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. It establishes a mathematical technique to deal with the relative displacements and orientations of mechanism components. The technique should not only deal with displacements but be extendible to velocity and dynamic analysis. The chapter defines the coordinate systems which are fixed on each link in the mechanism, and relates them through the mathematics of 3×3 dual-number coordinate transformations. A coordinate frame can be represented by unit vectors, vectors aligned with its axes and of unit length. Successive transformations about fixed coordinate axes are handled by successive left multiplication. A popular form of Euler angles is the ZYZ sequence. The coordinate-transformation matrices which have been developed deal with screw motions only with respect to the axes of coordinate frames.
