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Spherical Linkages Analysis and Synthesis by Special Unitary Matrices for Solution via Numerical Algebraic Geometry

[+] Author Affiliations
Saleh M. Almestiri, Andrew P. Murray, David H. Myszka

University of Dayton, Dayton, OH

Paper No. DETC2017-68318, pp. V05AT08A053; 10 pages
  • ASME 2017 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
  • Volume 5A: 41st Mechanisms and Robotics Conference
  • Cleveland, Ohio, USA, August 6–9, 2017
  • Conference Sponsors: Design Engineering Division, Computers and Information in Engineering Division
  • ISBN: 978-0-7918-5817-2
  • Copyright © 2017 by ASME


Numerical algebraic geometry is the field that studies the computation and manipulation of the solution sets of systems of polynomial equations. The goal of this paper is to formulate spherical linkages analysis and design problems via a method suited to employ the tools of numerical algebraic geometry. Specifically, equations are developed using special unitary matrices that naturally use complex numbers to express physical and joint parameters in a mechanical system. Unknown parameters expressed as complex numbers readily admit solution by the methods of numerical algebraic geometry. This work illustrates their use by analyzing the spherical four-bar and Watt I linkages. In addition, special unitary matrices are utilized to solve the five orientation synthesis of a spherical four-bar linkage. Moreover, synthesis equations were formulated for the Watt I linkage and implemented for an eight orientation task. Results obtained from this method are validated by comparison to other published work.

Copyright © 2017 by ASME
Topics: Linkages , Geometry , Algebra



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