Dimensional Synthesis of Open Path Generator of Four-Bar Mechanisms Using the Haar Wavelet

Abstract

This paper presents a synthesis method for the open path generation of a four-bar mechanism using the Haar wavelet. The synthesis method utilizes the wavelet transform and normalization to extract the wavelet output feature parameters (WOFP) of the open path. Analysis of the WOFP reveals a particular characteristic: for the same four-bar mechanism, not only do variations of the mechanism origin and angles and the proportional scaling of the linkage lengths have no influence on the details of the WOFP but the same holds true for the position of the point that generates the coupler curve. Based on this finding, a numerical atlas database comprises 192,596 groups of basic dimensional types was established and a method of matching recognition was proposed as well. According to the internal relationship of the wavelet characteristic dimension parameters (WCDP), the actual mechanism parameter values and position parameters of an objective four-bar mechanism can be calculated. Four examples are presented to verify the accuracy and practicality of the proposed theory.