The mathematical model of kinematic problems can be translated a multi-variables non-linear equations

and

it is a difficult problem to give the initial value for the no-linear equation. The homology continuation algorthm has resolved this difficult problem without given initial value and can find all solution

but a special programming is compiled at the same time and the quantity is very much.After builded initial equations

initial solutions are obtained.When initial solutions are used as initial value

all solutions or most of solutions are obtained with any finding method of non-linear equations.Now

this discovery couldn’t proved in theory

but it can finding all solutions of kinematic equations.The programming is compiled with Matlab6.1 & Maple programming language based on the discovery.The problem of function generation for planar four-link mechanism is solved by this method

and thus all solutions for this problem with maximum precision positions are obtained.This provide a simple realization method for homology method.