In this paper, a model is shown to predict the simultaneous deformations occurring when compliant robotic fingers are grasping soft objects. This model aims at providing an accurate estimation of the penetration, internal forces, and deformed shapes of both these fingers and the objects. A particular emphasis is placed on the case when the finger is underactuated but the methodology discussed in this paper is general. Usually in the literature, underactuated fingers are modelled and designed considering their grasps of rigid object because of the complexity associated with deforming objects. This limitation severely hinders the usability of underactuated grippers and either restricts them to a narrow range of applications or requires extensive experimental testing. Furthermore, classical models of underactuated fingers in contact with objects are typically applicable with a maximum of one contact per phalanx only. The model proposed in this paper demonstrates a simple algorithm to compute a virtual subdivision of the phalanges which can be used to estimate the contact pressure arising when there are contacts at many locations simultaneously. This model also pro- poses a computationally efficient approximation of isotropic soft objects. Numerical simulations of the proposed model are compared here with dynamic simulations, finite element analyses, and experimental measurements which all shows its effectiveness and accuracy. Finally, the extension of the model to other types of underactuated fingers, standard grip- pers, and fully actuated robotic fingers as well as potential applications is discussed and illustrated.

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