Kinematics of M Kinematics of Machinery

KINEMATICS OF MACHINERY

Subject code: ME402PC Regulations: R18-JNTUH Class: II Year B. Tech MECH II Sem

Department of Mechanical Engineering BHARAT INSTITUTE OF ENGINEERING AND TECHNOLOGY Ibrahimpatnam - 501 510, Hyderabad

MECH II Yr – II Sem. 1

KINEMATICS OF MACHINERY (ME402PC) COURSE PLANNER OBJECTIVE AND RELEVANCE:

The main objective of Design technology is integration of technology with management in planning and controlling the design, development and operation of manufacturing system. Rapid advances in manufacturing technology, e.g., computer controlled processes and management information systems, ERP and new manufacturing concepts like TPS, agile manufacturing, pull system etc., are reinforcing the recognition of technological, organizational, economic and human factors.

COURSE PURPOSE: A branch of engineering that involves the design, control, and continuous improvement of integrated systems in order to provide customers with high-quality goods and services in a timely, cost-effective manner In product design, the Design engineering team works with the designers, helping them to develop a product that can be manufactured economically while preserving its functionality. Features of the product that will significantly increase its cost are identified, and alternative, cheaper means of obtaining the desired functionality are investigated and suggested to the designers.

SCOPE OF COURSE:

Mechanical engineers are responsible for ensuring design aspects as smoothly as possible, which includes the specifications related with design development and procurement of special production and laboratory equipments for new product, line extensions or operational improvement projects.

PRE-REQUISITES:

Knowledge of engineering mechanics is required

SYLLABUS: JNTU: UNIT – I Mechanisms: Elements or Links – Classification – Rigid Link, flexible and fluid link – Types of kinematics pairs – sliding, turning, rolling, screw and spherical pairs – lower and higher pairs – closed and open pairs – constrained motion – completely, partially or successfully and incompletely constrained. Mechanism and Machines – Mobility of Mechanisms: Grubler’s criterion, classification of machines – kinematics chain – inversions of mechanism – inversions of quadric cycle chain, single and double slider crank chains, Mechanical Advantage.

UNIT – II Kinematics: Velocity and acceleration – Motion of link in machine – Determination of Velocity and acceleration – Graphical method – Application of relative velocity method.

MECH II Yr – II Sem. 2

Plane motion of body: Instantaneous center of rotation- centrodes and axodes – Three centers in line theorem – Graphical determination of instantaneous center, determination of angular velocity of points and links by instantaneous center method. Kliens construction - Coriolis acceleration - determination of Coriolis component of acceleration Analysis of Mechanisms: Analysis of slider crank chain for displacement- velocity and acceleration of slider – Acceleration diagram for a given mechanism.

UNIT – III Straight-line motion mechanisms: Exact and approximate copied and generated types – Peaucellier - Hart - Scott Russel – Grasshopper – Watt -Tchebicheff’s and Robert Mechanism - Pantographs Steering gears: Conditions for correct steering – Davis Steering gear, Ackerman’s steering gear. Hooke’s Joint: Single and double Hooke’s joint –velocity ratio – application – problems.

UNIT – IV Cams: Definitions of cam and followers – their uses – Types of followers and cams – Terminology – Types of follower motion - Uniform velocity, Simple harmonic motion and uniform acceleration and retardation. Maximum velocity and maximum acceleration during outward and return strokes in the above 3 cases. Analysis of motion of followers: Tangent cam with Roller follower – circular arc cam with straight, concave and convex flanks.

UNIT – V Higher pair: Friction wheels and toothed gears – types – law of gearing, condition for constant velocity ratio for transmission of motion – velocity of sliding Forms of teeth, cycloidal and involutes profiles – phenomena of interferences – Methods of interference. Condition for minimum number of teeth to avoid interference – expressions for arc of contact and path of contact of Pinion & Gear and Pinion & Rack Arrangements– Introduction to Helical – Bevel and worm gearing

Gear Trains: Introduction – Types – Simple – compound and reverted gear trains – Epicyclic gear train. Methods of finding train value or velocity ratio of Epicyclic gear trains. Selection of gear box - Differential gear for an automobile.

GATE SYLLABUS: Theory of Machines: Displacement, velocity and acceleration analysis of plane mechanisms; dynamic analysis of slider-crank mechanism; gear trains

IES SYLLABUS: Kinematic and dynamic analysis of planer mechanisms. Cams. Gears and gear trains LESSON PLAN:

Course Teaching Lect UNIT REFER Topics to be covered Learning Methodolo No. No. ENCES Outcomes gy UNIT-1 Elements or Links – Classification – Rigid Chalk and 1 Understanding 3,4 Link Talk

