Analysis of annulus-shaped compliant pivot with series-parallel leaves

Annulus-shaped compliant pivot, formed by well-proportioned compliant modules between the outer ring and inner ring, can be employed in precision mechanical systems due to good performances. Especially for the multi-series leaves in one module, the annulus-shaped compliant pivot can fulfill a large displacement range without any axial drift in theory. In the design of the annulus-shaped compliant pivot, the load-displacement behavior and the stress analysis with analytical forms are important consideration. However, in the literature, there is few detailed work. In this article, a general annulus-shaped compliant pivot model formed by series-parallel leaves is first analytically established for the load-displacement behavior and the stress prediction. These calculations are based on accurate approximation of a beam flexure. Firstly, a loaded moment is decomposed into universal loads by combining the geometric compatibility condition. The stiffness accurate approximation is then analytically obtained, which provides a simple design strategy. Furthermore, the stresses in every leaf are obtained so that the annulus-shaped compliant pivot with large motion range can be actualized by stress checking. Lastly, the analytical model has been verified by commercial finite element analysis software ANSYS.