Working and Assembly Modes of the Agile Eye

TL;DR

This paper provides a comprehensive kinematic analysis of the Agile Eye, a spherical parallel robot with unique workspace and singularity properties, revealing simple relationships between its assembly and working modes.

Contribution

It introduces the first detailed analysis of the Agile Eye's workspace, singularities, and the geometric relationship between its assembly and working modes.

Findings

Workspace is unlimited except for six singularity curves

Singularity curves are self-motions of the platform

Assembly modes have a simple geometric relation to working modes

Abstract

This paper deals with the in-depth kinematic analysis of a special spherical parallel wrist, called the Agile Eye. The Agile Eye is a three-legged spherical parallel robot with revolute joints in which all pairs of adjacent joint axes are orthogonal. Its most peculiar feature, demonstrated in this paper for the first time, is that its (orientation) workspace is unlimited and flawed only by six singularity curves (rather than surfaces). Furthermore, these curves correspond to self-motions of the mobile platform. This paper also demonstrates that, unlike for any other such complex spatial robots, the four solutions to the direct kinematics of the Agile Eye (assembly modes) have a simple geometric relationship with the eight solutions to the inverse kinematics (working modes).