Dimensional Synthesis Of Four Bar Mechanism Using Haar Wavelet

Four-bar mechanism is essential in mechanical transmission. It plays an important role in many applications such as industrial automation, electromechanical integration, agricultural modernization and military defense system. A number of methods for the dimensional synthesis of four-bar mechanism have been proposed. But in many applications, our interest lies in the open path or non-integer periodic function as opposed to the closed path or integer periodic function. The aim of this work was to propose a new numerical atlas method to apply to the non-integer periodic function synthesis and path synthesis problems of a four-bar mechanism. Contrasting with earlier work, this new method overcame the deficiency of the existing numerical atlas methods, which could not describe non-integer periodic functions or open path accurately. The influence of translation and dilation of the four-bar mechanism output on the wavelet feature parameters were considered, and a genetic algorithm was applied to the basic dimensional types of objective mechanisms. This process should yield, better results with regard to the shift and dilation parameters.Function synthesis of four-bar mechanismFirstly, a synthesis method for non-integer-periodic function generator of a four-bar mechanism through a Haar wavelet is presented. By using the wavelet theory, the mathematical model for the output of four-bar mechanism is established. Then the characteristics of the four-bar mechanism output variable are described as the wavelet feature parameters and the relationship of wavelet feature parameters between output and its translation or dilation is discovered. Based on this finding, three numerical atlas databases comprising of 148995 groups basic dimensional types of planar four-bar mechanism,148995 groups basic dimensional types of spherical four-bar mechanism and 11175 groups basic dimensional types of planar slider-crank mechanism are established. A method of matching recognition has been proposed as well. According to the internal relationship of wavelet feature parameters, the size of mechanism can be obtained by using fuzzy recognition. Based on the genetic algorithm, the optimization of the link parameters can be realized. Two examples are presented to prove the correctness and practicality of the proposed theory.Path synthesis of four-bar mechanismAt first, a synthesis method for open path generation of a four bar mechanism using a Haar wavelet. The synthesis method utilizes the wavelet transform and normalization to extract the wavelet output feature parameters of the open path. By analyzing the wavelet output feature parameters, a characteristic is presented:for the same four bar mechanism, not only do the variety of the frame position and angle and proportional scaling of the linkages length have no influence on the details of wavelet output feature parameters, but the same holds true for the position of the point that generates the coupler curve. Based on this finding, a numerical atlas database comprising of 148,995 groups of basic dimensional types has been established and a method of matching recognition has been proposed as well. According to the internal relationship of wavelet characteristic dimension parameters, the actual size and installation position of the objective four bar mechanism can be calculated. Two examples are presented to prove the correctness and practicality of the proposed theory.