MECH II Yr – II Sem. 3

Types of kinematic pairs – sliding, turning, Chalk and 2 1 Study 3,4 rolling, screw and spherical pairs Talk Lower and higher pairs – closed and open Chalk and 3 1 Understanding 3,4 pairs Talk Constrained motion – completely, Partially Chalk and 4 or successfully constrained and 1 Analysis 3,4 Talk incompletely constrained Revision MACHINES: Mechanism and machines Chalk and 5 1 Understanding 3,4 Classification of machines Talk Kinematic chain – inversion of mechanism Chalk and 6 1 Understanding 3,4 Talk Inversions of quadric cycle, chain Chalk and 7 1 Study 3,4 Talk Single and double slider crank chains Chalk and 8 1 Understanding 3,4 Talk Revision UNIT-2 3,4 Velocity and acceleration, Motion of link Chalk and 9 2 Study 3,4 in machine Talk Determination of Velocity and acceleration Chalk and 10 diagrams, Graphical method Application of 2 Analysis 3,4 relative velocity method four bar chain Talk Analysis of Mechanisms: Analysis of Chalk and 11 slider crank chain for displacement , 2 Analysis Talk Velocity and acceleration of slider Acceleration diagram for a given Chalk and 12 mechanism, Klein's construction, Coriolis 2 Analysis 3,4 Talk acceleration Determination of Coriolis component of Chalk and 13 acceleration, Plane motion of body: 2 Analysis Talk Instantaneous center of rotation Centroids and axodes – Relative motion between two bodies, Three centres in line Chalk and 14 2 Application 3,4 theorem – Graphical determination of Talk instantaneous centre Diagrams for simple mechanisms, Chalk and 15 2 Analysis 3,4 Talk Determination of angular velocity of points Chalk and 16 2 Analysis 3,4 and links Talk Revision 17 MOCK TEST – I UNIT-III Exact and approximate copiers and Chalk and 18 3 Analysis 3,4 generated types Talk Exact and approximate copiers and Chalk and 19 3 Analysis 3,4 generated types Talk

MECH II Yr – II Sem. 4

Peaucellier, Hart and Scott Russul Chalk and 20 3 Analysis 3,4 Talk Peaucellier, Hart and Scott Russul Chalk and 21 3 Analysis 3,4 Talk Grasshopper, Watt T. Chebicheff , Robert Chalk and 22 3 Analysis 3,4 Mechanisms Talk Grasshopper, Watt T. Chebicheff , Robert Chalk and 23 3 Analysis 3,4 Mechanisms Talk Straight line motion, Pantograph, Straight Chalk and 24 3 Analysis 3,4 line motion, Pantograph Talk Grasshopper, Watt T. Chebicheff , Robert Chalk and 25 3 Analysis 3,4 Mechanisms Talk Conditions for correct steering Chalk and 26 3 Analysis 3,4 Talk Davis Steering gear Chalk and 27 3 Analysis 3,4 Talk Ackerman’s steering gear – velocity ratio Chalk and 28 3 Analysis 3,4 Talk 29 HOOKE’S JOINT: Single Double Hooke’s joint Chalk and 30 3 Understanding 3,4 Talk Universal coupling Chalk and 31 3 Analysis 3,4 Talk Application – problems Chalk and 32 3 Understanding 3,4 Talk 33 Revision I Mid Examinations (Week 8) UNIT-IV Chalk and Analysis 3,4 Talk Definitions of cam and followers – their Chalk and 34 Analysis 3,4 uses – Terminology 4 Talk Definitions of cam and followers – their Chalk and 35 Analysis 3,4 uses – Terminology 4 Talk Types of followers and cams Chalk and 36 Understanding 3,4 4 Talk 37 Types of followers and cams 4 Understanding Chalk and 38 3,4 Revision 4 Talk Types of follower motion - Uniform Chalk and 39 Understanding 3,4 velocity (Max. & Min Acc) 4 Talk Chalk and 40 Types of follower motion – Simple Understanding 3,4 harmonic motion (Max. & Min Acc) 4 Talk Chalk and 41 Types of follower motion – Simple Understanding 3,4 harmonic motion (Max. & Min Acc) 4 Talk Chalk and 42 3,4 Revision 4 Talk 43 Analysis of motion of followers: Roller 4 Analysis Chalk and 3,4

