Closed-Form Nonlinear Analysis of Beam-Based Flexure Modules

The simple beam acts as a constraint element when used in flexure mechanisms. Non-linearities arising from the force equilibrium conditions in a beam significantly affect its properties as a constraint element. Consequently, beam-based flexure mechanisms typically suffer from performance tradeoffs in terms of motion range, accuracy and stiffness. This paper presents simple yet accurate approximations that capture this non-linearity and allow for the closed-form analysis of flexure mechanisms of moderate complexity. These general analytical tools enable a designer to parametrically predict key performance parameters of a conceived mechanism such as mobility, over-constraint, stiffness variation, and error motions, without resorting to tedious numerical or computational methods. To illustrate their effectiveness, these approximations are used in deriving the closed-form force-displacement characteristics of several important beam-based flexure modules, and the results are validated using Finite Element Analysis. Variations in the beam shape and flexure module geometry are also considered analytically.