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Title: A Study on Finding Finite Roots for Kinematic Synthesis
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 startpoints 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.  more » « less
Award ID(s):
1636302
PAR ID:
10062514
Author(s) / Creator(s):
;
Date Published:
Journal Name:
ASME 2017 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference Volume 5B: 41st Mechanisms and Robotics Conference
Page Range / eLocation ID:
V05BT08A083
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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