MECH II Yr – II Sem. 5

follower flanks Talk Analysis of motion of followers: Roller Chalk and 44 Analysis 3,4 follower flanks 4 Talk Circular cam with straight flank Chalk and 45 Analysis 3,4 4 Talk Chalk and 46 Analysis 3,4 Circular cam with straight flanks 4 Talk Circular cam with concave and convex Chalk and 47 Analysis 3,4 flanks 4 Talk UNIT-V Higher pairs, friction wheels and toothed Chalk and 48 5 Understanding 3,4 gears Talk Chalk and 49 5 Understanding 3,4 Gears– types Law of gearing, Talk Condition for constant velocity ratio for Chalk and 50 5 Analysis 3,4 transmission of motion Talk Form of teeth: cycloid and involute Chalk and 51 5 Analysis 3,4 profiles, Velocity of sliding Talk 52 Revision Chalk and 53 5 3,4 Revision Talk Phenomena of interferences , Methods of Chalk and 54 5 Analysis 3,4 interference Talk Phenomena of interferences , Methods of Chalk and 55 5 Analysis 3,4 interference Talk Condition for minimum number of teeth to Chalk and 56 5 Analysis 3,4 avoid interference Talk 57 Revision Condition for minimum number of teeth to Chalk and 58 5 3,4 avoid interference Talk Expressions for arc of contact and path of Chalk and 59 5 Analysis 3,4 contact Talk Expressions for arc of contact and path of Chalk and 60 5 Analysis 3,4 contact Talk 61 Revision Chalk and 5 Understanding 3,4 Talk Introduction to Helical, Bevel and worm 62 Understanding gearing Introduction to Helical, Bevel and worm Chalk and 63 5 Understanding 3,4 gearing Talk Introduction, Train value – Types of gear Chalk and 64 5 Understanding 3,4 trains Talk Simple and reverted wheel train – Chalk and 65 5 Analysis 3,4 Epicyclic gear Talk Train. Methods of finding train value or Chalk and 66 5 Analysis 3,4 velocity ratio – Epicyclic gear trains Talk

MECH II Yr – II Sem. 6

Train. Methods of finding train value or Chalk and 67 5 Analysis 3,4 velocity ratio – Epicyclic gear trains Talk Selection of gear box-Differential gear for Chalk and 68 5 Understanding 3,4 an automobile Talk Selection of gear box-Differential gear for Chalk and 69 5 Understanding 3,4 an automobile Talk

SUGGESTED BOOKS: TEXTBOOK: 1.) Theory of machines by Thomas Bevan, CBS 2.) Theory of machines – R.K.Bansal 3.) Theory of machines – R.S.Khurmi & J.K.Gupta

REFERENCES: 4.) Theory of machines – Rattan S.S., TMH , 2009 Edition 5.) Theory of machines – PL. Ballaney/Khanna publishers 6.) Theory of machines – sadhu singh pearsons edition

QUESTION BANK: DESCRIPTIVE QUESTIONS: JNTUH:

UNIT 1

1. a) Define “Inversion” of a mechanism. Describe how the Pantograph can be considered as an inversion of four bar chain.

b) In a crank and slotted lever mechanism, the driving crank is 50 mm long, and the time ratio of cutting stroke to return stroke is 1.8. If the length of working stroke of the ram is 120 mm, find the distance between the fixed centres, and the slotted lever length.

2. a) Distinguish between completely constrained motion and incompletely constrained motion with suitable examples.

b) Prove that a four bar chain is a constrained kinematic chain

3. Describe with a neat sketch the elliptical trammel mechanism as an inversion of the double slider crank chain. 4. a) What is the difference between quick return motion of crank and slotted lever Type and that of whit worth type?

MECH II Yr – II Sem. 7

b) Find the distance between the _xed centers of a Whitworth quick return motion Mechanism if the length of driving link is 40mm, return stroke is 150mm And time ratio of cutting to return stroke is 2. 5. In a whit worth quick return mechanism, the distance between the fixed centres is 60 mm and the driving crank length is 80 mm. The length of the slotted lever is 160 mm, and the length of connecting rod is 140 mm. Calculate the ratio of the times of cutting and return strokes. (b) Draw a sketch of the above mechanism and describe its function.

Unit-2

1. A double slider crank mechanism is shown in the figure 1 below. The crank 2 rotates at a constant angular velocity of 10 rad/s. O A = 100mm; AB = AC = 200mm. 2

Figure-1

Determine the velocity of each slider using the Instantaneous centre method

2. One cylinder of rotary engine is shown in Figure 2b. OA is the _xed crank and 200 mm long. OP is the connecting rod and is 520 mm long. The line of stroke is along AR and at the instant is inclined at 30o to the vertical. The body of the engine Consisting of cylinders rotates at a uniform speed of 500 rpm about the fixed centre A. Determine, (a) Acceleration of piston (slider) inside the cylinder (b) Angular acceleration of the connecting rod.

MECH II Yr – II Sem. 8

Figure 2b

3. In the mechanism shown in Figure 3. The crank OA rotates at 50 rpm and the lengths of the links are OA= 125 mm, AC= 600 mm, QC= 150 mm, QD= 150 mm, CD= 130 mm, BD= 550 mm and OQ= 625 mm. When the angle AOQ= 45 Degrees, determine, (a) The linear acceleration of the slider at B. (b) The angular acceleration of the links AC, CQD and BD. 4. The crank and connecting rod of a reciprocating engine are 125 mm and 500 mm long 0 respectively. The crank makes an angle of 40 with the inner dead centre, and revolves at a uniform speed of 250 rpm. Find the acceleration of the slider by Klein’s construction method. 5. a) Explain how you determine the various instantaneous centres in a crossed four Bar mechanism. b) The crank and connecting rod of a reciprocating engine are 150 mm and 600 Mm long respectively. The crank makes an angle of 60O with the inner dead Centre, and revolves at a uniform speed of 300 rpm. Find the velocity of the Mid-point of the connecting rod by Klein's construction method.

