PMC

Three time graphs representing a succession of three MVIC of 5 s each followed by 5 s of relaxation between contractions: (a) time graph of voltage during ankle plantar flexion with the period being represented in seconds (s) on the Ox axis and voltage represented in V on the Oy axis; (b) an example of the same time graph for ankle dorsiflexion with the period being represented in seconds (s) on the Ox axis and torque represented in Nm on the Oy axis; (c) torque represented in Nm during ankle plantar flexion, where the peak torque is highlighted with a red circle and the mean off-set level is marked with a red line; (d) torque represented in Nm during ankle dorsiflexion, where the peak torque is highlighted with a red circle and the mean off-set level is marked with a red line.

Construct the simulation model of the DC motor, based on the DC motor voltage balance equation, flux linkage equation and torque balance equation. Establish voltage balance equation given by where u_d is direct axis voltage, u_q is quadrature axis voltage. R_d and R_q denote direct axis resistance and quadrature axis resistance respectively. ,,,, represent direct axis current, direct axis current, direct axis flux and quadrature axis flux.Establish flux linkage equation given by where and denote the coefficient of direct axis self-inductance and quadrature axis self-inductance respectively. and are coefficient of mutual inductance. , represent electromagnetic torque and load torque.Establish torque balance equation calculated by .Build simulation model of the DC motor. ()

Illustration of the fact that rotation about an inertial eigenvector only requires a torque about the rotation axis. In each panel, a point-mass (p), fixed to the end of a weightless rod, rotates about an axis through O. In panel a, the axis of rotation is orthogonal to the rod’s longitudinal axis. This rotation only involves a tangential torque (T_t) along the axis of rotation to generate the tangential acceleration a_t. In panel b, the axis of rotation is not orthogonal to the rod’s longitudinal axis so that a_c is not directed at O. It thus involves a centripetal torque (T_c), oriented orthogonal to the rotation axis. Hence, the rotation axis in panel a represents an eigenvector whereas that in panel b does not

The two models demonstrate static equilibrium of the pelvis in the frontal plane during right single limb stance. In both models, the right hip is the axis about which torque is generated. The force generated by the hip abductors (Hip Abd.) times its moment arm (dotted line) generate a counterclockwise torque. Body weight (BW) times its moment arm (dashed line) generates a clockwise torque. The external load times its moment arm (solid line) generates a torque which is clockwise in direction and larger in magnitude when held in the left hand compared to the counterclockwise torque it creates when held in the right hand. In static equilibrium, the sum of the counterclockwise torques equals the sum of the clockwise torques. (A) Contralateral Load: The counterclockwise torque is from the Hip Abd. The clockwise torques include the torque due to BW and the torque due to the load. (B) Ipsilateral Load: The Hip Abd. and BW continue to generate counterclockwise and clockwise torques, respectively, while the load now generates a counterclockwise torque. In model A, the hip abductors must generate more force to counteract the clockwise torques generated by both BW and the load (with its large moment arm), whereas in model B, the hip abductors are assisted by the load to counteract the torque of BW.