Metric Relations and Displacement Groups in Mechanism and Robot Kinematics

Abstract

This paper presents a systematic theory for metric relations between the invariant properties of displacement groups, and shows this theory application to mechanism kinematics. Displacement groups, their invariant properties and operations are briefly described. Kinematic constraints are then introduced as tools for relating abstract group properties to actual mechanism constraints. Criteria and operating rules to employ metric relations for the generation of a meaningful set of closure equations for kinematic chains are detailed.