Analysis of Force Distribution in Grasps Using Augmentation

A new approach to the analysis of statically indeterminate restraint of a rigid body with any arrangement of point contact is presented in this paper. The paper associates the elasticity at restraint contacts with geometric compatibility of the contact points and constructs elastic compatibility equations, which are complementary to the restraint equations. The equations so obtained are then used to augment the restraint equations and lead to an agumented Jacobian matrix. The new approach enables grasps to be analysed and synthesized in a constraint of combined elasticity and geometric compatibility, in addition to the force equilibrium condition. This gives a mathematical basis for the analysis of force distribution of the statically indeterminate restraint. Detailed reasoning and derivations are given followed by both planar and spatial examples.

[1]  L. Brand.  Vector and tensor analysis , 1947 .

[2]  J. Kenneth Salisbury,et al.  Articulated Hands , 1982 .

[3]  J. K. Salisbury,et al.  Kinematic and Force Analysis of Articulated Mechanical Hands , 1983 .

[4]  B. Dizioglu,et al.  Mechanics of form closure , 1984 .

[5]  Mark R. Cutkosky,et al.  Robotic grasping and fine manipulation , 1985 .

[6]  Joseph Duffy,et al.  The Elliptic Polarity of Screws , 1985 .

[7]  Mark R. Cutkosky,et al.  Friction, Stability and the Design of Robotic Fingers , 1986 .

[8]  Van-Duc Nguyen,et al.  Constructing stable grasps in 3D , 1987, Proceedings. 1987 IEEE International Conference on Robotics and Automation.

[9]  D. J. Sanger,et al.  Restraint analysis of a rigid body using frictional elastic contacts , 1987 .

[10]  Tsuneo Yoshikawa,et al.  Manipulating and grasping forces in manipulation by multifingered robot hands , 1987, IEEE Trans. Robotics Autom..

[11]  Jeffrey C. Trinkle,et al.  On the stability and instantaneous velocity of grasped frictionless objects , 1992, IEEE Trans. Robotics Autom..

[12]  Audra E. Kosh,et al.  Linear Algebra and its Applications , 1992 .

[13]  D. John Sanger,et al.  Redundant grasps, redundant manipulators, and their dual relationships , 1992, J. Field Robotics.

[14]  Jian S. Dai,et al.  Analysis and Synthesis of Planar Grasping in an Image Space , 1992 .

[15]  Jian S. Dai.  Screw image space and its application to robotic grasping , 1993 .

[16]  Jian S. Dai,et al.  Synthesis of Grasps in Image Space Using Affine Augmentation , 1995 .