In this paper, dynamic modeling and slippage analysis of a three-link soft finger manipulating a rigid object on a horizontal surface is studied. In order to integrate the dynamics of soft tip with the finger linkage, power-law model and a linear viscous damper are used to model the elastic behavior and damping effect of soft tip respectively. Because of the enlarged contact area in the soft contact, a frictional moment can be exerted at the contact interface along with the normal and tangential forces. Furthermore, because of planar motion of object, frictional forces and moment are applied in the contact of object and ground. Therefore, friction limit surface is used as a mapping between contact forces/moment and sliding motions in both contacts. Instead of using equality and inequality equations of frictional contact conditions, a method is proposed to describe different states of the contact forces and moment by a single second-order differential equation with variable coefficients. This kind of formulation of the system dynamics facilitates the design of a controller to cancel the undesired slippage occurs between the soft tip and object during the manipulation.

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