Chasles' Motion Sphere—A Useful Tool to Visually Express the Motion Characteristics Over the Workspace of Robotic Mechanisms

Abstract

This paper presents a useful concept/tool, i.e., Chasles' motion sphere (CMSphere), that is able to visually express the motion characteristics over the workspace and capable of investigating the local motion performance of the end-effector of robotic mechanisms. The process of CMSphere generation is in line with people's habit of observing a mechanism. Under a researched pose, give a small pose change to the end-effector by translating with a small length or rotating with a small angle along a direction, then the corresponding Chasles' motion of the small pose change can be calculated. Two key parameters of Chasles' motion, the pitch and the position of the Chasles' axis, are chosen to represent the motion characteristics. This kind of mathematical operation can be carried along many directions to obtain a distribution of the motion characteristics at the researched pose, which can be drawn as a sphere. To illustrate this tool, Robotic Mechanisms with Three Independent Pose Variables (RMTIPVs) are discussed as the research objects. Three categories of RMTIPVs based on the types of independent pose variables are given. For each category, the detailed process of CMSphere generation is discussed. The 3R series mechanism, Tricept, and 3-RPS (the limb consisting of one revolute, one prismatic and one spherical joints) parallel mechanism are used as examples to demonstrate the methodology.