In stead of conventional kinematic pairs such as a revolute, prosmatic and spherical pairs, new kinematic pairs with multi-DOF which gave relative displacement described with mathmatical functions to adjacent links were proposed. The kinematic conditions between pair elements in case where a pair element moved along spatial line were revealed and then a 3 DOF pair of a sphere and a spiral pipe and a 2 DOF pair of a cylinder and a rectangular section spiral pipe were synthesized.
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