Finding all solutions to forward displacement analysis problem of 6-SPS parallel robot mechanism with chaos-iteration method

摘要

A numerical method was found, taking the iteration of Newton method as a nonlinear dynamitic system in which Julia sets leads to chaos. Those points of Julia set was in the neighborhood of those points where belong to the determinant of satisfies Jacobian matrix was equal to zero. Jacobian matrix equation was changed in a non\|linear equation with one variable by giving the other variable's value and the variable scope of the non\|given variable was confirmed, then all solutions of the equation with one variable were found. All values were given in the neighborhood of those points to given variables and the scope for the non\|given variable by the solution was confirmed, then all solutions of wanting problems were determined by rude and fine iteration method. The finding all solutions to forward displacement analysis problem of 6\|SPS parallel robot mechanism was solved by this method, general expression of Jacobian with Newton iteration was obtained, and thus all solutions for this problem were determined. This provides a simple and new realization method for robot mechanics design.