Unit-3 1. a) What do you understand by straight line motion mechanisms? Name the different mechanisms which are used for achieving approximate straight line motion. b) Derive the condition to be satisfied by a mechanism required to produce an exact straight line motion, Determine the diameters of the cone pulley joined by crossed belt. The driven shaft is desired to be run at speed of 60, 90 and 120 rpm while the driving shaft rotates at 160rpm. The centre distance between the axes of the two shafts is 2.5m. The Smallest pulley diameter can be taken as 150mm. 2. Show how the Hart mechanism satisfies the condition for exact straight line motion 3. Write a short notes on Tchebicheff mechanism

4. a) A coupler AB to form a simple Watt mechanism joins two bars OA and O1B.When the mechanism is in its mean position, the lines OA and O1B are perpendicular to AB. If OA=16cm, O1B=24cm and AB=12cm, find the position Of point P on connecting link which gives the best straight line motion.

b) Sketch and Describe the Scott-Russell and Robert's straight-line motion mechanisms.

5. A vehicle is moving in a straight path. The distance between the pivots of the front axle of a Davis steering gear is 1.2 m and the wheel base is 2.7 m. Find the inclination of the track arm to the longitudinal axis of the vehicle. 6. a) For an Ackermann steering gear, derive the expression for the angle of inclination of the track arms to longitudinal axis of the vehicle.

MECH II Yr – II Sem. 9

b) A Hooke's joint connects two shafts whose axes intersect at 1500. The driving Shaft rotates uniformly at 120rpm. The driven shaft operates against a steady Torque of 150 Nm and carries a wheel whose mass is 45 Kg and radius of Gyration 150mm. Find the maximum torque which will be exerted by the Driving shaft. 7. Write short notes on: a) Successfully constrained motion with examples

b) Double Hooke’s joint 8. In a double Hooke’s joint, the angles of the driving and driven shafts with the intermediate shaft are each equal to 200. The driving shaft is rotating at 500 rpm. If the forks of the intermediate shaft lie in a plane perpendicular to each other, And the max and min speeds of the driven shaft.

UNIT-4 1. a) Derive the expression for the velocity and acceleration during out stroke and Return stroke of the follower when it is in the uniform acceleration? 0 b) A roller of diameter 8 mm is moved outwards through 30 mm during 180 of a 0 cam rotation with cyclical motion. The roller dwells for 20 of cam rotation, and 0 returns with uniform velocity during the remaining 160 of the cam rotation. The base circle diameter of the cam is 28 mm, and the axis of the follower is offset by 6 mm to the left. Draw the profile of the cam, and determine the maximum velocity and acceleration of the follower during the outstroke if the cam rotates at 1500 rpm counter clockwise 2. Explain the pressure angle of the cam and discuss how it is influenced by the base circle at the cam. (b) A cam with a minimum radius of 25mm is to be designed for a knife-edge Follower with the following data: i. To raise the follower through 35mm during 600 rotation of the cam. ii. Dwell for next 400 of the cam rotation. iii. Descent of the follower during the next 900 of the cam rotation. iv. Dwell during the rest of the cam rotation. 3. Draw the profile of the cam if the ascent and descent of the cam is with simple harmonic motion and the line of stroke of the follower is to offset 10mm from the axis of the camshaft. What is the maximum velocity and acceleration of the follower during the ascent and the descent if the cam rotates at 150rpm

UNIT – 5 1. An internal spur gear having 200 teeth meshes with a pinion having 40 teeth and a module of 2.5mm. Determine

(a) The velocity ratio if the pinion is the driver (b) The centre distance, and (c) If the centre distance is increased by 3mm, find the resulting pressure angle.

MECH II Yr – II Sem. 10

0 2. If the angle of obliquity of a pair of gear wheels is 20 , and the arc of approach or recess is not less than the pitch, what will be the least number of teeth on the pinion? b) Derive the expression for the path of contact between two mating spur gears.

