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Implementation of a generic constraint function to solve the direct kinematics of parallel manipulators using Newton-Raphson approach

Abstract:

Newton-Raphson (NR) methods have been implemented to find the solution of the Direct Kinematics (DK) problem of Parallel Mechanism (PM) for a long time. However, all the objective functions presented so far are topology-dependent and can not be used for every PM. In this work this topic is addressed by introducing a generic constraint function that can be adapted effortlessly to other PMs. In order to demonstrate this capability the formulation is implemented for the most known PMs: the planar 3-RRR, the spherical 3-RRR, the Delta robot, and the Stewart-Gough manipulator. The rate of convergence, the accuracy and the velocity of the numerical method are analysed. Results show that the implementation of this generic constraint function within the NR algorithm provides a robust and accurate solution for the DK for suitable initial estimation. It is also shown that the simplicity of this constraint function may lead to a generic formulation for the DK of PMs.