The kinematic coefficients for the elliptic trammel linkage are 3 = 2 rad/m, 3 =

The kinematic coefficients for the elliptic trammel linkage are θ

3 = −2 rad/m, θ

3 = −6.928 rad/m2, R

4 = −1.732 m/m, and R

4 = −8 m/m2. A linear spring is attached between O and A with a free length L = 0.5 m and spring constant K = 2 500 N/m. A viscous damper with damping coefficient C = 45 N ·s/m is connected between the ground and link 4. The masses and mass moments of inertia of the links are m2 = 0.75 kg, m3 = 2.0 kg, m4 = 1.5 kg, IG2 = 0.25 N · m ·s2, IG3 = 1.0 N·m·s2, and IG4 = 0.35 N·m·s2. The velocity, acceleration, and force acting on input link 2 are VA2 = −5ˆj m/s, AA2 = −20ˆj m/s2, and F = −200ˆj N, respectively. If gravity acts in the negative y direction, determine:

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

(b) the equivalent mass of the linkage; and

(c) the horizontal force, P acting on link 4.