3. a) Explain the law of congurate action on a gear teeth. b) A toothed gear A is to drive another toothed gear B. The centre distance Between the shafts is to be exactly 300mm. Speed of A is to be 300rpm and That of B is to be 200rpm approximately. If each gear is of module 2, determine What should be the number of teeth on each gear? 4. Determine the maximum power that can be transmitted through a at belt having the following data: cross section of the belt = 300mm * 12mm,Ratio of belt tensions = 2.2 Maximum permissible tension in belt = 2N/mm2 Mass density of the belt material = 0.0011 g/mm3. 5. How is the creep under varying conditions of belt material determined? 6. Determine the maximum power that can be transmitted using a belt of 100mm 10mm with an angle of lap of 160deg. The density of belt 1 gm/cc and the Coefficient of friction may be taken as 0.25. The tension in the belt should not Exceed1.5 N/mm2 1) Classify gear trains. 2) In an epicyclical gear train, the internal wheels A and B and compound wheel C and D rotate independently about axis O. The wheels E and F rotate on pins fixed to the arm G. E gears with A and C and F gears with B and D. All the wheels have the same module and the number of teeth is: TC = 28, TD = 26, TE = TF = 18. (a) Sketch the arrangement; (b) Find the number of teeth on A and B; (c) If arm G makes 100 rpm clockwise and wheel A makes 10 rpm counter clock-wise, and the speed of wheel B. 7. An Epicyclic gear train consists of a sun wheel S, a stationary internal gear E, and three identical planet wheels P carried on a star-shaped planet carrier C. The sizes of th the different wheels are such that the planet C rotates at 1/5 of the speed of sun wheel S. If the wheels S, E, and P have 16, 64, and 24 teeth respectively, find the torque needed to keep the internal gear stationary. The driving torque on the sun wheel S is 100 Nm. 8. The Epicyclic gear train known as Ferguson's paradox is shown in figure 7. Gear 1 is fixed to the frame. The arm A and gears 2 and 3 are free to rotate on the shaft S. Gears 1, 2 and 3 have 100, 101, and 99 teeth respectively. The planet gear has 20 teeth. The pitch circle diameter of all the gears is the same so that the plant gear P meshes with all of them. Determine the revolutions of gears 2 and 3 for one Revolution of the arm A.

MECH II Yr – II Sem. 11

Figure 7

OBJECTIVE QUESTIONS

JNTUH:

Unit -1

1. In a reciprocating steam engine, which of the following forms a kinematic link ?

(a) cylinder and piston (b) piston rod and connecting rod

2. The motion of a piston in the cylinder of a steam engine is an example of

(a) completely constrained motion (b) incompletely constrained motion

3. The motion transmitted between the teeth of gears in mesh is

(a) sliding (b) rolling

(d) partly sliding and partly rolling

4. The cam and follower without a spring forms a

MECH II Yr – II Sem. 12

(a) lower pair (b) higher pair

5. A ball and a socket joint forms a

(a) turning pair (b) rolling pair (c) sliding pair (d) spherical pair

6. The lead screw of a lathe with nut forms a

(a) sliding pair (b) rolling pair (c) screw pair (d) turning pair

7. When the elements of the pair are kept in contact by the action of external forces, the pair is said to be a

(a) lower pair (b) higher pair

8. Which of the following is a turning pair ?

(a) Piston and cylinder of a reciprocating steam engine

(b) Shaft with collars at both ends fitted in a circular hole

(d) Ball and socket joint

9. A combination of kinematic pairs, joined in such a way that the relative motion between the links is completely constrained, is called a

(a) structure (b) mechanism

10. The relation between the number of pairs ( p ) forming a kinematic chain and the number of links (l) is

(a) l = 2p – 2 (b) l = 2p – 3 (c) l = 2p – 4 (d) l = 2p – 5

11. The relation between the number of links (l) and the number of binary joints ( j) for a kinematic chain having constrained motion is given by j= l - 2If the left hand side of this equation is greater than right hand side, then the chain is

(a) locked chain (b) completely constrained chain

MECH II Yr – II Sem. 13

12. In a kinematic chain, a quaternary joint is equivalent to

(a) one binary joint (b) two binary joints

13. If n links are connected at the same joint, the joint is equivalent to

(a) (n – 1) binary joints (b) (n – 2) binary joints

14. In a 4 – bar linkage, if the lengths of shortest, longest and the other two links are denoted by s, l, p and q, then it would result in Grashof’s linkage provided that

(a) l + p < s + q (b) l + s < p + q (c) l + p = s + q (d) none of these

15. A kinematic chain is known as a mechanism when

(a) none of the links is fixed (b) one of the links is fixed

16. The Grubler’s criterion for determining the degrees of freedom (n) of a mechanism having plane motion is

(a) n = (l – 1) – j (b) n = 2 (l – 1) – 2j (c) n = 3 (l – 1) – 2j (d) n = 4 (l – 1) – 3j where l = Number of links and j = Number of binary joints.

17. The mechanism forms a structure, when the number of degrees of freedom (n) is equal to

(a) 0 (b) 1 (c) 2 (d) – 1

18. In a four bar chain or quadric cycle chain

(a) each of the four pairs is a turning pair (b) one is a turning pair and three are sliding pairs

19. Which of the following is an inversion of single slider crank chain ?

(a) Beam engine (b) Watt’s indicator mechanism

MECH II Yr – II Sem. 14

20. Which of the following is an inversion of double slider crank chain ?

(a) Coupling rod of a locomotive (b) Pendulum pump

Unit-2

1. The total number of instantaneous centres for a mechanism consisting of n links are (a) (b) n () (c) (d) 2. According to Aronhold Kennedy’s theorem, if three bodies move relatively to each other, their instantaneous centres will lie on a

