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The Semigraphical Solution of Nonlinear Kinematics Problems

Authors: [tex2html_wrap4302]K. Etemadi-Zanganeh, J. Angeles

Investigator username: angeles

Category: robotics

Subcategory: modelling and simulation

In the majority of kinematics problems the mathematical models derived comprise a system of nonlinear algebraic equations, basically due to presence of trigonometric functions. In the context of kinematics, the methods of solving nonlinear algebraic systems (NAS) can be classified into two distinct groups, namely, [tex2html_wrap4298]) iterative numerical schemes like , that aim at finding one solution at a time, and [tex2html_wrap4300]) exhaustive numerical methods that lead to all possible solutions. As an alternative, we have proposed a semigraphical procedure for estimating all real solutions of the problems at hand. This method can be considered as a novel hybrid numerical-graphical approach that combines interactive features of computer graphics with symbolic/numerical computations. One great advantage of our approach is that it neither requires an initial guess like Newton-type methods nor a reduction to a monovariate polynomial, like exhaustive methods. The application of the method is not limited to kinematics, as it can be used in other fields of engineering that usually lead to systems of nonlinear algebraic equations.