Quantitative Analysis of Inner Force Distribution and Load Capacity of Grasps and Fixtures

Abstract

This paper focuses on a quantitative analysis for grasp planning and fixture design based on an analytical description of point contact restraint. In the framework, the analysis deals with the fundamental concepts of restraint cone, freedom cone, force-determinacy and relative form closure. A method is presented to quantify the performance of a fixture (or grasp) with two major characteristics of inner force distribution and load capacity. Two different fixturing (or grasp) models of simplex grasp and elastic grasp are presented. It is shown that the performance of these two types of grasp (or fixturing) could be measured with different performance indices. A minimax index (MMI) and a volume measure are defined for evaluating a simplex grasp, while a measure using the tolerable range of differential motion in the twist space or the allowable load polyhedron in the wrench space would be suitable for quantifying robustness and load capability of an elastic fixture system. Furthermore, for fixture system design a geometric analysis and reasoning procedure is described for the design of locators, clamps and supplementary supports. The aim of these proposed analysis and design techniques is to provide a scientific foundation for automated grasping/fixturing system design in the engineering practice.