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Design of Large Space Structures Derived from Line Geometry Principles

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Design of Large Space Structures Derived from Line Geometry Principles DESIGN OF LARGE SPACE STRUCTURES DERIVED FROM LINE GEOMETRY PRINCIPLES By PATRICK J. MCGINLEY A THESIS PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE UNIVERSITY OF FLORIDA 2002 Copyright 2002 by Patrick J. McGinley I would like to dedicate this work to Dr. Joseph Duffy - mentor, friend, and inspiration. My thanks also go out to my parents, Thomas and Lorraine, for everything they have taught me, and my friends, especially Byron, Connie, and Richard, for all their support. ACKNOWLEDGMENTS I would like to thank my advisor, Dr. Carl D. Crane, III, the members of my advisory committee, Dr. John Schueller and Dr. John Ziegert, as well as Dr. Joseph Rooney, for their help and guidance during my time at UF, and especially their understanding during a difficult last semester. iv TABLE OF CONTENTS page ACKNOWLEDGMENTS ................................................................................................. iv LIST OF TABLES............................................................................................................ vii LIST OF FIGURES ......................................................................................................... viii ABSTRACT...................................................................................................................... xii CHAPTER 1 INTRODUCTION ............................................................................................................1 2 BACKGROUND ..............................................................................................................5 2.1 In-Parallel Robotic Manipulators.............................................................................. 5 2.2 Definitions.................................................................................................................9 3 THEORETICAL DEVELOPMENT ..............................................................................14 3.1 Line Geometry Methods ......................................................................................... 14 3.2 Axial Loading Approximations .............................................................................. 23 3.3 Lateral Loading Approximations............................................................................ 24 3.4 Torsional Loading Approximation ......................................................................... 24 4 DUALITY OF POLYHEDRA .......................................................................................26 5 FINITE ELEMENT MODELING..................................................................................34 6 DATA ANALYSIS AND RESULTS.............................................................................46 6.1 Axial Specific Stiffness Performance ..................................................................... 48 6.2 Lateral Specific Stiffness Performance................................................................... 51 6.3 Torsional Specific Stiffness Performance............................................................... 53 6.4 Overall Performance Trends................................................................................... 55 7 NUMERICAL EXAMPLES...........................................................................................63 7.1 Dual Polyhedron ..................................................................................................... 63 7.2 Example Boom Design Problem............................................................................. 66 v 8 CONCLUSIONS.............................................................................................................67 8.1 Line Geometry ........................................................................................................ 67 8.2 Duality of Polyhedra............................................................................................... 68 8.3 Structural Simulation .............................................................................................. 68 9 FUTURE WORK............................................................................................................72 APPENDIX A MATLAB CODE FOR PSEUDO-INVERSE PROGRAM...........................................74 B ALTERNATE LEAST SQUARES MODELS ..............................................................82 C DESIGN OPTIMIZATION CHARTS...........................................................................87 D ADDITIONAL FIGURES .............................................................................................95 LIST OF REFERENCES...................................................................................................97 BIOGRAPHICAL SKETCH .............................................................................................99 vi LIST OF TABLES Table page 2.1 Optimal 3-3 manipulator ratio conversions .................................................................13 5.1 Comparison of AEC-Able specifications and SRTM model results [1]......................37 6.1 Maximum specific stiffness performance for 300m x 5m CFRP booms.....................56 7.1 List of vertices for mutual moment calculations..........................................................65 B.1 Ranges of key design parameters used to fit regression models.................................83 vii LIST OF FIGURES Figure page 1.1 Highway traffic sign support truss.................................................................................4 2.1 Top view of 3-3 in-parallel device platforms ................................................................6 2.2 Top view of 3-3 in-parallel device with actuated legs added ........................................7 2.3 Construction of an octahedral 3-3 manipulator with Rtop:Rbottom = ½............................8 2.4 Construction of a triangular truss unit cell...................................................................10 2.5 Triangular truss unit cell ..............................................................................................11 2.6 Octahedral truss unit cell .............................................................................................11 2.7 Symmetric reinforced octahedral truss unit cell ..........................................................12 3.1 Unit cell geometries and two-cell boom structures – triangular truss (a,d), symmetric reinforced octahedral (b,e), and octahedral (c,f)....................................................15 3.2 √det(JJT) vs. N {3,60} and φ {-180,180}, a=1 b=2 h=1 ............................................18 3.3 √det(JJT) vs. N {3,60} and φ {-180,180}, a=1 b=2 h=2 .............................................19 3.4 √det(JJT) vs. N {3,60} and φ {-180,180}, a=1 b=2 h=4 .............................................20 3.5 √det(JJT) vs. N {3,60} and φ {-180,180}, a=1 b=2 h=8 .............................................20 3.6 Corresponding length efficiency index plot to Figure 3.2 ...........................................21 3.7 Corresponding length efficiency index plot to Figure 3.3 ...........................................21 3.8 Corresponding length efficiency index plot to Figure 3.4 ...........................................22 3.9 Corresponding length efficiency index plot to Figure 3.5 ...........................................22 4.1 Regular octahedron to regular cube mapping ..............................................................27 4.2 Elongated octahedron dual to elongated cuboid ..........................................................30 viii 4.3 Optimal quality index octahedron configuration (w/perspective views) and dual (also with lines extended to accentuate intersections)....................................................31 4.4 Limit of scaling one set of vertices to ward the limit at which the octahedron approaches a tetrahedron........................................................................................32 5.1 Axial, lateral, torsional loads applied to center-plane constrained two-cell octahedral boom ......................................................................................................................34 5.2 AEC-Able boom for NASA STS-99 Shuttle Radar Topography Mission [1].............36 5.3 Conversion of SRTM cell to stacked 4-4 platform cell ...............................................37 5.4 AEC-Able SRTM boom finite element model, deformed under 10 lbf lateral end loading....................................................................................................................38 5.5 FEM model of 16 cell, 300m x 5m octahedral boom ..................................................39 5.6 FEM model of octahedron subjected to axial load ......................................................40 5.7 Deformed FEM model of octahedron subjected to axial load .....................................41 T 5.8 Induced leg stresses in a single octahedron, wapp= [0 0 –3 0 0 0] ..............................42 5.9 Deformed FEM model of octahedron subjected to lateral load...................................43 T 5.10 Induced leg stresses in a single octahedron, wapp= [-3 0 0 3h 0 0] ..........................44 5.11 Deformed FEM model of octahedron subjected to torsional load.............................44 T 5.12 Induced leg stresses in a single octahedron, wapp= [0 0 0 0 0 3] ..............................45 6.1 Specific axial stiffness vs. Rtop:Rbottom for various numbers of cells per SYM boom..49 6.2 Specific axial stiffness
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