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  K  INETOSTATIC D  ESIGN OF AN ARTICULATED LEG  - WHEEL LOCOMOTION SUBSYSTEM    by S  EUNG KOOK J  UN    J UNE 2004 A thesis submitted to the Faculty of the Graduate School of the State University of New York at Buffalo in partial fulfillment of the requirements for the degree of M  ASTER OF S  CIENCE    Department of Mechanical and Aerospace Engineering State University of New York at Buffalo Buffalo, New York 14260     ACKNOWLEDGEMENT My thanks go first and foremost to Professor Venkat Krovi as advisor, mentor and friend. His excellence in the field and enthusiasm to work has always been a source of inspiration. I also extend my gratitude to my committee members, Dr. Roger Mayne and Dr. John Crassidis for valuable suggestions and help. I spent many enjoyable hours with ARM Lab and department friends, Ajay, Annapurna, Chetan, Chin-pei, Dan, Glenn, Jae-jun, Jong-woo, Jong-rae, Leng-feng, Mike, Prasanna, Pravin, Rajan, Tao, Young-suk. I would like to thank them for help and advice inside and outside the school. I miss joyful friends, Deepak, JJ, Ken, Mrs. Krovi, Lei-tang, and Ravishankar giving me unforgettable recollections in Buffalo. Finally I would like to thank my family and ji-young who have encouraged me so much over years. ii    CONTENTS 1   INTRODUCTION   ..........................................................................1   1.1   Articulated leg-wheel subsystems for vehicle systems.......................................2  1.1.1 Articulated Degrees of Freedom.....................................................................2 1.1.2 Equilibration (Structural and Actuation-based)..............................................4 1.2   Single Degree-of-freedom Articulated Leg-Wheel Systems..............................5   1.3   Our Research Goals..............................................................................................6   1.4   Organization of the thesis.....................................................................................7   2   BRIEF BACKGROUND ON LEG-WHEEL SYSTEMS................8   3   DESIGN APPROACH................................................................11   3.1   Applied loads at the end-effector of a leg-wheel design...................................11   3.2   User-inputs for Problem Specification..............................................................12  3.2.1 Kinematic Design Factors under User-Control.............................................13 3.2.2 Force-related design factors under user-control...........................................14 3.3   Specific Test Scenario.........................................................................................15  3.3.1 Design of the kinematic trajectory for the test case......................................15 3.3.2 Design of the static trajectory for the test case.............................................15 3.4   Overview of Kinetostatic Design Approach.....................................................16   4   DESIGN/SYNTHESIS OF SDCSC LEG-WHEEL MECHANISM18   4.1   Coupled Serial Chain (CSC) mechanisms........................................................19   4.2   Kinematic Synthesis............................................................................................19  4.2.1 Planar Precision Point Synthesis of SDCSC.................................................19 4.2.2 Combined Kinematic Precision-Point Synthesis and Optimization.............21 4.3   Static Synthesis of SDCSC Mechanism.............................................................24  4.3.1 Precision Torque Synthesis...........................................................................24 4.4   Static Precision Point Synthesis and Optimization..........................................27  4.4.1 Two static precision points and no free choices...........................................27 iii    4.4.2 No static precision points and using both variables as free-choices.............30 5   DESIGN/SYNTHESIS OF FOURBAR LEG-WHEEL MECHANISM....................................................................................33   5.1   Kinematic Synthesis............................................................................................33  5.1.1 Planar Precision Point Synthesis of Fourbar.................................................34 5.2   Kinematic Synthesis............................................................................................34   5.3   Kinematic Optimization.....................................................................................35   5.4   Static Synthesis of Fourbar with Two Precision Points..................................37  5.4.1 Four static precision points and no free choices...........................................40 5.4.2 No static precision points and using four variables as free-choices.............42 6   STATIC EQUILIBRIUM ANALYSIS...........................................45   6.1   Background.........................................................................................................45  6.1.1 Structures and mechanisms...........................................................................45 6.1.2 Equilibrium Analysis....................................................................................46 6.2   Static Equilibration (in a mechanism context).................................................47  6.2.1 Static Balance and Gravity Compensation...................................................47 6.2.2 Methods for Equilibration.............................................................................48 6.3   Case Study of One-Link Mechanism.................................................................49  6.3.1 Examples of perfect static equilibration (using counterweight system).......49 6.3.2 Example of perfect gravity balancing (using Linear Springs)......................50 6.3.3 Examples for selective equilibria (using Hookian torsional springs)...........50 6.4   Analysis of Equilibria.........................................................................................52  6.4.1 Equilibrium Analysis for Spring equilibria...................................................52 6.4.2 Equilibrium Analysis for Counterweight......................................................53 6.5   Quantitative Measures for Evaluation of Equilibria.......................................54  6.5.1 Location of the equilibrium..........................................................................54 6.5.2 Sensitivity of the equilibrium........................................................................55 6.5.3 Basin of Attraction – magnitude and range..................................................56 6.6   Possible Equilibrium Configurations for a One-Link Mechanism................56   6.7   Most Useful Equilibrium Case of a One Link System.....................................58   6.8   Basin of Attraction Optimization......................................................................60  iv

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