Kinematic Analysis of a Family of 3R Manipulators

TL;DR

This paper systematically analyzes the workspace topologies of 3R manipulators, characterizing their singularities and cusps, and provides explicit conditions for cuspidality based on DH parameters.

Contribution

It introduces a comprehensive classification of workspace topologies and explicit conditions for cuspidality in 3R manipulators using DH parameters.

Findings

Workspace topologies are divided into five domains with constant cusp counts.

Explicit expressions for separating surfaces in DH-parameters are provided.

Necessary and sufficient conditions for a manipulator to be cuspidal are derived.

Abstract

The workspace topologies of a family of 3-revolute (3R) positioning manipulators are enumerated. The workspace is characterized in a half-cross section by the singular curves. The workspace topology is defined by the number of cusps that appear on these singular curves. The design parameters space is shown to be divided into five domains where all manipulators have the same number of cusps. Each separating surface is given as an explicit expression in the DH-parameters. As an application of this work, we provide a necessary and sufficient condition for a 3R orthogonal manipulator to be cuspidal, i.e. to change posture without meeting a singularity. This condition is set as an explicit expression in the DH parameters.