This paper presents a study on the effect of design parameters of an underactuated hand on its grasp performance. Three kinds of grasp performance characteristics are considered: grasp range, grasp strength, and immobilizing grasp range. Grasp strength is defined as the stiffness of the grasp. Immobilizing grasps are those in which the object cannot be moved for a force up to a certain threshold. In general, underactuated hands cannot produce immobilizing grasps. However, we show that immobilizing grasps can be created by including joint limits in the hand design. We consider the effect of two design parameters on the grasp performance: torque ratio and finger-base distance. Results show that an optimal finger-base distance and torque ratio exists that maximizes the grasp range and grasp strength. Also, the immobilizing grasp range is increased by decreasing the finger-base distance and increasing the torque ratio and joint limits.