For the rack-and-pinion mechanism in the posture shown in Fig. P2.15, the input link, 2, is vertical, and ∠BAO2 is 150◦. The dimensions are ρ5 = 2.5 in, RO5O2 = −8ˆi + 4ˆj in, RAO2 = 2 in, and RBA = 6 in.

(a) Show the locations of all instant centers.

(b) Using instant centers, determine the first-order kinematic coefficients of link 3, rack 4, and pinion 5.

(c) If ω2 = 10 rad/s cw, determine the angular velocity of link 3, the velocity of rack 4, and the angular velocity of pinion 5.