ABSTRACT
Title of Thesis: MECHANICAL DESIGN OF DEXTEROUS
MANIPULATOR LINKS
Christopher James Carlsen
Master of Science, 2018
Thesis directed by: Dr. David L. Akin
Aerospace Engineering
This paper explores the challenges of dense structure-electronics packaging,
specifically for a structural and electronics upgrade to the Ranger Tele-robotic Shut-
tle Experiment (RTSX) manipulators at the University of Maryland (UMD). Long
serial-link manipulators are popular in the space industry, where the need for a
long reach and high manipulability outweighs the need for high tip stiffness. For
larger systems with co-located electronics, such as those used to berth vehicles on
orbit, electronics packaging is not inhibited by the diameter of the link body. As
link diameter decreases, co-locating electronics in the manipulator becomes difficult
without adding external extensions to house them. In such densely packed bodies,
the control electronics are so integrated with structure that electronics maintenance
requires disassembly of primary structure.
MECHANICAL DESIGN OF DEXTEROUS
MANIPULATOR LINKS
by
Christopher James Carlsen
Thesis submitted to the Faculty of the Graduate School of the
University of Maryland, College Park in partial fulfillment
of the requirements for the degree of
Master of Science
2018
Advisory Committee:
Professor Dr. David Akin, Chair
Professor Dr. Norman Wereley
Professor Dr. Mary Bowden
©c Copyright by
Christopher James Carlsen
2018

Preface
Choosing a design based thesis has given me the opportunity to produce a
working system, in addition to the academic studies and rigor involved in any thesis
or dissertation. During my term at the University of Maryland College Park I
devoted my time nearly equally to academic course work and engineering design.
The design work detailed in this paper has been my most rigorous exercise yet,
encompassing several years of effort from both myself and my teammates at the
Space Systems Laboratory.
This paper is a demonstration of my own skills as well as the capabilities of my
peers. I am building upon the work, lessons learned, and creativity of a multitude
of people across multiple decades. The robot that I redesign in this thesis was con-
ceived, designed, and constructed by a group of highly skilled and dedicated people
years before I entered the university. My formative years in my undergraduate career
were spent learning from the design of Ranger and the mountain of documentation
that accompanies it. While I spend several chapters in this thesis analyzing and
critiquing the decisions made by the creators of Ranger, I do so having the benefit
of hindsight and wish to convey my utmost appreciation for the efforts expended
before me.
This thesis is also meant to be a reference text for my successors at the
Space Systems Laboratory, hopefully shedding some light into the inner workings of
Rangers design. To those students, I wish you good luck. I hope this is what you
need.
ii
Dedication
This thesis is dedicated to my late mother, Ann. She was there for every event
in my life, big or small. She drove me to do my best where ever I could, and see the
beauty in the world around me as often as I could.
Thank you so much.
iii
Table of Contents
Preface ii
Dedication iii
List of Tables viii
List of Figures ix
List of Abbreviations xiii
1 Thesis Motivation 1
1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Benefits of the Selected Commercial Motor Controllers . . . . . . . . 2
1.3 Challenges from the Selected Commercial Motor Controllers . . . . . 3
1.4 Motivation Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2 RTSX Overview 5
2.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.2 Internal Wiring . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2.3 Design Space Details . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
3 Introduction of New Motor Controllers 13
4 Design Requirements 15
4.1 Initial Requirements . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
4.2 Post-Prototype Additions and Alterations . . . . . . . . . . . . . . . 16
4.3 Prototype Lessons Learned . . . . . . . . . . . . . . . . . . . . . . . . 16
4.4 Materials Used . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
5 Controller Packaging Experiment 19
iv
6 Design Methods 25
6.1 Bottom-Up Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
6.2 Top-Down Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
6.3 Part Tree Generation . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
6.4 Design Methods Conclusions . . . . . . . . . . . . . . . . . . . . . . . 28
7 Second Design Revision Method 29
8 Structural Analysis 34
8.1 Analysis Assumptions . . . . . . . . . . . . . . . . . . . . . . . . . . 34
8.2 Gearbox Stiffness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
8.3 Analysis of Original System . . . . . . . . . . . . . . . . . . . . . . . 36
8.4 Prototype Link Layout . . . . . . . . . . . . . . . . . . . . . . . . . . 37
8.5 Prototype Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
8.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
9 Structural Inclusion of the Lid 42
9.1 Structural Connection Attempt . . . . . . . . . . . . . . . . . . . . . 42
9.2 Bolted Lid Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
9.3 Calculating Bolt Forces . . . . . . . . . . . . . . . . . . . . . . . . . . 44
9.4 Determining Parent Material Geometry . . . . . . . . . . . . . . . . . 48
10 Stiffness Analysis of Non-Axisymmetric Beams 49
10.1 Verification of Model . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
10.2 Evaluation of Characterization Data . . . . . . . . . . . . . . . . . . 53
10.3 Influence of Tool Tip Stiffness . . . . . . . . . . . . . . . . . . . . . . 55
10.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
10.5 Potential for Future Work . . . . . . . . . . . . . . . . . . . . . . . . 57
11 Tray Geometry Optimization Study 58
11.1 Varied Wall Thickness . . . . . . . . . . . . . . . . . . . . . . . . . . 59
11.2 Flange . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
11.3 Orthogrid . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
11.4 Isogrid . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
11.4.1 Base Geometric Design . . . . . . . . . . . . . . . . . . . . . . 62
11.4.2 External Mounting Points . . . . . . . . . . . . . . . . . . . . 63
11.5 Optimization Method . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
11.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
12 RTSX Standard Internal Interface 67
12.1 Load Transfer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
12.2 Surface Pressure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
12.3 Reducing Thermally Induced Stress . . . . . . . . . . . . . . . . . . . 72
12.4 Fatigue . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
12.5 Galvanic Corrosion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
v
13 Thermal Analysis of Original RTSX Design 77
13.1 Critical Components of Original Design . . . . . . . . . . . . . . . . . 77
13.2 Design Comparison to VPX Standard . . . . . . . . . . . . . . . . . . 79
13.3 Preliminary Inspection . . . . . . . . . . . . . . . . . . . . . . . . . . 80
13.4 Failure Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
13.4.1 PCB Flexure . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
13.4.2 Excessive Mating Pressure . . . . . . . . . . . . . . . . . . . . 81
13.4.3 Motor Driver Failure . . . . . . . . . . . . . . . . . . . . . . . 82
13.4.4 Separation of the Heat Spreader from the Card Cage . . . . . 82
13.4.5 Separation of Heat Spreader from Motor Driver . . . . . . . . 82
13.5 Steady State Thermal Design Investigation . . . . . . . . . . . . . . . 83
13.6 Contact Pressure Evaluation . . . . . . . . . . . . . . . . . . . . . . . 84
13.7 Failure Method Review . . . . . . . . . . . . . . . . . . . . . . . . . . 88
13.7.1 PCB Flexure . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
13.7.2 Excessive Mating Pressure . . . . . . . . . . . . . . . . . . . . 88
13.7.3 Motor Driver Flexure . . . . . . . . . . . . . . . . . . . . . . . 88
13.7.4 Separation of Heat Spreader from the Card Cage . . . . . . . 89
13.7.5 Separation of Heat Spreader from the Motor Driver . . . . . . 89
13.8 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
14 Thermal Redesign 92
14.1 Mechanical Isolation . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
14.2 Retaining Arm Design . . . . . . . . . . . . . . . . . . . . . . . . . . 94
14.2.1 Deformation Method . . . . . . . . . . . . . . . . . . . . . . . 95
14.2.2 Material Selection . . . . . . . . . . . . . . . . . . . . . . . . . 96
14.3 Thermal Transfer Between HPU and Link Body . . . . . . . . . . . . 96
15 RTSX Thermal Design Evaluation 98
15.1 Operating Environment . . . . . . . . . . . . . . . . . . . . . . . . . 98
15.2 Design Challenges . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99
15.3 Thermal Design Solutions . . . . . . . . . . . . . . . . . . . . . . . . 100
15.3.1 Built-In Heatsink . . . . . . . . . . . . . . . . . . . . . . . . . 100
15.3.2 Bolt-On Heatsink . . . . . . . . . . . . . . . . . . . . . . . . . 100
15.3.3 Thermal Electric Cooler . . . . . . . . . . . . . . . . . . . . . 101
15.3.4 Active Cooling . . . . . . . . . . . . . . . . . . . . . . . . . . 102
15.4 Impinged Nozzle Flow Design . . . . . . . . . . . . . . . . . . . . . . 102
15.5 Fabrication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108
16 Thermal Verification and Testing 110
16.1 Test Hardware . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110
16.2 Thermal Testing Results . . . . . . . . . . . . . . . . . . . . . . . . . 113
16.2.1 Junction Resistance . . . . . . . . . . . . . . . . . . . . . . . . 113
16.2.2 First Order Calculation of Steady State Values . . . . . . . . . 115
16.2.3 Passive Convection Performance . . . . . . . . . . . . . . . . . 117
16.2.4 Forced Air Convection Performance . . . . . . . . . . . . . . . 118
vi
16.2.5 Internal Radiative Heating . . . . . . . . . . . . . . . . . . . . 119
16.3 Thermal Design Conclusions . . . . . . . . . . . . . . . . . . . . . . . 119
17 Internal Electronics Mounting 121
17.1 Rack Construction Concepts . . . . . . . . . . . . . . . . . . . . . . . 122
17.1.1 Externally Framed Rack . . . . . . . . . . . . . . . . . . . . . 122
17.1.2 Monolithic Internally Framed Rack . . . . . . . . . . . . . . . 124
17.1.3 Built-Up Internally Framed Rack . . . . . . . . . . . . . . . . 124
17.2 Structural Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125
17.3 Wire Harnessing Consideration . . . . . . . . . . . . . . . . . . . . . 128
17.4 Parallel Design Development with Electronics Designs . . . . . . . . . 129
17.5 Electronics Mounting Conclusions . . . . . . . . . . . . . . . . . . . . 130
18 Link Extension Design 132
18.1 Thin Walled Beam . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132
18.2 Link Extension Interface . . . . . . . . . . . . . . . . . . . . . . . . . 134
18.3 Link Extension Design . . . . . . . . . . . . . . . . . . . . . . . . . . 135
19 Conclusions 138
Appendices 140
A RTSX DXE Kinematic Chain 141
B RTSX PXL Kinematic Chain 142
C Experimental Results Studying Minimal Parent Material Geometry About a
Threaded Surface 143
C.1 Experimental Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144
C.2 Comparison to Expected Values . . . . . . . . . . . . . . . . . . . . . 145
C.3 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147
D Conceptual Limits for Joint Design 150
D.1 Powertrain Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151
D.2 Piezoelectric Motors . . . . . . . . . . . . . . . . . . . . . . . . . . . 153
D.3 Bearing Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155
D.4 Kinematic Configuration . . . . . . . . . . . . . . . . . . . . . . . . . 156
D.5 Mechanical Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157
D.6 Design Study Conclusions . . . . . . . . . . . . . . . . . . . . . . . . 160
E Wire Harnessing Guide 162
E.1 Connector P4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162
F Interpart Connections 163
Bibliography 164
vii
List of Tables
4.1 Commonly used materials in RTSX . . . . . . . . . . . . . . . . . . . 18
5.1 Design constraints for RTSX links . . . . . . . . . . . . . . . . . . . . 20
5.2 HPU packaging cross sections . . . . . . . . . . . . . . . . . . . . . . 21
8.1 Stiffness stackup of the original and ideal links for RTSX . . . . . . . 36
8.2 Comparison of torsional stiffness between link designs . . . . . . . . . 39
9.1 Loading values for RTSX 2 bay link design . . . . . . . . . . . . . . . 44
9.2 Stress caluclated per bolt in selected configurations . . . . . . . . . . 48
9.3 Safety factor for bolts considered . . . . . . . . . . . . . . . . . . . . 48
10.1 Percentage error between the extended model in the compliance matrix 51
12.1 Coefficients of thermal expansion for selected materials . . . . . . . . 73
12.2 Galvanic index of materials used in RTSX . . . . . . . . . . . . . . . 75
13.1 Steady state motor drive temperatures . . . . . . . . . . . . . . . . . 84
15.1 Thermal system design requirements . . . . . . . . . . . . . . . . . . 99
15.2 Table of constants used in the impinged flow calculation . . . . . . . 103
16.1 Experimental results for various thermal interface models . . . . . . . 114
18.1 Design limits of a 0.33m link extension . . . . . . . . . . . . . . . . . 134
C.1 Experimental results of test sample failure . . . . . . . . . . . . . . . 146
E.1 Connector P4 Pinout Wire Chart . . . . . . . . . . . . . . . . . . . . 162
viii
List of Figures
2.1 RTSX system simulating DEXTER in neutural buoyancy . . . . . . . 5
2.2 RTSX DXE dexterous manipulator . . . . . . . . . . . . . . . . . . . 7
2.3 RTSX’s coarse positioning manipulator, PXL . . . . . . . . . . . . . . 9
2.4 Cross sectional view of the original RTSX DXE design . . . . . . . . 10
2.5 RTSX Configured as SPDM performing an ORU change out . . . . . 11
2.6 Wrist link with sheath removed . . . . . . . . . . . . . . . . . . . . . 12
3.1 Motor Drivers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
5.1 RTSX shoulder packaging study view 1 . . . . . . . . . . . . . . . . . 22
5.2 RTSX shoulder packaging study view 2 . . . . . . . . . . . . . . . . . 22
5.3 Cross section of prototype wrist housing . . . . . . . . . . . . . . . . 23
6.1 Example part tree structure . . . . . . . . . . . . . . . . . . . . . . . 27
7.1 Original Deisn Hierarchy . . . . . . . . . . . . . . . . . . . . . . . . . 33
7.2 Redesigned Heirarchy . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
8.1 Bending of original housing . . . . . . . . . . . . . . . . . . . . . . . 35
8.2 Cross section of prototype shoulder housing . . . . . . . . . . . . . . 37
8.3 Comparison of original and prototype wrist housings . . . . . . . . . 38
8.4 RTSX prototype flexibility being tested . . . . . . . . . . . . . . . . . 39
8.5 Final link design for RTSX . . . . . . . . . . . . . . . . . . . . . . . . 40
9.1 External view of an alternate lid design . . . . . . . . . . . . . . . . . 43
9.2 Cross section view of an alternate lid design . . . . . . . . . . . . . . 43
10.1 Extended characteristic equation for a link . . . . . . . . . . . . . . . 50
10.2 Characteristic compliance matrix of the final housing . . . . . . . . . 53
10.3 Ideal IPM distribution . . . . . . . . . . . . . . . . . . . . . . . . . . 54
10.4 Original link IPM distribution . . . . . . . . . . . . . . . . . . . . . . 54
10.5 Prototype link IPM distribution . . . . . . . . . . . . . . . . . . . . . 54
10.6 Final link IPM distribution . . . . . . . . . . . . . . . . . . . . . . . 54
10.7 Contribution to tip deflection . . . . . . . . . . . . . . . . . . . . . . 55
ix
11.1 Minimum wall geometry . . . . . . . . . . . . . . . . . . . . . . . . . 58
11.2 Thickness Optimized Wall Geometry . . . . . . . . . . . . . . . . . . 59
11.3 Flanged Wall Geometry . . . . . . . . . . . . . . . . . . . . . . . . . 60
11.4 Orthogrid lighteneing geometry . . . . . . . . . . . . . . . . . . . . . 60
11.5 Isogrid lightening geometry . . . . . . . . . . . . . . . . . . . . . . . 61
11.6 Reflective fiducial markers attached to a link . . . . . . . . . . . . . . 64
11.7 Isogrid geometry optimization, step 1 . . . . . . . . . . . . . . . . . . 65
11.8 Isogrid optimization, final iteration . . . . . . . . . . . . . . . . . . . 66
12.1 PXL electronics mounting interface . . . . . . . . . . . . . . . . . . . 67
12.2 DXE link mounting interfaces . . . . . . . . . . . . . . . . . . . . . . 68
12.3 Adapters used between joint module and link bodies in RTSX . . . . 69
12.4 Thermally invariant fastener chain . . . . . . . . . . . . . . . . . . . . 73
12.5 Galvanic corrosion of the threaded holes on the base of PXL . . . . . 75
13.1 Top view of the servo driver board . . . . . . . . . . . . . . . . . . . 79
13.2 Computer rendering showing the geometry of the heatspreader . . . . 79
13.3 Bottom view of the servo driver . . . . . . . . . . . . . . . . . . . . . 79
13.4 Servo drivers installed in RTSX . . . . . . . . . . . . . . . . . . . . . 79
13.5 Deformed original wrist link . . . . . . . . . . . . . . . . . . . . . . . 80
13.6 All controllers powered, Wedge-Lok conduction only . . . . . . . . . . 85
13.7 Single contoller powered, Wedge-Lok conduction only . . . . . . . . . 85
13.8 All controllers power, conduction through the full heat spreader . . . 85
13.9 Single controller powered, conduction through the full heat spreader . 85
13.10Unloaded heat spreader pressure distribution . . . . . . . . . . . . . . 86
13.11Applied moments to a FEA link model . . . . . . . . . . . . . . . . . 87
13.12DDC module unloaded pressure . . . . . . . . . . . . . . . . . . . . . 87
13.13DDC module worst case pressure . . . . . . . . . . . . . . . . . . . . 87
13.14Pressure loading, positive torsion . . . . . . . . . . . . . . . . . . . . 91
13.15Pressure loading, negative torsion . . . . . . . . . . . . . . . . . . . . 91
13.16Pressure loading, positive vertical bending . . . . . . . . . . . . . . . 91
13.17Pressure loading, negative vertical bending . . . . . . . . . . . . . . . 91
13.18Pressure loading, positive horizontal bending . . . . . . . . . . . . . . 91
13.19Pressure loading, negative horizontal bending . . . . . . . . . . . . . 91
14.1 Kinematic diagram of the servo driver retainer . . . . . . . . . . . . . 93
14.2 Grübler’s formula for calculating degrees of freedom in a mechanism . 93
14.3 New servo driver contact pressure . . . . . . . . . . . . . . . . . . . . 94
14.4 New servo driver contact pressure . . . . . . . . . . . . . . . . . . . . 94
15.1 Diagram of impinged flow across a surface . . . . . . . . . . . . . . . 103
15.2 Diagram of flowin the cooler . . . . . . . . . . . . . . . . . . . . . . . 105
15.3 Pressure-velocity diagram for the selected fan . . . . . . . . . . . . . 106
15.4 Calculated ideal impinged flow cooling per motor controller . . . . . . 106
15.5 Cooler assembled onto the thermal testbed . . . . . . . . . . . . . . . 107
15.6 Cross sectional view of the cooler as applied to a link . . . . . . . . . 107
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16.1 Thermal test link in an enviromental chamber . . . . . . . . . . . . . 111
16.2 Test electronics rack with dummy servo drivers . . . . . . . . . . . . 111
16.3 Thermal test platform being assembled . . . . . . . . . . . . . . . . . 111
16.4 Rendered graphic of the mock HPU . . . . . . . . . . . . . . . . . . . 112
16.5 Rendering of the interior of a HPU with sensor locations labeled . . . 112
16.6 First order temeperature prediction error . . . . . . . . . . . . . . . . 116
16.7 Free convection experimental results at room temparature . . . . . . 117
16.8 Maximum disapation from each motor controller as a funciton of ex-
ternal temperature . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118
17.1 Cross section of the link depicting volume allotments . . . . . . . . . 122
17.2 Prototype electronics mounting rack . . . . . . . . . . . . . . . . . . . 123
17.3 Internally framed rack with an underslung structure . . . . . . . . . . 124
17.4 Required Young’s Modulus for a given deflection . . . . . . . . . . . . 125
17.5 Natural frequency of a massless cantilever beam with a tip mass . . . 125
17.6 Finite element simulation showing the first vibratory mode . . . . . . 126
17.7 Concept for a stiffening beam for the top plate . . . . . . . . . . . . . 127
17.8 Final stiffening beam design . . . . . . . . . . . . . . . . . . . . . . . 127
17.9 Wire harness path . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128
17.10Gap in the built-up structure used for harnessing . . . . . . . . . . . 129
17.11Electronics interface example . . . . . . . . . . . . . . . . . . . . . . 130
18.1 Critical thickness for the link extension . . . . . . . . . . . . . . . . . 133
18.2 Proximal link extension inerface . . . . . . . . . . . . . . . . . . . . . 134
18.3 Distal link extension interface . . . . . . . . . . . . . . . . . . . . . . 134
18.4 Cross section of the link extension assembly . . . . . . . . . . . . . . 136
C.1 Detailed cross section of the test sample . . . . . . . . . . . . . . . . 143
C.2 Mechanical drawing for tensile test samples . . . . . . . . . . . . . . . 145
C.3 Index test of bolts until failure . . . . . . . . . . . . . . . . . . . . . . 146
C.4 Sample test results for 0.35 inch diameter billet . . . . . . . . . . . . 146
C.5 Comparison of experimental results against ideal results . . . . . . . . 147
C.6 Test sample 016 showing tensile failure . . . . . . . . . . . . . . . . . 149
C.7 Test Sample 040 showing pullout failure . . . . . . . . . . . . . . . . 149
D.1 Comparison of various hypocycloidal gearbox performances . . . . . . 151
D.2 Baseline arrangement of components inside a robotic joint . . . . . . 152
D.3 Surveyed actuator torque performances . . . . . . . . . . . . . . . . . 152
D.4 Standing Wave Motor . . . . . . . . . . . . . . . . . . . . . . . . . . 154
D.5 Traveling Wave Motor . . . . . . . . . . . . . . . . . . . . . . . . . . 154
D.6 Walking foot motion . . . . . . . . . . . . . . . . . . . . . . . . . . . 154
D.7 Geometry depicting how angular contact bearings resist rocking mo-
ments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 156
D.8 Mockup of Strongman actuators . . . . . . . . . . . . . . . . . . . . . 157
D.9 Strongman joint structural design . . . . . . . . . . . . . . . . . . . . 158
D.10 Strongman joint cross section . . . . . . . . . . . . . . . . . . . . . . 158
xi
D.11 Strongman joint-link interface . . . . . . . . . . . . . . . . . . . . . . 159
D.12 Strongman interface detail showing sealing surfaces . . . . . . . . . . 159
D.13 Comparison of Strongman shoulder with RTSX DXE Shoulder . . . . 160
E.1 Connector P4 Pinout . . . . . . . . . . . . . . . . . . . . . . . . . . . 162
E.2 Connector P4 cable cross section . . . . . . . . . . . . . . . . . . . . 162
F.1 Sample of RTSX Interpart Tree . . . . . . . . . . . . . . . . . . . . . 163
xii
List of Abbreviations
ABS Acrylonitrile Butadiene Styrene
CNC Computer Numerically Controlled
COTS Commercial Off the Shelf
CTE Coefficient of Thermal Expansion
DXE RTSX Dexterous Manipulator
EDM Electro-Discharge Machining
FEA Finite Element Analysis
HDT Heat Deflection Temperature
HPU High Power Unit
GPIO General Purpose In and Out
ICD Interface Control Document
IPM Impact Percentile Matrix
ISS International Space Station
MJM Multi Jet Manufacturing
MOSFET Metal Oxide Semiconductor Field Effect Transistor
MTBF Mean Time Between Failure
NASA National Aeronautics and Space Administration
ORU Orbital Replacement Unit
PCB Printed Circuit Board
PXL RTSX Positioning Leg
RTSX Ranger Tele-robotic Shuttle Experiment
SLM Selective Laser Melting
SLS Selective Laser Sintering
SPDM Special Purpose Dexterous Manipulator
SSL Space Systems Laboratory
SSRMS Space Shuttle Remote Manipulator System
STP Standard Temperature and Pressure
xiii
TEC Thermo-Electric Cooler
UMD University of Maryland
xiv
Chapter 1: Thesis Motivation
1.1 Introduction
This thesis was constructed to formally chronicle the redesign process of struc-
tural components in a robotic system. The system in question is a multi-armed
robotic manipulator, designed for mechanically servicing satellites and other such
systems while on orbit. This robotic system is known as the Ranger Tele-robotic
Shuttle Experiment (RTSX) platform and will be discussed at length throughout
this paper.
