ABSTRACT
This chapter serves as a text for a course using dual-number methods as well as a manual for the reader to develop his or her abilities for the design of machinery or evaluation of mechanical systems. The displacement analysis of a mechanism consists of determining the rotations and translations at the output and intermediate joints given the dimensions of the links and the displacements at the input joint. An organized way in which to analyze the displacements in this mechanism is to make up a table of the Denavit-Hartenberg parameters, establish the joint-link transforms, substitute into the condition-of-loop-closure equation and then manipulate that expression to obtain the desired results. A spherical mechanism is a spatial linkage whose joints have axes that intersect at a common point. The Cardan joint, often referred to as the Hooke's coupling or the universal joint, is a form of spherical four-bar mechanism widely used as a shaft coupling in automotive and machinery drive lines.
