A mathematical model for grasping analysis of flexible materials

The issue of grasping is fundamental as part of handling routines. Many gripping devices have been proposed and invented for flexible material handling, but a mathematical understanding of the relationship between the parameters of gripper and the properties of object to be grasped has not been obtained completely. With this, it is unrealistic to expect to develop a flexible grasping system - an intelligent grasping system. In this paper, a mathematical model for analysis of flexible materials pressed by a curved surface pinch gripper using the elasticity theory is presented. The relationship between an indenter, an external load and the properties of the material being handled is established. The distributions of stress and displacement within a sample have been derived. The contact interface between the indenter and the sample is solved with the aid of the Hertz elastic contact equations. A solution for calculating the contact length between a sample and a rigid table is developed. In order to model experimental behaviour the non-linear elastic response of the material and large deformations have to be incorporated in the model. Thus, this model provides a complete system for solving the problem of a small indenter pressing a flexible specimen of a much larger size. The predictions of the model are tested against experimental data and the results of finite element analysis, and reasonably good agreement is obtained. It is expected that the intelligent grasping system can adjust its grasping force systematically based on this model by adapting to the properties of the material to be grasped, and this should be of benefit for both grasping analysis and gripper design. © 2005 IOP Publishing Ltd.