RESEARCH PAPERS: Mechanisms and Robotics

On the Matrix Realization of the Theory of Biquaternions

[+] Author and Article Information
Q. J. Ge

Department of Mechanical Engineering, State University of New York at Stony Brook, Stony Brook, New York 11794-2300

J. Mech. Des 120(3), 404-407 (Sep 01, 1998) (4 pages) doi:10.1115/1.2829166 History: Received February 01, 1994; Revised April 01, 1998; Online December 11, 2007


This paper describes a matrix algebra realization of Clifford’s theory of biquaternions. By examining 4 × 4 skew-symmetric matrices, the paper shows the connection between infinitesimal screws in elliptic three-space and vector quaternions. By studying the matrix exponential of the skew-symmetric matrices, the paper also shows how finite screws in elliptic three-space lead to matrix realization of quaternions. Finally, it is shown that line transformations in elliptic three-space lead to double quaternions and that a dual quaternion is a limiting case of a double quaternion.

Copyright © 1998 by The American Society of Mechanical Engineers
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