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ME1252 KINEMATICS OF MACHINERY

(Common to Mechatronics Engineering)

(a) Instructions : 1. Answer ALL the questions.

(b) 2. Write brief procedure for graphical constructions.

(c) 3. Sketches should be drawn neatly.

(d) 4. Answers without units and with wrong units will carry less marks.

(e) 5. Symbols used should be explained atleast once in each solution.

(f) 6. Answers without writing the relevant equations and equations without substituting the data will carry ZERO

PART A — (10 ´ 2 = 20 marks)

1. How many inversions are possible from a four–bar kinematic chain? Name them based on their input–output motions.

2. What are the three conditions to obtain a four–bar crank–rocker mechanism?

3. Sketch the Geneva wheel indexing mechanism and state its application.

4. Distinguish normal component of acceleration and tangential component of acceleration.

5. State the advantages of cam mechanisms over linkage mechanisms.

6. Briefly write about undercutting in cam mechanisms.

7. State the relationship between circular pitch and the module.

8. Briefly write about reverted gear train with suitable sketch.

9. State the laws of dry friction.

10. The coefficient of friction between the belt and the pulley in a belt drive is 0.3. The angle of lap is 165°. If the tension on the tight side is 3000 N, determine the tension on the slack side.

PART B — (5 ´ 16 = 80 marks)

11. (i) Define transmission angle. Sketch a drag–link mechanism in maximum transmission angle and minimum transmission angle positions. (4)

(g) (ii) Define kinematic inversion. Describe in detail with neat sketches an elliptic trammel. (6)

(h) (iii) Design a four–bar crank rocker quick return mechanism for the following data : Rocker swing angle = 90°, Time ratio = 1.25 and output link length = 60 mm. (6)

12. (a) (i) How will you determine the magnitude and direction of the Coriolis Acceleration vector? (2)

(i) (ii) In a four–bar mechanism ABCD, the link lengths in mm are as follows : Input AB = 25, coupler BC = 85, output CD = 50 and frame AD = 60. The angle between the frame and the input is 100° measured anti–clockwise. The velocity of point B is 1.25 m/sec in the clockwise direction. Sketch the mechanism and determine the velocity and acceleration of the mid–point of the link BC. Also, find the angular velocity and angular accelerations of the links BC

and CD. (14)

Or

(j) (b) (i) State and prove the ARONHOLD–KENNEDY theorem involving instantaneous centres. (5)

(k) (ii) State the reasons for velocity and acceleration analysis. (3)

(l) (iii) Derive the analytical expressions to determine the angular position of the coupler and the angular position of the output link of a four bar crank–rocker mechanism in terms of the link lengths and input angular position. (8)

13. (a) (i) Sketch a cam–roller follower arrangement indicating important cam terminologies and explain them in detail. (8)

(m) (ii) Sketch and briefly compare the displacement, velocity and acceleration diagrams for uniform velocity, uniform acceleration and retardation, simple harmonic motion and cycloidal motion, used in cam mechanisms. (8)

Or

(n) (b) A disc cam used for moving a knife edge follower with simple harmonic motion during lift and uniform acceleration and retardation motion during return rotates in clockwise direction at 300 rpm. The line of motion of the follower has an offset 10 mm to the right of camshaft axis. The minimum radius of the cam is 30 mm. The lift of the follower is 40 mm. The cam rotation angles are : Lift 60°, dwell 90°, return 120° and remaining angle for dwell. Draw the cam profile and determine the maximum velocity and acceleration during the lift and return.

14. (a) Two gear wheels mesh externally to give a velocity ratio of 3 to 1. The involute teeth has 6 mm module and 20° pressure angle. Addendum is equal to one module. The pinion rotates at 90 rpm. Determine :

(i) Number of teeth on pinion to avoid interference and the corresponding number on the wheel (ii) the length of path and arc of contact (iii) contact ratio and (iv) the maximum velocity of sliding.

Or

(o) (b) In a reverted epicyclic gear train, the arm A carries two gears and and a compound gear . The gear meshes with gear and the gear meshes with gear . The numbers of teeth on , and are 80, 48 and 72 respectively. Find the speed and direction of gear when gear is fixed and arm A makes 400 rpm counter clockwise.

15. (a) (i) Prove or disprove the following statement : (p) ‘‘Angle of friction is equal to angle of repose’’. (6)

(q) (ii) A bolt is having V–threads. The pitch of the threads is 5 mm and the V–angle is 55°. The mean diameter of the bolt is 20 mm. The bolt is tightened by screwing a nut. The mean radius of the bearing surface of the nut is 25 mm. The load on the bolt is 5000 N. The coefficient of friction for nut and bolt is 0.1 whereas for nut and bearing surface is 0.16. Determine the force required at the end of a spanner 0.6 m long. (10)

Or

(r) (b) (i) Briefly explain the following :

(s) Slip of the belt and creep of the belt. (5)

(t) (ii) An open belt drive connects two pulleys of 1.2 m and 0.5 diameters on parallel shafts 4 m apart. The maximum tension in the belt is 1800 N. The coefficient of friction is 0.3. The driven pulley of diameter 1.2 m runs at 250 rpm. Calculate the length of the belt required, the power transmitted, and the torque on each of the two

shafts. (11)

TIRUCHIRAPPALLI/TRICHY

B.E./B.Tech. DEGREE EXAMINATION, APRIL/MAY 2003.