The RTSX platform is capable of operating in space, on land, and in water with
no modification. While its original application was intended for orbital operations,
it has been leveraged more recently as a testing and simulation platform for neutral
buoyancy and laboratory based operations. As operations moved away from the
need for flight ready hardware and towards long term ground operations, there was
a need to switch to commercial hardware with modern capabilities. The motion
control electronics for RTSX were the most repaired physical component and they
were purpose-built in-house, making them a large contributor to operational costs.
This paper focuses on the design changes that were necessary to implement
commercial motion controllers in RTSX. Multiple aspects of the original design were
1
also improved including thermal management, maintainability, and the total system
mass without impacting nominal performance.
1.2 Benefits of the Selected Commercial Motor Controllers
The commercial motor controllers selected improve the overall performance
of RTSX while reducing cost and labor. These units are capable of outputting six
times the original motor controller current at peak operation. This enables the
larger motors of RTSX to operate at full load, allowing the full system to operate
outside of a neutrally buoyant environment. This is a huge advantage for testing
and development of the full system, reducing the number of operators for testing
from a full dive team complement to only one operator and a safety. That reduces
the total test team from approximately eight personnel to two.
The commercial motor controllers selected also have onboard processing and
pre-made firmware. This means that there is low development overhead for initial
deployment and increased development speed for more complex functions. However
the total system capability is reduced, for example an external board needs to be
added to the system to expand the general purpose I/O (GPIO) bus from the motor
controllers in order to correctly read the absolute encoders used in the dexterous
arms of RTSX.
2
1.3 Challenges from the Selected Commercial Motor Controllers
Although the commercial motor controllers have a higher power density than
the existing controllers, they have a lower overall packing density. S side by side
comparison of the old and new controller is shown in figure 3.1. This means that
they are not able to fit into the existing volume for the motor controllers. The
entire mounting structure needed to be redesigned to accommodate the commercial
motor controllers. Subsequently, this meant that most of the mechanical structure
of RTSX needed to be redesigned. This is the crux of this paper and the most
challenging redesign component of RTSX.
Additionally, the commercial motor controllers have a much lower maximum
operating temperature from the original modules. As these modules have similar
thermal output, the thermal design of RTSX must be rethought. This is secondary
focus of this paper, consuming several chapters.
1.4 Motivation Summary
The higher level motivation for this thesis is to improve the state of the art of
robotic structure design. Most modern design work for robotics focuses on the soft-
ware development, end effector design, electronics, or even actuator design. This
thesis instead focuses on the design of the electronics mounting and structure of
a robotic manipulator. RTSX integrates the control electronics locally to the ac-
tuators. This reduces wiring bulk, allows the joint segments to be modular and
3
reconfigurable, and reduces total system volume. As most robotic manipulators do
not do this, it also presents a unique opportunity to lend further validity to this de-
sign style. Through better management of packing, thermal design, and structural
design, this thesis aims to open up the design space for future robotic manipulators.
4
Chapter 2: RTSX Overview
2.1 Overview
Figure 2.1: RTSX system simulating DEXTER in neutural buoyancy 1
RTSX is designed to perform servicing tasks while on orbit. In 1992, dexterous
manipulators in space were capable only of moving large components or collecting
samples on surface probes. The Ranger program, created by the University of Mary-
land Space Systems Laboratory and sponsored by the NASA Telerobotics program,
was intended to demonstrate dexterous robotics on-orbit in the near term. Origi-
nally designed for use on a dedicated free-flying servicing vehicle, it was redesigned in
1Photo courtesy of the Space Systems Laboratory, University of Maryland
5
1996 to be a shuttle-based experiment. RTSX never got to fly, although the ground
development/qualification unit continued to be used until 2015 as a laboratory and
neutral buoyancy research system. Problems with electronics systems dying far af-
ter end-of-life and desire to switch from custom to COTS for both electronics and
software were the driving factors for the redesign process.
Since the inception of the Ranger program, dexterous robotic manipulators
have become much more common. A number of different solutions are commercially
available for terrestrial operation. However, terrestrial robotic manipulators have far
different operating requirements such as tip velocity and a tool tip stiffness that is
orders of magnitude higher than space based robotic manipulators. For the purpose
of this thesis, the focus will be chiefly on space based manipulator design.
Broadly, there are two different categories for space manipulators, coarse and
dexterous. Coarse manipulators are those that move heavy loads long distances
with coarse positioning and low tip stiffness, similar to a crane. An example of
a coarse manipulator is the Space Station Remote Manipulator System (SSRMS),
also known as Canadarm2. Dexterous manipulators have fine positioning control
and much higher tip stiffness than coarse systems, and are generally intended to be
able of performing many tasks previously reserved for humans. The Special Pur-
pose Dexterous Manipulator (SPDM) is a dexterous manipulator system, designed
to replace orbital replacement units (ORU). RTSX features one coarse and two dex-
terous manipulators. The coarse manipulator moves the two dexterous manipulators
to their task, similar to how SSRMS moves SPDM about the International Space
Station (ISS).
6
The dexterous arms of RTSX feature eight degrees of freedom and two powered
tool drives. Although it is capable of being reassembled into multiple kinematic
configurations, RTSX is typically used in an anthropomorphic configuration. Each
dexterous manipulator is highly modular, and is designed as integrated shoulder,
elbow, and wrist modules incorporating both actuators and electronic controllers.
Each arm segment can be lengthened with simple link inserts to create the desired
reach.
The following section uses the yaw-pitch-roll notation to describe the sequenc-
ing of revolute joints. These are notated as Y-P-R respectively. This notation is
commonly used to give a brief description of how a serial-link manipulator behaves
kinematically. For example, a Y-Y manipulator would have two joints both in the
yaw plane, making it a planar manipulator. A Y-P manipulator would be for point-
ing to a spherical coordinate, such as you would need for a camera mount.
Figure 2.2: RTSX DXE dexterous manipulator
7
The shoulder module is built in a R-P-R configuration, giving it a simple kine-
matic chain. The drive electronics are not structural in this module, but attached
as an external extension. The elbow and wrist modules both have their drive elec-
tronics packaged into their kinematic chain, sitting proximal to the module that the
electronics control. The elbow is a P-R configuration featuring the only kinematic
offset in the whole system. This offset allows the dexterous arm to fold up for launch
and storage. Hidden in the image on the opposite side of the elbow are tie down
points for a flight releasable bolt to hold the arm in position.
The wrist is the mechanically densest of all of the modules featuring three
actuators and two tool drives. Joint 6 is non-orthogonal, mounted at a 45 degree
offset, allowing the kinematic axes of joints 6, 7, and 8 to intersect. This greatly
simplifies the arm kinematics mathematically.
The positioning leg of RTSX is far simpler kinematically. Each module con-
tains two joints and an external extension housing the control electronics. PXL
features a R-P-P-R-P-R configuration and is used for coarse maneuvering of the
dexterous arms to a task.
2.2 Internal Wiring
All wiring for each dexterous manipulator (DXE) and the positioning leg
(PXL) is internal to the manipulator. Keeping wiring internal eliminates the possi-
bility of abrasion of cables or entanglement with the arm itself or its environment.
Cabling passes through each actuator through its rotational axis inside of a shielded
8
Figure 2.3: RTSX’s coarse positioning manipulator, PXL
conduit. Internal wiring is limited by the geometry of the joint it passes through.
In DXE, internal cable diameter is very restricted because the majority of volume
in each joint is consumed by the powertrain. To make the most of this small cable
pass through, motor drivers and their control electronics were packaged into the arm
itself. Rather than pass all of the encoder, sensor, and motor cables through the
entire length of the arm to a control box at the base, only power and a data bus
are required. This also reduces problems associated with long cable runs, such as
resistive losses and inductance.
The RTSX platform can have link extensions inserted between each joint mod-
ule to increase its link length. With the power and data pass-through limited to
9
Figure 2.4: Cross sectional view of the original RTSX DXE design
a few wires, and electronics packaged in proximity to the joint modules they con-
trol, the link lengths of the arm can be modified with few modifications. The link
extensions use a common mechanical interface and contain a power and data bus
extension to pass through all necessary wiring. Changing the link lengths alter the
kinematics of the manipulator and allows the RTSX platform to mimic the kinemat-
ics and capabilities of other manipulators on orbit or under development. In 2005,
RTSX was used to mimic the kinematics of SPDM, pictured in Figure 2.5.
2.3 Design Space Details
The forearm and upper arm links of DXE are densely packed with both struc-
ture and electronics. The link is responsible for stiffly connecting proximal com-
ponents to distal components, protecting the electronics housed within from the
environment, and dissipating heat from those same electronics into the surrounding
environment.
Difficulties arise when trying to package electronics densely with primary struc-
10
Figure 2.5: RTSX Configured as SPDM performing an ORU change out
ture. Most electronics do not do well with strain and most primary structure does
not do well with large internal voids to hold electronics. In the case of RTSX, all
of the link volume that was not occupied by electronics or wiring was occupied by
primary structure 2.6. There are multiple schools of thought on whether this is a
good design limit. There is no residual volume for potential design expansion, but
as this was a purpose built robotic platform, is expansion volume necessary? We
will explore in chapter 3 why this highly-dense layout is counterproductive to the
upgrade process undertaken throughout this paper.
One downside to such a dense design was the difficulty of maintenance. For
space flight hardware this is frequently not an issue, since the cost of the mass of the
11
Figure 2.6: Wrist link with sheath removed. Dorsal view [left] and Ventral view
[right]
design greatly exceeds the maintenance and operations costs. As RTSX transitioned
in purpose from a flight experiment to a ground based testing and simulation plat-
form, maintenance time and cost became a larger factor. The original RTSX design
took measures to reduce volume and increase system reliability by limiting the num-
ber of electrical interconnects. As a result of this, the actuator wiring was soldered
directly to the backplane that controls it. This can be observed in Figure 2.6 on the
ventral side. This design choice was one of the largest contributors to maintenance
time. In order to modify any part of the backplane, all of the connections to the
PCB had to be de-soldered and tested, taking multiple days to complete.
As the links to house new electronics were redesigned, we had to keep in mind
that the design goals and the design space differs from RTSXs original intent. We
had to consider which design concepts to retain and which to rethink in order to
produce an effective manipulator for ground testing.
12
Chapter 3: Introduction of New Motor Controllers
The driving cause for this redesign is the introduction of new electronic motor
controller hardware. The original design used three daughter board control cards
in addition to the motor driver cards. It required a DC-DC regulator card, a com-
munications card, motion control card, and a motor driver card. Additionally, a
backplane board was required to connect all of these cards together and to pro-
vide additional signal filtering. This system performed all of the requisite functions,
but featured a large number of components. By extension, the large number of
components in this system lead to a reduced Mean Time Between Failure (MTBF).
The original motor driver was based on a DC motor torque controller manu-
factured by DDC. This module was designed to withstand high temperatures and
could output 10 amps of continuous current. This module was sufficient for driving
any actuator in PXL and DXE, and is used as a minimal baseline for future mod-
ules. This motor driver board had no other functionality beyond supporting and
driving the DDC module using the hall-effect sensors embedded in the motor stator
for feedback. The actuator control loop was run on the separate motion control
card.
All of this can currently be achieved on a single commercial module, available
13
Figure 3.1: Original Motor Driver (left) and new servo driver (right)
from a variety of different manufacturers. These new all-in-one modules are referred
to as servo drivers instead of motor drivers, as they have their own closed-loop
control system onboard which can slew the actuator to specific positions as well as
specific velocities. The module that was selected for this project is the DZCante-
020L0601made by Advance Motion Control, capable of outputting 12 amps of con-
tinuous current.
The 12 amp module was originally specified for use with all actuators in RTSX,
but an opportunity was found to increase total system performance. By using a
higher power controller in joints that are subjected to higher torque, RTSX can
increase in utility. By using the DZCante-060L080 in PXL and the DXE shoulder,
the maximum tip load of DXE is increased and PXL is capable of operating outside
of neutral buoyancy. This controller capable of supplying 30 amps of continuous
current and occupies the same volume as the 12 amp module. The only difficulty
created by using the 30 amp controller is an increased thermal load. Enhanced
methods of cooling need to be created, and are addressed in section 16.
1More information about this module is available at www.a-m-c.com
14
Chapter 4: Design Requirements
At the start of the redesign process a set of design requirements were estab-
lished. These were used to create a prototype link to determine the effectiveness of
the design modifications. After the prototype was completed, additions were made
to these requirements using the lessons learned.
4.1 Initial Requirements
P-1 The redesign shall package all appropriate electronic hardware and motor con-
trollers1into the link volume between joints in the dexterous arms, and into
the side mounted volumes on the positioning leg.
P-2 The redesign shall provide an adequate operating environment for the contained
electronics. This includes operation at 10 meters depth in chlorinated water.
P-3 The redesign shall be compatible with existing RTSX hardware.
P-4 The redesign shall be adequately stiff as to not impact the performance of RTSX
and adequately strong as to withstand all internal forces that can be exerted
by RTSX.
P-5 The redesign shall decrease maintenance time for replacing the contained elec-
15
tronics.
P-6 The redesign shall maintain current operable tip mass and should increase the
maximum allowable top mass.
4.2 Post-Prototype Additions and Alterations
P-4a The redesign shall result in a dexterous top stiffness greater than 10 N/mm
and should survive a tip force greater than 890N.
P-7 The redesign shall not exceed 137mm in diameter to eliminate self-collisions.
P-8 The redesign shall make large components common across all electronics hous-
ings to reduce manufacture tooling and setup.
P-9 The redesign shall have discrete allotments for wiring paths to avoid collisions
during assembly.
4.3 Prototype Lessons Learned
Additions were made to the initial design requirements after several proto-
types were completed, listed previously in section 4.2. After the prototype was
constructed, a series of laboratory tests help further define the tip deflection re-
quirement defined in P-4, resulting in the addendum P-4a. This update makes the
prototype unacceptably soft, necessitating another design revision. This is addressed
further in section 8.4.
1Hence forth known as the ”contained electronics”
16
Requirement P-7 sets a maximum link diameter. Although no self-collisions
occurred during testing of the prototype links, their diameter did increase from
the original design to the maximum permissible diameter. Unfortunately, additions
to the design for fastening the lid to the link extended outside of this maximum
permissible diameter and could have resulted in self-collisions. Operators had to
be careful to not collide with these fasteners when operating the elbow joint near
maximum flexion.
After the prototype housings were manufactured, an assessment was made of
the overhead requirements in the machine shop. Approximately 30% of the manufac-
turing person-hours were expended on creating unique tooling for each independent
housing. Requirement P-8 was created to reduce tooling time by creating a stan-
dard design for the bulk of the intricate components. This proved worthwhile and
reduced the total component cost approximately 20%.
4.4 Materials Used
The materials in table 4.1 are those used for the modifications covered in
this thesis. For reference, the critical parameters for each of these materials are
summarized in the table.
17
Table 4.1: Commonly used materials in RTSX
Young’s Yield Thermal
Material Density CTE
Modulus Strength Conductivity
Name (alloy) g/cm3 GPa MPa µm/m◦K W/m◦K
Aluminum (6061) 2.7 68.9 276 23.6 167
Aluminum (6063) 2.7 68.9 214 23.4 200
Aluminum (7075) 2.8 71.7 503 23.6 130
Stainless Steel (316) 8.0 193 290 16.0 16.3
Stainless Steel (A286) 7.9 200 938 16.9 12.6
Copper (101) 8.94 117 150 17.6 390
Titanium (6AL-4V) 4.43 113 880 8.6 6.7
18
Chapter 5: Controller Packaging Experiment
The first priority in starting this design was to establish a coarse structure.
All of the electronics housings in RTSX needed to be redesigned to accommodate
new electronic hardware. While each housing could have been designed on a case-
by-case basis to minimize mass across the system, this is often an expensive and
marginally futile effort. Instead, a common base design was created that was capable
of satisfying all design constraints and was modified for special cases.
All of the housings to be designed have a common set of design requirements.
They must be water tight to protect the internal electronics from the environment.
The structure must be sufficiently stiff so the total system stiffness is acceptable.
The housings must conduct heat from the servo drivers contained within to the
environment to be dissipated. Their internal electronics must be accessible and
replaceable; permanent installation is unacceptable. The link solution must be
compatible with existing joint module. Any design that does not meet all of these
basic requirements will be deemed unacceptable.
The electronics housings have three varying design requirements across four
types of housings. PXL uses three identical housings, and DXE uses six housings of
three different configurations across two manipulators. The variable design require-
19
Table 5.1: Design constraints for RTSX links
Housing Servo Low Power Major
Quantity Accessory
Location Driver Accessories Structural Loads
1x Brake Survive poor lift
PXL 3 2x 60A —–
Controller 6kN Load
Survive poor lift
DXE Shoulder 2 3x 60A —– —–
6kN Load
DXE Elbow 2 2x 20A —– —– 500 N-m bending
Wrist
DXE Wrist 2 5x 20A —– Camera 175 N-m bending
Processor
ments for each housing type and its location is listed in the table below. Finding
commonality in these sets of design constraints will allow for a faster design process
and a more affordable product.
These housings break down easily into three types by grouping how many
high power units (HPUs) each housing will need to contain. A HPU is considered
any component that consumes a large amount of power, such as motor controllers
and break drivers, which would require the high level of thermal dissipation this
mounting scheme achieves. Two housings will need to contain five HPUs, five will
house three HPUs, and two will house two HPUs. Further grouping of the housings
can be achieved, but is dependent on packaging geometry for the HPUs. For that
reason, the following packaging study was conducted to achieve maximum packing
density of HPUs.
Multiple packaging configurations were considered for orienting HPUs inside of
a housing. The geometry of DXE limits the cross sectional diameter to 5.375 inches.
Two basic orientations of the servo driver were considered, as well as facing the
heatsink inward or outward. Link cross sections were considered that packaged one,
20
two, or three HPUs. While it would have been advantageous to package three HPUs
into one section, in no configuration did they fit within the cross section without
modification. Several alternate designs were explored to package the HPUs, but it
was found that wiring allowances prevented any form of the three unit cross section
from working, even with modification to the HPU.
