Dynamics of rigid bodies undergoing multiple frictional contacts

Two key problem areas in the dynamics of rigid bodies with multiple frictional contacts are solved. First, the modeling of rigid body collisions is addressed. Second, an accurate model that will predict the contact forces is sought. The emphasis is on correct phenomenological and quantitative modeling. An approach to the simulation of mechanical systems with multiple, frictional constraints is proposed which is free of inconsistencies. This method is illustrated with the help of a simple planar example.<<ETX>>

[1]  É. Delassus.  Sur les lois du frottement de glissement , 1923 .

[2]  A. Ingleton.  A Probelm in Linear Inequalities , 1966 .

[3]  R. Knops,et al.  Three-Dimensional Problems of the Theory of Elasticity , 1967, The Mathematical Gazette.

[4]  G S A Shawki.  Rigidity considerations in fixture design—contact rigidity for eccentric clamping , 1967 .

[5]  R. Cottle.  On a Problem in Linear Inequalities , 1968 .

[6]  G. Dantzig,et al.  COMPLEMENTARY PIVOT THEORY OF MATHEMATICAL PROGRAMMING , 1968 .

[7]  A. I. Lur’e.  Three - dimensional problems of the theory of elasticity , 1968 .

[8]  J. J. Uicker,et al.  IMP (Integrated Mechanisms Program), A Computer-Aided Design Analysis System for Mechanisms and Linkage , 1972 .

[9]  J. M. Watt.  Numerical Initial Value Problems in Ordinary Differential Equations , 1972 .

[10]  S. Karamardian,et al.  The complementarity problem , 1972, Math. Program..

[11]  A. Ishlinsky.  On the dynamics of a system of rigid bodies , 1973 .

[12]  Baldine-brunel Paul,et al.  Analytical dynamics of mechanisms—a computer oriented overview , 1975 .

[13]  Ronald L. Huston,et al.  Eliminating singularities in governing equations of mechanical systems , 1976 .

[14]  J. Wittenburg,et al.  Dynamics of systems of rigid bodies , 1977 .

[15]  W. E. Schmitendorf,et al.  Analytical dynamics of discrete systems , 1977 .

[16]  Phillip Barkan,et al.  Kinematics and Dynamics of Planar Machinery , 1979 .

[17]  R. Cottle.  Numerical methods for complementarity problems in engineering and applied science , 1979 .

[18]  A. Browne.  The orientation of components for automatic assembly , 1980 .

[19]  B. Paul,et al.  Contact Pressures on Closely Conforming Elastic Bodies , 1981 .

[20]  Per Lötstedt.  Coulomb Friction in Two-Dimensional Rigid Body Systems , 1981 .

[21]  J. Ferziger.  Numerical methods for engineering application , 1981 .

[22]  E. Haug,et al.  Generalized Coordinate Partitioning for Dimension Reduction in Analysis of Constrained Dynamic Systems , 1982 .

[23]  Daniel E. Whitney,et al.  Quasi-Static Assembly of Compliantly Supported Rigid Parts , 1982 .

[24]  Per Lötstedt.  Mechanical Systems of Rigid Bodies Subject to Unilateral Constraints , 1982 .

[25]  Donald Goldfarb,et al.  A numerically stable dual method for solving strictly convex quadratic programs , 1983, Math. Program..

[26]  J. Oden,et al.  Nonlocal and Nonlinear Friction Laws and Variational Principles for Contact Problems in Elasticity , 1983 .

[27]  John E. Hopcroft,et al.  Motion of Objects in Contact , 1984 .

[28]  Per Lötstedt.  Numerical Simulation of Time-Dependent Contact and Friction Problems in Rigid Body Mechanics , 1984 .

[29]  K. Johnson.  Contact Mechanics: Frontmatter , 1985 .

[30]  Donald R. Riley,et al.  NEW DIRECTIONS FOR MECHANISM KINEMATICS AND DYNAMICS. , 1985 .

[31]  J. Keller.  Impact With Friction , 1986 .

[32]  Georges Giralt,et al.  Robotics research : the third international symposium , 1986 .

[33]  N. Harris McClamroch,et al.  Singular systems of differential equations as dynamic models for constrained robot systems , 1986, Proceedings. 1986 IEEE International Conference on Robotics and Automation.

[34]  E. Haug,et al.  Dynamics of mechanical systems with Coulomb friction, stiction, impact and constraint addition-deletion—I theory , 1986 .

