An Exhaustive Study of the Workspaces Tolopogies of all 3R Orthogonal Manipulators with Geometric Simplifications

TL;DR

This paper classifies three-revolute orthogonal manipulators with zero DH parameters based on workspace topology, identifying types with fully reachable, well-connected workspaces suitable for trajectory planning.

Contribution

It introduces a new classification scheme for 3R orthogonal manipulators based on workspace topology and kinematic properties, aiding manipulator design.

Findings

Several manipulators have fully reachable, well-connected workspaces.

Workspace topology characterized by cusps and nodes influences kinematic properties.

Classification helps identify manipulators with desirable trajectory feasibility.

Abstract

This paper proposes a classification of three-revolute orthogonal manipulators that have at least one of their DH parameters equal to zero. 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 manipulators are classified into different types with similar kinematic properties. Each type is evaluated according to interesting kinematic properties such as, whether the workspace is fully reachable with four inverse kinematic solutions or not, the existence of voids, and the feasibility of continuous trajectories in the workspace. It is found that several orthogonal manipulators have a "well-connected" workspace, that is, their workspace is fully accessible with four inverse kinematic solutions and any continuous trajectory is feasible. This result is of interest for the design of alternative manipulator geometries.