This paper introduces an extension to the energy map method for in-hand manipulation. Energy maps are used to predict how a part will evolve in the grasp given a specific actuation input to the gripper. Previous approaches assumed frictionless contacts, but we show analytically that friction can be included in the energy maps when using two-link underactuated fingers by understanding the evolution of the part-finger contact. These friction-based energy maps were used to evaluate the importance of various tendon-pulley gripper parameters across nearly 6 million simulated grasping scenarios. Specifically, a variable palm width is needed to manipulate parts of varying scales, and a variable transmission ratio, or the ratio of the distal to the proximal pulley radii, is needed to draw parts into a cage or to maintain a tip prehension grasp.