Kinematics of spatial linkages by group algebra: A structure-based approach

Abstract The theoretical fundamentals for a structure-based, unified approach to the kinematics of spatial linkages are presented according to the subdivision of rigid displacements into elementary subspaces of known properties. Subgroups of the rigid-transformation group are the basic tools that are used to single out the required properties. The geometric characteristics of these subgroups and their restrictions (constraints) are defined, and rules for constraint composition are given. The kinematic analysis of linkages is performed through the following two main steps: first a mobility analysis and constraint recognition are carried out; then, by using this mobility information and the invariant properties of transformation groups, a set of minimum-coupling compatibility equations is obtained.

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