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Finding Only Finite Roots to Large Kinematic Synthesis Systems

[+] Author Affiliations
Mark M. Plecnik, Ronald S. Fearing

University of California, Berkeley, CA

Paper No. DETC2016-60428, pp. V05BT07A094; 9 pages
  • ASME 2016 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
  • Volume 5B: 40th Mechanisms and Robotics Conference
  • Charlotte, North Carolina, USA, August 21–24, 2016
  • Conference Sponsors: Design Engineering Division, Computers and Information in Engineering Division
  • ISBN: 978-0-7918-5016-9
  • Copyright © 2016 by ASME


In this work, a new method is introduced for solving large polynomial systems for the kinematic synthesis of linkages. The method is designed for solving systems with degrees beyond 100,000, which often are found to possess a number of finite roots that is orders of magnitude smaller. Current root-finding methods for large polynomial systems discover both finite and infinite roots, although only finite roots have meaning for engineering purposes. Our method demonstrates how all infinite roots can be avoided in order to obtain substantial computational savings. Infinite roots are avoided by generating random linkage dimensions to construct start-points and start-systems for homotopy continuation paths. The method is benchmarked with a four-bar path synthesis problem.

Copyright © 2016 by ASME
Topics: Kinematics



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