(a) straight line (b) parabolic curve

3. In a mechanism, the fixed instantaneous centres are those centres which

(a) remain in the same place for all configurations of the mechanism

(b) vary with the configuration of the mechanism

(d) none of the above

Unit-3

1. In a pantograph, all the pairs are

(a) turning pairs (b) sliding pairs

2. Which of the following mechanism is made up of turning pairs ?

(a) Scott Russel’s mechanism (b) Peaucellier’s mechanism

MECH II Yr – II Sem. 15

3. Which of the following mechanism is used to enlarge or reduce the size of a drawing?

(a) Grasshopper mechanism (b) Watt mechanism

4. The Ackerman steering gear mechanism is preferred to the Davis steering gear mechanism, because

(a) whole of the mechanism in the Ackerman steering gear is on the back of the front wheels.

(b) the Ackerman steering gear consists of turning pairs

(d) both (a) and (b)

5. The driving and driven shafts connected by a Hooke’s joint will have equal speeds, if

(a) cos = sin (b) sin √tan

= Angle of inclination of the driving and driven shafts.

4. The instantaneous centres which vary with the configuration of the mechanism, are called

(a) Permanent instantaneous centres

(b) Fixed instantaneous centres

(d) None of these

5. When a slider moves on a fixed link having curved surface, their instantaneous centre lies

(a) on their point of contact (b) at the centre of curvature

6. The direction of linear velocity of any point on a link with respect to another point on the same link is

(a) parallel to the link joining the points (b) perpendicular to the link joining the points

MECH II Yr – II Sem. 16

7. The magnitude of linear velocity of a point B on a link AB relative to point A is

(a) AB (b) (AB)

8. The two links OA and OB are connected by a pin joint at O. If the link OA turns with angular velocity  rad/s in the clockwise direction and the link OB turns with angular velocity  rad/s in the anti-clockwise direction, then the rubbing velocity at the pin joint O is

(a)..r (b) ( – ) r

9. In the above question, if both the links OA and OB turn in clockwise direction, then the rubbing velocity at the pin joint O is

(a)..r (b) ( – ) r

10. In a four bar mechanism, as shown in Fig. 7.43, if a force is acting at point A in the direction of its velocity  and a force is transmitted to the joint B in the direction of its velocity  , then the ideal mechanical advantage is equal to

(a). (b) .

11. The component of the acceleration, parallel to the velocity of the particle, at the given instant is called

(a) radial component (b) tangential component

MECH II Yr – II Sem. 17

12. A point B on a rigid link AB moves with respect to A with angular velocity rad/s. The radial component of the acceleration of B with respect to A,

  (a)   AB (b)  × AB (c) (d) where  = Linear velocity of B with respect to A = × AB 13. A point B on a rigid link AB moves with respect to A with angular velocity rad/s. The angular acceleration of the link AB is

(a) (b)

 (c)  x AB (d) 14. A point B on a rigid link AB moves with respect to A with angular velocity rad/s. The total acceleration of B with respect to A will be equal to

(a) vector sum of radial component and coriolis component

(b) vector sum of tangential component and coriolis component

(d) vector difference of radial component and tangential component

15. The coriolis component of acceleration is taken into account for

(a) slider crank mechanism (b) four bar chain mechanism

Unit-4

1. The size of a cam depends upon

(a) base circle (b) pitch circle (c) prime circle (d) pitch curve

2. The angle between the direction of the follower motion and a normal to the pitch curve is called

(a) pitch angle (b) prime angle (c) base angle (d) pressure angle

3. A circle drawn with centre as the cam centre and radius equal to the distance between the cam centre and the point on the pitch curve at which the pressure angle is maximum, is called

MECH II Yr – II Sem. 18

(a) base circle (b) pitch circle (c) prime circle (d) none of these

4. The cam follower generally used in automobile engines is

(a) knife edge follower (b) flat faced follower (c) spherical faced follower (d) roller follower

5. The cam follower extensively used in air-craft engines is

(a) knife edge follower (b) flat faced follower (c) spherical faced follower (d) roller follower

6. In a radial cam, the follower moves

(a) in a direction perpendicular to the cam axis

(b) in a direction parallel to the cam axis

(d) along the cam axis

7. A radial follower is one

(a) that reciprocates in the guides (b) that oscillates

(d) none of the above

8. Offset is provided to a cam follower mechanism to

(a) minimise the side thrust (b) accelerate

9. For low and moderate speed engines, the cam follower should move with

(a) uniform velocity (b) simple harmonic motion

10. For high speed engines, the cam follower should move with

(a) uniform velocity (b) simple harmonic motion

11. Which of the following displacement diagrams should be chosen for better dynamic performance of a cam-follower mechanism ?

MECH II Yr – II Sem. 19

(a) simple hormonic motion (b) parabolic motion

12. For a given lift of the follower of a cam follower mechanism, a smaller base circle diameter is desired.

(a) because it will give a steeper cam and higher pressure angle.

