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In this work, we report on our progress in the development of a new anthropomorphic robot hand at the University of Malta. Following a brief overview of the work carried out in our laboratory so far, we discuss in some detail and through a fresh perspective a number of important lessons that can be learned from the human hand, and that can be very useful in the development of an artificial hand that can ultimately match the human counterpart in the execution of many tasks. We present a new design for a robot hand with joint position and grasping force sensing, based on the specific approaches brought up in this discussion, and targeted to reproduce many of the capabilities of the human hand. In particular, all of the actuation and sensing devices of the hand are located remotely from the device, therefore facilitating the development of a compact and lightweight hand design. A prototype of the new hand has been constructed and is presented herein. Finally, we present the initial results of our analysis to demonstrate how the magnitude and location of grasping forces can be inferred from the sensor readings.