Synthesis of Multi-DOF Pairs to Generate Relative Displacement Constraint Described with Mathematical Function

Abstract

Aiming to synthesize new mechanisms, new kinematic pairs with multi-DOF were proposed. In the pair, one element moved along a spatial curve with rotations about three axes relative to the other element. Spatial curves were classified with respect to their curvature and twist ratio. The condition that the one element can move along a spatial curve relative to the other element was derived. Consequently only a straight line, a circle and a constant spiral were obtained as a suitable spatial curve. Three kinds of pairs with 1,2 and 4 DOF which were composed of a spiral tube and a block with rectangular or circular closs-section were synthesized and built with a rapid prototyping method.