Chapter 5

Workspace of the End Effector of a Robot Mechanism

Abstract

The workspace of the spatial robotic mechanism and its symmetric homomorphism with the mechanism itself are discussed. The symmetry group of the kinematic chain structure must be a subgroup of that of the workspace of the end effector. Through mathematic proof, the analogous relationship between the workspace shape and the structure of the manipulator is revealed. The corresponding relationship between the workspace and the flexible workspace is homomorphic mapping. A quantitative description of such symmetry relations provides certain theoretical basis for the analysis, synthesis, and structure innovative design of robotic mechanisms. Examples demonstrate that this theorem ...

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