Solving the Geometric Design Problem of Spatial 3R Robot Manipulators Using Polynomial Homotopy Continuation-Reference-Cited by-同舟云学术

Solving the Geometric Design Problem of Spatial 3R Robot Manipulators Using Polynomial Homotopy Continuation

Published:2002-11-26 Issue:4 Volume:124 Page:652-661
ISSN:1050-0472
Container-title:Journal of Mechanical Design
language:en
Short-container-title:

Author:

Lee Eric¹,Mavroidis Constantinos¹

Affiliation:

1. Robotics and Mechatronics Laboratory, Department of Mechanical and Aerospace Engineering, Rutgers University, The State University of New Jersey, 98 Brett Rd., Piscataway, NJ 08854

Abstract

In this paper, the geometric design problem of serial-link robot manipulators with three revolute (R) joints is solved using a polynomial homotopy continuation method. Three spatial positions and orientations are defined and the dimensions of the geometric parameters of the 3-R manipulator are computed so that the manipulator will be able to place its end-effector at these three pre-specified locations. Denavit and Hartenberg parameters and 4×4 homogeneous matrices are used to formulate the problem and obtain eighteen design equations in twenty-four design unknowns. Six of the design parameters are set as free choices and their values are selected arbitrarily. Two different cases for selecting the free choices are considered and their design equations are solved using polynomial homotopy continuation. In both cases for free choice selection, eight distinct manipulators are found that will be able to place their end-effector at the three specified spatial positions and orientations.

Publisher

ASME International

Subject

Computer Graphics and Computer-Aided Design,Computer Science Applications,Mechanical Engineering,Mechanics of Materials

Link

http://asmedigitalcollection.asme.org/mechanicaldesign/article-pdf/124/4/652/5798688/652_1.pdf

Reference30 articles.

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