Muscular Mechanical Work/Power & Joint Energetics

Muscle mechanical work is an important biomechanical quantity in human movement. Power is defined as the rate of work or the rate of energy flow. Two power measures can be obtained from the joint kinetics: the joint power and the muscle power. The joint power is the scalar product of the net joint force and the joint velocity (P(j)=F*V)where P(j) = the joint power, F = the net joint force, and v = the velocity of the joint. Precisely speaking, the joint power is the rate of energy transfer through the joint caused by the linear motion of the joint.

where FAK/FT = the net joint force acting on the foot at the ankle, FAK/SH = the net joint force acting on the shank at the ankle, and vAK = the ankle velocity. [3] shows that both the foot and leg joint powers are of the same magnitude with an opposite sign at the ankle. This suggests that the ankle joint only transfers energy from foot to the leg and vice versa. Between the two segments forming a joint, one segment always gains energy at the rate the other loses its energy and vice versa.

Muscle power on the other hand is a scaler product of joint torque and the segment's angular velocity (P(m)=T*w)where P(M) = the muscle power, T = the joint torque, and w = the angular velocity. When looking at muscle powers of the foot and the leg at the ankle we can conclude...

where TAK/FT = the ankle joint torque acting on the foot, TAK/SH = the ankle joint torque acting on the lrg, wFT = the angular velocity of the foot, and wSH = the angular velocity of the leg. It appears that there is no apparent relationship between the muscle powers of the foot and leg since the angular velocities of the foot and leg can be very different.At the muscle, two things happen: (1) the muscle transfers energy from one segment it attaches to to the other, and (2) the muscle does work through contraction. The energy transfer happens from one segment to the other and the net change in the energy in the two segments due to the energy transfer must be 0. On the other hand, an individual muscle can either add (positive work) or drain (negative work) energy to or from both segments at the same time by doing work. The angular momentum is shown in figure 2.