For the elliptic trammel linkage in the posture shown, the velocity and acceleration of input link 2 are VA2 = −3ˆj m/s and AA2 = 7ˆj m/s2, respectively. The kinematic coefficients, masses, and second moments of mass about the mass centers of the links are shown in Table P12.55.

Figure P12.55 AG3 = G3B = 1.25 m.

The stiffness and free length of the spring are K = 200 N/m and R0 = 0.5 m, respectively, and the coefficient of the viscous damper is C = 15 N·

s/m. The only friction in the linkage is between links 1 and 4, where the coefficient of friction is μ = 0.35. The normal force at the point of contact between links 1 and 4 is Fn 41 = 500ˆj N, and gravity is vertically downward. Determine:

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

(b) the kinetic energy of the linkage, and

(c) the external force P acting at point H.