Geometrical approach of planar hyper-redundant manipulators: Inverse kinematics, path planning and workspace

A new method for inverse kinematics for hyper-redundant manipulators is proposed in this paper to plan the path of the end-effector. The basic idea is that for a given smooth path consisting of points close enough to each other; computing the inverse kinematics for these points is carried out geometrically using the proposed method. In this method, the angles between the adjacent links are set to be the same, which makes lining up of two or more joint axes impossible; therefore, avoiding singularities. The manipulability index has been used to show how far the manipulator from the singularity configuration is. The determination of the workspace of the manipulator using the proposed method has been presented in this paper. The simulation results have been carried out on a planar and a three dimensional manipulators. The effectiveness of the proposed method is clearly demonstrated by comparing its result with results calculated by the well-known method of measuring manipulability which is used for singularity avoidance for the last two decades.

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