Kinematic Simulation of Planar and Spatial Mechanisms Using a Polynomial Constraints Solver

AbstractThe connection between kinematics and mechanisms to algebraic constraints is well known. This work presents a general kinematics simulator that allows end users to define planar and/or spatial arrangements, even along freeform curves and surfaces. The mechanical arrangement is then converted into a set of algebraic constraints and the motion of the arrangements is computed with the aid of a multivariate polynomial constraint solver.

[1]  Glenn A. Kramer,et al.  Solving Geometric Constraint Systems , 1990, AAAI.

[2]  Jean-Claude Latombe,et al.  Robot motion planning , 1970, The Kluwer international series in engineering and computer science.

[3]  Gershon Elber,et al.  Efficient solution to systems of multivariate polynomials using expression trees , 2008, 2008 IEEE International Conference on Shape Modeling and Applications.

[4]  Gershon Elber,et al.  Topologically guaranteed univariate solutions of underconstrained polynomial systems via no-loop and single-component tests , 2010, SPM '10.

[5]  A. Morgan,et al.  Numerical Continuation Methods for Solving Polynomial Systems Arising in Kinematics , 1990 .

[6]  I. Artobolevsky.  Mechanisms in Modern Engineering Design , 1979 .

[7]  I. I. Artobolevskiĭ.  Mechanisms in modern engineering design , 1975 .

[8]  B. Roth,et al.  Synthesis of Path-Generating Mechanisms by Numerical Methods , 1963 .

[9]  Alan C. Carr,et al.  VIRTUAL PROTOTYPING OF A WHEELCHAIR LIFT FOR THE DISABLED FITTED TO A CL-600 CHALLENGER AIRCRAFT , 1998 .

[10]  Leo Joskowicz,et al.  Understanding Mechanical Motion: From Images to Behaviors , 1999, Artif. Intell..

[11]  Bruno Buchberger,et al.  Algebraic methods for geometric reasoning , 1988 .

[12]  G. Laman.  On graphs and rigidity of plane skeletal structures , 1970 .

[13]  Howard E. Shrobe.  Understanding Linkages , 1993, AAAI.

[14]  Jan Verschelde,et al.  Advances in Polynomial Continuation for Solving Problems in Kinematics , 2002 .

[15]  Gershon Elber,et al.  Subdivision termination criteria in subdivision multivariate solvers using dual hyperplanes representations , 2007, Comput. Aided Des..

[16]  J. Merlet,et al.  Five Precision Point Synthesis of Spatial RRR Manipulators Using Interval Analysis , 2004 .

[17]  John E. Hopcroft,et al.  Movement Problems for 2-Dimensional Linkages , 1984, SIAM J. Comput..

[18]  M. Barton,et al.  Topologically guaranteed solution of surface – surface intersections via no – loop and single – component tests , 2009 .

[19]  Gershon Elber,et al.  Subdivision Termination Criteria in Subdivision Multivariate Solvers , 2006, GMP.

[20]  C. Mavroidis.  A SPATIAL OVERCONSTRAINED MECHANISM THAT CAN BE USED IN PRACTICAL APPLICATIONS , 1999 .

[21]  Arthur G. Erdman,et al.  Mechanism Design : Analysis and Synthesis , 1984 .

[22]  Christoph M. Hoffmann,et al.  Geometric constraint solver , 1995, Comput. Aided Des..

[23]  David A. Cox,et al.  Using Algebraic Geometry , 1998 .

[24]  M.L. Husty,et al.  Self-motions of Griffis-Duffy type parallel manipulators , 2000, Proceedings 2000 ICRA. Millennium Conference. IEEE International Conference on Robotics and Automation. Symposia Proceedings (Cat. No.00CH37065).

[25]  J. Merlet,et al.  Five Precision Points Synthesis of Spatial RRR Manipulators Using Interval Analysis , 2002 .