(b) because it will give a profile with lower pressure angle

(d) none of the above.

13. The linear velocity of the reciprocating roller follower when it has contact with the straight flanks of the tangent cam, is given by

(a) ( − )sin (b) ( − )cos

= Minimum radius of the cam,

= Radius of the roller, and

= Angle turned by the cam from the beginning of the displacement for contact of roller with the straight flanks.

14. The displacement of a flat faced follower when it has contact with the flank of a circular arc cam, is given by

(a) R(1cos) (b) R(1sin) (c) (R  )(1cos) (d)(R  ) (1sin)

where R = Radius of the flank,

= Minimum radius of the cam, and

= Angle turned by the cam for contact with the circular flank.

15. The retardation of a flat faced follower when it has contact at the apex of the nose of a circular arc cam, is given by

(a) OQ (b) OQ sin

MECH II Yr – II Sem. 20

Unit-5

1. The two parallel and coplanar shafts are connected by gears having teeth parallel to the axis of the shaft. This arrangement is called

(a) spur gearing (b) helical gearing (c) bevel gearing (d) spiral gearing

2. The type of gears used to connect two non-parallel non-intersecting shafts are

(a) spur gears (b) helical gears (c) spiral gears (d) none of these

3. An imaginary circle which by pure rolling action, gives the same motion as the actual gear, is called

(a) addendum circle (b) dedendum circle (c) pitch circle (d) clearance circle

4. The size of a gear is usually specified by

(a) pressure angle (b) circular pitch (c) diametral pitch (d) pitch circle diameter

5. The radial distance of a tooth from the pitch circle to the bottom of the tooth, is called (a) dedendum (b) addendum (c) clearance (d) working depth

6. The product of the diametral pitch and circular pitch is equal to

(a) 1 (b) 1/(c) (d) 2

7. The module is the reciprocal of

(a) diametral pitch (b) circular pitch (c) pitch diameter (d) none of these

8. Which is the incorrect relationship of gears?

(a) Circular pitch × Diametral pitch = (b) Module = P.C.D/No.of teeth

9. If the module of a gear be m, the number of teeth T and pitch circle diameter D, then

(a) m = D/T (b) D = T/m (c) m = D/2T (d) none of these

10. Mitre gears are used for

MECH II Yr – II Sem. 21

(a) great speed reduction (b) equal speed

11. The condition of correct gearing is

(a) pitch line velocities of teeth be same

(b) radius of curvature of two profiles be same

(d) none of the above

12. Law of gearing is satisfied if

(a) two surfaces slide smoothly

(b) common normal at the point of contact passes through the pitch point on the line joining the centres of rotation

(d) addendum is greater than dedendum

13. Involute profile is preferred to cyloidal because

(a) the profile is easy to cut

(b) only one curve is required to cut

(d) none of the above

14. The contact ratio for gears is

(a) zero (b) less than one (c) greater than one

15. The maximum length of arc of contact for two mating gears, in order to avoid interference, is

(a) (r + R) sin (b) (r + R) cos (c) (r + R) tan (d) none of these where r = Pitch circle radius of pinion,

R = Pitch circle radius of driver, and Pressure angle.

MECH II Yr – II Sem. 22

16. When the addenda on pinion and wheel is such that the path of approach and path of recess are half of their maximum possible values, then the length of the path of contact is given by

( )  ( )  (a) (b)

( )  (c) (d) none of these 17. Interference can be avoided in involute gears with 20° pressure angle by

(a) cutting involute correctly

(b) using as small number of teeth as possible

(d) using more than 8 teeth

18. The ratio of face width to transverse pitch of a helical gear with as the helix angle is normally

(a) more than 1.15/tan (b) more than 1.05/tan 

19. The maximum efficiency for spiral gears is

() () (a) (b) () ()

() () (c) (d) () () where = Shaft angle, and = Friction angle.

20. For a speed ratio of 100, smallest gear box is obtained by using

(a) a pair of spur gears

(b) a pair of helical and a pair of spur gear compounded

(d) a pair of helical and a pair of worm gear compounded

MECH II Yr – II Sem. 23

where T = Number of teeth on the sprocket.

21. In a simple gear train, if the number of idle gears is odd, then the motion of driven gear will

(a) be same as that of driving gear

(b) be opposite as that of driving gear

(d) none of the above

22. The train value of a gear train is

(a) equal to velocity ratio of a gear train (b) reciprocal of velocity ratio of a gear train

23.When the axes of first and last gear are co-axial, then gear train is known as

(a) simple gear train (b) compound gear train

24.In a clock mechanism, the gear train used to connect minute hand to hour hand, is

(a) epicyclic gear train (b) reverted gear train

25.In a gear train, when the axes of the shafts, over which the gears are mounted, move relative to a fixed axis, is called

(a) simple gear train (b) compound gear train

26.A differential gear in an automobile is a

(a) simple gear train (b) epicyclic gear train

27.A differential gear in automobilies is used to

MECH II Yr – II Sem. 24

(a) reduce speed (b) assist in changing speed

ii) GATE QUESTIONS:

1. Which of the following mechanism is used to enlarge or reduce the size of a drawing?

(a) Grasshopper mechanism (b) Watt mechanism

2. The Ackerman steering gear mechanism is preferred to the Davis steering gear mechanism, because

(a) whole of the mechanism in the Ackerman steering gear is on the back of the front wheels.

