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
Copyright
Copyright © 2016, American Society of Mechanical Engineers
Publisher
American Society of Mechanical Engineers
Volume
8
Issue
4
Peer Reviewed
yes
eCommons Citation
Brake, Daniel A.; Hauenstein, Jonathan D.; Murray, Andrew P.; Myszka, David H.; and Wampler, Charles W., "The Complete Solution of Alt–Burmester Synthesis Problems for Four-Bar Linkages" (2016). Mechanical and Aerospace Engineering Faculty Publications. 167.
https://ecommons.udayton.edu/mee_fac_pub/167
COinS
Comments
Permission documentation is on file.