List of top Theory of Machines Questions

The Whitworth quick return mechanism is shown in the figure with link lengths as follows: OP = 300 mm, OA = 150 mm, AR = 160 mm, RS = 450 mm. The quick return ratio for the mechanism is _______

A tappet valve mechanism in an IC engine comprises a rocker arm ABC that is hinged at B as shown in the figure. The rocker is assumed rigid and it oscillates about the hinge B. The mass moment of inertia of the rocker about B is \( 10^{-4} \, \text{kg.m}^2 \). The rocker arm dimensions are \( a = 3.5 \, \text{cm} \) and \( b = 2.5 \, \text{cm} \). A pushrod pushes the rocker at location A, when moved vertically by a cam that rotates at \( N \, \text{rpm} \). The pushrod is assumed massless and has a stiffness of 15 N/mm. At the other end C, the rocker pushes a valve against a spring of stiffness 10 N/mm. The valve is assumed massless and rigid. 

Resonance in the rocker system occurs when the cam shaft runs at a speed of ________ rpm (round off to the nearest integer).

The figure shows an arrangement of a heavy propeller shaft in a ship. The combined polar mass moment of inertia of the propeller and the shaft is 100 kg.m². The propeller rotates at \( \omega = 12\ \text{rad/s} \). The waves acting on the ship hull induce a rolling motion as shown in the figure with an angular velocity of 5 rad/s. The gyroscopic moment generated on the shaft due to the motion described is ________ \text{N.m} (round off to the nearest integer).