Theory Of Machine And Mechanism

a) Explain the concept of degrees of freedom in kinematic chains. How does it affect the motion of mechanisms?

b) A four-bar linkage consists of the following link lengths:
AB = 100 mm, BC = 250 mm, CD = 200 mm and DA = 300 mm. Link AB rotates counterclockwise at 30 rad/s. Using the instantaneous center method, calculate:
i) Angular velocities of BC and CD,
ii) The velocity of a point on BC located 100 mm from B.

a) Why are inversions of mechanisms important? Explain with the help of a four-bar linkage example.

b) A mechanism has 10 links and 15 pairs, including one higher pair. Determine:
i) The degree of freedom in using Kutzbach's criterion.
ii) The possible motion characteristics of the mechanism.

a) Compare and contrast the graphical and analytical methods for determining displacement, velocity, and acceleration in mechanisms.

b) For a four-bar linkage with link lengths L₁ = 50 mm, L₂ = 120 mm, L₃ = 140 mm, and L₄ = 160 mm:
i) Determine if the linkage satisfies the Grashof condition.
ii) Calculate the maximum and minimum angular displacement of the coupler link.

a) What are the constraints in designing a cam profile for a high-speed follower motion?

b) The following particulars relate to a symmetrical circular cam operating a flat faced follower.
Least radius = 25 mm, nose radius = 8 mm, lift of valve = 10 mm, angle of action of cam = 120°, cam shaft speed = 1000 rpm. Determine the flank radius and maximum velocity, acceleration and retardation of the follower. If the mass of the follower and valve with which it is in contact is 4 kg, find the minimum force to be exerted by the spring to overcome inertia of the valve parts.

a) Explain the concept of friction axis in power screws. How does it affect the efficiency of screw mechanisms?

b) A flat belt transmits 20 kW at 1440 rpm. The pulley diameters are 500 mm and 1 m, and the center distance is 3 m. If the coefficient of friction is 0.25
Calculate:
i) The tension in the tight and slack sides of the belt.
ii) The maximum stress in the belt material.

a) Discuss the law of gearing and its significance in ensuring smooth power transmission.

b) Design a compound gear train for a speed reduction ratio of 100:1. The input speed is 3000 rpm, and the power transmitted is 20 kW. Assume each gear pair has a speed reduction of 5:1. The gears have a module of 3 mm and face width 40 mm.
Tasks:
i) Determine the number of teeth for all gears.
ii) Verify the torque capacity of the gear teeth under the transmitted power.

a) Explain the difference between epicyclic and compound gear trains. Where are these types of gear trains commonly used?

b) An epicyclic gear train has a sun gear with 20 teeth, a planet gear with 30 teeth, and a ring gear with 70 teeth. The sun gear is fixed, and the ring gear rotates at 300 rpm clockwise.
Tasks:
i) Calculate the speed and direction of the planet carrier.
ii) If a torque of 500 Nm is applied to the ring gear, determine the torque transmitted to the planet carrier.

a) A shaft transmitting 50 kW at 200 rpm is supported by two collars. If the coefficient of friction is 0.05 and the diameter of the collar is 300 mm, calculate the friction torque.

b) A mechanism has 8 links and 12 pairs. Determine the degree of freedom using Kutzbach's criterion.

c) A four-bar linkage is designed with link lengths as follows:
Shortest link: 80 mm,
Second shortest link: 160 mm,
Third shortest link: 200 mm,
Longest link: 240 mm.
Tasks:
i) Check if the linkage satisfies the Grashof's condition.
ii) Identify which link (if any) can rotate continuously.