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A Study on Finding Finite Roots for Kinematic Synthesis

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

University of California, Berkeley, CA

Paper No. DETC2017-68341, pp. V05BT08A083; 8 pages
  • ASME 2017 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
  • Volume 5B: 41st Mechanisms and Robotics Conference
  • Cleveland, Ohio, USA, August 6–9, 2017
  • Conference Sponsors: Design Engineering Division, Computers and Information in Engineering Division
  • ISBN: 978-0-7918-5818-9
  • Copyright © 2017 by ASME


This study presents new results on a method to solve large kinematic synthesis systems termed Finite Root Generation. The method reduces the number of startpoints used in homotopy continuation to find all the roots of a kinematic synthesis system. For a single execution, many start systems are generated with corresponding startpoints using a random process such that start-points only track to finite roots. Current methods are burdened by computations of roots to infinity. New results include a characterization of scaling for different problem sizes, a technique for scaling down problems using cognate symmetries, and an application for the design of a spined pinch gripper mechanism. We show that the expected number of iterations to perform increases approximately linearly with the quantity of finite roots for a given synthesis problem. An implementation that effectively scales the four-bar path synthesis problem by six using its cognate structure found 100% of roots in an average of 16,546 iterations over ten executions. This marks a roughly six-fold improvement over the basic implementation of the algorithm.

Copyright © 2017 by ASME
Topics: Kinematics



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