The accurate modeling and performance analysis of cross-spring pivot as a flexure module

The load-displacement behavior of a cross-spring pivot as a kind of rotational element or module in compliant mechanisms is a subject of keen interest for many researchers. The model allowing not only quick design but also characteristics capture is pursued. This paper addresses some accurate closed-form results via approximations. These expressions are simple for a designer to understand the parameters without resorting to a tedious iterative procedure. The rotational displacement and center shift of the pivot are analyzed both qualitatively and quantitatively, with a general-purposed load applied including bending moment, horizontal and vertical forces. Meanwhile, a concise expression for center shift without approximations is proposed. The validity of the model is verified by finite element analysis (FEA). The relative error of the rotational displacement is less than 1.8% even if the rotational angle reaches ±20°; the relative errors for the two components of center shift are less than 6% and 4% respectively, in the case of typical but general configurations and loads.