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

ω2 = −5kˆ rad/s and α2 = 3kˆ rad/s2, respectively, and the acceleration of the mass center of link 3 are α3 = 15.75kˆ rad/s2 and AG3 = 9.60ˆi −

15.20ˆjin/s2, respectively. The weights and second moments of mass of the links are w2 = w3 = 13.2 lb,w4 = 2.2 lb,IG2 = IG3 = 45.69 lb · in ·

s2, and IG4 = 4.56 lb · in · s2. The torque acting on link 4 is T14 = −17.7kˆ in · lb, and there is an unknown torque, T12, acting on link 2.

Gravity is in the negative y direction. Determine:

(a) the magnitude, direction, and location of the reaction force between links 3 and 4, and

(b) the magnitude and direction of the torque, T12.

Figure P12.56 O2A = 2.0 in, AO4 = 4.0 in, and AG3 = 2.40 in.