Table 5.2: Packaging cross sections considered for RTSX links
One HPU Two HPUs Three HPUs
21
Orientation D Orientation C Orientation B Orientation A
A test packaging was created to explore orientation D2 and B2, placing three
servo drivers onto a central structure to be used for development on the shoulder
of RTSX. The assembly was designed to use the same waterproof covering as the
original housing, which constrained the exterior bounds of the packaging. This unit
was fully assembled and implemented to observe any issues in packaging. It was
immediately found that the limited clearance between controllers in configuration
D2 proved difficult for wiring. It was also found that the geometry required to
interface with the I-beam section was costly and required tighter tolerances than
desired. Later versions of the D2 or B2 configuration forewent the use of I-beam
stock, switching to a monolithic structure to eliminate as many tolerance stack-ups
as possible.
Figure 5.1: Packaging study of RTSXFigure 5.2: Obverse side of RTSX shoul-
shoulder der packaging study
This test packaging was an attempt at reusing the sheath made for the original
design. While this did reduce cost, it imposed highly limited volume constraints.
22
This design approach was abandoned as it caused more problems than it solved.
After this trial, the length and diameter of the link housing was treated as variable
as well.
In its place a new format was created, using a modified form of layout 2A. The
HPUs were oriented into a V configuration, so they could be mounted to an internal
structure and wedged into the outer structure to conduct heat. This configuration
required a 12% larger diameter than the original design to make allotments for wire
paths and to fit the stock heat spreader packaged with the servo drives.
Figure 5.3: Cross section of prototype wrist housing
This prototype housing was a study in both packaging and maintainability.
Arguably the most important component of this design was the inclusion of a lid,
allowing the internals of the link to be accessed from the side. This side-access
23
concept has variety of benefits which are enumerated in chapter 8 and discussed
throughout this paper. It provides a great benefit for reducing system maintenance
and electronics development time by allowing direct access to the driving electronics.
While the design pictured in Figure 5.3 was not selected for the final revision, many
features and concepts from this design are used.
24
Chapter 6: Design Methods
As computer aided design software progresses, there is an increasing focus on
the methodology used to design a product in the software. This design process used
two different software packages, PTC Creo for the prototype links and Siemens NX
10 for the final design. Both software packages are capable of the top-down and
bottom-up design methods discussed in this chapter. However, bottom-up design
was practiced in PTC Creo and top-down was practiced in Siemens NX, largely due
to operator experience.
6.1 Bottom-Up Design
This methodology was used for the packaging test unit in the shoulder and
the prototype links. Bottom-up design is commonly used in assemblies with a low
part count. In this method, all of the parts are designed individually and edited
individually to interface with the final assembly. Only at the final assembly of all the
components does the larger system exist. This is like designing a house by drawing
the foundation, then the floor, the walls, and finally the roof. Overall, if the user
has enough experience and design intuition, this method can be very quick, but will
rarely produce optimal results.
25
6.2 Top-Down Design
A top-down design methodology was implemented for the final link design.
This flow defines the geometry and features of all the components in an assembly
from a top-level assembly file, sometimes referred to as a skeleton design. While
seemingly more complicated than a bottom-up design process, top-down flow allows
for faster system design studies and for quick spawning and destruction of compo-
nents in the system. Top-down design also removes ambiguity by focusing on the
interfaces and utility of each component, rather the details of the component itself.
Using the same house analogy, the entire house would be sketched roughly and re-
fined multiple times and then used as a template to design individual parts of the
house separately.
6.3 Part Tree Generation
Top-down design flow reduces total design time for large and complex designs,
but does little to reduce the design time for individual components. To eliminate
the time spent designing multiple similar components, such as fasteners or gaskets,
a design tool known as family trees was used. A template part governed by a series
of equations was created for each family of parts, and all parts in that family were
generated from a parameter table.
This method can also be used for more complex components and was imple-
mented for multiple major components in the link design. An example of this can be
26
Figure 6.1: Example part tree structure
found in figure 6.1 in the generation of the electronics tray body and link tray. Two
versions of each component were required, one supporting two HPU bays, and one
supporting three HPU bays. Instead of designing two permutations of the same base
design separately, a single template part was created. This template took in inter-
face requirements from multiple sub-level components as well as exterior interfaces.
From this template, both two- and three-bay versions of the link were generated
automatically.
Generated parts were used extensively throughout the final link design. It was
found that to use this method properly, extensive notes and mapping were required
in order to understand the flow of design-driving constraints. Unfortunately, this
design technique is somewhat obtuse to new users and takes an inordinate amount
of time to train new designers on. It is suggested that future designs focus heavily
27
on documenting the flow of variables inside the generated parts tree. It is likely
that a project of this scale is too small to benefit from this design method, however
more iterations and refinement of documentation methods will be needed to fully
understand this.
6.4 Design Methods Conclusions
The study of design methods within this process yielded useful results. The
design of the prototype links, both the built up shoulder design and the monolithic
tray designs, were constructed using the bottom up design method. These parts
were designed quickly, taking approximately six months from conception to final
design review. However, these parts had multiple fit-up issues as well as a large
total system mass. The final design took approximately one year to complete but
was able to achieve a far better performing design, as is detailed in the rest of this
paper. The overall conclusion reached is that the balance between performance and
design time should be weighed when selecting a design method.
28
Chapter 7: Second Design Revision Method
Using the lessons learned from the test packaging, the design was reconsidered
abstractly. Ease of maintenance and speed of operations greatly outweigh the need
for simplicity of design. Accepting harder-to-manufacture and -calculate designs
allows for a system with higher utility. Tolerance stack-up is also detrimental to
the system, making assembly difficult and reducing the positioning accuracy of the
manipulator. Switching from a built-up primary structure to a monolithic design
again increases cost and design complexity, but allows a more accurate product.
There are two major design concerns for operation and repair of RTSX, the
length of the thermal path and disassembly procedures for maintenance. Thermal
energy must be conducted from motor though the intermediate components in the
manipulator, where it will be dissipated into the environment. Common materials
used in space robotics have a thermal conductivity between 6.7 to 390 W/mK.
Active heat pumping methods such as liquid cooling or refrigeration loops are to be
avoided as the added complexity reduces the total system reliability. So when the
thermal path between the heat load and the environment proves to be insufficient,
the options for resolving the problem is limited to either switching to a higher
thermal conductivity or reducing the characteristic length of the geometry.
29
Improving the disassembly procedures reduces the time for maintenance as
well as development time. For the original design hierarchy, three major features
limit the disassembly procedure. First, disassembly requires that all joints distal to
the link must be removed before the link may be disassembled. This is problematic
as each assembled joint segment is over 15kg, making them ungainly to maneuver
precisely. Secondly, there is no method to disconnect the backplane from the joint
actuators it controls. This can be seen in figure 2.6. earlier in this paper, where the
backplane is soldered directly onto the harness. To replace the backplane due to
a failed component, it must be painstakingly unsoldered, modified, and re-soldered
to the harness. Third, the primary structure chain within the link must be broken
to remove any electronics for maintenance. This is caused by the sheath which is
used to seal the link internals from the environment. It resists hydrostatic pressures
while allowing the card cage to transfer all the primary loads. While this design
simplifies the flow of forces inside the link, it makes it impossible to access the
internal electronics without breaking the primary structure chain.
To improve both of these design concerns, the following top level changes were
made. Observe the differences in figure 7.1 and figure 7.2 . The flow between
“Proximal Interface” and “Distal Interface” remains continuous, but the compo-
nents between them are manipulated. Also note the change in the “Remove for
Maintenance” region and how this will affect disassembly procedures. As is dis-
cussed later in this chapter, extracting the distal interface from the maintenance
region has great benefit for the maintainability of the system.
Leaving the primary structure path unbroken during maintenance is the first
30
concern. The sleeve was eliminated in favor of a non-structural side access door
with a face seal, so the internals of the link can be accessed while leaving the link
structure intact.
In addition to making the electronics easier to access, a modification was
made to ease the bulk of operational issues. An external, water tight connector was
added to the lid, giving the operators a direct connection to all of the debugging
ports onboard the electronics, the communication bus, and the power buses. While
the connector will not resolve all of the difficulties in trouble shooting the internal
electronics, it makes the majority of modifications easier.
An electrical disconnect was added between the joint actuators and their con-
trolling electronics, eliminating the need to solder the wiring harness for any regular
maintenance. The servo drivers were packaged into a removable electronic bay along
with all other electronic components inside the link. All of the electronics inside the
link may now be exchanged by disconnecting the tray connector and removing the
entire rack.
The thermal path from the servo driver to the environment was simplified
in the new methodology. Instead of flowing through multiple components to heat
sink to the ambient environment due to the poor thermal characteristics of the
waterproofing sleeve, heat is conducted directly through the sidewall of the tray and
into the environment. This change removes three thermal interfaces and shrinks
the characteristic length from several inches to a fraction of an inch. All of these
modifications will lead to a greatly improved thermal profile.
Top level modifications to the design were not conducted in isolation from the
31
detail design. What figure 7.2 shows is the result of multiple design iterations and
design space explorations.
32
Figure 7.1: Original Design Hierarchy
Figure 7.2: Redesigned Hierachy
33
Chapter 8: Structural Analysis
A concern for primary structure components in a robotic arm is stiffness. The
stiffness of a serial manipulator directly impacts its harmonic frequency and posi-
tioning accuracy. With a decrease in either, the load carrying capacity and operating
speed must be decreased for stable operation. For most serial revolute robotic sys-
tems, the bulk of the tool tip flexure is due to the spring rate of the gearboxes, but
this is not necessarily true if the drive electronics are packaged into the interstitial
links. The packaging and accessibility requirements inherent in placing drive elec-
tronics inside serial robotic links may cause a reduction in flexure stiffness that must
be accounted for in determining total system stiffness.
8.1 Analysis Assumptions
Serial link manipulators have a structure with a large length to width ratio,
which allows for some simplifications in the following analysis. RTSX is accurately
modeled using Euler-Bernoulli beam theory, as the dominant forces on the link body
are bending moments. The individual link segments of RTSX have a relatively
low length to width ratio but are integral into a longer system, so the deflection
of interest will be angular displacement, not linear. Note that this is the same
34
Figure 8.1: Bending in XX, YY, and ZZ respectively
flexure metric by which the revolute joints are analyzed. By these assumptions,
the flexibility of RTSX will be modeled as a series of torsional springs spaced at
geometric nodes across the length of the arm.
8.2 Gearbox Stiffness
As stated before, torsional stiffness of revolute joints has the greatest influence
on tool tip stiffness for the majority of serial link manipulators. For comparison,
the following are the performance characteristics of the gearboxes used in RTSX.
As stiffness is a critical factor in gearbox selection, two types of gearing systems
dominate the robotics market: strain wave and hypocycloidal (colloquially known
as cycloidal drive). Both have high gear ratios with good torque to mass ratios,
are compact, and have theoretically zero backlash. Strain wave gearboxes have
two distinct programmatic advantages over hypocycloidal: they have been used
in space flight since 1971, and they are readily available on the market. Given
these criteria, RTSX was constructed with strain wave gearboxes manufactured by
Harmonic Drive.
Harmonic Drive gearboxes have a non-linear torque response. In the region
of torque that RTSX operates in, the response can be approximated as linear. The
35
torsional stiffness of the gearbox models used is approximately 67 kNm/rad and
yields an approximate first mode harmonic frequency of 4.0Hz.
8.3 Analysis of Original System
To calculate the torsional stiffness of the RTSX links, a finite element model
was created and analyzed using NASTRAN SOL 101. For the maximal loading
conditions, their response was found to be roughly linear and their spring constants
are listed in table 8.3. For comparison, an ideal link was formulated using the same
volume of aluminum, length, and diameter, to show what the ideal performance
would be for a link without internal electronics. While bending can occur across a
number of axes, the chosen alignment gives the minimum and maximum bending
stiffness for the body. For the system wide analysis, the bending axis of lowest
stiffness will be used. As seen below, stiffness is reduced when using non-optimal
link geometry by an order of magnitude. Thus, the assumption that the link stiffness
has little influence on system harmonic frequency and stiffness is no longer true.
Table 8.1: Stiffness stackup of the original and ideal links for RTSX
Ideal Original
Ideal Link Original Link Gearbox Joint/Link Joint/Link
Axis of
Stiffness Limit Stiffness Stiffness Combined Combined
Torsion
kNm/rad kNm/rad kNm/rad Stiffness Stiffness
kNm/rad kNm/rad
Bending (XX) 6066 50.7 67 66 59
Bending (YY) 6066 3437 67 66 65
Torsion (ZZ) 13714 181.3 67 67 49
36
8.4 Prototype Link Layout
Figure 8.2: Cross section of prototype shoulder housing
After exploration of the design space, a prototype shoulder module was con-
structed with the goal of minimizing cost. As mentioned in figure 5.2, the shoulder
module was constructed using the B2 and D2 cross section design, which necessi-
tates an endoskeleton type structure. To reduce cost, the system was sized to use an
American Standard I beam as stock. Assembly tolerances prevent any welding along
the structure, so all components in the primary structure chain must be bolted to-
gether. This results in more components in the assembly and requires more precise
machining tolerances to reduce error stack-up.
This design was quickly abandoned for future links because of assembly diffi-
culties, torsional stability, and the quantity of components. The next housing design
37
Figure 8.3: Side-by-side comparison of original and prototype wrist housings
to be produced was constructed in an attempt to greatly reduce the number of crit-
ical mechanical components. Instead of bolting together fittings to the primary
structure, both ends of the link were limited to using the original marman band
fasteners only. The challenge exists in trying to find a common bolting design that
can be adapted to fit each of the multiple interfaces on the RTSX platform, as well
as survive all of the forces that the arm is subjected to.
8.5 Prototype Analysis
One redesign goal for RTSX was to make the electronics more accessible to re-
duce maintenance time. After several design iterations considering tradeoffs between
structure, machinability, and operation, a side-loading design with a removable lid
was selected. To assess the usefulness of such a design, a prototype was constructed
and implemented on RTSX. This design concept was found to be effective, but it
came with several disadvantages. Most importantly to this analysis, the side-loading
housing created an open cross section, which proved to be unacceptably flexible.
38
Figure 8.4: RTSX prototype link flexibility being tested using a visual tracking
system.
Table 8.2: Comparison of torsional stiffness between link designs
Prototype Side-
Original Link Final Side-Access
Access Link
Stiffness Link Stiffness
Stiffness
Worst Case Bending kNm/rad 507 161 584
Torsion kNm/rad 181 127 345
Average Link mass kg 8.6 8.0 4.3
The prototype side-loading design greatly decreased servicing time for RTSX,
but its open cross section did not meet the required stiffness in bending or torsion.
Flexibility tests were conducted in neutral buoyancy 8.4, evaluating the tool tip
deflection throughout a variety of poses and tip forces. Tip deflection was measured
using a multi-camera motion capture system. Over the range of forces RTSX was
designed to output, tip deflection was found to be as much as 11mm, which is out
of acceptable bounds for many of the intended operations. To improve performance
to acceptable levels and still use the side-loading design, the lid must be integrated
to the link structurally to close the cross section.
While there are several structural disadvantages to using a side loading link
39
Figure 8.5: Final link design for RTSX
configuration, it is possible to mitigate these through analysis and design. By loading
the electronics into the side of a structural link, the cross section must be split to
allow for access. This is problematic as the torsional stiffness of the link is greatly
reduced and the shear center is moved outside of the link body. Unless the link body
is sufficiently built up, which would be very massive, a lid must be firmly bolted to
the link body to close its cross section. While we have found it possible to operate
the robotic system without closing the links, the tool tip stiffness is noticeably
reduced. Machinability is easier as the geometry of the link is restricted to the
outside perimeter, but machine time is increased to support lightening features such
as isogrids. Accepting these requirements, allowing link-integral electronics to be
accessed through the side of the link reduces maintenance time from days to hours.
The side-loading housing was updated to use a series of shear bolts to pin the
lid of the housing to the body of the link. This design change reduced the flexibility
of the link to acceptable ranges. Due to packaging constraints, it was not possible
40
to bolt continuously along the length of the lid. Some flexure and slippage occurs
in the interstitial space between the bolts, but the increase in stiffness was found to
be acceptable. Lightening features were also added to the link body to increase the
allowed tip mass of RTSX, reducing the total assembled mass of the link by 30%.
A geometric optimization was also performed on the link design to determine its
isogrid geometry while still maintaining adequate stiffness.
8.6 Conclusions
Integrating electronics into the link of a robotic arm is a non-trivial design pro-
cess. While there are several advantages to doing this for the electrical system and
general operations, it invalidates the standard assumption that the tool tip spring
rate is calculated using only the stiffness of the gearboxes. The structural design
process now relies on finite element methods to evaluate the link stiffness instead of
simple Euler-Bernoulli beam theory due to the non-symmetric and irregular geom-
etry inherent in electronics packaging. Given the benefits to electrical systems and
operations, packaging the drive electronics in a side-loading link design was found
to be preferable to the original design.
Implementing non-symmetric link cross sections requires a higher level of mod-
eling than the simplistic results found in table 8.2. To fully quantify the geometric
feature impact on performance of the asymmetric link, we must form a characteri-
zation matrix for the response of the link to external loads. The following chapters
are a detailed expansion of this analysis.
41
Chapter 9: Structural Inclusion of the Lid
A preliminary design analysis shows that even if the entire structural volume
allowed for the tray, pictured in Figure 8.3, were occupied with titanium, the tray
would still be too torsionally flexible to produce an acceptable design. To increase
the stiffness of the link in the designated design volume, it is necessary to either
reinforce the tray using stiffer materials such as carbon composites, or to use the lid
as a structural component.
9.1 Structural Connection Attempt
The prototype design assumed no structural connection between the lid and
the tray, as they were secured together with marman bands. The bands were de-
signed to impart only enough force to compress the perimeter face seal between the
lid and the tray. If the lid is to contribute to the torsional stiffness of the link, it
needs to transmit shear forces between the lid and the tray.
An attempt was made to provide a high normal force between the lid and the
tray and transmit the forces via friction between the tray and the lid. The design
selected used two tension members running through the diameter of the assembled
link. They can be seen at either end of the link shown in figure 9.2. These members
42
were tensioned by a set of Belleville springs to provide a high, but known tensile
force. The springs were compressed by a 7/16 double hight hex fitting, seen in
figure 9.1, and locked into place by a spring loaded retaining fixture to prevent
unintentional actuation.
Figure 9.1: External lid of an alternate lid Figure 9.2: Cross section view of an alter-
design nate lid design
While this design is simple for an operator to actuate, the tensile members were
not able to produce adequate surface friction between the lid and the tray. This
design was simulated using a linear static FEA with surface contact and friction
between the lid and the tray. The lid was not capable of distributing the normal
pressure across a wide enough surface to be effective, resulting in concentrated areas
of shear transmission only at the ends of the lid. Limits on the structural geometry
of the link prevented a sufficiently rigid design of the lid. A design had to be devised
to transmit shear across the length of the lid/tray connection, preferably by means of
a mechanical joint rather than frictional connection. After some design exploration,
it was found that shear bolts placed along the perimeter of the lid could be sufficient.
43
9.2 Bolted Lid Analysis
To alter the stiffness of the side-loading link design, a lid must be bolted
to the open face of the link to close its cross section. While forces on the bolts
spaced at regular intervals and placed on an infinite beam can be simply calculated,
understanding their interaction with the stiffness of the system is not as clear. A set
if system level loads were established and used to generate table 9.1. The following
analysis shows the numerical methods used to characterize the forces that the lid
bolts will be subjected to. These methods were then used for fastener selection and
placement, documenting the motivation behind the bolts selected.
Table 9.1: Loading values for RTSX 2 bay link design
Symbol Value [units] Description
V 1000 N Shear force imparted to the link
T 240 N-m Axial torque imparted to the link
R 0.068 m Radius of the link cross section
M 440 N-m Bending moment imparted to the link
L 0.2286m Effective length of the link
P 41000 Pa Internal differential pressure in the link
9.3 Calculating Bolt Forces
By bolting along the edge of the link housing, shear forces can be transmitted
between the link body and the lid. To simplify analysis, the link body was calculated
as a tube of constant wall thickness, bisected along its axis. The region of this
bisection is of interest. The goal of the analysis was to determine the forces to be
reacted by N number of bolts placed along the bisected edge to effectively “glue”
44
the sides of the tube back together. This calculation is done using the following
parameters.
For a hollow shaft under axial torque and small deflections equation 9.3 relates
geometry and torque to shear force.
T
τtorque = (9.1)
2πtr2
Pressure forces are also a significant contributor to the forces on the bolts.
These forces are calculated by observing the hoop stress generated for the cross
section of the link, detailed in equation 9.3. As we are not concerned with the hoop
stress across the link/lid system, merely the stress along their 1D interface, the thin
walled assumption can be used to simplify calculation. This yields the following.
PrL
Fh = (9.2)
2
Bending of the beam will also impart a shear stress across the bolt head. This
load is approximated by the resultant force from the moment as reacted through
the centroids of each shell half, shown in equation 9.3.
Mπ
Fbending = (9.3)
4r
For calculating the shear force involved in the transverse shear loading of the
link section, equation 9.3 was used.
These forces generate a tensile, shear, and moment force on the bolt. To
implement this design without failure, the following relations must be true:
45
V L
Fshear = (9.4)
2πr
1. The sum of all forces on the bolt must result in a Von-Mises stress lower than
the yield stress of the bolt.
2. The clamping force across the effective seam length of the bolt must be high
enough to overcome the moment generated along the seam. This prevents the
bolt shank from bending and breaking.
3. The preload force must be greater than the sum of all tensile forces required
of the bolt.