(b) the Ackerman steering gear consists of turning pairs

(d) both (a) and (b)

3. The magnitude of linear velocity of a point B on a link AB relative to point A is

(a) AB (b) (AB)

where = Angular velocity of the link AB.

4. The two links OA and OB are connected by a pin joint at O. If the link OA turns with angular velocity  rad/s in the clockwise direction and the link OB turns with angular velocity  rad/s in the anti-clockwise direction, then the rubbing velocity at the pin joint O is

(a)..r (b) ( – ) r

5. In a radial cam, the follower moves

(a) in a direction perpendicular to the cam axis

MECH II Yr – II Sem. 25

(b) in a direction parallel to the cam axis

(d) along the cam axis

6. A radial follower is one

(a) that reciprocates in the guides (b) that oscillates

(d) none of the above

7. Two pulleys of diameters and and at distance x apart are connected by means of an open beltdrive. The length of the belt is

 ( )  ( ) (a) ( + )+2x+ (b) ( − )+2x+

 ( )  ( ) (c) ( + )+2x+ (d) ( − )+2x+

8. In a cone pulley, if the sum of radii of the pulleys on the driving and driven shafts is constant, then

(a) open belt drive is recommended

(b) cross belt drive is recommended

(d) the drive is recommended depending upon the torque transmitted

9. The train value of a gear train is

(a) equal to velocity ratio of a gear train (b) reciprocal of velocity ratio of a gear train

10. When the axes of first and last gear are co-axial, then gear train is known as

(a) simple gear train (b) compound gear train

11. In a clock mechanism, the gear train used to connect minute hand to hour hand, is

MECH II Yr – II Sem. 26

(a) epicyclic gear train (b) reverted gear train

1.The ratio of face width to transverse pitch of a helical gear with as the helix angle is normally

(a) more than 1.15/tan (b) more than 1.05/tan 

2. The maximum efficiency for spiral gears is

() () (a) (b) () ()

() () (c) (d) () () where = Shaft angle, and = Friction angle.

3. For a speed ratio of 100, smallest gear box is obtained by using

(a) a pair of spur gears

(b) a pair of helical and a pair of spur gear compounded

(d) a pair of helical and a pair of worm gear compounded

When the addenda on pinion and wheel is such that the path of approach and path of recess are half of their maximum possible values, then the length of the path of contact is given by

( )  ( )  (a) (b)

( )  (c) (d) none of these 4. Interference can be avoided in involute gears with 20° pressure angle by

(a) cutting involute correctly

MECH II Yr – II Sem. 27

(b) using as small number of teeth as possible

The radial distance of a tooth from the pitch circle to the bottom of the tooth, is called

(a) dedendum (b) addendum (c) clearance (d) working depth

5. The product of the diametral pitch and circular pitch is equal to

(a) 1 (b) 1/(c) (d) 2

6. Offset is provided to a cam follower mechanism to

(a) minimise the side thrust (b) accelerate

7. For low and moderate speed engines, the cam follower should move with

(a) uniform velocity (b) simple harmonic motion

8. For high speed engines, the cam follower should move with

(a) uniform velocity (b) simple harmonic motion

WEBSITES:

1) www.nptel.iitm.ac.in/courses.php 2) www.khannapublishers.in/categories.php 3) www.books.google.com 4) www.ebookee.org 5) www.sme.org 6) www.springer.com

SUBJECT EXPERTS: 1. Dr.Jayaram S R, MCE, Hassan 2. Prof.V.V.Bongale, MCE, Hassan 3. Dr.B.Suresh, NIE, Mysore 4. Prof.Y.M.Shashidhar, MCE, Hassan JOURNALS: 1) Modelling of Mechanical Systems 2) International Journal of Mechanical Sciences 3) Journal of Mechanical Working Technology 4) International Journal of Engineering Science and Research 5) Archives of Civil and Mechanical Engineering

MECH II Yr – II Sem. 28

6) International Journal of Engineering Science and Innovative Technology Impact Factor 7) International Journal of Engineering Science and Technology Impact Factor 8) International Journal of Engineering Science and Innovative Technology

SEMINARS:

1. Belt Rope and Chain Drives 2. STEERING Mechanisms 3. STRAIGHT LINE MOTION MECHANISMS 4. GEAR TRAINS

CASE STUDIES/SMALL PROJECTS: 1) Prepare the models of Inversions of 4 bar mechanisms 2) Single slider crank mechanism 3) Double slider crank mechanism 4) Cam and follower

MECH II Yr – II Sem. 29