Path Synthesis Method for Planar Four-Bar Linkages Based on Wavelet-Fractal Analysis

Feature extraction for coupler curves is a key technique for the approximate synthesis based on the electronic atlas. A new extraction based on wavelet multiresolution analysis (MRA) and fractal theories is presented. The suitable basic wavelet, the decomposition level for MRA and algorithm for fractal dimensions were determined through experiments. The features, obtained from wavelet coefficients and their Lipschitz exponents, have the characteristics that they are independent of the directions and the scales of curves, and consist of only with 1 global fractal dimension and 2 local fractal dimensions. The atlas database, therefore, can be created with smaller capacity and the result curves can be retrieved from it quickly. Redemonstrating the curves, comparing the closeness with the least squares of the distance between two corresponding points on desired curves and the generated coupler curves prove that the method can arrange the result curves in a good order when retrieving curves from the database. Fractal features are very suitable to create larger electronic atlas.