Analysis of the Rigid Motion of a Developable Conical Mechanism

Abstract

We demonstrate analytically that it is possible to construct a developable mechanism on a cone that has rigid motion. We solve for the paths of rigid motion and analyze the properties of this motion. In particular, we provide an analytical method for predicting the behavior of the mechanism with respect to the conical surface. Moreover, we observe that the conical developable mechanisms specified in this paper have motion paths that necessarily contain bifurcation points which lead to an unbounded array of motion paths in the parameterization plane.