In this research project, a theoretical basis is developed for the solution of a set of nonlinear equations which are used for the design and analysis of mechanical systems. The approach allows a rapid numerical determination of all possible solutions. The main advantage of having all possible solutions is that design optimization can be performed simply by selecting the best from amongst alternative solutions. For equations with symbolic coefficients, the method yields a mathematical model from which theoretical advances can be derived. The solutions of the system equations are formulated with physical system parameters expressed as literal coefficients of a characteristic matrix or polynomial. Whereas the results are generated in the context of analysis and design of linked mechanisms, e. g., a serial jointed manipulator, they are applicable to a wide variety of engineering problems.*** //
