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

Mon Nov 13 10:43:02 EST 1995