The complete solution of mixed Burmester synthesis problems for four-bar linkages (2015)

Content Provider	CiteSeerX
Author	Brake, Daniel A. Myszka, David H. Wampler, Charles W.
Abstract	Approaches to precision-point synthesis of four-bar linkages have typically spec-ified only path-points or only poses, i.e., path-points with orientation. The former is known as “path synthesis, ” while the latter is known as “rigid-body guidance, ” sometimes referred to as a “Burmester problem. ” We consider the family of “mixed Burmester ” synthesis problems in which some combination of path-points and poses are specified, with the extreme cases corresponding to the traditional approaches. The mixed problems that have, in general, a finite num-ber 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 generalized Burmester family, and provide more details concerning all the zero- and one-dimensional cases. 1
File Format	PDF
Publisher Date	2015-01-01
Access Restriction	Open
Content Type	Text