Stiffness characteristics of inner–outer ring flexure pivots applied to the ultra-precision instruments

The inner-outer ring flexure pivot (IORFP), composed of three straight springs that cross each other in space, is studied in this work. First, to emphasize the study value of IORFP, qualitative comparison is applied to IORFP and some of most commonly used flexure pivots. Then an analytical model for the rotational stiffness of IORFP is developed based on the strain energy formulation of a beam flexure, and model applicability is provided as well. Analysis of stiffness, buckling load, and the nonlinear of moment–rotation relation is then carried out. Subsequently, the analytical model is verified by finite element analysis. After that, seven prototypes of IORFP are manufactured, and their rotational stiffnesses are tested. The results show that the analytical model can be used for analysis and designing of compliant mechanisms that contain IORFP. Finally, the study quantitatively compares stiffness characteristics and axis drift of IORFP and the generalized cross-spring pivot, indicating that the former significantly outperforms the latter. IORFP possesses excellent performances and can be widely used to supplant generalized cross-spring pivot in compliant mechanisms and ultra-precision instruments.