A Classification of 3R Orthogonal Manipulators by the Topology of their Workspace

TL;DR

This paper classifies 3R orthogonal manipulators based on the topology of their workspace, characterized by singular curves, cusps, and nodes, dividing the design space into nine distinct topology domains.

Contribution

It provides a novel classification framework for 3R manipulators based on workspace topology, with explicit expressions for the separating surfaces in DH-parameters.

Findings

Nine distinct workspace topology domains identified.

Explicit expressions for separating surfaces in DH-parameters.

Manipulators within each domain share similar kinematic properties.

Abstract

A classification of a family of 3-revolute (3R) positining manipulators is established. This classification is based on the topology of their workspace. The workspace is characterized in a half-cross section by the singular curves. The workspace topology is defined by the number of cusps and nodes that appear on these singular curves. The design parameters space is shown to be divided into nine domains of distinct workspace topologies, in which all manipulators have similar global kinematic properties. Each separating surface is given as an explicit expression in the DH-parameters.