A Null-Space Analysis Method for Solving Bilinear Equations in Kinematic Synthesis of Planar and Spherical Dyads

摘要

Many problems in kinematic synthesis of mechanisms and robots lead naturally to systems of bilinear equations in design parameters. Such systems are typically solved using well-known methods for solutions of systems of polynomial equations, e.g., Dialytic Elimination, Grobner bases, and Polynomial Continuation. This paper presents a new null-space analysis method for solving a system of bilinear equations in the context of kinematic synthesis of planar and spherical four-bar linkages. The resulting algorithm is simple, efficient and is applicable to the problem of synthesizing both planar and spherical mechanisms and robot manipulators with revolute and prismatic joints. Numerical examples are given to illustrate the effectiveness of the algorithm.