Optimization-Based Design of a Fully-Compliant Bistable Micromechanism

Micro-bistable mechanisms are used in microswitches and microvalves to reduce power consumption as power is applied only to switch states. Many of the bistable mechanism designs that have been presented incorporate rigid-body joints. These joints introduce unwanted friction and poor repeatability into the mechanism motion. A fully-compliant mechanism avoids these problems. Optimization techniques were used to find fully-compliant bistable micromechanism designs. The chosen objective was to minimize the displacement required between the two stable positions. Two families of designs were considered: those where the actuator was integral to the device and those where it remained in contact only during actuation. Mechanism designs are presented and are currently in the process of fabrication. INTRODUCTION Mechanically bistable micromechanisms maintain either of two stable positions without the need of constant power input. This is attractive for systems with power constraints because power is supplied only to switch the mechanisms between states. For example, several examples of bistable mechanisms for micro-relays or micro-switches have been presented (Hälg, 1990; Matoba et al., 1994; Kruglick and Pister, 1998; Sun et al., 1998, Jensen et al., 1999). Bistable microvalves have also been discussed which remain either open or closed (Wagner et al., 1996; Goll et al., 1996; Shinozawa et al., 1997; Schomburg and Goll, 1998). A bistable fiber-optic switch (Hoffman et al., 1998) and a bistable system to produce a force for assembling mi parts (Vangbo and Bäcklund, 1998) have also been suggeste These bistable micromechanisms generally fall into one two broad categories. Many of the devices presented residual stress in deposited films to create beam buckling well-known bistable phenomenon. Other devices use str energy storage and a mixture of rigid-body and compliant joi to create bistable mechanisms. This approach is espec useful in standard MEMS fabrication processes, such Cronos’ MUMPs or Sandia National Laboratories’ SUMMiT The goal of stress-free polysilicon inherent in these proces makes small-size buckling designs infeasible. Unfortunate however, friction in rigid-body joints creates a considerab increase in power requirements, as well as a correspond reduction in reliability due to stiction. Moreover, bistabl micromechanisms which include rigid-body joints suffer fro poor repeatability. The large clearances typical of these jo induce variation in the locations at which the mechanism stable (Jensen et al., 1999). Hence, a more robust design w consist of one flexible piece of material which would not rely o residual stress for its bistable behavior. Such a design wo realize the advantages of compliant mechanisms, such friction-free operation, no backlash, and no we (Ananthasuresh and Kota, 1996). Several design constraints peculiar to MEMS impose add complexity to the design problem. For example, stress in t flexural pivots tends to prevent large motions, requiring that mechanism design involve only small angular motions over range of deflection. In addition, during mechanism motio some of the energy stored in the mechanism would have to w 1 Copyright  2000 by ASME to force the mechanism into a second stable position, while some of the stored energy would necessarily work to return to the initial fabrication position. In order to better explore the design space, we decided to use optimization techniques, which would allow us to evaluate many designs very quickly, examining feasible designs in further depth while discarding infeasible designs. MECHANISM TYPOLOGY The first step in the mechanism design was to choose a basic topology for the device. For simplicity in attaching the device to an actuator, linear motion was desired for the input. A kinematic slider was therefore chosen as the input link. With this basic stipulation, we considered two basic mechanism typologies, the slider-crank and the double-slider mechanisms, shown in Figure 1. Each type contains the required slider joint, and prior work had shown both to be excellent candidates for bistable mechanisms (Jensen, 1998). A preliminary analysis was performed for each mechanism type to determine its suitability for fully-compliant bistable mechanism design. For this analysis, each mechanism type was modeled as a fully-compliant mechanism. The details of the modeling for the double-slider type are given below, and the modeling of the slider-crank type is similar. Preliminary optimization performed on each model showed that while the double-slider design space contained feasible bistable designs, the slider-crank design space contained few, if any, feasible bistable designs. Thus, the double-slider mechanism type was chosen for further study. MODEL DEVELOPMENT To make the mechanism fully compliant, thin flexible segments could be used in place of the pin joints, and any of several common linear suspensions, such as the folded beam suspension, could be used in place of the sliders. A simple kinematic model of a fully-compliant doubleslider mechanism requires torsional or translational springs to be placed at each mechanism joint, as shown in Figure 2. This mechanism model is based on pseudo-rigid-body modeling, in which thin flexible segments (known as small-length flexural pivots) are modeled as pin joints, with torsional springs to represent bending stiffness (Howell and Midha, 1994). For simplicity, we require that the two small-length flexural pivots have the same geometry and consequently the same stiffness k. The mathematical model of the mechanism may then be formulated. First, the dependent design variables must be calculated from the independent variables: