Sample Question Paper (Kinematics of Machines) Maximum marks: 75 Time allowed: 3 Hours Note: Attempt any five questions selecting at least two from each part. (Part – A) 1. (a) What is degree of freedom of a mechanism? How is it determined? (b) Define Grashof’s law. State how is it helpful in classifying the fourlink mechanisms into different types? (c) Find the maximum and minimum transmission angles for the mechanisms shown in Fig. 1. The figures indicate the dimensions in standard units of length. 5 5 5 S R G 300 350 3 b B a 1 A 200 O 120 o c 700 400 2 (mm) 3 Fig.1 2. P on slider Q on AR C d D A Fig. 2 Fig. 2 shows the link mechanism of a quick-return mechanism of the slotted lever type, the various dimensions of which are OA = 400 mm, OP = 200 mm, AR = 700 mm, RS = 300 mm. For the configuration shown determine the acceleration of the cutting tool at S and the angular acceleration of the link RS. The crank OP rotates at 210 rpm. 3. (a) What is Freudenstein’s equation? How is it helpful in designing a fourlink mechanism when three positions of the input (θ1, θ2, θ3) and the output link (ϕ1, ϕ2, ϕ3) are known? (b) Design a four-link mechanism when the motions of the input and the output links are governed by a function y = x2 and x varies from 0 to 2 15 5 with an interval of 1. Assume 80° to 160°. 4. to vary from 50° to 150° and from (a) Prove that a Kempe’s mechanism traces an exact straight line using two identical mechanisms. (b) The two shafts of a Hooke’s coupling have their axes inclined at 20°. The shaft A revolves at a uniform speed of 1000 rpm. The shaft B carries a flywheel of mass 30 kg. If the radius of gyration of the flywheel is 100 mm, find the maximum torque in shaft B. 10 8 7 (Part – B) 5. 6. 7. 8. (a) Why is a cycloidal motion programme the most suitable for high-speed cams? (b) The following data relate to a symmetrical circular cam operating a flat-faced follower: Minimum radius of the cam 40 mm Lift 24 mm Angle of lift 75o Nose radius 8 mm Speed of the cam 420 rpm Determine the main dimensions of the cam and the acceleration of the follower at (i) the beginning of the lift (ii) the end of contact with the circular flank (iii) the beginning of contact with the nose (iv) the apex of nose. (a) What are uniform pressure and uniform wear theories? Deduce expressions for the friction torque considering both the theories for a flat collar. (b) Explain the terms: friction circle, friction couple and friction axis. (c) Describe the working of a mitchell thrust bearing. T1 = e µθ for a flat belt drive with usual notations. (a) Derive the relation, T2 (b) A leather belt transmits 10 kW from a motor running at 600 rpm by an open-belt drive. The diameter of the driving pulley of the motor is 350 mm, centre distance between the pulleys 4 m and speed of the driven pulley 180 rpm. The belt weighs 1100 kg/m3 and the maximum allowable tension in the belt is 2.5 N/mm2. µ = 0.25. Find the width of the belt assuming the thickness to be 10 mm. Neglect the belt thickness to calculate the velocities. (a) State and prove the law of gearing. (b) In the epicyclic gear train shown in Fig. 3, the compound wheels A and B as well as internal wheels C and D rotate independently about the 3 12 7 3 5 7 8 5 axis O. The wheels E and F rotate on the pins fixed to arm a. All the wheels are of the same module. The number of teeth on the wheels are TA = 52, TB = 56, TE = TF = 36 Determine the speed of C if (i) the wheel D fixed and arm a rotates at 200 rpm clockwise (ii) the wheel D rotates at 200 rpm counter-clockwise and the arm a rotates at 20 rpm counter-clockwise. 10 E a A O F Fig. 3 B C D