From these relations the following loads on each bolt can be estimated. They
are calculated on the surface of the thin walled cylinder at the seam. The sum of
shearing forces are denoted in equation 9.3 and the sum of compressive stresses are
in equation 9.3, totaling into equation 9.3
T Mπ V L
τx = [ + + ] (9.5)
2πr2 4rL 2πr NAbolt
Pr 1 T L
σy = [ + ] R (9.6)
2 2 2πr2
PL
NAbolt
Given the known values, and with a preload ratio (Rpl) of 2, the previous
equations simplify to equation 9.3.
After some examination of this design space, it was found that a likely solution
was by using between 2 and 5 bolts per side, using either 10-32, 1/4-28, or 5/16-32
bolts.
46
√
σ = σ2von y + 3τ
2
x (9.7)
33100
σvon = (9.8)
NAbolt
Packaging requirements made using four or more bolts difficult, as it impinged
on the packaging cross sectional area for the servo drivers. Finite element models
revealed that using less than three bolts per side caused the lid to lift free of the
gasket under certain loading conditions, leaving only the option of using three bolts
per side. For this application, high strength National Aerospace Standard (NAS)
or Military Standard (MS) bolts should be used, the yield strength of which is
approximately 1.1 GPa (160 Ksi), to reduce or eliminate the probability of fatigue-
based failure.
Another loading scenario must be considered. If the bolts are not preloaded at
all, they are subjected to a bending moment. This moment is equivalent to bending
the bolt shank with the sum of all shear loads at a distance of the lid thickness, in
this case 0.2 inches. Observing the yielding safety factor using a 1.1 GPa bolt, the
following holds true.
Operating RTSX with untightened bolts due to human error is possible. In
order to not yield the lid bolts in this case, bolt size 10-32 should not be used.
While the higher safety factor of 5/16-32 bolts is appealing, it makes packaging
more difficult and would add 5% to the length of the housing. Given these factors,
a 1/4-28 bolt size was selected for mating the lid to the link body.
47
Table 9.2: Stress caluclated per bolt in selected configurations
Von-Mises stress in bolt [MPa]
Bolt Size 2 bolts per side 3 bolts per side 4 bolts per side 5 bolts per side
10-32 807 538 403 323
1/4-28 437 291 218 175
5/16-32 272 181 136 108
Table 9.3: Safety factor for bolts considered
Bolt Size Nominal Safety Factor Untightened Safety Factor
10-32 2.0 0.6
1/4-28 3.8 1.6
5/16-32 6.1 3.1
9.4 Determining Parent Material Geometry
With bolt geometry selected, the geometry and properties of the parent ma-
terial must be selected to ensure proper operation. The goal of this design is to
minimize geometry volume without compromising the maximum bolt load. An
experiment was conducted to examine the minimum volume of material required
about a threaded surface in the parent material. Details about this experiment can
be found in Appendix C.
The results of this study were used to create keep out boundaries for subtrac-
tive features that could intersect threaded features. These boundaries are modeled
as tapered cylinders with the base of the cylinder starting at the face of the threaded
surface. This was very useful for the design process and provided a better sense of
what subtractive features would be allowed. The final geometry was selected as to
not intersect with the keep out boundaries at all, so the tapered cylinder surface is
not visible. This method may be of more utility in other designs were a subtractive
feature must intersect a threaded surface.
48
Chapter 10: Stiffness Analysis of Non-Axisymmetric Beams
This section details mathematical and analytical methods for characterizing
the structure of the link. Typically, the link stiffness would conform to the structure
in equation 10. This matrix is created as a characteristic equation of a link section
assuming it is analogous to an Euler-Bernoulli beam. When the center of shear of
a beam is coincident with the centroid and neutral bending axis, there is limited
coupling between shear and moment forces in a beam. Figure ?? illustrates the
minimum characteristic matrix for a cantilevered beam. However, once the center
of shear beginsto deviate from the centroid, cross coupling becomes rampant.
 L
3 2
0 0 0 L 0
3EIxx 2EIxx 30 L 0 −L2  0 0 3EIyy 2EIyy [ ] [ ]L 0 0 0 0 0 EA V δ zz −L2 L  = (10.1) 0 0 0 02EIyy EIyyL2 0 0 0 L 02EI EI 
M φ
xx xx
0 0 0 0 0 L
GJzz
When an eccentricity exists between the shear center and the center of bending,
the effective bending stiffness is reduced and axial torsion is coupled with beam
deflection. This interferes with the system in two ways: decreasing the stiffness and
causing out-of-plane responses to forces. The results of such an eccentric distance ε
in the X and Y axis can be found in equation 10.1.
49
 L3 0 −εxL2 2 0
L −εyL
 3EIxx 2EIxx 2EIxx 2GJzz3 2 2  0
L −εyL −L 0 εxL
3EIyy 2EIyy 2EIyy 2GJ

zz
 [ ] [ ] 0 0
L 0 0 0 
EA V δ
 zz 2 2 = 0 −L
εyL L 0 0  M φ
2EIyy 2EIyy EIyy 
L2 0 −ε L
2
x 0 L

0 
2EIxx 2EIxx EIxx
−εyL εxL 0 0 0 L
2GJzz 2GJzz GJzz
Figure 10.1: Extended characteristic equation for a link accounting for eccentricity
of the center of shear
It should be noted that the coordinate frame for this transformation is not
typical for Euler-Bernoulli beam bending. As this design will be applied to robotics,
a different frame was selected. Denavit-Hartenberg parameters, a common coordi-
nate frame convention for robotics, aligns the Z axis along the axis of rotation for
the previous joint.
10.1 Verification of Model
This modeling method of deriving offsets and gross geometry properties from
experimental finite element analysis was tested using a simplified model. The test
beam was a 25.4mm diameter, 305mm long cylinder with a Youngs modulus of 68.9
GPa. The orthogonal test forces were applied individually to solve for each column
of the matrix, using a tip force of 90 N and a tip moment of 2.26 N-m. Two more test
cases were run, using a -25.4mm eccentricity in the x and then y axis. Solving for
the magnitude of error between the predicted matrix and FEA matrix, the following
error range was found, averaging across all solutions.
Very little deviation exists between a finite element model and the Euler-
Bernoulli model except in C16 and C26. There is almost no correlation between
50
Table 10.1: Percential error between the extended model in the compliance matrix
modeled in equation 10.1
Cx1 Cx2 Cx3 Cx4 Cx5 Cx6
C1y 1.92% 0% 0.783% 0% 2.38% 100%
C2y 0% 1.92% 0.783% 2.37% 0% 100%
C3y 0% 0% 0.569% 0% 0% 0%
C4y 0% 0.562% 0.011% 0.059% 0% 0%
C5y 0.562% 0% 0.011% 0% 0.059% 0%
C6y 0.766% 0.766% 0% 0% 0% 2.27%
these values in the model and the results from the finite model simulation, showing
a breakdown in the simplified model. Fortunately, these values are relatively small
and have little influence on the overall performance of the link. Considering these
error ranges to be reasonable without refining the finite element mesh, the same
methods were applied to the original, prototype, and final upper arm link.
Deviation of a link design from a predictable Euler-Bernoulli model can be
considered detrimental to the control and operation of a robotic manipulator. Very
simple control models do not account for the flexure of components in the system.
More complex models predict and compensate for the flexure of components, but
only in simple terms to reduce controller complexity. It is expected that deflection
will be in plane with the deforming forces. Deviating from a simply predictable
Euler-Bernoulli model causes deflections to deviate out of the plane of the deform-
ing forces. While this will occur in axisymmetric cases due to out-of-plane warping,
limiting this deformation to an insignificant level is important. The resulting com-
pliance matrix of the original housing is shown in equation 10.1
The dominating region in the compliance matrix in equation ?? is C44 C55
C66, equating applied moments directly to angular deflection about the same axis.
51
  28.6 0.3 0.5 −1.1 337.2 40.8 0.2 199.9 0.4 −110.4 8.5 −33.6 0.4 0.4 2.6 −2.7 6.9 −1.8−0.9 −98.1 −2.0 772.3 −35.9 35.6 
 = C 9original × 10 (10.2)
313.9 7.8 7.8 −35.7 3861.3 −42.4
39.2 −39.2 −1.8 18.9 −24.1 5405.9
As mentioned before, due to the geometry of a long serial-link manipulator, angular
deflections in manipulator components dominate the stiffness of the tool tip. While
the largest component is C66, this deflection only affects tip stiffness in off-axis poses
where a significant torque can be applied to the link body.
  85.7 −0.1 11.4 −0.7 449.6 −0.7 −0.1 228.4 0.0 −112.4 1.9 1123.9 

−11.4 0.0 5.7 −0.1 −86.4 −0.2  9 − − − = C × 10 (10.3)0.7 137.3 0.1 772.3 −5.8 55.6  prototype412.0 1.4 78.5 −6.4 3089.1 1.9 
−0.6 1569.5 −0.3 49.7 7.2 14673.1
A large amount of coupling can be observed in C62 and C26 of equation 10.1.
This is attributed to the open cross section of the prototype link, which places the
center of shear away from the neutral bending axis. It should also be noted that
the magnitude of C66 is much greater in the prototype housing, denoting that is is
more compliant. This too is due to the open cross section of the link tray. Note
that the magnitude of C44 and C55 are nearly comparable between the original and
prototype housing, which follows as one was used as the design basis for the other.
The final housing compliance matrix, shown in figure 10.2 shows an overall
stiffer link. Coupling has been greatly limited from previous designs. To fully
understand how this improvement impacts the performance of RTSX, an evaluation
52
  85.7 0 −8.6 0.2 337.2 −0.2 0 28.6 0 −112.4 −0.3 56.5  −8.6 0 5.7 0 −70.4 0 0.2 −117.7 0 772.3 1.7 31.9 
 = C 9final × 10
333.5 −0.2 −78.5 1.5 3089.1 1.8 
−0.4 58.9 0.0 33.7 1.2 2316.8
Figure 10.2: Characteristic compliance matrix of the final housing, shown in N, m,
N-m, and radians
method was constructed to compare how the link designs flex, not just their overall
magnitude.
10.2 Evaluation of Characterization Data
To demonstrate the impact of coupling terms on the tool tip stiffness, we can
examine a simplified scenario in Cartesian space. Say the link is the most proximal
component of a serial-link manipulator with a tool tip located at [1,1,1]m. A linear
force is applied to the tool tip and the resulting forces on the link are [1,1,1,1,1,1].
Using these components as generic inputs, the impact of each value in the compliance
matrix can be calculated. This result will be referred to as the Impact Percentile
Matrix (IPM).
An ideal distribution for the IPM was created using the ideal link geometry
described in section 18. Note that in an ideal IPM P44=P55=P66, P15=P24=P42=P51,
P11=P22 and all other values have little impact on the deflection of the tool tip.
This observation again confirms the starting simplification of this design process,
that angular deflection of the link due to applied moments has the largest impact
on tool tip stiffness.
53
 6.58 0 0 0 2.58 0  
 
0.25 0 0 0.01 2.93 0.35 0 1.74 0 0.96 0.07 0.29  0 6.58 0 2.58 0.01 0.01    0 0 0.02 0.02 0.06 0.02  0 0 0.06 0 0.01 0  

0.01 0.85 0.02 6.70 0.31 0.31 
0 2.58 0 25.42 0.03 0 
2.73 0.07 0.07 0.31 33.52 0.37 
2.58 0.01 0 0.03 25.42 0 
0.34 0.34 0.02 0.16 0.21 46.93
0 0.01 0 0.04 0.04 25.42
Figure 10.4: Original link IPM distribu-
Figure 10.3: Ideal IPM distribution
 tion 0.37 0 0.05 0 1.96 0    1.13 0 0.11 0 4.46 0 0 0.99 0 0.49 0.01 4.89 0 0.38 0 1.49 0 0.75 0.05 0 0.02 0 0.38 0   0.11 0 0.08 0 0.93 0  0 0.60 0 3.36 0.03 0.24   0 1.56 0 10.22 0.02 0.42 1.79 0.01 0.34 0.03 13.44 0.01 4.42 0 1.04 0.02 40.90 0.02 
0 6.83 0 0.22 0.03 63.85
0.01 0.78 0 0.45 0.02 30.67
Figure 10.5: Prototype link IPM distribu-
Figure 10.6: Final link IPM distribution
tion
The out of plane deformations observed in the finite element results are due
to warping and the location of the shear center. A cross sectional center of shear
that is not coincident with the neutral axis of bending of the beam will result in
torsion of the beam in addition to Euler-Bernoulli based deflection. This out-of-
plane deflection is problematic as the tool-tip deflection is no longer in line with the
applied forces.
Unequal contribution of C44 C55 C66 to the tool tip stiffness will result in
a higher influence of manipulator pose on the stiffness. To simplify the control
scheme of the manipulator, it is desirable to have equal contributions from all three
components. A comparison between the origina, prototype, and final redesign link
is shown in figure 10.7. Note that the magnitudes of C44 C55 C66 deviate more
than the original design in the prototype, and less than the original design in the
final version. This shows a significant improvement in performance between the
54
prototype and final design.
Figure 10.7: Spread of tip deflection contribution
10.3 Influence of Tool Tip Stiffness
Tool tip stiffness is one of the driving design characteristics of a robotic ma-
nipulator. In terms of positioning error; the stiffer the tool tip, the lower the force
deflection, the more accurate positioning becomes. Compliance control uses a force-
torque sensor at the tool tip to observe the tool force and to allow the manipulator to
be compliant in desirable ways. Ideally, this would be conducted with a manipulator
of infinite stiffness, but this is unfortunately impossible.
When performing a task that requires an accurate tip force, such as making
an incision in surgery or laying carbon fiber on a form, the manner in which the
tip deflects can affect the performance. If the tip deflection is not symmetric to the
tip force, unintended motion will result. As an example, let‘s consider a 6 degree
of freedom manipulator with an asymmetric tip stiffness that is being programed
55
to cut out a pattern with a knife. A simple method would be to make a trajectory
across the surface with the tool tip and apply a specific force normal to the cutting
surface. As the blade edge presses in, it will react with a force normal to the surface,
but lateral forces will also be generated due to the asymmetry. The robot may be
able to trace a perfectly straight line across the face of the surface, but when trying
to cut using the same trajectory the line will warp.
Predictability of motion is extremely important for any robotic task. If a
robot tasked with surgery or welding cannot keep a straight line, it is of little use
for automation beyond coarse positioning. While it is possible to leave the task
of correcting this malfunction to the controls engineers, by using the analysis and
design techniques in this paper, it can be corrected in the mechanical design instead.
10.4 Conclusions
Based on the metrics created and evaluated in this chapter, the final struc-
tural design of the link is empirically better. The final link design is more rigid in all
bending axes, but more importantly it is more uniform in its deflection. Eccentric
Euler-Bernoulli type beam loading is limited with the final design by reducing the
eccentricity of the shear center, compared to the prototype link. In making the
link design similar to an ideal beam, dominated by the torsional deflection compo-
nents C44, C55, and C66, the link will deflect in a more predictable manner when
implemented in a long serial-link manipulator.
56
10.5 Potential for Future Work
This method of analysis has shown that eccentricity between the center line
of shear and the load axis causes a moment about the center of shear, resulting in
a torque applied to the link. In robotic manipulator design the joints are frequently
offset from one another, either to increase the range of motion, or for stowing the
manipulator. A serial link robotic manipulator can be designed with asymmetric
links such that the position of the center line of shear intersects the joint, and
virtually eliminates the structural offset. This would allow the use of massively
asymmetric link structures and would increase the tip stiffness of the manipulator.
However, this may result in reduced torsional stiffness of the link, which should be
studied and manipulated as needed.
57
Chapter 11: Tray Geometry Optimization Study
A study was conducted to find the optimum material geometry for the tray.
Previous design requirements have determined the bounding inner and outer cross
sections. Initial deflection simulations determined that leaving the sidewalls of the
link solid resulted in a design that was rigid, but excessively heavy. However, if the
sidewalls are reduced to the minimum machinable thickness of 0.125 inches, shown
in Figure 11.1, the link becomes unacceptably compliant.
Figure 11.1: Cross section of the link featuring the minimum wall thickness
Using these two extreme cases as bounds, the following designs were explored.
To limit degrees of freedom in this design study, the base material was set to 7075-
T6 aluminum, no other materials could be added to the system, and the final design
must be machined using subtractive methods.
58
11.1 Varied Wall Thickness
The simplest method to lighten the outer walls was to find the minimum wall
thickness that achieves the desired stiffness. This was a simple process, allowing the
optimizer to manipulate the thickness of each of the three walls independently while
targeting a minimum torsional stiffness. The result, shown in Figure 11.2, reduced
the mass of the link marginally, but not to any desired range.
Figure 11.2: Cross sections of the link featuring optimized wall thicknesses.
11.2 Flange
To reduce mass but maintain bending stiffness while keeping machining simple,
a stiffening fin design was created, pictured in Figure 11.3. The concept was to add
I-beam-like flanges to the exterior of the link housing to increase bending stiffness.
While this design did function properly in bending, it was not stable in torsion. This
design was not put through the optimizer, as it was determined to not be viable at
even its extreme cases.
59
Figure 11.3: Cross section of the link featuring flanged wall features
11.3 Orthogrid
Figure 11.4: External view of the orthogrid geometry tested for the link 1
Orthogrid geometry is orthotropically stiff across the surface it occupies. This
is frequently used on the exterior of a pressurized cylinder, given the two primary
forces: hoop stress and axial stress. This can be found everywhere in aerospace,
from the fuselage of a plane to the pressurized modules on the space station. It is
1Due to a computer error, the archived copy of this design was lost. This is the best image
available, taken from an uncorrupted thumbnail.
60
a useful geometry to prevent buckling of a thin outer shell. Coincidentally, when
applied to this design, the minimum machinable thickness for the inner wall is not
very susceptible to buckling. Extremes of this geometry were unsatisfactory when
the structure was subjected to torsion. Geometry optimization was not conducted.
11.4 Isogrid
Another common geometry used for stiffening structures is isogrid. This geom-
etry was created with the intention of creating a surface that is isotropically stiff at
the node points. Unlike the flange and orthogrid geometry, this has a high torsional
stiffness and optimization was allowed to proceed. Isogrid has multiple geometry
features that can be varied for optimization, so preliminary manual searches were
conducted to down-select optimization variables.
Figure 11.5: External view of the tray featuring isogrid lightening geometry
61
11.4.1 Base Geometric Design
The Isogrid Design Handbook [1] describes various methods of analytically
designing isogrid for certain scenarios. Isogrid designs on cylinders are generally
optimized for two primary loading conditions: axial and torsional stiffness. This is
achieved by aligning one of the three rib chords either along the axis of the cylinder
or along the diameter respectively. In this case, the latter orientation was selected,
as the biggest design limitation has been the torsional stiffness of the link.
It should be noted that due to the ratio in this design between rib height,
node separation, and wall thickness, it does not observe the classical properties of
an isogrid. In a classic isogrid, the wall of the structure carries the bulk of the load,
and the ribs exist to stiffen the wall from buckling and other phenomena. In the
case of the design in Figure 11.5, the ribs take the bulk of the load of the structure.
This makes the structure more of an isotruss than an isogrid, since it behaves as if
there is no wall. We are able to design in this region because of improvements in
finite element methods since the creation of the Isogrid Design Handbook.
Node spacing is another important aspect to isogrid design. While it can be
used as a variable for improving the specific stiffness of a design, node spacing is
more frequently altered to improve mounting point position. In this design, nodes
are spaced to align with the fasteners for the lid. Coincidentally, this eliminates
the geometry generated through an extensive study to find the minimum parent
material geometry about a threaded hole. The results of this study are noted in
Appendix C.
62
11.4.2 External Mounting Points
A beneficial design aspect for isogrid is the geometry of the nodal points.
Because of the rounded corners of the equilateral triangle pockets, a somewhat
massive region of featureless volume remains at the nodal points. In some instances
this volume is diminished by a circular hole bored into the node. This feature can
be sized to have little to no impact on the performance of the isogrid surface and
is an additional mass saving measure. However, the nodal area can also be used as
a mounting point, taking advantage of the unused material volume and the flexural
properties of the isogrid at its nodes.
External mounting points on a link body are of great utility for several reasons.
Fiducial based visual tracking systems require accurate knowledge of the locations
of the markers. By adding an absolute set of mounting points on the surface of a
robotic manipulator, visual tracking markers can be attached and calibrated easily.
Mounting points also allow for the addition of additional structure. During
testing of robotic manipulators it is not uncommon for them to suffer collisions,
either with themselves or with the environment. This is true of RTSX as well. How-
ever, while industrial robotic systems are capable of withstanding such collisions,
aerospace manipulators are far more fragile. To reduce the probability of damage
to the system due to collision, a sacrificial cover was designed to be mounted to the
exterior of the link. In the event of a collision, this plastic cover will crush to absorb
energy from the impact. Thanks to the recent reduction of cost in 3d printing tech-
nologies, we are able to produce replacement cages cheaply and quickly in house,
63
Figure 11.6: Reflective fiducial markers attached to a protective housing
making a disposable crash cage affordable. A rendering of this design is shown in
figure 11.6
11.5 Optimization Method
Optimization was carried out by using the Geometric Optimization toolkit
built into Siemens NX [2]. This toolkit navigates the design space by manipulating
selected variables, such as the thickness of the isogrid web, and testing the design in
finite element analysis (FEA) software. In this instance, the optimization was carried
out using the NX NASTRAN Solver 101, observing maximum angular deflection of
the link. The finite element analysis performed used the extreme tip loading cases
found in Table 5.1.
