Geometric nonlinearities often complicate the analysis of systems containing largedeflection members. The time and resources required to develop closed-form or numerical solutions have inspired the development of a simple method of approximating the deflection path of end-loaded, large-deflection cantilever beams. The path coordinates are parameterized in a single parameter called the pseudo-rigid-body angle. The approximations are accurate to within 0.5 percent of the closedform elliptic integral solutions. A physical model is associated with the method, and may be used to simplify complex problems. The method proves to be particularly useful in the analysis and design of compliant mechanisms

Parametric Deflection Approximations for End-Loaded, Large-Deflection Beams in Compliant Mechanisms

A modified Lagrangian formulation is presented for the dynamic analysis of constraint mechanisms. The proposed method is based on a Hamiltonian description of the dynamics which leads to the Lagrange's equations. However, the constraint conditions are not appended to the Lagrange's equations in the form of algebraic or differential constraints, but instead inserted in them by means of a penalty formulation, and therefore the number of equations of the system does not increase. In addition, this approach directly leads to a system of ordinary differential equations, as opposed to the classical Lagrange's formulation which results in differential algebraic equations. The resulting set of equations is of the form dot y =g(y,t) , which can be integrated by standard numerical algorithms. Finally, the proposed method is very systematic and general, and can model any type of constraint conditions, either holonomic or nonholonomic. A series of illustrative examples are analyzed. The results demonstrate the capabilities of the proposed method for simulation analysis.

A modified Lagrangian formulation for the dynamic analysis of constrained mechanical systems

A new class of fully compliant bistable mechanisms with the added benefit of integrated self-retraction has been developed (hereafter identified as Self-Retracting Fully compliant Bistable Mechanism or SRFBM). A technique using tensural pivots to manage compressive loading in compliant mechanisms is introduced and implemented in the SRFBM. The elimination of traditional kinematic joints and their associated clearance allows a total displacement between stable positions of 8.5 /spl mu/m, and the mechanism size is less than 300 /spl mu/m square when using 2.0 /spl mu/m minimum line widths. Maximum actuation force is approximately 500 /spl mu/N. The SRFBM's small linear displacement and reasonable actuation force facilitate integration with efficient thermal actuators. Furthermore, fully compliant mechanisms allow greater freedom in fabrication as only one mechanical layer is needed. Systems with on-chip actuation have been fabricated and tested, demonstrating bistability and on-chip actuation, which requires approximately 150 mW. A single fatigue test has been completed, during which the SRFBM endured approximately 2 million duty cycles without failure.

Burton Paul

Papers

Kinematics and Dynamics of Planar Machinery