On Double Leaf Spring Mechanism for Fine Positioning : Theoretical and FEM Analyses for Designing (1st Report)

Abstract

The characteristics of cantilever are theoretically well known in the field of strength of materials. In case of analyzing behaviors of complicated mechanical structures, it is, in general, required to solve a lot of simultaneous equations derived from given equilibriums and constraints. In order to simplify equations mentioned above, the authors want to introduce a unique method in which only the cantilever theories are used. The method in which the cantilever theory and the principle of superposition are combined brings easily in results regarding to angular and translational displacement at any point of intricate mechanisms, by solving a few of simultaneous equations, the number of which is equal to arbitrary constraints of mechanism. The idea itself is not newly developed by the authors. The way shown here, however, surely seems to be peculiar and unconventional for analyses of complicated mechanical structures. After describing the beam theory on a cantilever, the principle of superposition and characteristics of the well known single leaf spring mechanism, the author theoretically analyze both angular and translational displacements of a newly developed double leaf spring mechanism and compare them with the results obtained numerically by FEM for designing the equipment. It is clarified from the theoretical and numerical results that the double leaf spring mechanism shows an excellent translational displacement with no angular displacement for fine positioning at the origin of the stage Based on theoretical and numerical analyses described above, the authors finally designed two modeled mechanisms, that is, one side supported double leaf spring mechanism and both side supported one. Both are much superior to single leaf spring mechanism from the view of structural balance and the distance to be traveled.