Analysis of Spatial Chains

Abstract

In this chapter we study spatial linkages. These systems have at least one link that moves through a general spatial displacement. We examine the TS and CC chains that are important to our design theory, as well as the TPS and TRS chains that appear in robotics. In addition, we study the 3R wrist which is actually a spherical linkage, however, it provides a convenient parameterization of the S-joint that is an important part of our spatial open chains. We determine the joint angles for these chains that position the end-effector in a desired location.