Abstract
The movements of the spherical mechanisms take an important place in the robotic studies. In this paper, the design and the trajectory motion equations of the joints in the spherical mechanisms were presented by the methods of the sequential SLERP, sequential fast SLERP, sequential SLERP with De-Moivre, and modular SLERP interpolation that we firstly defined. Additionally, the Serret Frenet frame and curvatures of the geometrical SLERP interpolation curve for the locations of the joints in the spherical mechanisms were computed, and then, several numerical examples on the interpolation equations that produce the motion equations of the spherical mechanisms with 2 and 3-degree of freedom were given at the end of the paper.
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