For the linkage in the posture shown, the angular velocity and acceleration of input link 2 are

ω2 = −5kˆ rad/s and α2 = 3kˆ rad/s2, respectively.

The kinematic coefficients are R

AO2 = −10.40 in/rad, R

CA = 14.80 in/rad, R

AO2 = −18.00 in/rad2, R

CA = −14.80 in/rad2, x

C = −14 in/rad, y

C = 14 in/rad, x

C = −14 in/rad2, and y

C =

−14 in/rad2. Gravity is in the negative y direction. The distances, the free length and spring rate of the rectilinear spring, the damping constant of the viscous damper, and the weights and second moments of mass about the mass centers of links 2, 3, and 4 are shown in Table P12.54.

Determine:

(a) the first-order kinematic coefficients of the spring and the damper;

(b) the kinetic energy of the linkage; and

(c) the torque, T12.