Rigid Body Motion Characteristics and Unified Instantaneous Motion Representation of Points, Lines, and Planes

Abstract

The article presents a unified algebraic approach for the modeling of the instantaneous motions of all linear elements, such as points, lines, and planes, embedded in a rigid body. The paper first addresses the Clifford algebra based displacement operator and its higher derivatives from which the coordinate-independent characteristic numbers with simple geometric meaning are defined. With Clifford algebra, the paper also presents the computation method and examples to demonstrate the process of obtaining the displacement operator and the characteristic numbers. Because of the coordinate independent feature, no tedious coordinate transformation typically found in the conventional instantaneous invariants method is needed.