On the forward and inverse displacement of spatial parallel manipulators

In engineering applications, the singularity, and the forward and inverse displacement of spatial parallel manipulators have received a great deal of attention. This paper presents a new simple but effective methodology to investigate these problems based on the analysis of the degree of freedom (DoF) of the spatial parallel manipulator. Through numerical method, the singularity and the forward displacement problems can be cracked simultaneously. With a numerical example, we point out that the Newton-GMRES algorithm is quite a good redeeming method to solve the forward displacement of spatial parallel manipulators, in which cases the differential coefficient matrix of the Newton?Raphson method is nearly singular.