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

被引:35
作者
Brake, Daniel A. [1 ]
Hauenstein, Jonathan D. [1 ]
Murray, Andrew P. [2 ]
Myszka, David H. [2 ]
Wampler, Charles W. [3 ]
机构
[1] Univ Notre Dame, Dept Appl & Computat Math & Stat, Notre Dame, IN 46556 USA
[2] Univ Dayton, Dept Mech Engn, Dayton, OH 45469 USA
[3] Gen Motors R&D Ctr, Warren, MI 48090 USA
来源
JOURNAL OF MECHANISMS AND ROBOTICS-TRANSACTIONS OF THE ASME | 2016年 / 8卷 / 04期
基金
美国国家科学基金会;
关键词
GEOMETRY;
D O I
10.1115/1.4033251
中图分类号
TH [机械、仪表工业];
学科分类号
0802 ;
摘要
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.
引用
收藏
页数:8
相关论文
共 25 条
[1]   Concerning the manufacture given level curves with the aid of jointed quadrilateral [J].
Alt, H .
ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND MECHANIK, 1923, 3 :13-19
[2]  
[Anonymous], NUMERICALLY SOLVING
[3]   Defects in link mechanisms and solution rectification [J].
Balli, SS ;
Chand, S .
MECHANISM AND MACHINE THEORY, 2002, 37 (09) :851-876
[4]  
Bottema O., 1990, Theoretical Kinematics, V24
[5]  
Brake Daniel A., 2014, Mathematical Software - ICMS 2014. 4th International Congress. Proceedings. LNCS: 8592, P175, DOI 10.1007/978-3-662-44199-2_29
[6]  
Burmester L., 1886, LEHRBUCH KINEMATIC
[7]  
Erdman A., 2001, MECH DESIGN ANAL SYN, V1
[8]  
Freudenstein F., 1959, ASME, Journal of Engineering for Industry, Series B, V81, P159
[9]   Witness sets of projections [J].
Hauenstein, Jonathan D. ;
Sommese, Andrew J. .
APPLIED MATHEMATICS AND COMPUTATION, 2010, 217 (07) :3349-3354
[10]  
Lu Y, 2007, CONTEMP MATH, V448, P183