Determine The Spatial Linkage Assembly Configuration Elimination Method

This thesis comes from the shanghai city's scientific development project of colleges and universities.This thesis is aimed to: l)find a universal method in establishing the mathematic model f(u; x) = 0 for spatial linkage configuration ; 2)put forward a synthetic elimination method for m n by which the equations (PS) = 0 can be eliminated as polynomial solutions (TS) = 0 ; 3)solve a number of common spatial linkage configuration for industry project.A synthetic elimination method for m n is suggested by making use of advantages of synthetic division ,the method of elimination by resultant and the method of elimination by principal power product in order to find a Groebner basis (GS) of a (PS) , and an algorithm of the method is constructed .Calculation results of many examples illustrate that the method has some merits , such as high calculating efficiency and good elimination effect,etc.For a series spatial linkage configuration with single closed loop and single degree of freedom which contains revolve pair(R) , parallel pair(P) and column pair(C), a method of availing all effective elements is employed to create position equations according to acknowledged information of the types of kinematic pairs and corresponding framework parameters, etc 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 .The method can eliminate (PS) into (TS) and obtain all kinematics solutions by fully making use of 12 equations of position equations and solving the equations unitedly. The merits are obvious which is compared with the traditional method.The general program DCSL which is programmed according to this method is characteristic of easy input, formulaic output and accurate results in founding the spatial linkage configuration .In this thesis the author makes a series of calculation to spatial linkage configuration, which is a testimony of this method in its correctness and feasibility.Multiply solution problem is one of the most difficult and advanced subjects in mechanistic research. The research work of this thesis is of theoretical value to improve mechanics and the calculation result is of practical value to the application of spatial linkages.