Research On The Theory And Approach Of Optimal Synthesis For Planar Linkages Based On Self-Adapted Approximation Of Simple Curves

A new approach of approximate synthesis for planar linkages is presented in the dissertation, which includes regenerating position, function and path, and forming three types of mechanisms, such as four-bar linkage (4R), crank-slider (RRRP) as well as inverting linkage (RRPR). And then, based on constraint curves of characteristic points or straight lines of mechanisms, an opening chain with two degree of freedoms is utilized to regenerate the given motion, in which the kinematic model of the float link is established and the characteristic points or straight lines on the float link can be certained. Different mechanisms can be constructed by combining the characteristic points or straight lines on the moving rigid body. As a result, a unified model of synthesis of different planar linkages is set up. The question of searching characteristic points or straight lines on moving rigid body is decomposed into two relatively independent sub-questions. The first one is to evaluate the characteristic of points and straight lines on moving rigid body, whose mathematics model is a kind of special non-differential max-mini optimal problem with inequality constraints. By the method of Saddle-point Programming and maximum entropy, the problem can be transformed as a differential optimal problem with single objective. The second oner is to search approximative character points or straight lines on moving rigid body within design space, whose mathematic model is nonlinear and non-differential problem with multiple constraints. By genetic algorithm followed by BFGS抯 method, the problem can be resolved. For a general optimal approach, the results depend on the initial point. In this dissertation, a new approach is presented by means of shape of centrodes on moving rigid body. By genetic algorithm, a series of good initial points can be produced automatically. III Finally, the new approach is extended to synthesis planar six-bar linkages, so that a unified model is established from synthesis of planar four-bar linkages to that of planar six-bar linkages. Results of different synthesis examples are given to illustrate the effectiveness of the approach. In each case, the optimization algorithm was run automatically with several initial parameters.