A Fourier Approach to Kinematic Acquisition of Geometric Constraints of Planar Motion for Practical Mechanism Design

Abstract

This paper studies the problem of geometric constraint acquisition from a given planar motion task using Fourier descriptor. In the previous work, we established a computational geometric framework for simultaneous type and dimensional synthesis of planar dyads by extracting line or circle constraints from a sequence of task poses. In cases where six or more poses are specified as the desired movement, the resulting optimal constraint may be nowhere in the accuracy neighborhood to be viewed as an approximate line or circle. The approach herein enhances the framework by exploiting Fourier transform to capture the feasible constraint of a continuous motion with a large set of poses. Theoretically, any arbitrary point trajectory on the task motion can be transformed to an array of harmonics and used as a constraint; on a practical level, only those with low number of harmonics could allow accurate realization by simple planar mechanisms suitable for real applications, e.g., four and sixbar linkages, cams, and coupled serial chains. Therefore, the practical goal is to find the simple Fourier constraint defined with the least number of harmonics. Two examples of designing assistive mechanisms for upper and lowerlimb rehabilitation are provided in the end to illustrate the effectiveness of our approach.