Computational models for predicting the deflected shape of a non-uniform, flexible finger

Motivated by the applications of flexible fingers (capable of offering large deflections to accommodate object variations) in grasping, we present several computational models that characterize the large deflection of a flexible finger (beam). Specifically, we develop analytical methods for analyzing the design of cantilever-like fingers or elements of a machine that is designed primarily to support forces acting perpendicular to the axis of the member. Both uniform and non-uniform beams are considered. The methods were numerically validated by comparing the computed results against those obtained using the closed-form solutions, where exact solutions are available for fingers with a uniform cross-section. To extend the closed-form solution for predicting the shape of a non-uniform finger, we compute numerically an effective EI that approximates the non-uniform finger as a uniform finger at the point of contact. The approximate model has been examined experimentally. The results show excellent agreement. We expect that the methods presented here will have other engineering applications.