kom basics of mechanisms

7/31/2019 Kom Basics of Mechanisms

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SUGGESTED READINGS :

1. Khurmi,R.S and Guptha,J.K - Theory of machines

2. Ballaney,P.LTheory of machines

3. Rattan,S.S - Theory of machines

4. Jayakumar,V - Kinematics of machinery

5. Green,W.G - Theory of machines

6. Shigley,J.E - Mechanical Engineering7. Malhotra,D.R and Guptha,H.CTheory of machines

8. Abdulla Shariff and Shariff,N.A - Theory of machines

9. John Hannah and Stephens,R.CMechanics of machines


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1. BASICS OF MECHANISMS

2. KINEMATIC ANALYSIS

3. KINEMATICS OF CAM

4. GEARS

5. FRICTION

SYLLABUS :


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BASICS

OF

MECHANISMS

UNIT : 1


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BASICS OF MECHANISMS:

1.Terminology and Definitions

2.Degree of freedom.

3.Mobility

4.Kutzbach criterion(Grueblers equation)

5.Grashoffs law.

6.Kinematic inversions of 4-bar chain and slider crankchains.

7.Mechanical advantage.

8.Transmission angle.

:


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BASICS OF MECHANISMS:

9.Description of common mechanisms-offset slidermechanism as quick return mechanisms

10.Pantograph

11.Straight line generators (Peaucellier & Wattmechanisms)

12. Steering gear for automobile13.Hookes joint

14.Toggle mechanism15.Ratchets and escapements16.Indexing mechanisms


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It is branch of science which deals with the study of relative

motion between the various parts of a machine, and force

which acts on them.


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TYPE :

Divided into

1.Kinematics (no force consider)

2.Dynamics. (force consider)

i) kineticsii) statics


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It is a device which receives energy and transforms it intosome useful work.EXAMPLE:

fig


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It is the part of a machine which has motion relative tosome other part.

CHARACTERISTICS:

1.It should have relative motion and

2.It should be a resistant body


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TYPES OF LINK :

Three Types:

1.Rigid link (connecting rod and crank pin)

2.Flexible link (belt, ropes, chains, spring)

3.Fluid link (fluid in hydraulic press, jack, crane)


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Structure is an assemblage of number of resistant bodieshaving no relative motion between them.

EXAMPLE:

Roof trusses, bridges, buildings, machine frames.


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The two links or element of a machine, when in contactwith each other, are said to form a pair. If the relativemotion between them is completely or successfully

constrained, the pair is known as kinematic pair.

fig

EXAMPLE: Crank and connecting rod, Piston and enginecylinder.


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CLASSIFICATION OF KINEMATIC PAIR :

1.Type of contact:lower pair, higher pair.

2.Type of relative motion:sliding pair, turning pair, rolling pair, screw pair,spherical pair.

3. Type of constraint:

closed pair, unclosed pair.


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CLASSIFICATION OF KINEMATIC PAIR :

1.LOWER PAIR:

2.HIGER PAIR:

3.SLIDING PAIR:

4.TURNING PAIR:

9.UNCLOSED PAIR:

6.SCREW PAIR:

7.SPHERICAL PAIR:

8.CLOSED PAIR:

5.ROLLING PAIR:


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1.LOWER PAIR:

A kinematic pair is known as lower pair if the two linkshas surface contact or area contact between them. Alsothe contact surfaces are similar. Eg.: shaft rotating in abearing and Nut turning on a screw.


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2.HIGER PAIR:


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3.SLIDING PAIR:


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4.TURNING PAIR:


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5.ROLLING PAIR:


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6.SCREW PAIR:


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7.SPHERICAL PAIR:


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When the motion between the pair is limited to a definitedirection then the motion is said to be a constrainedmotion.

TYPES OF CONSTRAINED MOTION :

1. Completely constrained motion.

2. Incompletely constrained motion.

3. Successfully constrained motion.

TYPES OF CONSTRAINED MOTION


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TYPES OF CONSTRAINED MOTION :

1.Completely constrained motion.

2. Incompletely constrained motion 3. Successfully constrainedmotion.


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A Kinematic chain is defined as a combination of kinematic

pair, joined in such a way that the relative motion betweenthe links or elements is completely or successfully constrained.

To determine the given assemblage oflinks forms the kinematic chain or not:

The two equations are:

1. l = 2p - 4

2. J = 3/2 * l - 2

l = number of linksp = number of pairsj = number of joints

Three possible cases are:

(ii) If L.H.S>R.H.S

(i) If L.H.S=R.H.S

(iii) If L.H.S


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ILLUSTRATIONS:

1.Arrangement of three links:

2.Arrangement of four links:

3.Arrangement of five links:

4.Arrangement of six links:


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1.Arrangement of three links:

Link-1

Link-2Link-3

A B

C

Number of links, l=3

Number of pair, p=3Number of joints j=3

1. l = 2p - 4

3 = 2 * 3 - 43 = 2L.H.S>R.HS

2. J = 3/2 * l - 2

3 = 3/2*3 - 23 = 2.5L.H.S>R.HS


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2.Arrangement of four links:

l = 4p = 4j = 4

1. l = 2p - 4

4 = 2 * 4 - 44 = 4L.H.S=R.H.S

2. J = 3/2 * l - 2

4= 3/2*4 - 24 = 4L.H.S=R.H.S

Link-1

Link-2

Link-3

Link-4

A B

C

D


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3.Arrangement of five links:

l = 5p = 5j = 5

1. l = 2p - 4

5 = 2 * 5 - 45 = 6L.H.S


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4.Arrangement of six links:

l = 6p = 5j = 7

1. l = 2p - 4

6 = 2 * 5 - 46 = 6

L.H.S=R.H.S

2. J = 3/2 * l - 2

7 = 3/2*6 - 27 = 7L.H.S=R.H.S

Link-1

Link-2

Link-3

Link-4

Link-5

Link-6

A B

CD

E

F


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The usual types of joints in a chain are:

