Approximate equations for circular hinge stiffnesses

Abstract

Flexure hinges are widely used for very high precision mechanisms, such as a high precision linear guide, a nano positioning stage, a robot hand and etc., because of no gap and no friction. Regarding circular hinge stiffnesses, Paros and Weisbord derived exact solutions, but they are unwieldly because of the complexity. Simpler equations are preferred to use in analyses of the assembled mechanisms composed of flexure hinges. Therefore, in this paper, approximate stiffness equations for the semicircular hinge are discussed. The approximate equations were also derived by Paros and Weisbord, but their tensile stiffness equation does not give a good result. And, many studies were performed for the circular hinge, but their stiffness equations are apart from the exact solutions when the hinge thickness is large. In this paper, new approximate stiffness equations are derived by substituting approximate functions of series for the small terms of the exact solutions. Errors between the delivered approximate solutions and the exact solutions are less than 3 percentages in the wide range of the hinge thickness. The derived approximate stiffness equations give better results than other approximate equations in the wide range of the hinge thickness. And, they are useful for the actual design because it is easily recognized how design parameters contribute to the stiffnesses.