Angle of Twist of a Double-Bent Leaf Flexure under Torsion

Abstract

310 INTRODUCTIONLeaf springs and hinges are two kinds of flexure guide; they have many applications in precision machines, especially in nanoelectromechanical systems (NEMs) and microelectromechanical systems (MEMs). These flexure guides have outstanding advantages such as a lack of friction, and their guiding resolution is on the order of a nanometre. However, they have a short working range (from micrometre to millimetre). Therefore, the new flexure guides, which have a large working range and nano-resolution, have become very important in recent years. For example, a parallel leaf spring flexure has been presented with increasing displacement [1]; a displacement reduction mechanism based on torsional leaf spring hinges has been developed [2]; a novel flexure-based leaf spring has been presented with a large range (25 × 25) μm 2 [3]; a mechanism for a single-axis flexure-based nano-positioning stage with a large range of motion (up to a millimetre) is described in [4]; a multi-axis positioning system with nanometric resolution over a 1 mm stroke is described in [5]; a novel flexure parallel-kinematics precision positioning stage with a centimetre range has been designed and developed [6], and many hinge flexure guides have been reported [7] to [11]. In comparison with a hinge, the leaf spring has a smaller size and a minimum use of materials for the same displacement. Thus, we examined leaf spring flexure guides for the large range travel in this study.In general, a leaf spring can be divided into three types: single, single-bent, and double-bent leaf [12]. The single leaf has two degrees of freedom (DoF)