1.Binary joint 2.Ternary joint 3.Quaternary joint

A.W.Kliens criterion of constraint:

J +h/2 = 3/2 * l - 2 l = number of linksh = number of higher pairs

j = number of binary joints


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A.W.Kliens criterion of constraint: J +h/2 = 3/2 * l - 2

j=4; l=4; h=0

j+h/2 = 3/2*l - 24+0 = 3/2*4 - 24 = 4L.H.S=R.H.S

j=7; l=6; h=0

j+h/2 =3/2*l - 27+0 =3/2*6 - 27 =7L.H.S=R.H.S

j=12; l=9; h=0

j+h/2 = 3/2*l - 212+0 = 3/2*9 - 212 = 11.5L.H.S>R.H.S


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Degree of freedom is defined as the number of independentmotion (both translation and rotational) a body can have.

fig

1.A body have 6 independent motions.2.This body is said to have 6 degrees of freedom.3.Mathematically degree of freedom in a space is given by

Degree of freedom=6-number of constraints


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n = 3(l 1) 2j - h

l = number of linksh = number of higher pairsj = number of binary joints or lower pairs

n = number of degree of freedom.

1.Application of kutzbach criterion to plane mechanismsmechanisms with lower pair:

(i) three bar (ii) four bar (iii) five bar (iv) six barmechanisms with higher pair:(i) cam and follower.

2.Application of kutzbach criterion to spatial mechanisms


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1.Three bar: 2.Four bar: 1.Five bar:

1.Six bar:


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Mechanism with higher pair


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1.Three bar mechanism:

n = 3(l 1) 2j - h

l = 3j = 3

n = 3(3-1) 2 * 3n = 0

Structure, no motion


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2.Four bar mechanism:

n = 3(l 1) 2j - h

l = 4j = 4

n = 3(4-1) 2 * 4n = 1

Mechanism is driven by single input motion


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3. Five bar mechanism: n = 3(l 1) 2j - h

l = 5j = 5

l = 5j = (f)=6

n = 3(5-1) 2 * 4n = 2

n = 3(5-1) 2 * 6n = 0

To drive, two input motionStructure, no motion


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1.Six bar mechanism:

l = 6j = 6

l = 6j = (f)=7

l = 6j = (f)=8

n = 3(6-1) 2 * 6n = 3

n = 3(6-1) 2 * 7n = 1

n = 3(6-1) 2 * 8n = -1

To drive, 3 input

motion

To drive, 1 inputmotion

Staticallyindeterminatestructure.

n = 3(l 1) 2j - h


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l = 3j = 2h = 1

n = 3(l 1) 2j - h

n = 3(3-1) (2 * 2) - 1n = 1

Mechanism is driven by single input motion


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l = 4j = 3

h = 1

n = 3(l 1) 2j - h

n = 3(4-1) (2 * 3) - 1n = 2

To drive, two input motion


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KUTZBACH CRITERION FOR SPATIAL MECHANISMS:

n = 6(l 1) 5p1 4p2 3p3 2p4 1p5

l = number of linksn = number of degree of freedomp1=number of pair having one degree of freedomp2=number of pair having two degree of freedom


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GRUBLERS CRITERION FORPLANE MECHANISM:

GRUBLERS CRITERION FORSPATIAL MECHANISM:

3l 2j 4 = 0

6l 5p1 7 = 0

l = total number of linksp1 = number of pairs having single degree of

freedom


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- When one of the links of kinematic chain is fixed, thenthe chain is known as mechanism.

- To transmit motion.

- type writers

TYPES: 1.SIMPLE . 2.COMPOUND

Four link More than 4 links

INVERSION OF MECHANISM:The method of obtaining different mechanisms by fixingdifferent links in a kinematic chain, is known as inversion of themechanism


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Grashofs law states that the sum of the shortest andlongest links cannot be greater than the sum of theremaining two links lengths, if there is to be continuousRelative motion between two members.

l = length of the longest link.s = length of the shortest link.p & q = length of the other two links.

s + l < p + q

fig


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1.Four bar chain

2.Single slider crank

3.Double slider crank

(i) Beam engine (crank and lever mechanism)(ii) Coupling rod of a locomotive (double crank mechanism)(iii) watts indicator mechanism (double lever mechanism)

(iv) Pantograph (v) Ackermann steering

(i) Pendulum pump (bull engine) (ii) Oscillating cylinder engine

(ii) rotary internal combustion engine (gnome engine)(iii) Crank and slotted lever quick return motion

(i) Elliptical trammels. (ii) scotch yoke mechanism

(iii) Oldhams coupling.


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(i) Beam engine (crank and lever mechanism)


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(ii) Coupling rod of a locomotive (double crank mechanism)


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(iii) watts indicator mechanism (double lever mechanism)


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(iv) Pantograph (v) Ackermann steering


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(i) Pendulum pump (bull engine)


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(ii) Oscillating cylinder engine


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(iii) rotary internal combustion engine (gnome engine)


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(iv) Crank and slotted lever quick return motion


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(i) Elliptical trammels.

(iii) Oldhams coupling


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(iii) Oldham s coupling.

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