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Precision positioning and alignment are critical to an emerging class of small-scale manufacturing and numerous motion control applications. The drive for better performance steers design and control effort into achieving high tolerances and stringent specifications in terms of parameters, such as resolution, range, load-capacity, and bandwidth. Examples of applications needing precision positioning and alignment include (i) high-bandwidth steering of mirrors in telecommunication applications [1], (ii) tool-sample alignment in stamping applications such as imprint lithography [2, 3] and micro-contact printing [4], and (iii) alignment of optically flat surfaces brought in close proximity to characterize fields and forces on small-scales, such as the Casimir force [5, 6]. A widely used set of designs for precision applications described above involve compliant mechanisms based on slender beam modules, also referred to as flexures [7, 8]. The advantages flexures offer are mainly smooth elastic motion without non-linearities such as friction or backlash [9]. Flexure-based mechanisms such as the diaphragm flexure involve the payload suspended on a radial or tangential arrangement of flexural beams. Various forms of such flexures have appeared over the past few decades for applications such as MEMS mirrors, and in angle alignment and guidance applications [4, 10, 11]. Analysis of the statics and dynamics of flexure-based mechanisms have been extensively studied [9, 12]. While flexure-based engineering designs have been around for many decades [13], designing them for dynamic performance has sought little attention. Few publications [14, 15] have appeared in this context. The design for dynamical performance of flexures in the context of mechanical advantage is detailed in [14]. A finite-element approach based on Euler-Bernoulli beam bending theory is formulated for analyzing dynamics in [15] and optimizing the design space for precision flexure-based applications in [16].

Dynamic Modeling and Performance Trade-offs in Flexure-based Positioning and Alignment Systems