Optimization of the isogrid geometry was done by varying the wall thickness
of the tray and the web thickness of the isogrid. The test case was torsional loading
64
of the assembled link and lid, using the maximum angular deflection as the output
for the optimizing function. Additional geometry was attached to either end of the
simulated link in order to mimic the properties of the joint hardware at either end
of the assembly. The goal of this process is to engineer a link with the required
stiffness and minimum mass.
Initial finite element runs were conducted using an initial wall and web thick-
ness of 0.04 inches. While not easily machinable, it is within a generous span
of potentially manufacturable geometries. The results of this first simulation are
shown in figure 11.7, which depicts the absolute nodal displacement. In this figure,
the center of shear is visualized by the blue dot on the closest face, the area of least
displacement since it is the center of the rotation. Note that with this very thin
geometry, the center of shear is almost centered on the mid-line of the link.
Figure 11.7: Isogrid geometry optimization, step 1
The design converged to a nominal thickness of 1/8 inch, an easily machin-
able geometry. Figure 11.8 shows the results of the final simulation, depicting the
absolute nodal displacement again. Observe that not only is the magnitude of dis-
65
placement smaller, but the center of shear has shifted. While previously considered
to be undesirable, it was found that a moderate amount of eccentricity of the shear
center is allowable if a higher torsional stiffness can be achieved.
Figure 11.8: Isogrid optimization, final iteration
11.6 Conclusions
This design method explored the possible lightening geometry for the exterior
of the link tray. The process was conducted assuming the interior boundaries were
invariable and predefined by the motor controller packaging study which was previ-
ously conducted. The exterior boundary was formed by the diameter of the original
link, a geometry which prevents self-collision of the links. This study explored five
different methods for lightening the exterior geometry while maintaining adequate
bending and torsional stiffness. Further lightening methods could be explored, but
the performance produced by the selected isogrid design was found to be acceptable
and the iteration study stopped, although further iteration is possible.
66
Chapter 12: RTSX Standard Internal Interface
The RTSX platform features six unique mechanical interfaces between the joint
modules and their accompanying link body, or the previous link. These are shown
in figures 12.1 and 12.2. A question arises as to approach: should a unique link
body be manufactured to interface with each joint module, or should a component
be manufactured to adapt each joint module to a standard mechanical interface?
This was prototyped to understand the constraints imposed on the design space.
The original design for DXE used stainless steel fittings for both side of the
marman band interface. This served as the only adapter in the kinematic chain of
DXE. PXL used a large mounting plate to attach the electronics housing to the joint
module, which when removed allowed for access to the internals of the transverse
Figure 12.1: PXL electronics mounting interface
67
Figure 12.2: DXE link mounting interfaces
link. Both of these adapters in DXE and PXL are heavy, constructed from stainless
steel or thick aluminum. This approach was re-thought for the DXE prototype
housing, opting to make the marman interface an integral feature on the link body,
rather than a separate part.
A survey was taken of all of the mechanical interfaces across the reused hard-
ware from the original RTSX design, depicted in figure 12.3. It was found to be
possible to remanufacture the mating components to have a more advantageous
connection scheme. This was investigated but deemed too costly given the size
and complexity of the components involved. Therefore, a common link design was
created, using adapters to connect to existing hardware.
68
Figure 12.3: Use of adapters between joint modules and link bodies in all three
RTSX revisions
12.1 Load Transfer
The RTSX standard link interface is the point of highest stress in the entire
RTSX kinematic chain. The available area for fasteners is very limited by packaging
concerns, drastically reducing options for connecting the link body to the system.
A regular distribution of fasteners across a surface will react an out of plane
moment about the elastic center of the distribution. For symmetric distributions
such as bolt circles or four bolts in a square, the elastic center is also the center of
the bolt circle or square. As the bending plane is rotated about this elastic center,
a set of limber and stiffer axes of bending are established. The most limber axis
of bending will yield the maximum pullout force on a single fastener for a regular
distribution. For a rectangular bolt pattern, the worst case pullout force applied to
69
each bolt given an applied moment is defined by equation 12.1 and 12.1, produced
by Moo-Zung Lee [3].
√
M M a2 + b2
F = = ( ), a ≤ b (12.1)
2a sin θd 2a b
4M
F = , N ≤ 3 (12.2)
ND
A variety of bolting patterns were analyzed to find an acceptable mounting
pattern. Exploration of the geometry found that the maximum dimensions of a
rectangular bolt pattern were 1.375 by 2.5 inches with a 5/16 bolt diameter. Using
the formula in figure ?? and the loading conditions in Table 5.1, the maximum
tensile force on the bolt is 3200 lbf with a fastener stress of 41 ksi. Circular bolting
patterns were limited by the half-moon shaped mounting area, making the maximum
possible bolt circle approximately 1.5 inches in diameter with 6 fasteners and limited
to 0.250 inch diameter bolts. The maximum tensile force is 1700 lbf with a fastener
stress of nearly 35 ksi.
Since both bolting patterns yield approximately the same fastener stresses,
other factors must be considered in selecting an appropriate layout. Finite element
models were constructed of both fastener patterns to explore potential issues re-
sulting from stress flow. This revealed that the bolt circle layout generated a large
bending moment across the bolted face. The moment is caused by the increased
distance between the fastener and side walls of the tray. The rectangular bolt pat-
tern places each fastener as close to the side walls as possible, reducing the bending
distance to a minimum.
70
12.2 Surface Pressure
In most cases, fasteners are constructed from materials with a higher yield
force than the parent material they interact with. This has an unfortunate effect
on the fastened joint in where the parent material may start yielding before the
fastener. The contact surface between a bolt head and the parent material must be
examined for potential wear and eventual loosening of the fastener.
The bolts implemented on the standard RTSX interface are NAS6307-8 bolts,
a 7/16-20 hex head bolt constructed from A-286 stainless steel. Each bolt has a
tensile breaking strength of 17000 lbf and a contact area of 0.146 in2, resulting
in a maximum contact pressure of approximately 116 ksi. The parent material is
constructed from aluminum 7075 with a yield strength of 73 ksi, which will cause
the contact surface to plastically deform if the bolt is ever subjected to forces that
high. If such an event occurs, it would be advantageous if the bolt deformed and
broke before the parent material.
Shigley [4] models the compressed member under a bolt head as a frustra
spreading from the bolt head to the midpoint of the grip. There is some debate over
the half-angle of this cone, ranging from 45◦ to as small as 25◦. Based on this range,
the bolted connection would need to have a stiff washer to spread out the load to
the maximum acceptable surface pressure with a thickness between 0.09 and 0.04
inches.
71
12.3 Reducing Thermally Induced Stress
There are several concerns in a bolted interface outside of load transfer and
surface pressure. Galvanic corrosion and fatigue can lead to cycle induced failure
of a bolted connection, but there is another more frequently overlooked phenomena
that can be more damaging. Bolted connections are frequently built up with several
different materials, all with different coefficients of thermal expansion (CTE). The
defining equation showing thermally induced axial forces on the bolt are shown in
equation 12.3 Considerations must be made for thermally induced stress caused by
a differential between CTE in materials used in the connection.
Σn mi=1Li∆T (CTE)i − Σj=1Lj∆T (CTE)j
∆FT = 1 1 (12.3)+
n EiAi n E AΣ L j ji=1 i L Σi j=1Lj Lj
Fy > ∆Ft + ∆Fpl > 0,∆Fpl > 0 (12.4)
If the system exceeds the boundaries in Figure 12.3, it will be considered to
have failed. If the sum of preload and thermally induced forces exceed the yield
strength of any material in the chain, yielding will occur. Yielding would cause
the fastened connection to loosen, possibly enough to remove all preload once the
connection returns to its assembled temperature. If the sum of forces are negative,
the connection will become loose, resulting in the same complications.
It is possible to create a bolted connection that is thermally invariant. If
the proportions and CTEs of all components in the connection chain are selected
carefully, the fastener and the sum of the parent materials will have the same effec-
72
∑n ∑m
Li(CTE)i = Lj(CTE)i
i=1 j=1
Figure 12.4: Thermally invariant fastener chain
tive CTE. This is useful for decoupling the fastener preload from the CTE of the
materials. This was done for the bolted connection in the RTSX standard interface.
The bolted section of the interface uses three different materials. The bolt is
constructed from A286 stainless steel, the tray is aluminum 7075, and the thrust
plate is titanium 6AL-4V. For simplicity, their CTEs from Table 1 have been copied
to Table 11 below.
Table 12.1: Coefficients of thermal expansion for selected materials
Material Location CTE (µm/m◦C)
A286 Fastener 16.9
7075-T651 Tray Body 23.6
Ti 6Al-4V Thrust Plate 8.6
The wall of the tray body has a known thickness of 0.333 inches and the thrust
plate has a minimum thickness of 0.15 inches, as determined in Section 12.2. Solving
for the thickness of the thrust plate, we find that the invariant plate thickness exists
at about 0.27 inches thick. For flight designs this is highly desirable, but was not
possible for this design iteration due to cost.
12.4 Fatigue
It is easy to overlook the loading cycles for fasteners in any design. For a
robotic manipulator, the number of cyclic stresses the system will endure throughout
73
its lifetime is quite large. For that reason, the fatigue life of the fasteners used in
the primary structure must be considered. While there are many different schools of
thought and analytical methods for determining fastener fatigue life, NAS standards
for fastener design were used. Design standards for high cycle fatigue dictate that
the fastener must be loaded to 10% of its total yielding strength at maximum. This
results in a fastener that is greatly over-sized for all other purposes, but will not
fatigue through the lifetime of RTSX.
12.5 Galvanic Corrosion
RTSX is designed to operate in a submerged environment, making it suscep-
tible to galvanic corrosion. To combat this, the exterior of RTSX is constructed
almost entirely from anodized aluminum. While the anodized coating is effective at
eliminating galvanic corrosion, difficulties arise at bolted interfaces. These fastener
assemblies feature bolts that do not match the galvanic potential of the aluminum
it is bolted into. Unaddressed, this will cause the interface to quickly corrode. For
that reason, the following mitigation measures were taken to reduce or eliminate
galvanic corrosion. The abrasion caused by the tightening of fasteners or applying
threaded inserts allows for oxidation and other coatings to wear. This can be seen
in the exterior bolts used to hold the base of PXL to its test platform in Figure 12.5.
To eliminate galvanic corrosion in the primary structure chain, fasteners are
shielded from the environment by o-rings. This allows for material selection for the
primary structure to be conducted without concern for the galvanic index of the
74
Table 12.2: Galvanic index of materials used in RTSX, taken from [5]
Min. Galvanic Max. Galvanic
Material Area of Use
Index [Volts] Index [Volts]
7075-T651 -0.78 -0.7 Primary Structure
316 Stainless -0.18 -0.1 Helical inserts and pins
Ti-6Al-4V -0.12 -0.04 Exterior fasteners
A286 -0.19 -0.11 Primary structure fasteners
Figure 12.5: Galvanic corrosion of the threaded holes on the base of PXL
materials, but is difficult to package correctly.
Note the pattern of corrosion found on the PXL base, shown in figure 12.5
as a white chalky buildup about the threaded feature. This galvanic corrosion
is caused by interaction between the parent material, fastener, and stainless steel
threaded inserts. Outside of the threaded feature and the countersunk hole it sits
in, no corrosion can be observed other than mild discoloration. Neither the coating
standard specified [6] nor the production drawing states that this feature should
be masked before or machined after the anodizing process. This corrosion is most
likely due to damage sustained while assembling the helical inserts. Note that the
threaded feature on the left has not sustained the same level of corrosion.
The prevalence of corrosion between parent material and threaded inserts is
75
problematic for the implementation of the threaded feature for the lid. This feature
must be exposed to the environment, so an adequate barrier between the thread
insert and the parent material must be formed. To solve this, a barrier coating is
pre-applied to the inserts used on the lid which should inhibit any potential corrosion
caused by assembly abrasion.
76
Chapter 13: Thermal Analysis of Original RTSX Design
The DXE link design integrated the servo drivers directly with the primary
structure. This reduced the number of parts and the number of thermal and me-
chanical interfaces. The electrical system was subject to several failures during
development. Multiple failures of the motor driver module and digital to analog
converter occurred due to an unknown and inconsistent mechanism. Failure was
attributed to assembly error and thermal issues by the operators, who remedied
this with a few design adjustments. In this section, a theory will be proposed as to
why these components suffered frequent failure, demonstrate how this mechanism
occurred, and justify several aspects of the redesign of the system.
13.1 Critical Components of Original Design
The original RTSX link structure was heavily integrated with a modular back-
plane design. The servo drivers sat perpendicular to the link body and penetrated
all the way through the structure. The link was produced by casting to allow for
several internal features unavailable with subtractive machining. The majority of
the design was finish machined with computer numerically controlled (CNC) milling,
but the card cages were finished via wire electro-discharge machining (EDM) due
77
to their thin but deep geometry. To waterproof the link design, the card cage was
encased with a stainless steel sheath which did not touch the cage. This meant that
all thermal load generated by the servo drivers must be conducted along the link
to either end where it could then be conducted to the environment. This design
feature limited the arm operationally, as it could not run on a continuous duty cycle
without overheating.
Wedge-Lok fasteners sat on either end of the servo driver board. They serve
two functions: locking the servo driver daughter card into place, and compressing
the heat spreader against the body of the link. The Wedge-Lok design was intended
to transfer heat out of the system through the clamped area directly under the
Wedge-Lok, similarly to the VPX standard discussed later. The final design used
this to also compress thermal grease across the entire motor driver card to increase
its transfer area.
The motor driver module was a large rectangular module and accounted for
nearly all of the thermal load generated in the drive electronics for RTSX. The
module was heat sunk through a milled hole in the back of the servo driver PCB,
against the heat spreader. This module contained only the drive electronics to
commutate signals from the motor, and to apply appropriate voltages and currents
to the brushless motor it controls. While its thermal output varied, it was estimated
at forty watts peak.
The servo driver heat spreader, pictured in Figure 13.2, conducted heat from
the motor driver directly into the link body behind it and to the Wedge-Lok interface
at both ends of the card. There are several points where it contacted the PCB, which
78
conducted away some heat, but more importantly prevented the heat spreader from
shorting against the servo driver. Thermal grease was applied between the motor
driver module and the heat spreader, as well as the heat spreader and the link body
to increase conductivity and account for any surface imperfections.
Figure 13.1: Top view of the servo driverFigure 13.2: Computer rendering showing
board the geometry of the heatspreader
Figure 13.4: Servo drivers installed in
Figure 13.3: Bottom view of the servo
RTSX
driver
13.2 Design Comparison to VPX Standard
This design bears a similarity to the VPX/VME64 standard frequently found
in military and aerospace computer systems. The standard connects a daughter
79
Figure 13.5: Finite element simulation of original forearm link showing out of plane
warping of the card cage
card to a backplane, and conducts all heat out of the system through a cold plate
and into the clamped Wedge-Lok ends. However, the heat spreader on RTSX is
insubstantial compared to the normal VPX implementations. The thermal flow in
this component should be studied further.
13.3 Preliminary Inspection
Inspection of the link structure reveals that its basic shape is two parallel rails
connecting the proximal and distal end of the structure, tied together with multiple
thin plates. In bending and torsion, this design proved sufficiently stiff for nominal
operation. This part suffers from a reduced torsional stiffness, as it features only two
separate continuous rails that run the length of the casting. As the link is torqued,
the card cages deform and warp. The planar feature separating each card is no
longer planar and has deflections up to one millimeter. This is of great concern as
its surface is the only conduction path for the servo drivers.
80
13.4 Failure Theory
While the failure of the motor driver modules was originally attributed to
thermal failure, the elements of the failure may be much more complex. As seen in
the preliminary analysis, the link body, and by extension the card cage, cannot be
considered rigid. This can allow for the following failure mechanisms for the servo
driver.
13.4.1 PCB Flexure
Flexure of the card cage can lead to flexure of the printed circuit board (PCB)
and its components, leading to premature failure. As this is a difficult mechanism to
examine due to the intricacy of the assembled board, we will leave this mechanism
mostly unexamined analytically.
13.4.2 Excessive Mating Pressure
The heat spreader directly contacts the motor driver. As the assembly bends
and flexes, it is possible to generate regions of high force from excessive mating
pressure on the module. This mechanism can be examined through finite element
analysis, though interpreting the results may be too subjective as even a low pressure
could cause fatigue failure.
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13.4.3 Motor Driver Failure
Similar to PCB flexure, this mechanism may play a large role in failure, but
is very dependent on the complex interaction of electrical components inside the
module. This should be observed, but further study was not possible within the
scope of this project.
13.4.4 Separation of the Heat Spreader from the Card Cage
We can safely assume that the area of the heat spreader located below the
Wedge-Lok clamps are held firmly in place. However, it is possible that the majority
of the area for the heat spreader could separate from the card cage. This is not a
critical failure point, as the heat able to transfer through the Wedge-Lok should be
sufficient.
13.4.5 Separation of Heat Spreader from Motor Driver
This mechanism is arguably worse than separating the heat spreader from
the card cage. Once separated, there is no thermal path out of the motor driver
module, save for the pins connecting it to the PCB. This has the added effect of
disconnecting the temperature monitor located on the PCB, which would allow for
unobserved thermal run away of the servo driver.
With the possible failure modes established, we can form a finite element model
to better judge these failure mode influences. Model geometry for the upper arm
link, PCB, Wedge-Lok, heat spreader, and the motor driver were all created and
82
then greatly simplified. Geometry that is of the most influence; the heat spreader,
PCB, and link body was preserved as accurately as possible. Connector pins were
replaced on the motor driver with a thin wall, and nearly all of the geometry on the
Wedge-Lok was eliminated. Only a single card was modeled near the center of the
housing for mechanical stress simulation, as this is the region of largest warping of
the card cage.
13.5 Steady State Thermal Design Investigation
To understand the impact on heat spreader separation, nominal thermal oper-
ation was studied. Using finite element analysis, the card cage design was evaluated
to examine performance with or without conduction through the back of the heat
spreader. For completeness, this is also explored for one or all servo drivers at max
thermal flux. The following evaluation was done using NASTRAN SOL153 and
observed only steady state temperatures.
The motor driver module has a maximum thermal flux of approximately 40
watts, and the joints that the link conducts heat out of has an approximate max-
imum temperature of 60 degrees centigrade. The motor drivers have a maximum
operating temperature of 125 degrees centigrade, above which we can assume they
will incur damage.
All of these simulations were performed assuming perfect conduction across
mating surfaces, most importantly the card cage to the heat spreader and the heat
spreader to the motor driver module. As there is no margin or even negative margin
83
Table 13.1: Steady state motor driver temperatures under various contact and load-
ing conditions
Maximum Failure
Test Condition Temperature Margin
◦C ◦C
Single controller with only Wedge-Lok conduction 125 0
All controllers with only Wedge-Lok conduction 170 -15
Single controllers with full heat spreader conduction 87 38
All controllers with full heat spreader conduction 100 25
allowed for operating without conducting through the rear of the heat spreader, it
can be concluded that some amount of rear conduction is required. This is evident
from the physical hardware, as many motor driver cards had thermal paste applied
to the rear of their heat spreader with the intent of doing just that. With this
knowledge, it can be safely assumed that separation of the heat spreader from the
link body is capable of causing thermal damage to the motor driver module.
13.6 Contact Pressure Evaluation
Analysis was performed using NASTRAN to calculate contact loops and ob-
serve contact pressures. Initial contact pressure for the motor driver module was
established by enforcing the maximum tolerance interference with the heat spreader.
Seven different loading conditions were simulated to observe the various loading
pressures on the heat spreader from both the motor control module and the card
cage. For the purposes of this analysis, a contact pressure of zero is considered not
contacting and therefor thermally insulated.
The highlighted region in Figure 13.10 shows the contact pressure on the in-
terface between the heat spreader and the card cage, directly behind the motor
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Figure 13.6: All controllers powered, Figure 13.7: Single contoller powered,
Wedge-Lok conduction only Wedge-Lok conduction only
Figure 13.8: All controllers power, con- Figure 13.9: Single controller powered,
duction through the full heat spreader conduction through the full heat spreader
driver module. Contact pressure between the heat spreader and the motor control
module is concentrated sharply along one outer edge. This appears to be due to
the increased stiffness around this region. Observing Figure 13.10 it can be noted
that this region of high pressure is close to the edge of the card, and also features a
larger volume of the heat spreader. Due to an access window cut into the body of
the heat spreader, the centerline of the component has nearly no bending stiffness
and is unable to react the forces evenly. Already we are able to observe a point of
thermal resistance, as the heat spreader does not apply pressure to the majority of
the surface it is conducting to and from.
To test mechanical deflection and change and surface pressure, one end of the
link housing was fixed and moments were applied to the other. As a long serial
85
Figure 13.10: Unloaded heat spreader pressure distribution. The area under the
motor driver module is higlighted with a red dashed box.
manipulator such as RTSX is accurately modeled using Euler-Bernoulli beam the-
ory, the dominant forces on the link body are bending moments. This analysis was
done using the maximum nominal bending moments the link will experience. Im-
pacts, overloading, and manufacturing defects will likely yield more extreme results;
however, that is beyond the scope of this analysis.
