In this paper, we propose a complete methodology for deriving task-specific force closure grasps for multifingered robot hands under a wide range of uncertainties. Given a finite set of external disturbances representing the task to be executed, the concept of Q distance is introduced in a novel way to determine an efficient grasp with a task compatible hand posture (i.e., configuration and contact points). Our approach takes, also, into consideration the mechanical and geometric limitations imposed by the robotic hand design and the object to be grasped. In addition, incorporating our recent results on grasping , the ability of the robot hand to exert the required contact forces is maximized and robustness against positioning inaccuracies and object uncertainties is established. Finally, the efficiency of our approach is verified through an experimental study on the 15 DoF DLR/HIT II robotic hand attached at the end effector of the 7 DoF Mitsubishi PA10 robotic manipulator.