Kinematic analysis of spatial fixed-axis higher pairs using configuration spaces

We present a kinematic analysis algorithm for spatial higher pairs whose parts rotate around or translate along fixed spatial axes. The part geometry is specified in a parametric boundary representation consisting of planar, cylindrical, and spherical patches bounded by line and circle segments. Kinematic analysis is performed by configuration space construction following the method that we developed for planar pairs. The configuration space of a pair is a complete encoding of its kinematics, including contact constraints, contact changes, and part motions. The algorithm constructs contact curves for all pairs of part features, computes the induced configuration space partition, and identifies the free space components. Spatial contact analysis is far harder than planar analysis because there are 72 types of contact versus 8. We have developed a systematic analysis technique and have used it to derive low-degree equations for all cases, which are readily solvable in closed form or numerically. We demonstrate the implemented algorithm on three design scenarios involving spatial pairs and planar pairs with axis misalignment.

[1]  Elisha Sacks,et al.  Computer-aided synthesis of higher pairs via configuration space manipulation , 2001, Proceedings 2001 ICRA. IEEE International Conference on Robotics and Automation (Cat. No.01CH37164).

[2]  David Baraff,et al.  Dynamic Simulation of Non-penetrating Rigid Bodies , 1992 .

[3]  Leo Joskowicz,et al.  Computational Kinematics , 1991, Artif. Intell..

[4]  Jean-Paul Laumond,et al.  Algorithms for Robotic Motion and Manipulation , 1997 .

[5]  John Canny,et al.  Impulse-Based Dynamic Simulation , 1995 .

[6]  Randy C. Brost,et al.  Analysis and planning of planar manipulation tasks , 1992 .

[7]  William H. Press,et al.  Numerical recipes in C , 2002 .

[8]  Elisha Sacks,et al.  Practical Sliced Configuration Spaces for Curved Planar Pairs , 1999, Int. J. Robotics Res..

[9]  L. Joskowicz,et al.  Computational Kinematic Analysis of Higher Pairs with Multiple Contacts , 1995 .

[10]  Bruce Randall Donald,et al.  A Search Algorithm for Motion Planning with Six Degrees of Freedom , 1987, Artif. Intell..

[11]  Elisha Sacks,et al.  Parameter synthesis of higher kinematic pairs , 2003, Comput. Aided Des..

[12]  Russell H. Taylor,et al.  Interference-Free Insertion of a Solid Body Into a Cavity: An Algorithm and a Medical Application , 1996, Int. J. Robotics Res..

[13]  Leo Joskowicz,et al.  Dynamical simulation of planar systems with changing contacts using configuration spaces , 1998 .

[14]  Leo Joskowicz,et al.  Parametric kinematic tolerance analysis of planar mechanisms , 1997, Comput. Aided Des..

[15]  Jean-Daniel Boissonnat,et al.  A practical exact motion planning algorithm for polygonal objects amidst polygonal obstacles , 1988, Proceedings. 1988 IEEE International Conference on Robotics and Automation.

[16]  S M Barnes,et al.  Computer-Aided Kinematic Design of a Torsional Ratcheting Actuator , 2001 .

[17]  Mark de Berg,et al.  Computational geometry: algorithms and applications , 1997 .

[18]  F. Litvin,et al.  Gear geometry and applied theory , 1994 .

[19]  E. J. Haug,et al.  Computer aided kinematics and dynamics of mechanical systems. Vol. 1: basic methods , 1989 .

[20]  Dinesh Manocha,et al.  Collision Detection: Algorithms and Applications , 1996 .

[21]  E. Sacks,et al.  MEMS Functional Validation Using the Configuration Space Approach to Simulation and Analysis , 1999 .

[22]  Jorge Angeles,et al.  Optimization of cam mechanisms , 1991 .

[23]  Arthur G. Erdman,et al.  Modern kinematics : developments in the last forty years , 1993 .

[24]  Leo Joskowicz,et al.  Parametric kinematic tolerance analysis of general planar systems , 1998, Comput. Aided Des..

[25]  Leo Joskowicz,et al.  Computer-assisted Kinematic Tolerance Analysis of a Gear Selector Mechanism with the Configuration Space Method , 1999 .