Third Semester

Mechanical Engineering

ME1252 KINEMATICS OF MACHINERY

(Common to Mechatronics Engineering)

(a) Instructions : 1. Answer ALL the questions.

(b) 2. Write brief procedure for graphical constructions.

(c) 3. Sketches should be drawn neatly.

(d) 4. Answers without units and with wrong units will carry less marks.

(e) 5. Symbols used should be explained atleast once in each solution.

(f) 6. Answers without writing the relevant equations and equations without substituting the data will carry ZERO

PART A — (10 ´ 2 = 20 marks)

1. How many inversions are possible from a four–bar kinematic chain? Name them based on their input–output motions.

2. What are the three conditions to obtain a four–bar crank–rocker mechanism?

3. Sketch the Geneva wheel indexing mechanism and state its application.

4. Distinguish normal component of acceleration and tangential component of acceleration.

5. State the advantages of cam mechanisms over linkage mechanisms.

6. Briefly write about undercutting in cam mechanisms.

7. State the relationship between circular pitch and the module.

8. Briefly write about reverted gear train with suitable sketch.

9. State the laws of dry friction.

10. The coefficient of friction between the belt and the pulley in a belt drive is 0.3. The angle of lap is 165°. If the tension on the tight side is 3000 N, determine the tension on the slack side.

PART B — (5 ´ 16 = 80 marks)

11. (i) Define transmission angle. Sketch a drag–link mechanism in maximum transmission angle and minimum transmission angle positions. (4)

(g) (ii) Define kinematic inversion. Describe in detail with neat sketches an elliptic trammel. (6)

(h) (iii) Design a four–bar crank rocker quick return mechanism for the following data : Rocker swing angle = 90°, Time ratio = 1.25 and output link length = 60 mm. (6)

12. (a) (i) How will you determine the magnitude and direction of the Coriolis Acceleration vector? (2)

(i) (ii) In a four–bar mechanism ABCD, the link lengths in mm are as follows : Input AB = 25, coupler BC = 85, output CD = 50 and frame AD = 60. The angle between the frame and the input is 100° measured anti–clockwise. The velocity of point B is 1.25 m/sec in the clockwise direction. Sketch the mechanism and determine the velocity and acceleration of the mid–point of the link BC. Also, find the angular velocity and angular accelerations of the links BC

and CD. (14)

Or

(j) (b) (i) State and prove the ARONHOLD–KENNEDY theorem involving instantaneous centres. (5)

(k) (ii) State the reasons for velocity and acceleration analysis. (3)

(l) (iii) Derive the analytical expressions to determine the angular position of the coupler and the angular position of the output link of a four bar crank–rocker mechanism in terms of the link lengths and input angular position. (8)

13. (a) (i) Sketch a cam–roller follower arrangement indicating important cam terminologies and explain them in detail. (8)

(m) (ii) Sketch and briefly compare the displacement, velocity and acceleration diagrams for uniform velocity, uniform acceleration and retardation, simple harmonic motion and cycloidal motion, used in cam mechanisms. (8)

Or

(n) (b) A disc cam used for moving a knife edge follower with simple harmonic motion during lift and uniform acceleration and retardation motion during return rotates in clockwise direction at 300 rpm. The line of motion of the follower has an offset 10 mm to the right of camshaft axis. The minimum radius of the cam is 30 mm. The lift of the follower is 40 mm. The cam rotation angles are : Lift 60°, dwell 90°, return 120° and remaining angle for dwell. Draw the cam profile and determine the maximum velocity and acceleration during the lift and return.

14. (a) Two gear wheels mesh externally to give a velocity ratio of 3 to 1. The involute teeth has 6 mm module and 20° pressure angle. Addendum is equal to one module. The pinion rotates at 90 rpm. Determine :

(i) Number of teeth on pinion to avoid interference and the corresponding number on the wheel (ii) the length of path and arc of contact (iii) contact ratio and (iv) the maximum velocity of sliding.

Or

(o) (b) In a reverted epicyclic gear train, the arm A carries two gears and and a compound gear . The gear meshes with gear and the gear meshes with gear . The numbers of teeth on , and are 80, 48 and 72 respectively. Find the speed and direction of gear when gear is fixed and arm A makes 400 rpm counter clockwise.

15. (a) (i) Prove or disprove the following statement : (p) ‘‘Angle of friction is equal to angle of repose’’. (6)

(q) (ii) A bolt is having V–threads. The pitch of the threads is 5 mm and the V–angle is 55°. The mean diameter of the bolt is 20 mm. The bolt is tightened by screwing a nut. The mean radius of the bearing surface of the nut is 25 mm. The load on the bolt is 5000 N. The coefficient of friction for nut and bolt is 0.1 whereas for nut and bearing surface is 0.16. Determine the force required at the end of a spanner 0.6 m long. (10)

Or

(r) (b) (i) Briefly explain the following :

(s) Slip of the belt and creep of the belt. (5)

(t) (ii) An open belt drive connects two pulleys of 1.2 m and 0.5 diameters on parallel shafts 4 m apart. The maximum tension in the belt is 1800 N. The coefficient of friction is 0.3. The driven pulley of diameter 1.2 m runs at 250 rpm. Calculate the length of the belt required, the power transmitted, and the torque on each of the two

shafts. (11)