A Graphical, User-Driven Newton-Raphson Technique for Use in the Analysis and Design of Compliant Mechanisms

Abstract

The analysis and design of compliant mechanisms, undergoing large (geometrically nonlinear) deflections, have been assisted by the Newton-Raphson method to find the load which satisfy a prescribed set of force and displacement boundary conditions. This paper introduces a graphical, user-driven Newton-Raphson technique that allows easy access to good initial design variable estimates, and subsequently accurate and expeditious solutions. These design variables may include loads as well as material and geometric properties of the beam segments composing the mechanism. A line search step-restriction technique is included to enhance the stability of the method. The method uses six-degree-of-freedom planar beam elements in a chain calculation that cumulatively evaluates the large deflections corresponding to a given load set.