Analyse Comparative des Manipulateurs 3R \`a Axes Orthogonaux

TL;DR

This paper classifies the workspace topologies of 3R orthogonal manipulators without offset, evaluates their performance based on condition number and inverse kinematic solutions, and identifies topologies with optimal performance.

Contribution

It provides a detailed classification of workspace topologies for a family of manipulators and links these topologies to performance metrics.

Findings

Nine distinct workspace topologies identified.

Performance correlates with the number of inverse kinematic solutions.

Optimal manipulators belong to specific workspace topologies.

Abstract

A family of 3R orthogonal manipulators without offset on the third body can be divided into exactly nine workspace topologies. 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. Based on this classification, we evaluate theses manipulators by the condition number related to the joint space and the proportion of the region with four inverse kinematic solutions compared to a sphere containing all the workspace. This second performance number is in relation with the workspace. We determine finally le topology of workspace to which belong manipulators having the best performance number values.