For a practical mechanism synthesis problem, extreme accuracy is not really necessary due to inherent limitations in manufacturing processes and arbitrariness in the design specification. In this sense, the Selective Precision Synthesis(SPS) developed by Kramer and Sandor has been proved to be a useful design tool with different limits of accuracy at various discrete positions. This method, however, is still not amenable to practical routine utilization, because of the difficulty of handling often inevitable mechanism construction errors and of applying to slider-crank mechanisms. In this study, the Conventional SPS(CSPS) is modified to resolve these problems by adopting the displacement matrix approach and using binary links as basic elements. This Modified SPS(MSPS) can thus be applied to the synthesis of slider-crank mechanisms as well. The mechanism construction procedure proposed in this paper permits deviation at the first point of the design path which is not the case in the CSPS. With the introduction of "maximum allowable angular deviation," the mechanism construction error (MCE) at a design point can be eliminated. The link length adjustment is also found to be a useful tool for the case of infinite MCE. These new MCE elimination techniques are shown to be more efficient than the previously developed strategies.
The proposed MSPS has two steps. In the optimization stage, all possible binary links satisfying the given motion requirements are found passing through accuracy circles. Once this is done, a four-bar mechanism is then constructed by taking any two binary links which are distinct or manufacturable. For a mechanism to be practically designed, several other conditions on link length ratio, Grashof criteria, transmission angles, and so on, have to be satisfied. The more candidates there are from the first step, the more probable it is to satisfy these and reach the best mechanism. To produce as many binary links as possible, an exhaustive method of generating initial guesses for the optimization is proposed. A clustering procedure is used to classify the resulting local solutions. An unsupervised learning procedure of the neural network study is adopted and modified for the clustering. The proposed learning rules including the threshold and decision of the cluster centers have physical meanings and are found practicable.
Several realistic design problems are taken to emphasize the rationale of the proposed MSPS and to show practical results. The proposed procedure has all the flexibility necessary to deal with real-life problems and effectively generates solutions. The extra effort of deciding angular deviation is more than justified from a practical point of view.
