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Technical Brief

Special Unitary Matrices in the Analysis and Synthesis of Spherical Linkages

[+] Author and Article Information
Saleh M. Almestiri

University of Dayton, Dayton, Ohio 45469
almestiri@gmail.com

Andrew P. Murray

University of Dayton, Dayton, Ohio 45469
murray@udayton.edu

David Myszka

University of Dayton, Dayton, Ohio 45469
dmyszka@udayton.edu

1Corresponding author.

ASME doi:10.1115/1.4041633 History: Received April 14, 2018; Revised September 21, 2018

Abstract

This work seeks to systematically model and solve the equations associated with the kinematics of spherical mechanisms. The group of special unitary matrices, SU(2), is utilized throughout. SU(2) is widely acknowledged as a method for writing rotations yet rarely utilized. Elements of SU(2) are employed here to analyze the three-roll wrist and the spherical Watt I linkage. Additionally, the five orientation synthesis of a spherical four-bar mechanism is solved and solutions are found for the eight orientation synthesis of the Watt I linkage. Using SU(2) readily allows for the use of a homotopy-continuation-based solver, in this case Bertini. The use of Bertini is motivated by its capacity to calculate every solution to a design problem.

Copyright (c) 2018 by ASME
Topics: Linkages , Design , Kinematics
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