Mechanics of Machines

SATHYABAMA UNIVERSITY

(Established under section 3 of UGC Act, 1956)

Course & Branch: B.E - Mechanical & Production/ Aeronautical  

Title of the paper: Mechanics of Machines

Semester: IV                                                               Max. Marks: 80     

Sub.Code: 6C0070                                                     Time: 3 Hours

Date: 28-04-2008                                                         Session: FN       

                                                PART – A                       (10 x 2 = 20)

Answer All the Questions

1.     Define: Grashoff’s law.

2.     Draw a four bar mechanism and show that it has one degree of freedom as per Kutzbach criterion.

3.     What is meant by balancing?

4.     What is the cause for swaying coupling?

5.     Construct the displacement diagram for the follower motion to be cycloidal.

6.     Define law of gearing?  

7.     Write the equation to determine the efficiency of a screw jack.

8.     Define velocity ratio.

9.     What is viscous damping?

10.   Define single degree of freedom.

PART – B                       (5 x 12 = 60)

Answer All the Questions

11.   Sketch and explain the following inversions of a double slider crank chain.     

        (i) Elliptic trammel

        (ii) Scotch yoke mechanism

        (iii) Oldham’s coupling.

(or)

12.   A four bar linkage has following dimensions:

        Crank AO₂ = 150mm                      Link AB = 450 mm

        Link BO₄ = 300 mm                       Link O₂O₄ = 200 mm

        Link O₂O₄ is fixed.

Find the angular acceleration of links AB and BO₄ when  the crank is rotating with a constant angular velocity of 200 rad/s counter clockwise and also positioned 45° to horizontal.

13.   Four masses m₁= 90 kg; m₂ = 180 kg; m₃ = 210 kg and m₄ = 140 kg are fixed to the cranks of 250 mm radius and revolve in planes 1,2,3 and 4 respectively.  The angular position of the cranks in the planes 2,3 and 4 with respect to the crank in plane 1 are 70°, 140° and 245° taken in the same sense.  The distance of planes 2,3 and 4 from plane 1 are 500 mm, 1500 mm and 2500 mm respectively.  Determine the position and magnitude of the balancing mass at the radius at 300 mm in planes L and M located at the middle of planes 1 and 2 and middle of planes 3 and 4 respectively.

(or)

14.   A four cylinder  vertical engine has cranks 300 mm long.  The planes of rotation of the first, third and fourth cranks are 750 mm, 1050mm and 1650 mm respectively from that of the second crank and their reciprocating masses are 150 kg, 400 kg and 250 kg respectively.  Find the mass of the reciprocating parts for the second cylinder and relative angular position of the cranks in order that the engine may be in complete primary balance.

15.   The following data are for the a disc cam mechanism with roller follower:

        Minimum radius of the cam   =      35 mm.

        Lift of the follower                 =      40 mm.

        Roller diameter                       =      15 mm.

        Cam rotation angles are as mentioned below:

                        During ascent = 120°,    Dwell = 80°

                        During descent = 80°,     Dwell = 80°

        Cam rotates in clockwise direction and the follower motion is uniform acceleration during both ascent and descent.  Draw the displacement diagram and cam profile of the follower and indicate the relevant data.

(or)

16.   A pair of involute spur gears with 16° pressure angle and pitch of module 6 mm is in mesh.  The number of teeth in pinion is 16 and its rotational speed is 240 rpm.  The gear ratio is 1.75.  In order to avoid the interference, determine

                (iv) Addenda on pinion and wheel.

                (v) Length of path of contact.

(vi) Maximum velocity of sliding on either side of pitch point.

17.   A square threaded bolt of root diameter 22.5 mm and pitch 5 mm is tightened by screwing a nut whose mean diameter of bearing surface is 50 mm.  If the coefficient of friction between nut and bolt is 0.1 and nut and bearing surface is 0.16, determine the force required at the end of spanner 500 mm long when the load on the bolt is 10 kN.

(or)

18.   A belt drive is required to transmit 12 kW from a motor running at 720 rpm.  The belt is 12 mm thick and has a mass density of 0.003 gm/mm³. Safe stress in the belt is not to exceed 2.5 N/mm². Diameter of driving pulley is 250 mm where as the speed of the driven pulley is 240 rpm.  The two shafts are 1.25 m apart.  Coefficient of friction is 0.25.  Determine the width of the belt.

19.   A cantilever shaft of 50 mm diameter, 300 mm long has a disc of 100 kg attached to the free end.  The Young’s modulus is 200 GN/m². Determine (i) Frequency of longitudinal vibration (ii) Frequency of transverse vibration.

(or)

20.   A shaft 25 mm diameter and 0.5 m long carries a mass of 2 kg at its mid point. The density of shaft material = 40 x 10³ kg/m³, E = 200 GN/m². Assume shaft is freely supported.  Calculate the whirling speed of shaft?