There was no appreciable change in contact pressure for the interface between
the heat spreader and the motor driver module while under bending. Similarly, at
the interface between the heat spreader and the card cage, only the very edge of the
heat spreader makes any measurable contact. While there may be a growing gap
in the non-clamped region of the module, analyzing the effects of that accurately
is beyond the scope of this study. What can be said from this analysis is that the
contact pressure is not distributed across the component, and that the efficiency of
thermal transfer will be reduced.
86
Figure 13.11: Applied moments. The red, green, and blue arrows represent positive
vertical bending, positive horizontal bending, and positive torsion respectively.
Figure 13.12: Contact pressure on the mo- Figure 13.13: Contact pressure on the mo-
tor driver module, unloaded tor drive module, worst case loading
Several observations can be made by examining the contact pressure distri-
butions of the six primary loading cases shown in figures 13.14 through 13.19. As
predicted, torsion of the link does affect the pressure distribution on the motor
driver, though they are comparable to the distribution change for vertical bending.
This is to be expected, as vertical bending produces comparable bending in the card
cage. Vertical bending causes nearly no change in pressure distribution.
The severity of change in contact pressure as a result of nominal structural
loads is of great concern. While a vertical bending event does not greatly affect the
87
contact pressure, torsion and horizontal bending nearly separate the contact area
completely.
13.7 Failure Method Review
Earlier in this chapter, five possible failure modes were stated. Given the
analysis above, the following statements can now be made.
13.7.1 PCB Flexure
Mechanical stresses and strains measured in the simplified finite element model
were far below yielding for any part of the board. While it was found that flexure
did occur, it is not known if that would have definitively impacted any component.
13.7.2 Excessive Mating Pressure
Mating pressures were concentrated into small regions across the entire motor
driver board and its components. However, there was no evidence that any of these
pressures were large enough to cause any component to fail.
13.7.3 Motor Driver Flexure
The motor driver module was modeled as a solid epoxy block of equivalent
dimensions. While the module did flex and had some mechanical stresses, they
were nowhere near the estimated yielding strength. Similarly to the PCB Flexure
theory, this may have impacted the component performance, but it is not possible
88
to estimate that given our knowledge of the system.
13.7.4 Separation of Heat Spreader from the Card Cage
As demonstrated, this is the most problematic mechanism and was most likely
the root cause of failure.
13.7.5 Separation of Heat Spreader from the Motor Driver
Pressure distributed across the motor driver module was insufficient and cre-
ated a poor thermal path. This pressure also varied and lessened during flexure
of the card cage. Overall, this region is under-performing and may have led to a
reduced operational duty cycle.
13.8 Conclusions
With this knowledge, several simple modifications can be made to this card
system to improve its performance. If the heat spreader material is changed from
aluminum to copper, the peak temperatures while only conducting through the
Wedge-Loks changes from 170◦C to 108◦C. The geometry of the heat spreader could
also be altered to equalize bending stiffness across the component to distribute
clamping force evenly and reduce inefficiencies in the system. By not depending
on contact through the rear of the heat spreader and by increasing the efficiency
of the thermal junction between the motor driver module and the heat spreader,
the coupling of mechanical flexure and thermal performance should be substantially
89
reduced.
Systematically, this has demonstrated multiple problems with prior packaging
of electronics which require large thermal dissipation inside of the primary structure
of a robotic arm. The primary structure cannot be assumed to be rigid, and its
flexure could be quite problematic to sensitive electronic components. Due to this
flexure, it is suggested that the electronic systems are mechanically decoupling from
the primary structure as much as possible. This can be problematic where thermal
junctions or high vibrations exist, but as is demonstrated later in this paper, it is
possible. It is also suggested that the length of the thermal path be reduced to
increase thermal efficiency. In the original RTSX design, heat must travel at least
half the length of the link before it can be dissipated. This can be greatly improved
if a few design aspects are changed.
90
Figure 13.14: Pressure distribution on the Figure 13.15: Pressure distribution on the
heat spreader under positive torsion heat spreader under negative torsion
Figure 13.16: Pressure distribution on Figure 13.17: Pressure distribution on
the heat spreader under positive vertical the heat spreader under negative vertical
bending bending
Figure 13.18: Pressure distribution on the Figure 13.19: Pressure distribution on the
heat spreader under positive horizontal heat spreader under negative horizontal
bending bending
91
Chapter 14: Thermal Redesign
To improve performance and reliability, the thermal management system for
RTSX was completely redesigned from the original concept. The redesign considers
mechanical isolation, packaging, and thermal flow with the goal of reducing the
system temperature while preventing flexure of the link body from flexing the servo
drivers.
14.1 Mechanical Isolation
In the previous design, servo drivers were rigidly clamped on both sides by
Wedge-Loks. This rigid connection caused the forces in the card to be statically
indeterminate, and allowed the PCB to be twisted and bent by the flexure of the
link housing. To prevent this from occurring, the connection method was rethought
assuming the link body it mates to will flex under load.
Grüblers formula, equation 14.2, solves for the number of degrees of freedom
(F) of a system. The input is the number of links (L) (including the world frame),
the number of joints (N), and the degrees of freedom for each joint (fi). Figure 14.1
details the kinematic diagram for holding a servo driver against the inside wall of a
link, showing five link bodies (including the world frame), six joints, and a sum total
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Figure 14.1: Kinematic diagram of the servo driver retainer
∑N
F = 6(L−N − 1) + fi
i=1
Figure 14.2: Grübler’s formula for calculating degrees of freedom in a mechanism
93
of 15 degrees of freedom. Using Grüblers formula, three degrees of freedom remain
in this system. These degrees of freedom are the three rotational degrees that the
motor controller can move in to compensate for primary structure flex, allowing
it to maintain constant contact with the wall. As it is assumed that the heatsink
has a sliding contact against the inner wall of the link, the only forces imparted to
the servo driver as a consequence of the link flexing are a small change in contact
pressure due to the linear spring rate of the retaining arms. This is discussed further
in section 14.2.
Figure 14.3: Finite element analysis show- Figure 14.4: Finite element analysis show-
ing surface pressure gradient at the servo ing stress in the pre-loaded retaining arm
driver contact for the servo driver
14.2 Retaining Arm Design
One of the unique challenges in this design is to apply rigid clamping pressure
to the heatsink of the HPU across a wide gap. Normally such a design is accom-
plished with spring loaded bolts or wedge-loks. Instead, a novel method of retaining
electronics must be created to satisfy this design. This uses two semi-flexible can-
94
tilevered arms to hold the motor controller against the outer wall and provide a
constant clamping force by virture of their spring rate.
14.2.1 Deformation Method
The retaining arms themselves can take on several forms. Original concepts
had the retaining arms use torsion springs to push a solid lever arm. While this
has the benefit of a discrete moving part and high stiffness outside of the intended
motion, it does suffer from several drawbacks. At the scale required by the design
volume, there are few commercially available springs that will exert the desired
force. It is nearing the limit of simple torsion spring design.
Tension spring based articulations were also explored, but they suffered from
similar problems. These discrete-spring based articulations are costly due to the
number of components required. They also suffer from high surface pressures, mak-
ing their durability low. Instead, a flexible structure was explored.
The final spring arm design uses a flexible cantilevered arm with all necessary
geometry machined into it. The geometry of the design was dictated by three factors:
desired tip stiffness of the cantilevered beam, maximum stress in the cantilever beam,
and maximum stress in the interface between the beam and the mounting rack. The
former two are defined by the Euler-Bernoulli slender beam equations, and the latter
is defined by a simple finite element analysis. To determine geometry, the properties
of the material it is constructed from must also be known.
95
14.2.2 Material Selection
A search was conducted to find a material with a high strength to stiffness ra-
tio, while not causing yielding to occur under small deformations. Nearly all metals
were incompatible with these when fully stressed. Many plastics have an unaccept-
ably low yield strength, making them also incompatible. Several compatible plastics
in the search area were found, including several 3D printed materials. Prototypes
were produced using the appropriate geometries and were tested. The 3D printed
plastics were found to be too brittle, and their allowable deformations to be too
small. All of the prototypes eventually fractured and failed catastrophically.
It was necessary to return to the original material search and select for materi-
als with very high safety factors which fail ductilely. Now the concern was no longer
ease of manufacture, so non-additively manufactured materials were considered. Ul-
tem 1000 was selected as it met all of these factors, and can still be machined. New
prototypes were manufactured and found to be superior to the 3d printed models,
and more than adequate to implement.
14.3 Thermal Transfer Between HPU and Link Body
The original RTSX card cage systems used thermal paste to improve con-
duction between the heat spreader on the motor controller card and the link body.
While it is possible to use thermal paste in this updated design, RTSX would benefit
greatly operationally by abstaining from the use of any pastes or fluids. Several dif-
ferent connection methods were tested, including bare metal on metal, and a brass
96
coated thermal gap filler was selected. Details about this test can be found in the
thermal testing section in Section 16.2.1.
97
Chapter 15: RTSX Thermal Design Evaluation
In order for RTSX to operate in numerous environments, it must be able
to output the heat generated by its servo drivers. Space manipulators typically
expel their generated thermal energy by radiation, and by conducting heat back to
the base vehicle [7]. RTSX will only be operating on land and in water now, so
redesigning the thermal path to transfer heat directly into the surrounding fluid by
free convection is a sensible solution.
15.1 Operating Environment
The operating environment for RTSX consists of three locations: laboratory,
water, and on deck at the Neutral Buoyancy Research Facility (NBRF). Laboratory
testing will be conducted in an air conditioned and dry short=sleeve environment,
which will account for the bulk of Ranger‘s use. In-water testing occurs fully sub-
merged in a pool of chlorinated water kept at 30◦C. A staging area, known as the
“deck” of the NBRF is a temporary testing area for RTSX between water operations,
which can reach temperatures of up to 44◦C and 100% humidity.
98
Table 15.1: Thermal system design requirements
Geometric property of a sing servo driver’s external surface area Surface Area
Simplified cylindrical link without stiffening geometry 0.014
Final link geometry with isogrid 0.02
Minimum
Environmental and operational conditions Required
that the thermal solution must survive Surface
Area
Q T T H
Scenario Description # mc inf min 2
[watts] [◦C] [◦
[m ]
C] [W/m2 ◦C]
Wrist stall in laboratory 1 11 65 20 0.5 0.49
PXL stall in laboratory 2 27 70 20 0.5 1.08
Wrist stall in water 3 11 65 30 20 0.02
PXL Stall in water 4 27 70 30 20 0.03
Wrist stall on deck 5 11 65 44 0.5 1.05
PXL stall on deck 6 27 70 44 0.5 2.08
15.2 Design Challenges
The tray of the new RTSX link serves as both as primary structure and the
only thermal path for the servo drivers. As was discussed earlier in this text, the
geometry of the tray was optimized for structural stiffness with minimal mass, with
only basic consideration given to thermal issues. Examining the outer surface of the
tray, the isogrid paneling increases external surface area by 40%.
Table 15.1 above illustrates several issues with the base design. The values
for free convection were taken from [8], and represent the approximate minimum
value for natural convection in that respective medium. Operation of DXE and
PXL in the water is roughly in the acceptable range; tests will need to be conducted
to demonstrate that this is acceptable. Operation on deck or in the laboratory
appears to fall at least one order of magnitude short of the acceptable range for
free convection. By the data above, the surface area of the link would need to be
99
increased by more than a factor of 100 to be within acceptable operating conditions
for scenario #6.
15.3 Thermal Design Solutions
Several options were considered to increase the rate of thermal transfer be-
tween the link body and the environment. Two active and two passive options were
considered: active cooling, solid state heat pumps, bolt-on heatsinks, and built-in
heatsinks respectively. The goal was to produce a design that can be physically
implemented on RTSX with low mass and preferably low cost.
15.3.1 Built-In Heatsink
Possibly the simplest solution would be to added additional features, such as
fins or pin heatsink geometry into the outside of the tray. No additional components
would be added and, as the geometry of the tray already requires a four axis CNC to
create, adding additional surface features is arguably simple. After some preliminary
design, this concept was found to require fin geometry that is too small for normal
milling. A built-in heatsink is not possible at this power density and free convection
coefficient.
15.3.2 Bolt-On Heatsink
A bolt on heatsink would be able to conduct thermal energy to a much larger
surface area to then be dissipated into the environment. The addition of a bolt on
100
heatsink was found to be viable, with several possible solutions. This solution ne-
cessitates two costly but critical design features: mating geometry to the base of the
external isogrid to conduct heat into the heatsink, and finned geometry to increase
surface area to the environment. After a review of options with manufacturing, it
was found that machining finned geometry was prohibitively expensive. Pursuing
other methods, two options were found: to create a monolithic part containing both
features using additive manufacturing, or to machine the isogrid adapter and bolt
on an off-the-shelf heatsink. The former option is effective and compact, but is far
more costly than the latter. Designs for both were created and judged against the
other solutions.
15.3.3 Thermal Electric Cooler
By increasing the operating temperature of the external surface, the surface
area would not need to be modified. The operating temperature required to extract
the thermal energy through free convection is prohibitively high, nearing 1400◦C. In
this regime, thermal transfer by radiation dominates, stabilizing at around 185◦C.
While more manageable, this is still too high for both human safety and is beyond the
operational temperatures for thermal electric coolers. It is not possible to implement
thermal electric coolers on RTSX.
101
15.3.4 Active Cooling
The only environments of operational concern are in air, which allows the con-
sideration of powered cooling. Forced air convection has the possibility to increase
the convection coefficient from 0.5 to 200 W/m2 ◦C or higher, though it is highly
dependent on fluid flow. The isogrid surface is a challenging structure to remove
heat from through forced air convection, as the pocketed structure will create re-
gions of high pressure but stagnant flow inside of them. With this in mind, ducted
flow paths are a necessity. After some review, impinged nozzle flow was found to
be a practical solution with the possibility of high convection coefficients, while re-
maining simple to calculate. This design was compared to the only other possible
option, the bolt-on heatsink. As the bolt-on heatsink required a number of ther-
mal connections and was a great deal more massive, the active cooling solution was
selected for prototyping and testing.
15.4 Impinged Nozzle Flow Design
Cooling the bottom of a milled pocket with convective airflow is challenging.
Without properly shaped airflow, the closed shape of the pocket can stagnate. As
computation of flow across a non-planar surface can be complex, a solution that
only cools with flow against the bottom of the pocket feature, rather than the
sides, greatly simplifies calculation and design. Impinged nozzle flow forces airflow
normal to a planar surface to transfer heat effectively by creating a turbulent region
of airflow known as the impingement region. Compared with flow parallel across
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Figure 15.1: Diagram of impinged flow across a surface [9]
a surface, the turbulent region of impinged flow allows for high thermal transfer
across a small area. This method of cooling also has the benefit of being simple to
calculate numerically.
As the following calculations are done for air starting at standard temperature
and pressure (STP), the following constants will be used.
Table 15.2: Table of constants used in the impinged flow calculation
Symbol Name Value Units
ν Dynamic Viscosity 1.589× 10−5 m2/s
Pr Prantel Number 0.707 Unitless
ρ Density 1.3947 kg/m3
κ Kinematic Viscosity 2.63× 10−2 W/m◦K
Effective area (equation 15.4) is a dimensionless ratio between the diameter of
the nozzle (D) and the radius of the impinged region (r).
D2
Ar = (15.1)
4r2
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The Reynolds Number (equation 15.4) is calculated as follows, where ν is the
dynamic viscosity for the fluid.
VeD
Re = (15.2)
ν
The Grashof number (equation 15.4) is the dimensionless ratio between buoy-
ant and viscous forces in a fluid, where H is the height of the nozzle opening above
the surface.
√ √1− 2.2 (Ar)
Gr = 2 Ar √ (15.3)
1 + 0.2(H − 6) (A )
D r
The thermal convection coefficient (equation 15.4) generated in the impinged
flow region is then calculated as follows. The Prandtel number and κ are empirical
values specific to the working fluid, they are listed in table 15.2.
P 0.42κ
h = r G (2R0.5(1 + 0.005R0.55 0.5r e e ) ) (15.4)D
As stated by [9], the calculations for impinged flow cooling are only valid for
the following regions.
1. Reynolds number between 2000 and 400000
2. Nozzle exit velocity below Mach 0.3
3. An effective area between 0.004 and 0.04
4. Nozzle height to nozzle diameter ratios between 2 and 12
104
Using the prior equations and bounds, the convection coefficient can be calcu-
lated given nozzle geometry and exit velocity. A relation between nozzle geometry
and exit velocity (equation 15.4) must be formed to create a design space. By as-
suming that air passes from the environment, into a compressor, and then into a
stagnant plenum from which the nozzles are fed, exit velocity can be calculated as
a function of plenum pressure. √
2P
Ve = (15.5)
ρ
Nozzle diameter is governed by the operating limits of the compressor used
to pressurize the plenum. A compressor has a nearly linear relationship between
volumetric flow rate (equation 15.4) and operating pressure. The pressure and
volumetric flow equation for a pump can be simplified by observing volumetric free
flow, flow at maximum pressure, and maximum pressure.
Using this relation, a market survey was performed analyzing a wide range
of fans and compressors. The surface area directly external to the servo driver
Figure 15.2: Diagram of flow in the cooler
105
P
Qdot = (Qopen −Qclosed) (15.6)
Pmax
features a set of twelve full isogrid pockets. Using one nozzle per each of the pockets
yielded the best total heat transfer from the servo driver. A search was conducted
considering packaging, thermal transfer, mass, and decibel level. The initial study
attempted to use a single compressor to cool all three HPUs in the links considered,
but the commercially available options were too large to package easily and ducting
was found to be too complex to quickly design. Diaphragm pumps were initially
considered to be the optimal pump for this design, but the survey found that the
permissible flow rate and pressure fall outside of the acceptable design space for
impinged flow.
Figure 15.4: Calculated ideal impinged
flow cooling per motor controller
Figure 15.3: Pressure-velocity diagram for
the selected fan [10]
The market survey yielded multiple acceptable fans. The selected high static
pressure fan has a useful operating pressure for nearly half of its operating regime.
106
Figure 15.5: Cooler assembled onto the thermal testbed
Figure 15.6: Cross sectional view of the cooler as applied to a link
Unfortunately RTSX only has two power buses, 48v and 5v, so the selected fans will
require some form of voltage regulator to operate. Each prototype fan was equipped
with its own buck-boost converter packaged into the plenum area directly under the
flow of the fan.
107
15.5 Fabrication
The structure for each cooler module was fabricated using Multi Jet Manufac-
turing 1 (MJM) in a matter of hours. To reduce manufacturing time and support
material volume, the plenum was bisected at its mid-plane and assembled using
bolts. The plenum was constructed from RGD840 on a Stratasys Objet30. The
print area and orientation of the design was manipulated to reduce print time as
the printing process is very sensitive to certain features, such as object height and
cavity orientation. The full list of optimizing practices can be found in the Objet30
Users Guide [11]. These rules dictated many of the small design choices in the shape
of the plenum/nozzles.
While the MJM process is well suited for this design because of its speed
and geometry, the material used proved to be problematic. RGD840 has a heat
deflection temperature (HDT) of 45-50◦C at 0.45 and 1.82 MPa. While the operating
environment does not extend exceed 44◦C (Table 15.1), the close vicinity of the HDT
caused warping to occur over time. This opened the seam between the bisected
components, venting the pressure of the plenum to ambient. As a design revision,
the plenum should be constructed from a material with a higher HDT to prevent
further issues.
Attachment to the isogrid of the link was done using nylon 4-40 bolts. This
mounting requirement is strictly enforced to prevent damage to the link body. In
the event of an unexpected failure or collision, the attached bolts will be sheared off
1Also known as polyjet manufacturing
108
rather than damaging the aluminum housing. Two threaded features are located by
each servo driver and are used to secure each cooling unit. To stabilize this design,
four hemispherical contact points are included in the geometry for the plenum. As
the fasteners are tightened, these points are pre-loaded against the exterior of the
link to eliminate vibration.
109
Chapter 16: Thermal Verification and Testing
To verify the thermal design and to refine uncertain design features, a series
of experiments were conducted, using a mixture of mock-up and final hardware to
reduce testing costs.
16.1 Test Hardware
A prototype test link was created to validate the design of the thermal system
in RTSX and the values in Table 15.1. The prototype link consists of a tray and
electronics rack with dummy servo drivers designed to emulate the thermal load
from a stalled servo driver. To eliminate unknown or unpredictable components
of thermal transfer, all other exterior components were created using ABS plastic.
Free convection can be greatly influenced by the orientation of the geometry, as it is
dependent on buoyant forces. For that reason a two degree of freedom poseable joint
was designed and placed between the test link and its stand, allowing the cylindrical
link to be placed into any orientation.
The test electronics rack features three dummy servo drivers and five thermal
probes. Four additional thermal probes were placed about the test tray. This
array of sensors was designed to measure maximum temperatures about the system
110
Figure 16.1: Thermal test link in an environmental chamber
as well as the resistance across thermal junctions and free convection coefficients.
Each dummy servo driver can be heated in two different zones, up to 50 watts per
zone. The servo drivers these are approximating have multiple MOSFETs across
their heatsink which are individually activated based on motor commutation, so
two zones were made to examine the possibility of MOSFET location dependent
heating.
