Design of flexure-based precision transmission mechanisms using screw theory

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 a multiplicity of feasible concepts that possess 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 bodyʹs 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. It is also significant to the design of transmission-based microstructural architectures for creating new materials with extraordinary mechanical properties. The microstructural architecture for a material that achieves a negative Poissonʹs ratio as well as a hand-actuated two degree of freedom (DOF) microscopy stage are designed as case studies to demonstrate the utility of this theory.