Pseudo-rigid-body models for circular beams under combined tip loads

Circular beams can offer potential advantages to designers of compliant mechanisms and provide useful alternatives to other types of compliant elements. However, they pose unique challenges due to lack of effective models for predicting deformation upon loading. In this work, the kinematic and stiffness properties of circular beams with uniform cross sections subjected to combined force and moment loads are represented using pseudo-rigid-body models. The pseudo-rigid-body models serve as numerical approximations for easy derivation of mechanism equations, and also enable quick solutions using multi-body software packages. The models are derived by comparisons against beam theory, and the values of the parameters are presented in the form of fitting functions for a large range of arc angles. The validity and applicability of these models in analysis are demonstrated with the example of a micro-force sensor. Their use in design is demonstrated with the case of developing flexure mechanisms for microspines in grasping applications, with comparisons against Finite Element Analysis to prove their accuracy and speed. The PRB models can serve as tools facilitating design of compliant mechanisms with circular beams.