A Fourier Descriptor Based Approach to Design Space Decomposition for Planar Motion Approximation

Abstract

This paper deals with the classical problem of dimensional synthesis of planar four-bar linkages for motion generation. Using Fourier Descriptors, a given motion is represented by two finite harmonic series, one for translational component of the motion and the other for rotational component. It is shown that there is a simple linear relationship between harmonic content of the rotational motion and that of the translational motion for a planar four-bar linkage. Furthermore, it is shown that the rotational component can be used to identify the initial angle and the link ratios of a four-bar linkage. The rest of the design parameters of a four-bar linkage such as location of the fixed and moving pivots can be obtained from the translational component of the given motion. This leads naturally to a decomposed design space for four-bar motion synthesis for approximate motion generation.