Automated kinetostatic modeling approach for flexure-based mechanisms

Modeling the kinetostatics of a flexure-based mechanism is crucial for characterizing its performances and optimizing its parameters. However, the kinetostatic modeling is always a very complicated and error-prone process because it involves formulating not only the loop-closure equations, but also a large number of load equilibrium equations. In this work, we present a general approach that can automatically generate kinetostatic models for planar flexure-based mechanisms. The proposed approach represents the topological structure of a flexure-based mechanism using an incidence matrix and a path matrix, based on which the loop-closure equations and load equilibrium equations are uniformly formulated. These equations are simultaneously solved for the kinetostatic behaviors of the mechanism. All the load equilibrium equations are formulated at vertices instead of links, which eliminates the need of introducing virtual hinges. The automated approach is implemented in an integrated software package with graphical user interface to facilitate the kinetostatic modeling of various flexure-based mechanisms. The effectiveness of the proposed approach is demonstrated by three examples, including a flexure-based displacement amplifier, a microscopic rotation converter, a planar parallel 3-DOF nanopositioner, and a double-output mechanism showing its accuracy and broad applicability.