In the engineering field of fine positioning, a small input displacements obtained by such actuator as an electrical element is often magnified by using mechanical levers with elastic hinges. To the contrary, such a small input displacement is sometimes required to be reduced further to as fine as subnanometer order in the field of, for example, molecular manipulation technique. The authors studied so far both experimentally and theoretically on the apparatus for magnification and reduction of input displacement, comprising of some elastic hinges and rigid blocks. In this paper, the authors discuss theoretically on the relation between the input displacement and output displacement of a fundamental mechanism. The mechanism consists simply of elastic beams and rigid block ,which creates a very high reduction of input displacement. It is clarified that though the mechanism provides fairly higher reduction ratio, the output displacement obtained here is nonlinear with respect to the input displacement, leading to an unfavorable effect for fine positioning. The results shown in this paper will ,however, will be useful for the development of advanced mechanism with high reduction ratio by redesigning the structure.
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