This paper enables the synthesis of flexure-based transmission mechanisms that possess multiple decoupled inputs and outputs of any type (e.g. rotations, translations, and/or screw motions), which are linked by designer-specified transmission ratios. A comprehensive library of geometric shapes is utilized from which every feasible concept that possesses the desired transmission characteristics may be rapidly conceptualized and compared before an optimal concept is selected. These geometric shapes represent the mathematics of screw theory and uniquely link a body's desired motions to the flexible constraints that enable those motions. This paper is significant to the design of nano-positioners, motion stages, and optical mounts. Recently, these principles have been applied to the design of transmission mechanisms that constitute the microstructure of new materials with extraordinary properties (e.g. zeroegative thermal expansion coefficients and Poisson's ratios). A hand-actuated microscopy stage was designed, fabricated, and tested to demonstrate the utility of this theory.
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