Title

The Complete Solution of Alt–Burmester Synthesis Problems for Four-Bar Linkages

Document Type

Article

Publication Date

4-2016

Publication Source

Journal of Mechanisms and Robotics

Abstract

Precision-point synthesis problems for design of four-bar linkages have typically been formulated using two approaches. The exclusive use of path-points is known as “path synthesis,” whereas the use of poses, i.e., path-points with orientation, is called “rigid-body guidance” or the “Burmester problem.” We consider the family of “Alt–Burmester” synthesis problems, in which some combination of path-points and poses is specified, with the extreme cases corresponding to the classical problems.

The Alt–Burmester problems that have, in general, a finite number of solutions include Burmester's original five-pose problem and also Alt's problem for nine path-points. The elimination of one path-point increases the dimension of the solution set by one, while the elimination of a pose increases it by two. Using techniques from numerical algebraic geometry, we tabulate the dimension and degree of all problems in this Alt–Burmester family, and provide more details concerning all the zero- and one-dimensional cases.

Inclusive pages

041018-1 to 041018-8

ISBN/ISSN

1942-4302

Comments

Permission documentation is on file.

Publisher

American Society of Mechanical Engineers

Volume

8

Issue

4

Peer Reviewed

yes