Planar Linkage Analysis With The Integrated Polynomial Solution

This paper bases on the Through Program?project of the Ministry of Communication ~ progression of science and technology, whose name is the similar analytic solution of analysis and synthesis of planar linkages.The paper summarized the common linear and nonlinear mathematics model in the research of mechanism science, focusing on the comment on the methods to solve nonlinear algebraic system of equations. Especially elaborating on the theories and methods of polynomial elimination of system of equations systematically. The paper proposes the elimination by eliminant with aid of basic sets (EEABS), in order to solve the problems in the theories and methods of polynomial system of equations 慹limination at present, and to find the multi-solutions of mechanism science ~ research. The main idea of this method is to choose a set according to the order of polynomials, to eliminate by making use of Bezout eliminant, get zero set from the improved formula about set of zero points, so that a polynomial system of equation ~ set of zero points can be got only by one time arrangement. The EEABS has some advantages such as the workload of eliminating is greatly reduced and the degree of eliminating result is lowered, and so on. The method not only solves the problem of how to choose a suitable initial value that needed in solving nonlinear system of equations on analysis and synthesis of mechanism by iteration method, but also better thoroughly solves the problem of multi-solutions on the assembly configurations of mechanism and multi-scheme about the synthesis of mechanism. In addition, the paper proposes a polynomial method to define the limited position of mechanism and to design a mechanism based on its quick-return characteristic. The foresaid two methods are the most important achievements in the field of theoretic research in this paper.The paper has totally solved 206 problems on the analysis and synthesis of planar links and linkages by the EEABS, and compiled the program of EEABS. The program can automatically turn a system of equations that include triangle functions into polynomial system of equations in the analysis and synthesis of the mechanism, to eliminate and get the polynomial solutions of the original system of equations. The software system of analysis and synthesis of planar linkages is formed at last by author. A great number of calculating results show that EEABS is effective and practicable. In addition, the method has been successfully applied into optimum design of two types of range-changing mechanism of gantry crane and the software systems of optimization design and analytical calculation of straight-arm gantry crane and 憃ptimization design and analytical calculation of balance pulley compensation gantry crane?has been compiled. The above-mentioned three software systems are the most valuable achievements in the field of practical research.