Dual Cayley-Klein parameters and Möbius transform: Theory and applications

The paper focuses on the use of Cayley-Klein (CK) parameters in the description of rigid-body kinematics. After a brief historical overview, an introduction to this concept is offered. New formulas for first and second time derivatives of 2×2 transforms based on the CK parameters are herein derived. These formulas are extended also to dual numbers. Based on these results, the kinematic analysis methodology originally due to Denavit is completed, thereby allowing for the velocity and acceleration analysis of spatial linkages. Different numerical examples with applications of the concepts proposed here are included.