[35]  Klaus Schittkowski,et al.  NLPQL: A fortran subroutine solving constrained nonlinear programming problems , 1986 .

[36]  Matthew T. Mason,et al.  Mechanics and Planning of Manipulator Pushing Operations , 1986 .

[37]  Edward J. Haug,et al.  Dynamics of mechanical systems with Coulomb friction, stiction, impact and constraint addition-deletion—II Planar systems , 1986 .

[38]  V. T. Rajan,et al.  Dynamics of a rigid body in frictional contact with rigid walls: Motion in two dimensions , 1987, Proceedings. 1987 IEEE International Conference on Robotics and Automation.

[39]  J. Oden,et al.  Contact Problems in Elasticity: A Study of Variational Inequalities and Finite Element Methods , 1987 .

[40]  John E. Hopcroft,et al.  Simulation of physical systems from geometric models , 1987, IEEE J. Robotics Autom..

[41]  Manfred Hiller,et al.  A Computer-Oriented Approach for the automatic Generation and Solution of the Equations of Motion for Complex Mechanisms , 1987 .

[42]  Yu Wang,et al.  Modeling impact dynamics for robotic operations , 1987, Proceedings. 1987 IEEE International Conference on Robotics and Automation.

[43]  Arthur C. Sanderson,et al.  Planning robotic manipulation strategies for sliding objects , 1987, Proceedings. 1987 IEEE International Conference on Robotics and Automation.

[44]  Edmund Taylor Whittaker,et al.  A Treatise on the Analytical Dynamics of Particles and Rigid Bodies: INDEX OF TERMS EMPLOYED , 1988 .

[45]  John C. Platt,et al.  Constraints methods for flexible models , 1988, SIGGRAPH.

[46]  Katta G. Murty,et al.  Linear complementarity, linear and nonlinear programming , 1988 .

[47]  Robert H. Sturges,et al.  A Three-Dimensional Assembly Task Quantification with Application to Machine Dexterity , 1988, Int. J. Robotics Res..

[48]  Vijay R. Kumar,et al.  Force distribution in closed kinematic chains , 1988, IEEE J. Robotics Autom..

[49]  Yu Wang,et al.  On the inconsistency of rigid-body frictional planar mechanics , 1988, Proceedings. 1988 IEEE International Conference on Robotics and Automation.

[50]  R. Brach.  Rigid Body Collisions , 1989 .

[51]  Hamid M. Lankarani,et al.  A Contact Force Model With Hysteresis Damping for Impact Analysis of Multibody Systems , 1989 .

[52]  David Baraff,et al.  Analytical methods for dynamic simulation of non-penetrating rigid bodies , 1989, SIGGRAPH.

[53]  W. Stronge.  Rigid body collisions with friction , 1990, Proceedings of the Royal Society of London. Series A: Mathematical and Physical Sciences.

[54]  Bruce Randall Donald,et al.  On the motion of compliantly-connected rigid bodies in contact. II. A system for analyzing designs for assembly , 1990, Proceedings., IEEE International Conference on Robotics and Automation.

[55]  D. H. Bacon,et al.  42 – Computers in mechanical engineering , 1990 .

[56]  Norman I. Badler.  Human Factors Simulation Research at the University of Pennsylvania , 1990 .

[57]  R. Vijay Kumar,et al.  Analysis and simulation of mechanical systems with multiple frictional contacts , 1994 .

[58]  V. Kumar,et al.  A kinestatic analysis of cooperating robot system , 1991, Fifth International Conference on Advanced Robotics 'Robots in Unstructured Environments.

[59]  Vijay Kumar,et al.  Control of contact conditions for manipulation with multiple robotic systems , 1991, Proceedings. 1991 IEEE International Conference on Robotics and Automation.

[60]  Xiaoping Yun,et al.  Coordination of two-arm pushing , 1991, Proceedings. 1991 IEEE International Conference on Robotics and Automation.

[61]  Pramath R. Sinha,et al.  A contact stress model for multifingered grasps of rough objects , 1992, IEEE Trans. Robotics Autom..

[62]  M. T. Mason,et al.  Two-Dimensional Rigid-Body Collisions With Friction , 1992 .

[63]  Inhwan Han,et al.  Multi-Body Impact Motion with Friction—Analysis, Simulation, and Experimental Validation , 1993 .

[64]  Edward R. Champion.  Numerical Methods for Engineering Applications , 1993 .