This paper presents the mechatronic design of a new anthropomorphic hand. It has been developed in the context of a multidisciplinary project which aims at understanding how humans perform the manipulation of objects in order to replicate grasping and in-hand movements with an artificial hand. This has required the development of a new hand with a high level of both anthropomorphism and dexterity. The hand must exactly replicate the kinematics of the human hand, adding up to 24 degrees of mobility and 20 degrees of freedom, which is a design challenge if a high level of dexterity must be guaranteed. Three key concepts have guided the mechanical design: modularity, backdrivability and mechanical simplicity. A modular approach simplifies the complex hand assembly and permits us to concentrate our efforts on one basic unit which will be replicated throughout the hand. Mechanical simplicity and backdrivability ensure a good natural mechanical behavior, essential for stable control of contact forces. Likewise, a better controllability will enhance the dexterity of the hand. A thorough mechanical design assures backdrivability through the whole mechanism, including actuators and transmission of movement to the joints. Experimental results confirm the validity of the design approach and will open new lines of research into robotic hands.