The kinematic synthesis applied to tree topologies is a tool for the design of multifingered robotic hands, for a simultaneous task of all fingertips. Even though traditionally wrists and hands have been designed separately, the wrist usually being part of the robot manipulator arm, it makes sense to consider the wrist as a part of the hand, as many grasping and manipulation actions are a coordinated action of wrist and fingers. The manipulation capabilities of robotic hands may also be enhanced by considering more than one splitting stage, as opposed to the single-palm traditional hand. In this work, we present the dimensional synthesis for a family of multifingered hands, the binary hands, which have a 2R wrist and several splitting stages, each of them spanning two branches consisting of a revolute joint for each edge. For these topologies, it is proved that a three-position task can be defined for each fingertip, regardless of the number of fingers. One example is presented to show the possible design strategies and uses for this family of hands.