Design and stiffness evaluation of a compliant joint with parallel architecture realizing an approximately spherical motion

This paper introduces the design of a fully-compliant Spherical Joint (SJ), obtained by the in-parallel connection of two identical open chains each composed of three equal circular flexible beams, having coincident centers of curvature and mutually orthogonal axes of minimum rotational stiffness. Thanks to its particular topology, the SJ provides a fully isotropic behavior, the two chains being placed in space so as to be symmetric with respect to the beams' center of curvature. At first, the overall system compliance matrix is derived by means of an analytical procedure, in order to obtain a parametric formulation of the SJ behavior within the small deflection range. Then, after finite element validation of the analytical model, an optimization study of the beam geometry is developed, with the aim of maximizing the ratio between the SJ primary to secondary compliance factors. At last, the potential advantages and drawbacks of the proposed design are discussed by numerically evaluating the joint performance in terms of parasitic motions within the large deflection range (namely, when large external loads are applied to the envisaged center of spherical motion).