Dual Cayley–Klein parameters and Möbius transform: Theory and applications. (December 2016)

• Record Type: Journal Article
• Authors: Pennestrì, E.; Valentini, P.P.; Figliolini, G.; Angeles, J.
• Is Part Of: Mechanism and machine theory. Volume 106(2016:Dec.)
• Page Start: 50
• Page End: 67
• Publication Date: 2016-12
• Subjects: Clifford algebra -- Cayley–Klein parameters -- Quaternions -- Kinematics; Machine theory -- Periodicals; Machinery -- Periodicals; Machines -- Périodiques; Génie mécanique -- Périodiques; Machine theory; Machinery; Periodicals; 621.81
• DOI: 10.1016/j.mechmachtheory.2016.08.008
• Languages: English
• ISSNs: 0094-114X

Abstract

Abstract: 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.