Figure 16.3: Thermal test platform being
Figure 16.2: Test electronics rack with
assembled
dummy servo drivers
One mock HPU was sensored in greater detail than the others, to observe phe-
nomena inside of the HPU. In Figure 16.5, the location of sensor 1 is common across
111
Figure 16.4: Rendered graphic of the Figure 16.5: Rendering of the interior of
mock HPU a HPU with sensor locations labeled
all three mock HPUs and is located approximately where the built in thermistor is
on the servo drivers. This will provide a more accurate estimate as to when the
servo drivers will enter an over temperature state. Sensor 2 is located at the clos-
est point between the heater units and the outside wall, providing the temperature
just before heat is transferred to the outside wall. Sensor 3 is located on the outer
plastic wall to study internal radiation. How this functions is explained later in this
chapter.
Four resistive heaters are located on the heat sink, pictured in Figure 16.5,
and grouped into two pairs. The motor controllers these are imitating have six
separate MOSFETs spaced across the length of the heatsink, which are activated
in pairs. This mock grouping is to verify that the variation in thermal loading
location across the heatsink does not impact the performance of the unit. Thermal
load is established by measuring total electrical power input to each heater group
to produce accurate measurements.
112
16.2 Thermal Testing Results
The thermal test was conducted to study a range of attributes. In total,
approximately 100 hours of testing was performed on this system in a wide variety of
configurations. For all test procedures, steady state conditions are assumed to have
been achieved when the change in temperature is less than 0.01◦C/min. Monitoring
mechanisms were used to make sure that temperatures did not exceed acceptable
limits to prevent damage to the test hardware.
16.2.1 Junction Resistance
Thermal resistance was studied across the thermal junction between the servo
driver heatsink and the link body. Several options were considered at the start of
this experiment for this thermal junction as it provides a unique challenge: a sliding
thermal junction. As mentioned earlier, thermal paste was used in the original VPX
rack for Ranger. While this is effective, it leads to operational challenges when the
paste needs to be cleaned and reapplied after de-mating to ensure proper contact.
The prototype housing manufactured to test the side loading design did not make
use of any thermal joining compound, merely placing two relatively flat aluminum
plates against each other. While this was permissible for the simple kinematic
checkouts that DXE was subjected to, it was insufficient for operation near the load
limit of the arm and overheated in those conditions. Junction resistance was never
characterized for the prototype system, but was deemed unacceptable and it was
noted that thermal conductivity would need to be improved on the final design.
113
The thermal test link was used as a test platform to evaluate thermal junction
designs. Three baseline designs were tested: bare metal, thermal paste, and a
gap filler. The gap filler selection was investigated with the cooperation of the
manufacturer. Off-the-shelf foamed gap filler has a very high coefficient of friction,
practically adhering to any clean surface. This is incompatible with the assembly
method used to contact the HPUs to the outer walls. During assembly, the HPU
must slide across the surface while the retaining arm is pre-loaded. Gap filler would
bind and tear during this assembly. Ultimately, a thin brass coating on the gap
filler was found to have little impact on the materials thermal performance, while
allowing the HPU to slide across the now brass coated surface during assembly.
Table 16.1: Experimental results for various thermal interface models
Bare Metal Thermal Paste Brass Coated Gap Filler
∆ T [◦C] 32.8 12 13.8
Junction Resistance [◦C/W] 1.27 0.466 0.536
The results of the thermal junction test are shown in Table 13.1. During test-
ing it was found that the bare metal junction resistance, approximately 1.27 K/W,
was too high to allow any HPU to operate at capacity for more than a few min-
utes. However, both the thermal paste and gap filler had acceptable performances.
Although it is possible to gain a slightly better thermal connection by the use of
thermal paste, the brass coated gap filler is far easier to work with. This junction
method is now used for every HPU connection in the system.
114
16.2.2 First Order Calculation of Steady State Values
It was theorized that during testing, it is possible to predict the steady state
temperature of the system from a set of initial values. This method was derived
assuming that the heating system acted like an ideal first order system. This assumes
the system can be modeled as having a linear dissipation rate of energy to the
environment, a constant rate of energy input, and a linear heat capacity. Given
that, when the system is at ambient temperature and the heat is turned on, the
temperature rise will act as Heavyside step function with arbitrary inputs. This can
be modeled as follows where h(x) is the Heavyside step function.
Experimental data is gathered in the time domain. It is thus useful to have a
final form using a time constant to make its form easily understandable. Manipu-
lating equation 16.2.2 to use time constants yields equation 16.2.2.
dT 1
+ T = Ah(t) (16.1)
dt τ
−t −t
T (t) = T0e τ + Aτ(1− e τ ) (16.2)
In this form, T0 is the initial system temperature, A is a scalar, and is the time
constant of the system. This is a very useful form, as A/tau is also our steady state
temperature, which will be denoted as Tss from now on. Given that there are three
unknown variables in this equation, the system should be able to be characterized
by fitting the curve to a series of three data points.
A 6 hour test was conducted to gather data to verify this model. The first
115
Figure 16.6: First order temeperature prediction error
order model was applied to a set of linearly spaced data points taken from the
experimental results. As was expected, when the sampled data increases in size the
steady state error decreases. Depending on the accuracy of Tss desired, this model
may be useful for reducing testing time by 60% or more.
Multiple attempts were made to create a more accurate predictive model. Pos-
sible sources of deviation examined were increases in ambient temperature, unequal
heating rates of the bulk materials, and radiative thermal dissipation. Increasing the
system order and adding additional linear terms had limited success in consistently
lowering the prediction error. Ultimately this prediction method was abandoned for
collecting experimental data as the repeatable accuracy was deemed unacceptable.
This method was used extensively during the testing process, but not for any
gathered data. This was used as a safety check, in addition to finite element models
predicting the steady state temperature of the experiment. To prevent potential
damage of the hardware, the steady state error was continuously predicted using
the data gathered. When an egregious overshoot of the maximum temperature was
116
Figure 16.7: Free convection experimental results at room temparature
predicted, the experiment was carefully monitored until the predicted steady state
error returned to acceptable ranges or was shut down.
16.2.3 Passive Convection Performance
The majority of the testing conducted was to observe the free convection based
cooling of a link. Free convection performance was limited by the maximum oper-
ating temperature of the motor controller. The test was concluded when the steady
state motor controller temperature exceeded 50 degrees Centigrade. The test was
operated at 22 degrees ambient temperature and the maximum operating thermal
load was 7.25 watts. Detailed results can be found in figure 16.7. It was found that
the average free convection coefficient is approximately 14 W/m-K.
It was predicted that the orientation of the link with relation to gravity would
have a large effect on the cooling rate of the link. However, after some experimenta-
tion it was found that in practice this had a 10% impact on the total performance of
117
Figure 16.8: Maximum disapation from each motor controller as a funciton of ex-
ternal temperature
the system. When the axis of the link was oriented vertically, the convective cooling
had a higher impact. This follows with free convection theory, as the buoyant forces
are able to increase the velocity of the fluid across the surface of the link body. All
other tests were performed horizontally to create a worst case heating scenario.
16.2.4 Forced Air Convection Performance
Actively cooling the structure of the link provides a generous boost in per-
formance. After a few tests, it was determined that the cooling performance of
the impinged nozzle design greatly exceeded the capacity of the motor controller.
It averaged a surface dissipation of 50 W/m-K, more than 3.5 times greater than
free convection cooling. This accounts for the total surface area fraction that the
heatsink can dissipate heat through, not just the bottom of the Isogrid as calculated
in Figure 15.4, which account for the perceived 5 times reduction in performance
from the simulated forced cooling design.
Cooling the motor controller below 50C is not a useful metric for normal
operation. The forced air convection performance was measured by holding the
118
motor controller at 50C, using the environmental temperature as the independent
variable, and the thermal power emitted from the motor controller as the dependent
variable.
16.2.5 Internal Radiative Heating
To prevent damage to the selective laser sintered (SLS) plastic holddown points
on the motor controller, it is important to study the internal heating effects, not
just the stable system temperatures.
The location of the resistive heater on the mock motor controllers was observed
to have a direct effect on the heating rate of the holddown points. When the heater
closest to the holddown point was activated (heater group 1 in Figure 16.5), the
plastic surface drastically rose in temperature despite the isolating air gap. Sensors
placed across the motor controller heatsink showed that there was little variation
in the heatsink temperature gradient based on which heater set was activated. If
this phenomena presented a greater change in temperature it would be of concern.
However, as the materials used in this design are all capable of surviving the tem-
peratures presented, this phenomena should merely be noted for when observing
temperatures inside the final design.
16.3 Thermal Design Conclusions
The thermal design and analysis of Ranger resulted in a functional design
that can be used in a neutral buoyancy environment. However, the design required
119
several special considerations to be made when operating on land. An active cooling
device had to be constructed to produce acceptable operating temperatures while
on land. The thermal design of RTSX is functional, but should be iterated again
to see if there is a possible design that works in all required environments without
modification.
120
Chapter 17: Internal Electronics Mounting
Mounting electronics inside of a flexible body is a non-trivial process. As
discussed earlier in this paper, flexure of printed circuit boards and electronic com-
ponents can have catastrophic consequences. In a typical design, a printed circuit
board should be kept as rigid as possible to avoid any problems, which sits in oppo-
sition to the assumption that the link body is flexible. The following section details
the design process for mounting the electronics internal to the link body of RTSX.
The overarching design concept for this refit is to sequester all electronic com-
ponents in the link to a removable rack to facilitate repair and upgrades. After
multiple design iterations of the rack with the electrical engineers for RTSX, it be-
came clear that it is more efficient to set known interfaces between hardware and
electronics at the expense of design flexibility. For that reason, the layout of elec-
tronics in the rack was separated into discrete regions.
Packaging of the HPUs into the wedge configuration only allows for a few
regions in the cross section for continuous structure along the length of the link.
As the allowed volumes for the HPUs are very well known, the design volume for
all additional electronics to be housed must be maximized. After several design
revisions, a minimum “accessory electronics allotment” was created. This was the
121
Figure 17.1: Cross section of the link depicting volume allotments
driving factor in determining the maximum thickness of the top plate, which could
be no thicker than 0.125 inches.
17.1 Rack Construction Concepts
The electronics rack must be structured to hold all components securely and
with adequate stiffness. The design must also be within the allowed budget to
construct. Due to the complexity of the required geometry, multiple concepts were
tested to find an affordable design.
17.1.1 Externally Framed Rack
Placing the bulk of the structure for the rack about the external perimeter
certainly has its benefits. With a large separation between the mounting plates, the
structure is very resistant to bending. It also affords an additional layer of protection
122
Figure 17.2: Prototype electronics mounting rack demonstrating an externally
framed rack concept
for the electronics contained within. The design in Figure 68 uses a series of thin
beams to separate the two mounting plates. As the plates are compressed together
during insertion into the link, these beams act as high stiffness springs. They are
designed to buckle when compressed to apply a firm contact between the mounting
plates and the body of the link for thermal transfer.
This design was used in the original prototype link. Multiple issues were
found with the implementation of this design. The rack design is fairly massive,
and should be mass optimized on future iterations. The contact area between the
mounting plates and the link structure is extensive, but does not contact evenly,
resulting in poor thermal transfer. The clamping method is not statically determi-
nant, making the vibrational properties of the cage unknown, even varying between
assembly/disassembly cycles.
123
Figure 17.3: Internally framed rack with an underslung structure
17.1.2 Monolithic Internally Framed Rack
For completeness in the design space, we must entertain the idea of machining
the rack from a single monolithic piece of stock. This has the benefit of eliminating
all structural fasteners and can allow an overall lighter structure. However, given the
complexity of the geometry inside the design volume, the complexity of machining
and its associated costs will greatly outweigh any performance benefit.
17.1.3 Built-Up Internally Framed Rack
Two layouts were pursued for an endoskeleton-style rack. Early design explo-
ration created the concept of the cantilever retaining arms, which are detailed in
chapter 14 However, the structure that mounts all of the retaining arms together
takes on a variety of shapes. The structure can fill the entire volume, but it was
limited to either above or below the HPUs.
124
4FL3
E =
(∆y)bt3
Figure 17.4: Required Youn√g’s Modulus for a given deflection
4 3EI √−2
fn = 2π
ml3
Figure 17.5: Natural frequency of a massless cantilever beam with a tip mass
17.2 Structural Analysis
It is assumed that the mass of electronics on the top plate is approximately
2 kg and the vibrational loading on the link will not exceed 5Gs. Based on these
estimations, the maximum loading across the face of the top plate is approximately
100N. Packaging provides limiting geometry for the design of the top plate. The
plate will be 208mm by 111mm to give the most amount of useful surface area to the
electronics team. The plate has a maximum thickness of 3.2mm and a maximum
allowed deflection of 1.2mm. Given these constraints, the required stiffness of the
plate can be calculated by modeling it as a cantilevered beam.
The required Young‘s Modulus for the top plate to prevent static deflection
based collisions is an order of magnitude less than the Young‘s Modulus for alu-
minum. Since static deflection is of no concern, we must examine the fundamental
frequencies of the rack.
Initial analysis yields a harmonic frequency of the electronics rack of approxi-
mately 6 Hz. As the expected harmonic frequency of the arm is below 10 Hz, this
would be unacceptable. However, if the top plate is manufactured from high modu-
lus carbon fiber, the harmonic frequency of the rack becomes 45 Hz. As construction
125
Figure 17.6: Finite element simulation showing the first vibratory mode
with carbon composites can be costly, alternates must be considered. By adding
several stiffening struts across the body between HPU bays, the first harmonic node
is eliminated. This structure becomes far more difficult to calculate analytically with
the addition of the struts, so instead finite methods are used. A mesh model was
generated from the existing geometry and a set of idealized springs were added in
place of the HPU spring arms. Vibratory analysis was performed using NASTRAN
SOL 103, Real Eigenvalues, to find the un-damped fundamental frequencies of the
whole system. This analysis revealed that the first harmonic frequency of the rack
is increased to approximately 700 Hz.
The stiffening struts are a critical component of the rack body, and are a
good candidate to optimize for manufacture. Initial assessment of manufacturing
techniques rules out the use of low scale sheet metal forming as too inaccurate and
of subtractive milling as too costly. Instead, additive manufacturing methods were
considered.
Multiple geometry options such as the design above were considered. These
designs were optimized using the manufacturer‘s costing function using several dif-
126
Figure 17.8: Final stiffening beam design,
tessellated to reduce manufacturing cost
Figure 17.7: Concept for a stiffening beam
for the top plate
ferent starting designs, such as the multi-node truss pictured above. Ultimately it
was found that the costing function was most effective if the design can be tessellated
into the smallest build area per strut. The final design was created considering Euler
buckling and the potential for manufacturing defects, leading to a simple geometry
that is thicker than normally required.
The shear clips used to retain the top plate to the vertical plate in the elec-
tronics rack design were limited by machining requirements. To eliminate as many
vibrational nodes as possible, the shear clips were attached through the contiguous
length of the vertical plate. The rivets used to affix the plates to the shear clips are
double-countersunk, designed to sit flush on both sides of the material, to prevent
any damage to the wiring harness that will be occupying the same area. This type
of rivet is a new design is relatively new, so a large safety factor must be used to
avoid any unexpected failures. To prevent any corrosion between the aluminum of
the rack and any of the fasteners used to hold it together, the aluminum components
127
Figure 17.9: Wiring harness path generated in NX for the power cabling for the
servo drives
were individually Alodined1 to provide a wear resistant oxide layer which electrically
insulates the fasteners from the structure.
17.3 Wire Harnessing Consideration
Allotments must be made for wiring harness paths in the design of the elec-
tronics rack. To calculate the cable harness diameter, a series of interface documents
were created for each electronic module. An example page taken from this docu-
ment can be found in appendix E. Paths were then generated in NX, using these
documents to generate approximate cable harness diameters.
As can be seen in figure 17.9, the wiring harness for the motor controllers
passes between the stiffening rib and the tray body. This method makes good use
of the space, but required multiple design considerations to prevent abrasion of the
cable harness. All corners in this area are curved to prevent abrasion, including the
stock used to create the shear clips used to assemble the tray.
1Also known as yellow chromate, a conversion coating applied to the surface of metals to inhibit
oxidation.
128
Figure 17.10: Gap in the built-up structure used for harnessing
The double-countersunk rivets have a fairly small range of acceptable plate
thicknesses. Compounding that with the need for building up the joint with two
shear clips and the tolerances for countersinking holes (figure 17.10), the required
precision for constructing this section becomes very strict. This increases the cost
of the shear clips greatly, but is an allowable trade off for the gained harnessing
volume.
17.4 Parallel Design Development with Electronics Designs
One of the major challenges in designing the upgrades for RTSX were the
parallel development of electrical and mechanical design. Multiple methods for
coordinating this design process were tried with varying degrees of success. While
current detail designs could be conveyed with relative ease, design intent is frequently
lost. The use of Interface Control Documents, colloquially known as ICDs, was
found to be the most effective in retaining design intent and establishing design
requirements. This frequently took the form of allowed design volumes, mounting
129
Figure 17.11: Subsection of the mechanical ICD issued for the status indicator
housing
regions and methods, as well as enforced keep-out zones. Expanding ICD constraints
to be as overreaching as possible was useful for design iteration, reserving extra area
as a system level allowance.
17.5 Electronics Mounting Conclusions
Building up an internal mounting rack in this manner allows for a wide variety
of mounting options for electronics. The concept behind this design was to maximize
internal mounting volume while still retaining good heat sinking and rigid structures.
While this has been shown to be true in the preceding sections, such a design is not
inherently easy to manufacture. Cable harnessing is a non-trivial task for such a
design. Although it was shown to be possible in Section 17.3, there is little margin
for error in creating such a harness. Given the design constraints of this system,
there is little alternate for this design. Implementing a floating connector between
all of the electronics and the rest of the system reduces the manual labor executed on
the manipulator itself during maintenance, but also increases cost and part count.
130
In all, this design works appropriately and no design defects have yet to be found,
but designing for such a large bulk of cabling inside a small housing is difficult.
131
Chapter 18: Link Extension Design
Up until this chapter, we have alluded to the existence of link extensions, a
method by which the kinematics of RTSX can be modified. This chapter details
both the mechanism for extension, as well as the governing equations for designing
an extension link. Link extensions add to the existing link length. They range in
extension from a few centimeters to multiple meters. Of course, the longer the link,
the lower the allowable tip mass. For very long lengths, it is not possible to operate
RTSX without a gravity offset, such as in neutral buoyancy or microgravity. We can
extend the operability region of RTSX slightly by applying lightening techniques to
minimize the material used in their construction.
18.1 Thin Walled Beam
A formula [12] for determining the buckling stress of a thin walled tube in
bending was empirically derived by a team of NASA researchers to form equations
for space vehicle design. The equations 18.1 and 18.1 defining the critical buckling
stress are taken from that monograph.
√
1 r
γ = 1− 0.731(1− e− 16 t ) (18.1)
132
σB = √ γE t (18.2)
(3(1− /mu2)) r
Figure 18.1: Critical thickness of the link extension given various material properties
Using equation 18.1 we can examine the design space to determine the wall
geometry. Both yielding and buckling loads must be observed to establish a mini-
mum wall thickness. Materials with a smaller modulus ratio1 are more susceptible
to failure by buckling than by yielding. This can be observed in figure 18.1.
Given these design limitations, aluminum 7075 was selected for the link. Al-
though greater performance can be achieved using titanium, the added material and
subsequent machining cost makes the design too expensive. Stainless steel is to be
avoided for large structures, as its specific stiffness is too low to produce a tenable
system mass. However if manufacturability is desired over performance, it is sim-
pler to weld and form stainless steel; this would be a good alternate for producing
extremely long link lengths.
1The modulus ratio is termed here as E/σyield, the ratio of the Young‘s Modulus to the yielding
stress
133
Table 18.1: Design limits of a 0.33m link extension
Modulus Stock
Safety Factor of 1 Safety Factor of 2
Ratio Cost
Defining Thickness Mass Defining Thickness Mass
Material E/σyield USDFactor (mm) (kg) Factor (mm) (kg)
6061 250 Yielding 1.7 0.65 Yielding 3.4 1.3 26
7075 143 Buckling 1 0.4 Yielding 1.8 0.71 55
316 666 Yielding 1.6 1.8 Yielding 3.2 3.62 125
Ti-6AL-4V 128 Buckling 0.8 0.5 Buckling 1.1 0.69 455
Figure 18.2: Proximal link extension iner- Figure 18.3: Distal link extension inter-
face face
18.2 Link Extension Interface
The link extension interface uses several features to align and transfer loads.
These features are original to the first RTSX design, and have been reused to reduce
the remanufacture of mating components. The inter-link connection is done with
a marman clamp, which preloads the connection, and transfers bending and axial
loads. A lip machined into the connection transfers shear loads across the joint, and
works in combination with a pin to transfer torsional loads.
134
Internal to the mechanical interface are interconnects for the electrical system.
RTSX uses three high power connector modules manufactured by Smith Connectors,
known as Hypertronics connectors. These have the power density and the connection
density required to pass the power and data busses through the links. The original
design used a purpose built floating connector housing which aligned the connectors
physically before mating. The new design standard has made use of a COTS floating
connector housing manufactured by Smiths Connectors to house these modules.
This makes manufacturing cheaper and tolerance simpler for the extension interface,
eliminating the tight tolerance parts from the design.
