Visualizing Path Synthesis Of Planar Four-bar Linkage

The planar four-bar linkage is one kind of the most commonly used mechanisms. With many advantages, such as simple structure, being manufactured easily, large bearing capacity and easy maintenance, it obtains widespread application both in actual production and life. The path synthesis problem of planar four-bar linkage is one kind of problems that are frequently met in applications of planar four-bar linkage.With rapid development of computer technology; the method of visual synthesis, which uses computer as the tool to complete path synthesis task, was appeared and hewed out new approach to theoretical research on path synthesis and creative design of mechanism.Taking the planar four bar linkage as the research object, a novel visually synthesizing method on path generation, including the theory of visualizing path synthesis and its technical realization, was studied.The visually synthesizing theory was firstly presented. After analyzed the influence of mechanism parameters on the shape of the coupler curve and defined the path error between two curves, six parameters were selected as the variables. For comparison two curves, the curves should be parameterized as arc length and normalized. After the only one of coordinate system was set up on the curve according to some rules, the origin point was selected as the starting point of the curve, and the positive sense of the curve can be decided on every curve, and each points'arc length s along the path were got and then their corresponding coordinates equally spaced along the natural coordinate system on the curve were calculated. The mathematical calculating model of the path error between coupler curve and desired curve was established with least square of the distance between them, that is, the coupler curves must be scaled, rotated and translated to overlap the desired curve and to minimize the difference between two curves, the relation between the path error and 6 parameters of the generated mechanism was got.The techniques to realize the visualization on path synthesis were then discussed. The representation of the path error to the computer with computer visualization was mainly discussed. The three kinds of representation, such as cloud map, contour map and shapes of two curves were chosen as the visualizing images of the difference between desired curve andcoupler curve on generated mechanism and software about visualizing path synthesis was developed with computer programming language. The software core was the relationship between path error and parameters of generated mechanism and their visualization, and not only can be used to visually synthesize the path generation, but also can be displayed the trajectory and the kinematical simulation of mechanism.The problems of the Complex Method applying to the path synthesis were also studied and the non-optimal solution problem with optimal method was solved by the application of visualizing synthesis technology, in the other words, the latter can be used to further optimize the existing mechanism to reduce the path error.