In this work, we address the problem of kinematic modeling and control design of a multifingered robot hand. Each robot finger is modeled as a parallel manipulator and its kinematic constraints are computed from empirical analysis due to the inherent mechanical complexity of the mechanism. The motion control problem for a grasped object is solved by using the kinematic control approach, which is able to ensure the asymptotic stability of the output tracking error and the prehension of the object. The kinematics-based control scheme is designed to include the contact model in the hand Jacobian matrix, allowing for the simultaneous control of the object position as well as the relative position between the fingers. Experiments are carried out with a three-fingered robot hand executing grasping and manipulation tasks of soft objects. Practical results are shown to illustrate the performance and effectiveness of the proposed methodology.