Compliant Serial 3R Chain with Spherical Flexures

Abstract

A spherical flexure is a special kind of compliant hinge specifically conceived for spherical motion. It features an arc of a circle as centroidal axis and an annulus sector as cross-section, circle and annulus having a common center coinciding to that of the desired spherical motion. This paper investigates a compliant spherical 3R open chain that is obtained by the in-series connection of three identical spherical flexures having coincident centers and mutually orthogonal axes of maximum rotational compliance. The considered spherical chain is intended to be used as a complex flexure for the development of spatial parallel manipulators. The compliance matrix of the proposed chain is first determined via an analytical procedure. Then, the obtained equations are used in a parametric study to assess the influence of spherical flexure geometry on the overall stiffness performances of the considered 3R open chain.