Cuspidal and Noncuspidal Robot Manipulators

TL;DR

This paper reviews the kinematic properties of cuspidal and noncuspidal robot manipulators, providing conditions for their classification and detailed analysis of orthogonal and 6R types.

Contribution

It offers a comprehensive classification and explicit conditions for identifying cuspidal manipulators based on DH parameters and workspace analysis.

Findings

Classification of 3R orthogonal manipulators into cuspidal and noncuspidal types

Explicit DH-parameter-based conditions for cuspidality

Analysis of cuspidal properties in 6R manipulators

Abstract

This article synthezises the most important results on the kinematics of cuspidal manipulators i.e. nonredundant manipulators that can change posture without meeting a singularity. The characteristic surfaces, the uniqueness domains and the regions of feasible paths in the workspace are defined. Then, several sufficient geometric conditions for a manipulator to be noncuspidal are enumerated and a general necessary and sufficient condition for a manipulator to be cuspidal is provided. An explicit DH-parameter-based condition for an orthogonal manipulator to be cuspidal is derived. The full classification of 3R orthogonal manipulators is provided and all types of cuspidal and noncuspidal orthogonal manipulators are enumerated. Finally, some facts about cuspidal and noncuspidal 6R manipulators are reported.