Mechanical hands have become of greater interest in robotics due to the advantages they offer over conventional grippers in tasks requiring dextrous manipulation. However, mechanical hands also tend to be more complex in construction and require more sophisticated design analysis to determine the forces in the system. A mechanical hand can be described as a kinematic chain with time-varying topology which becomes redundantly actuated when an object is grasped. When this occurs, care must be exercised to avoid crushing the object or generating excessive forces within the mechanism. In the present work, this problem is formulated as a constrained quadratic optimization problem. The forces to be minimized form the objective, the dynamic equations of motion form the equality constraints and the finger-object contacts yield the inequality constraints. The quadratic-programming approach is shown to be advantageous due to its ability to minimize ‘internal forces’ A technique is proposed for smoothing the discontinuities in the force solution which occur when the toplogy changes.