In this paper, the kinematics of a joint with three degrees of freedom for a novel hyper-redundant robot arm is investigated. This joint is able to achieve a superposed rotation about two axes (roll and pitch) and a translational motion along one axis as a common prismatic joint. The forward and inverse kinematics of the so-called Multi-Joint will be determined in a closed-form solution. Next, the reachable and suitable workspace will be worked out to determine the solution space of the inverse kinematics. Finally, the differential kinematics to compute the cartesian velocity and statics will be determined.
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