Kinematic Analysis of Mechanisms Based on Parametric Polynomial System

Many kinematic problems of mechanisms can be expressed in the form of polynomial systems. Gröbner Bases computation is effective for algebraically analyzing such systems. In this research, we discuss the cases in which the parameters are included in the polynomial systems. The parameters are used to express the link lengths, the displacements of active joints, hand positions, and so on. By calculating Gröbner Cover of the parametric polynomial system that expresses kinematic constraints, we obtain segmentation of the parameter space and valid Gröbner Bases for each segment. In the application examples, we use planar linkages to interpret the meanings of the algebraic equations that define the segments and the Gröbner Bases. Using these interpretations, we confirmed that it was possible to enumerate the assembly and working modes and to identify the geometrical conditions that enable overconstrained motions.