A uniform geometric-algebraic framework for the forward kinematic analysis of 6-6 Stewart platform manipulators of various architectures and other related 6-6 spatial manipulators

This paper presents a generic geometric-algebraic framework to solve the forward kinematic problem (FKP) of 6-6 Stewart platform manipulators (SPM) in which both the fixed and moving platforms can be either planar or non-planar/general. The FKPs of the SPMs having some of these architectures, e.g., one with a planar moving and general fixed platform, have not been solved explicitly in the existing literature, to the best of the knowledge of the authors. Moreover, some of the existing algorithms applicable to some other classes of SPMs are seen to fail in this case. The algorithms proposed in this paper solves the FKP of this class SPMs, and also that of the 6-RSS manipulator, by relating it to the former. Apart from generating these novel results, the algorithm is amenable to fast and reliable implementation in a generic programming language, such as C, and is able to solve a typical FKP in about 0.7 ms on an ordinary PC. The formulation is illustrated via applications to a number of SPMs and 6-RSS manipulators of different architectures.