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 presents a list of definitions based on dual-number. A dual number, which perhaps should be called a "duplex" number in analogy with complex numbers. All formal operations of dual number are the same algebra followed by setting as those of ordinary. The dual angle represents the relative displacement and orientation between two lines in space. The trigonometric functions of a dual angle are obtained using the Taylor-series expansion. A free vector has the qualities of magnitude and direction and is represented pictorially as a line with an arrowhead whose length corresponds to its magnitude and whose orientation corresponds to its direction. A vector constrained to lie upon a definite line in space is called a "line vector".