The link extension interface geometry was retained in the redesign because it
is effective and simple. However, the interface hardware was changed from stainless
steel to hard anodized aluminum to reduce mass. There were many concerns for
this interface originally. Galling and cold welding are a big concern for a high stress
joint like this when operating in vacuum. However, as this joint will be operated
terrestrially, and the chance of cold welding is highly reduced when aluminum is
hard anodized, this design choice was deemed acceptable.
18.3 Link Extension Design
With the link extension wall thickness and the end interfaces established, the
method of manufacture needed to be established. With such a thin outer wall and
thick end features to be made, the possibility of welding the components had to
be entertained. After a brief dimensional analysis looking at the shrinkage and
135
Figure 18.4: Cross section of the link extension assembly
warping due from welding process, this method was deemed unsuitable for a part
of this scale, due to the inaccuracies in parallelism between the two end interfaces
from welding. A built-up assembly was also considered; however, in a bid to reduce
component count, this was not pursued.
The final assembly consists of a monolithic structure bored from a single piece
of stock, with both the thin walled beam and the RTSX link extension interface
integral. The connection to the floating connector assembly is made with a retaining
ring and an alignment notch. This simplifies the manufacturing to two lathe setups
and two milling setups. If this can be manufactured on a milling lathe then the setup
is reduced to only two lathe positions. There is a challenge to boring a component
this long, as a useful length for this link extension design is between 5 and 20
inches in length. A survey of several machine shops showed that while this is not
commonly possible to manufacture, specialty lathes exist with a long enough bed to
136
manufacture this component.
This design for the link extension provides a nearly perfect stiffness to strength
ratio using aluminum. Although it is theoretically possibly to achieve a more op-
timum design by using more complex geometry, ie isogrids, the design selected sits
nearly perfectly between yielding and shell buckling. Unfortunately this design is
not scalable beyond about 15 inches for manufacturability reasons. For such an arm,
using a built up design with a common extrusion is preferable. No such extrusion
is commercially available, so a custom extrusion is a likely but costly alternative.
137
Chapter 19: Conclusions
The design of new electronics housings for RTSX transformed from a simple
structure with complicated electronics to a complex structure with simple electron-
ics. While the utility of altering the electronics in such a manner is beyond the
scope of this paper, this new design is far more capable both electronically and
mechanically. We have formed a much more comprehensive understanding on the
interplay between electronics packaging and structural design. By taking a holistic
approach to design, the new system has improved thermal performance, structural
stiffness, and maintainability without the use of exotic materials or drastic changes
to the manipulator‘s architecture.
Many design guidelines were established in the production of this thesis. Min-
imum parent material geometry for a threaded feature is useful knowledge, however
the real life performance of this method was never established as the feature was
rendered unnecessary in the final design. The ultem hold down arms for the HPUs
appear to be very effective, however the design will need to be proved with further
testing, including vibratory and vacuum tests. The utility of forcing such a rigorous
top-down method for this design has yet to be established. It is certainly effective
for larger projects, but the size of this study boarders on being too small to be
138
effective. As of the completion of this thesis, all of the design guidelines created
appear to be of great value, but further testing will be required.
A goal of this design was to reduce the part count and manufacturing complex-
ity from the previous design. Comparing current production costs with accounts of
previous costs, this appears to have been an effective method. This design makes
use of off-the-shelf components as much as possible, even using the prototyping
breakout board for the servo drivers instead of producing our own. Using so many
off-the-shelf components does present many other design constraints, as evidenced
from the extensive design work done to package the large servo driver package. This
appears to have been a worth while pursuit, but this may not be fully understood
until the improved RTSX design has been in service for several years.
139
Appendices
140
Appendix A: RTSX DXE Kinematic Chain
141
Appendix B: RTSX PXL Kinematic Chain
142
Appendix C: Experimental Results Studying Minimal Parent Mate-
rial Geometry About a Threaded Surface
In order to better understand the failure mode of a threaded surface and
to establish minimum geometry for surrounding material, a test was designed to
examine parent material during a bolt pullout event. Prior to this experiment, it
was conceptualized that failure could occur at any of the helical threads, depending
on the ratio of the tensile road taken by each thread [13]. The thread loading
distribution is assumed to be approximately 30% on the first three threads because
helical inserts are used. Otherwise it may be near 80% on the first thread.
Figure C.1: Detailed cross section of the test sample
143
C.1 Experimental Setup
Forty two test samples were machined from 5/8 inch aluminum stock with
varying diameters about the threaded area. Six samples of each diameter, rang-
ing from 0.35 to 0.6 inches were machined and inspected in multiple dimensions to
conform to the mechanical drawing in Figure C.2.This inspection included four di-
ameters taken about the necked area to ensure concentricity and a Go-NoGo gauge
inspection of the tapped feature. Six samples were rejected for not conforming to
one or more dimension. It was noted that although all accepted threaded features
conformed to the acceptable helical manufacturers standard, their frequency of fail-
ure increased along with their batch number, likely due to the wear of the tap used.
Six samples were rejected for not conforming to one or more dimension. A helical
threaded insert, part number 1185-4CN250, was then inserted into each accepted
test sample and its insertion tang was recovered.
The material used was chemically and mechanically evaluated by the manu-
facturer. A material test report was received from the manufacturer and used as the
bulk material properties for this test. While this could have taken into account the
statistical deviation of the material, the material properties were merely the average
measured properties for simplicity. No significant deviation was found between the
samples used in the results of this experiment.
The test was performed using 1/4-20-3B bolts with a yield strength of 160
Ksi, all from the same batch. To ensure there was no damage to the threads due to
plastic deformation, bolts were tagged with each destroyed sample and not reused.
144
Figure C.2: Mechanical drawing for tensile test samples
An index test was performed using several samples from the batch to confirm their
properties. In place of a test sample, the bolts were indexed by being threaded into
a Grade 2H double height steel nut with a yield strength of 180 Ksi. This index
test found that the bolts were sufficiently strong as to not interfere with the test
results. Additionally, no batch defects were found across all of the index bolts. A
force-strain chart of all index bolts can be found in figure C.3 below.
C.2 Comparison to Expected Values
Stanley Engineering estimates the pullout force for a 1D helical to be approxi-
mately 4200 lbf in aluminum 6061. In this experimental setup, the maximum pullout
force was found to be near 4000 lbf, falling close to the manufacturer‘s value but
not matching it. This is of some concern and is addressed in the conclusion of this
145
Figure C.4: Sample test results for 0.35
Figure C.3: Index test of bolts until failure
inch diameter billet
Table C.1: Experimental results of test sample failure
Sample Ultimate Yield Tensile Tensile Stress (ksi) Shear Stress (ksi)
Diameter (inches) Tesile Force (kip) Force (kip) Ultimate Yield Ultimate Yield
0.35 0.9 0.7 31.7 24.6 5.5 4.2
0.375 1.5 1.3 35.2 30.5 9.1 7.9
0.4 2.2 1.75 38.0 30.3 1.4 10.6
0.45 3.75 3.2 4.1 35.1 22.8 19.4
0.5 4 3.5 31.1 27.2 24.3 21.2
0.55 4 3.5 23.6 20.6 24.3 21.2
0.6 4 3.5 18.6 16.3 24.3 21.2
appendix.
Comparing these values to the experimental material properties provided by
the material manufacturer, the effect of parent material geometry becomes very
apparent. Observing the failure methods visually during testing, the transition
region between failing in tension and thread pullout is about the 0.45 diameter
region. Inspection of the results in Figure 86 show 0.45 inches as the region of
maximum tensile failure. As a point of comparison, % of Max Load compares the
tensile failure force to the maximum pullout force according to the helical insert
manufacturer. Total yield and ultimate forces reach their maximum at a diameter
146
Figure C.5: Comparison of experimental results against ideal results
of one-half inch.
Figure C.6 and figure C.7 illustrate the differences between tensile failure and
thread pullout. Note the region one-quarter of the length from the top of the test
sample in Figure C.6. This is a tensile failure point directly after the helical insert.
This showed that there was no failure within the helical insert itself, but the exact
distribution of yield within the last few threads is questionable.
C.3 Conclusions
This experiment demonstrated that, for a bolted connection, the maximum
tensile strength can achieved by having the parent material threads fail in shear
before the parent material fails in tension. For a 1/4-20 1D helical connection, the
tensile yield force was found to be approximately 85% of the manufacturers yield
strength. While this may have been due to a manufacturing defect, it would be wise
to apply a 1.2 safety factor to the presumed failure load of a helical connection.
147
The region of peak strength begins just after the intersection between tensile
and pullout failure. By this observation we can infer that the minimum amount
of bulk material about a threaded feature should result in a shearing or pullout
failure to maximize strength to weight ratio of the joint. This is in keeping with the
“One-Horse Shay” design principle by the American writer Oliver Wendell Holmes
Sr., where in all failure modes should occur at once to maximize the lifetime of the
design.
148
Figure C.6: Test sample 016 showing ten- Figure C.7: Test Sample 040 showing pull-
sile failure out failure
149
Appendix D: Conceptual Limits for Joint Design
All of the design work contained in this thesis studies the design of the link
segments of a serial-link manipulator with revolute joints. To complement this
study, an additional design study was conducted to characterize the design limits of
the revolute joints themselves. This study was conducted using data from previous
space-based manipulators and actuators, as well as off the shelf industry designs for
powertrains.
This design study was conducted for a specific application. Many space based
manipulators are currently used through a long series of tasks, such as the Space
Shuttle Remote Manipulator System (SSRMS). Now there is a push for mission-
specific robotic manipulators. For example, an asteroid retrieval mission would
require a manipulator to contact and capture a rock for return to earth. Such a
task would benefit greatly from a dexterous manipulator, but the mass required
to make the manipulator resilient and long-lasting would be much better used for
sensors and propulsion systems. To better align with future robotic missions, this
conceptual design was conducted for a dexterous manipulator with a very limited
lifetime.
150
Figure D.1: Comparison of various hypocycloidal gearbox performances
D.1 Powertrain Design
RTSX and many other space-based serial link manipulators have a similar de-
sign for their powertrains. The design typically consists of a brushless DC motor
that drives a hypocycloidal gearbox, typically a flexspline design such as a harmonic
drive gearbox. A systems level review of available brushless DC motors revealed
that the high performance torque densities are relatively the same. Various hypocy-
cloidal gearboxes were surveyed, comparing the maximum operating torque with
their masses. It was found that the CPL series manufactured by Harmonic Drive
was able to yield the highest torque density, which is unsurprising as this model was
designed explicitly as a light weight variant of the CSD model.
Several revolute joints were designed using drive train components that were
optimized for their specific torque output. This resulted in an actuator torque
density on par with flight heritage actuators such as those used on the Pathfinder
mission. The number of mechatronic components in the actuator were minimized
to a motor, harmonic gearbox, joint bearing, motor bearing and encoder. From
151
Figure D.2: Baseline arrangement of components inside a robotic joint
Figure D.3: Surveyed actuator torque performances
this layout it was considered that all intermediate structures could be optimized for
minimal mass.
Surveying available actuators and their performances resulted in an unex-
pected insight. Actuator designs follow the rough formula shown in equation D.1.
Values for a and c are dependent on the design of the actuator. The higher the
constant values are, the higher the specific torque of the actuator, and thus the
more desirable it is in a mass constrained manipulator. While classic brushless di-
rect current motors follow a fairly tight trend, piezoelectric actuators greatly exceed
152
their performance.
Torque ≈ a×mass1.5 + c (D.1)
D.2 Piezoelectric Motors
Piezoelectric motors are a comparatively recent technology, but are already
wide spread in their use. Ultrasonic motors, a subset of piezoelectric motors, were
first invented by Toshiiku Sashida [14] in 1980 and are now widely used in areas
where a high packing factor and high precision is needed. These motors can com-
monly be found in the focus mechanism in high end camera lenses.
There are three basic designs for a piezoelectric motor. A standing wave
ultrasonic motor, such as Toshiiku Sashida invented, generates harmonic vibrations
in a stator ring using an array of piezoelectric devices equally spaced about the
stator. Varying the driving frequency results in motion. A traveling wave motor
excites a flexible shaft, causing contact points about the perimeter to process as
they are forced against each other. The traveling wave motor requires much more
hardware than the standing wave motor to generate motion, but locks the rotor
in place when unpowered, where the standing wave motor cannot. A walking foot
motor uses a pair of conjoined piezo devices to allow the contact point to bend and
pull the stator along. This design generates considerably higher forces and has a
much higher positioning accuracy.
Piezoelectric motors have had limited implementation in the field of robotics.
More commonly, they are found in micro manufacturing, where their exceptionally
153
Figure D.5: Traveling
Figure D.4: Standing
Wave Motor [15]
Wave Motor [15] Figure D.6:
Walking foot
motion [16]
high precision and stiffness is required. These technologies are very mature for that
field, but have yet to be designed for a high torque to mass ratio. Even so, this
technology has exciting potentials for the field of robotics for several benefits.
1. High Torque Output Using Direct Drive: Designs like the Walking Foot
actuator have a high power to torque output, eliminating the need for gearing.
This also greatly reduces the inertia of the actuator.
2. High Precision: High positional accuracy and movement are a must for any
robotic actuator. This technology is already being implemented in precision
manufacturing for this.
3. Unpowered Braking: The Traveling Wave and the Walking Foot actuator
both clamp the stator to the rotor when unpowered, eliminating the need for
a discrete brake to be added to the powertrain in an actuator.
4. Low Part Count: Compared to conventional actuators, the Walking Foot
154
and the Standing Wave actuator have only two moving parts.
5. Compact: With no need to generate a magnetic field and manipulate mag-
netic flux, all of the volume in Standing Wave and Walking Foot actuators is
devoted to mechanical support of the actuator and movement.
After examining these technologies on a systems level, I believe that there is
great potential to using piezoelectric motors in robotics and their application should
be further researched and matured.
D.3 Bearing Design
A trade study was conducted for selecting bearing sets to be used in the
actuator. The force that governs the sizing of bearings is the rocking moment on
the joint. Instead of relying on the separation distance and radial reaction force
of a pair of bearings to resist a rocking moment, angular contact bearing pairs are
treated differently. The rocking moment does not push radially on the bearings,
instead it uses the virtual distance between the conical tips of the contact lines of
the ball bearings. This virtual distance, also known as the resistance moment arm, is
visualized in Figure 96. While matched angular contact bearings are typically used
to resist rocking moments, there is a design space in which they are not necessarily
as efficient.
Thin section angular contact bearings are frequently used in the configuration
above. They can be pre-loaded by external geometry and fasteners, eliminating any
non-linearity in the system. However, two angular contact bearings packaged back
155
Figure D.7: Geometry depicting how angular contact bearings resist rocking mo-
ments [17]
to back have approximately 15% higher moment carrying capacity than a single four
point contact bearing, while massing twice as much. Four point contact bearings
can be pre-loaded by assembling them with oversized ball bearings, eliminating
their non-linearity. This method of preloading works but is not nearly as precise
or as fatigue resistant as that used for a pair of angular contact bearings. For our
purposes, this is acceptable.
D.4 Kinematic Configuration
The minimal mass joint concept was designed into a notional serial-link ma-
nipulator called Strongman. This serial-link manipulator was envisioned to mimic
the basic kinematics of the human arm while matching the performance. The design
156
Figure D.8: Mockup of the light weight actuators inside the kinematic chin of Strong-
man
goal for the whole manipulator system was to mass under 5kg for use on a small
satellite. RTSX omitted as many joint offsets as possible to reduce the systems
kinematic complexity. This means that pitch joints such as in the elbow and wrist
require bearings on both sides of the joint to react the load. Strongman ignores
this requirement to reduce the total mass of the system at the cost of increased
computational complexity.
Strongman is designed to operate with a tip load of 9 kg on earth and generate
a torque at the tool tip of 20 Nm. To increase the tip mass, the powertrain for each
joint is reduced successively to optimize for total system mass. The shoulder joints
require a maximum torque of 90 Nm, the elbows need 54 Nm, and the wrist requires
an output of 20 Nm. The mass of all the actuators in the system is 2.2 kg, leaving
2.8 kg for structure, wiring, and electronics.
D.5 Mechanical Design
The preliminary mechanical design of Strongman was conducted to minimize
the mass of the manipulator while still maintaining the same waterproofing that
157
Figure D.10: Strongman joint cross sec-
tion
Figure D.9: Strongman joint structural
design
RTSX has. The intent was to maintain a minimum safety factor of two above the
maximum actuator loads. The joint structure was designed to be manufactured
from aluminum using an additive process such as Selective Laser Melting (SLM).
Strongmans structure was limited to a minimum thickness of 0.040 inches for man-
ufacturability.
The structural ribs surrounding the brushless DC motor, pictured in green in
Figure D.10, serve to fill the void left by the small diameter of the stator. These
also serve as a radiative cooler for the motor, increasing the effective view factor
directly about the motor. The ribs are sized to withstand buckling modes; however,
vibrational modes were not studied, and would need to be.
Another mass minimization technique used in the design of Strongman was
the use of composite layup for the thin walled link tubes. This presents a myriad of
challenges, including how to properly seal the composite from water intrusion, how
158
Figure D.12: Strongman interface detail
showing sealing gasket (Shown in orange)
Figure D.11: Strongman joint-link inter-
face
to mechanically mate to the composite, and how to design for the large difference
in coefficient of thermal expansion. Preliminary solutions were found for all of these
challenges and were added to the link design.
To allow for a bolted interface, a pre-fabricated composite flange is adhered
to the exterior of the composite link tube. The composite link is attached to the
metallic structure of Strongmans joints by a series of circumferential shear clips.
These are designed to eliminate stresses caused by radial thermal expansion of the
joint, and still carry the structural loads of the serial link manipulator. The ta-
pered parent material about the threaded feature uses geometry established in the
experimental study detailed in Appendix C. At the base of the joint sits an o-ring
to seal the interior of Strongman from the environment. This o-ring is highlighted
in orange in Figure D.12.
159
D.6 Design Study Conclusions
This design study was conducted to observe the highest performance design
space possible for a serial link manipulator. The design was conducted with the goal
of minimizing the manipulator mass, which in turn reduced the load requirement
for the joints when operating in Earth‘s gravity. Strongman is designed to lift 9
kg in earth gravity and has a mass of under 5kg. By comparison, RTSX DXE is
designed to lift 9kg at full extension and has a mass of nearly 200kg. The DXE
design emphasized tip manipulability, packing three motors and two tool drives into
the wrist. This had a large weight penalty associated with it, but resulted in a more
dexterous system.
Figure D.13: Comparison of Strongman shoulder with RTSX DXE Shoulder
Strongman would present a new design paradigm for space robotics. By mak-
ing system mass and cost lower by an order of magnitude, it may make the use of
robotic manipulators far more appealing to systems engineers. Many actuators and
160
mechanisms used in space today operate for only a limited number of cycles, but
this has not been allowed for robotic manipulators yet. Assuming a very limited
cycle life on a dexterous robotic manipulator could allow a single manipulator to re-
place many of the deploying actuators on a vehicle, and there by reducing mass and
cost. Strongman may also be an enabling technology for more complex experiments
on small satellites, allowing experiments to be conducted on-board a small satellite
that would normally be performed by a human.
161
Appendix E: Wire Harnessing Guide
This appendix page is an example of one of the wiring control documents
for the design of RTSX. This is designed to include all necessary information and
background for mechanical design.
E.1 Connector P4 Table E.1: Connector P4 Pinout Wire
Chart
Pin# USED AWG Logical Name
Connection Overview:
1 YES 20 +5V Logic
This connector provides the power
2 YES 20 GND
to run the Servo Driver logic (known col-
3 YES 26 PDI-3
loquially as Control Power) and multi-
4 YES 26 PAI-1+(REF +)
ple I/O connections to the distribution
5 YES 26 PDI-2
board. Pins 1 and 2 carry control power,
6 NO - PAI-1-(REF -)
pin 4 is an analog pin read by the Servo
7 YES 26 PDI-1
Drivers ADC, and all remaining pins are
8 YES 26 PDO-3
for digital communication. Not all digital
9 YES 26 GND
pins may be used, but for the purpose of
10 YES 26 PDO-2
this document we will treat them as fully
11 YES 26 PDI-5+
populated.
12 YES 26 PDO-1
Connector Type:
13 YES 26 PDI-5-
Molex: P/N 51353-1600 (housing)
14 YES 26 PDI-5+
56134-9100 (contacts)
15 YES 26 GND
16 YES 26 PDI-4-
Figure E.2: Connector P4 cable cross sec-
Figure E.1: Connector P4 Pinout tion, showin in inches
162
Appendix F: Interpart Connections
The flow of design requirements and interfaces is traditionally done by form-
ing interface control documents and manually checking for compliance. To decrease
design time, this process was automated within the Siemens design software. Inter-
faces in the form of numerical values, two dimensional geometry, and even complex
surfaces are linked between components in this design.
The Interpart connections follow almost the exact same structure as the design
tree. Note the similarities between Figure 6.1 and Figure F.1. The only discrep-
ancies occur between the structures are due to the design history associated. The
Interpart tree persists across all design revisions, so components that were depre-
cated still exist on the tree. In Figure F.1 the part “BackBone Top Template V3”
was eliminated from the design, but its model is still dependent on variables in
“Rack Template V4. ”
Figure F.1: Sample of RTSX Interpart Tree, generated using Siemens NX
163
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