MMC – a new numerical approach to the kinematics of complex manipulators

A numerical approach (MMC-model; MMC – mean of multiple computations) is proposed for solving the kinematics of manipulators of nearly arbitrary configuration. It is applicable to serial, parallel and hybrid-chain-manipulators (HCMs). Even changing configurations of the manipulator are possible, because the structural analysis of the current manipulator configuration is done automatically. This approach does not make a strict distinction between the direct and inverse kinematics, but solves both tasks as well as mixed control tasks in a single model. With a slight modification over-constrained problems can also be solved. These properties make the model especially suitable for the simulation of reconfigurable HCMs. The advantages of the MMC-model arise from splitting the structural analysis into two parts. The first, linear part performs the topological analysis without any constraints. Only this part performs the numerical approximation. The second, generally non-linear part adds the constraints and thus allows versatile control of the movement without changing the equations of the approximation procedure in the first part. After a general description of the model we present a hexapod walking system as a complex application of a HCM.