Moment-Dependent Pseudo-Rigid-Body Models for Beam Deflection and Stiffness Kinematics and Elasticity

This thesis introduces a novel parametric beam model for describing the kinematics and elastic properties of ortho-planar compliant Micro-Electro-Mechanical Systems (MEMS) with straight beams subject to specific buckling loads. Ortho-planar MEMS have the ability to achieve motion out the plane on which they were fabricated, characteristic that can be used to integrate optical devices such as variable optical attenuators and micro-mirrors. In addition, ortho-planar MEMS with large output forces and long strokes could be used to develop new applications such as tactile displays, active Braille, and actuation of micro-mirrors. In order to analyze the kinematics and elasticity of a curved beam contained in a Micro Helico-Kinematic Platform (MHKP) device, this thesis offers an improved model of straight and curved flexures under compressive loads. This model uses an approach similar to the one applied to develop a regular Pseudo-Rigid -Body Model but it differs in the definition of a key parameter, the characteristic radius factor, γ, which is not a constant, but a function of the moment, γ*=γ(M) . This approach allows for the Pseudo-Rigid-Body Model (PRBM) to describe the motion taken by the deflected beam precisely over a large range of motion. In developing the model, this thesis describes kinematic and elastic parameters such as the angle coefficient, C9, the characteristic radius, γl, and the torque coefficient, Tθ. Furthermore, the torque coefficient is divided into two component functions, Tf, and, Tm, which can be used to find the working loads (force and moment) on the beam. The input displacement is the only needed state variable, object variables, which describe the beam, include the material modulus of elasticity, E, the moment of inertia, I, and its length, l