A mathematical approach to the mechanical capabilities of limbs and fingers.

Neuromuscular function is the interaction between the nervous system and the physical world. Limbs and fingers are, therefore, the ultimate mechanical filters between the motor commands that the nervous system issues and the physical actions that result. In this chapter we present a mathematical approach to understanding how their anatomy (i.e., physical structure) defines their mechanical capabilities. We call them "mechanical filters" because they attenuate, amplify, and transform neural signals into mechanical output. We explicitly distinguish between limbs and fingers because their subtle anatomical differences have profound effects on their mechanical properties. Our main message is that many aspects of neuromuscular function such as co-contraction, posture selection, muscle redundancy, optimality of motor command, are fundamentally affected (if not defined) by the physical structure of limbs and fingers. We attempt to present the fundamental filtering properties of limbs and fingers in a unified manner to allow for a direct and useful application of powerful mathematical concepts to the study of neuromuscular function. Every researcher of motor control is well advised to consider these filtering properties to properly understand the co-evolution and synergistic interactions between brain and body. At the end of the day, every inquiry in neuromuscular function can be reduced to the fundamental question whether and how the nervous system can perform the necessary sensorimotor functions to exploit and reach the mechanical capabilities of limbs and fingers.