The Polynomial Solutions Of Mechanism Synthesis

This paper primarily aims to solve the precision kinematics synthesis problems of mechanism by solving the equation set derived from the mechanism. The item is imbursed by shanghai city's scientific development project of colleges and universities.If you apply this method to solve problem, most of mechanism synthesis problem will turn into one problem, that is to solve the equation set. The most difficult point is get full solution of the equation set, thus it can provide a wider range for optimized project.The main points of this paper is as follow:1) find a method of establishing mathematic model that can be easily eliminated variable; 2)bring forward asynthetic elimination method for m≥n by which the equation set (PS)=0 can beeliminated as polynomial solutions(TS)=0; 3)get the polynomial solutions of some typical linkage mechanism for industry.Employing the advantage of synthetic division, the method of elimination by resultant and the method of elimination by principal power product, this paper formed a synthetic elimination method which can be used to find a Groebner basis (GS) of a (PS), and an algorithm of the method is also constructed . Calculation results of many examples show that this method has many merits such as high calculating efficiency and good elimination effect, etc.For a series spatial and planar mechanism synthesis, synthetic equation set can be established according to the kinematics requirement and characters of the mechanism. Then trigonometric functions are rationalized so as to create a polynomial system (PS) =0 , and the polynomial solution (TS)=0 is obtained with synthetic elimination method. Using the solutions, the unknown mechanism parameter can be calculated.Based on this synthetic elimination method, a general program called SLGBU is written. And this program requires simple input, provides formulaic output and accurate results. Many kinds of spatial and planar mechanism synthesis is solved by this program, so it proves the correctness and reliability of the method in this paper.The polynomial solutions obtained by the synthetic elimination method has more completely solved multiple solutions and other difficult subjects in mechanistic research. The distinguished character of these achievements is its strong practicality and convenience for application and spread.