Session: MR-1-5: Mechanisms Synthesis and Analysis

Paper Number: 114960

114960 - Approximate Motion Synthesis of Four-Bar Linkages Using Poles: A Bi-Invariant Approach 

This paper presents a technique for the approximate motion synthesis of planar four-bar mechanisms based exclusively on the locations of displacement poles. Approximation motion synthesis is the same as motion generation or rigid-body guidance when a mechanism cannot be synthesized to meet all of the kinematic constraints and a best-fit solution must be determined. One challenge in approximate motion guidance methods is that incompatible measures are used to identify the best-fit displacement and orientation angle. Thus, the optimal solution provides a match between the task positions and positions generated by the resulting linkage that is conditional on the function used to combine the displacement and orientation. Such solutions are said to lack bi-invariance.

This work focuses on the locations of the displacement poles, which are sufficient to characterize the relative task positions. Further, the displacement poles are described solely by their locations. The optimization minimizes the distance between the poles of the task position and the poles of the positions generated by a synthesized linkage. Further, a technique is presented that does not use the entire set of displacement poles, thereby reducing the size of the optimization. The advantage of the method is that the exclusive use of pole locations results in a bi-invariant metric. The technique is illustrated with several examples and compared to other established methods.

Presenting Author: David Myszka Univ Of Dayton

Presenting Author Biography: Dave Myszka is a professor at the University of Dayton

Authors:

Tianze Xu University of Dayton
David Myszka Univ Of Dayton
Andrew Murray University of Dayton