Flexural stiffness evaluation of leaf spring compliant mechanisms

Compliant mechanisms are widely used in precision mechanism and microsystem design. A commonly used compliant mechanism configuration makes use of leaf spring of rectangular cross section loaded in bending. The section is characterized by a high width to thickness ratio. This design solution is employed in a great variety of precision instruments and microdevices, i.e. accelerometers, RF MEMs and usually an accurate evaluation of the flexural stiffness is required. The bending of such leaf springs is a not well developed topic, in the classical engineering literature, two models being available in literature: beam model, referring to the case when the anticlastic curvature is free to occur, and cylindrical flexure of thin plates, when the anticlastic curvature is precluded. The aim of this work is to develop a solution based on the von Kármán non linear theory of thin plates in order to analyze intermediate cases between anticlastic and cylindrical bending, depending on width to thickness ratio of the leaf spring cross-section.