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The Semigraphical Solution of Nonlinear Kinematics Problems

In the majority of kinematics problems the mathematical models derived comprise a system of nonlinear algebraic equations, basically due to the presence of trigonometric functions. In the context of kinematics, the methods for solving nonlinear algebraic systems (NAS) can be classified into two distinct groups, namely, i) Newton-type numerical schemes that deal with systems of multivariate nonlinear equations and aim at finding one solution at a time, and ii) elimination procedures based on computer algebra that lead to a monovariate polygonial equation, thereby enabling the computation of 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 and numerical computations. One great advantage of our approach is that it neither requires an initial guess like Newton--type methods nor a complete reduction to a monovariate polynomial, like the second class of 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.

K. Etemadi--Zanganeh, J. Angeles

Thierry Baron
Mon Nov 13 10:43:02 EST 1995