Unit-i Basics of Machines

8/8/2019 Unit-i Basics of Machines

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UNIT I BASICS OF MACHINES

DefinitionsKinematic linkor simply link

Each part of a machine, which moves relative to some other part, is known as a

kinematic link (or simply link) or element.

Example: Reciprocating Steam Engine

A link should have the following two characteristics:

1. It should have relative motion2. It must be a resistant body (capable of transmitting the required forces

with negligible deformation)

Types of Links

In order to transmit motion, the driver and the follower may be connected by the

following three types of links:

1. Rigid link. A rigid link is one which does not undergo any deformationwhile transmitting motion. Strictly speaking, rigid links do not exist. However, as

the deformation of a connecting rod, crank etc. of a reciprocating steam engine is

not appreciable, they can be considered as rigid links.

Binary link A link has two ends is called Binary link. Ternary link A link which forms three connections is called Ternary

link.

Quaternary link A link having four ends is known as Quaternary link2. Flexible link. A flexible link is one which is partly deformed in a manner notto affect the transmission of motion. For example, belts, ropes, chains and wires

are flexible links and transmit tensile forces only.

3. Fluid link. A fluid link is one which is formed by having a fluid in areceptacle and the motion is transmitted through the fluid by pressure or

compression only, as in the case of hydraulic presses, jacks and brakes.


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Kinematic Pair

The two links or elements of a machine, when in contact with each other, are said toform a pair. If the relative motion between them is completely or successfully constrained(i.e. in a definite direction), the pair is known as kinematic pair.

Classification of Kinematic Pairs

1.According to the type of relative motion between the elements.The kinematic pairs according to type of relative motion between the elements may

be classified as discussed below:


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(a)Sliding pair.When the two elements of a pair are connected in such a way that one can only

slide relative to the other, the pair is known as a sliding pair. The piston and cylinder,

cross-head and guides of a reciprocating steam engine, ram and its guides in shaper, tail

stock on the lathe bed etc. are the examples of a sliding pair. A little consideration will

show, that a sliding pair has a completely constrained motion.(b) Turning pair.

When the two elements of a pair are connected in such a way that one can onlyturn or revolve about a fixed axis of another link, the pair is known as turning pair. A

shaft with collars at both ends fitted into a circular hole, the crankshaft in a journal

bearing in an engine, lathe spindle supported in head stock, cycle wheels turning overtheir axles etc. are the examples of a turning pair. A turning pair also has a completely

constrained motion.

(c) Rolling pair.

When the two elements of a pair are connected in such a way that one rolls overanother fixed link, the pair is known as rolling pair. Ball and roller bearings are examples

of rolling pair.(d)Screw pair.When the two elements of a pair are connected in such a way that one element can

turn about the other by screw threads, the pair is known as screw pair. The lead screw of

a lathe with nut, and bolt with a nut are examples of a screw pair.

(e)Spherical pair.

When the two elements of a pair are connected in such a way that one element

(with spherical shape) turns or swivels about the other fixed element, the pair formed is

called a spherical pair. The ball and socket joint, attachment of a car mirror, pen standetc., are the examples of a spherical pair.

2. According to the type of contact between the elements. The kinematic pairs

according to the type of contact between the elements may be classified as discussedbelow:

(a)Lower pair.When the two elements of a pair have a surface contact when relative motion

takes place and the surface of one element slides over the surface of the other, the pair

formed is known as lower pair. It will be seen that sliding pairs, turning pairs and screwpairs form lower pairs.

(b)Higher pair.

When the two elements of a pair have a line or point contact when relative motiontakes place and the motion between the two elements is partly turning and partly

sliding,then the pair is known as higher pair. A pair of friction discs, toothed gearing, belt

and rope drives, ball and roller bearings and cam and follower are the examples of higher

pairs.

3.According to the type of closure. The kinematic pairs according to the type of closurebetween the elements may be classified as discussed below :

(a)Self closed pair.

When the two elements of a pair are connected together mechanically in such away that only required kind of relative motion occurs, it is then known as self closed pair.

The lower pairs are self closed pair.


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(b)Force - closed pair.

When the two elements of a pair are not connected mechanically but are kept incontact by the action of external forces, the pair is said to be a force-closed pair. The cam

and follower is an example of force closed pair, as it is kept in contact by the forces

exerted by spring and gravity.

Kinematic Chain

When the kinematic pairs are coupled in such a way that the last link is joined to the

first link to transmit definite motion (i.e. completely or successfully constrained motion),

it is called akinematic chain.

Examples for Kinematic Chain


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MechanismWhen one of the links of a kinematic chain is fixed, the chain is known as

mechanism. It may be used for transmitting or transforming motion.

ApplicationsEngine indicatorsTypewriter


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Standard mechanisms

Figure 1. Plane linkwork Figure 2. Cam mechanism

Grublers Criterion for Plane MechanismsSince in a kinematic chain each link forms a part of two pairs, therefore there

will be as many links as the number of pairs.

Relation between the number of links (l) and the number of joints ( j ) which

constitute a kinematic chain is given by the expression :

j = (3/2) l- 2

MachineA mechanism with four links is known as simple mechanism, and the mechanism

with more than four links is known as compound mechanism. When a mechanism isrequired to transmit power or to do some particular type of work, it then becomes a

machine.


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Degrees of Freedom:It is defined as the number of input parameters (usually pair variables) which

must be independently controlled in order to bring the mechanism into a useful

engineering purpose.An unconstrained rigid body moving in space can describe the following

independent motions.

1. Translational Motions along any three mutually perpendicular axes x, y and z

2. Rotational motions along these axes.

Thus a rigid body possesses six degrees of freedom. The connection of a link with

another imposes certain constraints on their relative motion. The number of restraints cannever be zero (joint is disconnected) or six (joint becomes solid).

Degrees of freedom of a pair is defined as the number of independent relativemotions, both translational and rotational, a pair can have.

Degrees of freedom = 6 no. of restraints.

To find the number of degrees of freedom for a plane mechanism we have an

equation known as Grublers equation and is given by

F = 3 (n 1) 2j h

F = Mobility or number of degrees of freedomn = Number of links including frame.j = Joints with single (one) degree of freedom.h = number of higher pair.

F > 0, results a mechanism with F degrees of freedom.F = 0, results in a statically determinate structure.F < 0, results in a statically indeterminate structure.


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Type of joint Nature of Motion Degrees of freedom

Hinges (Revolute)

Slider (prismatic)

Cylindrical, Cam, Gear andBall Bearings

Rolling Contact

Spherical

Pure rolling

Pure Sliding

Rolling and Sliding

Pure Rolling

1

1

2

1

3

Inversion of MechanismWhen one of links is fixed in a kinematic chain, it is called a mechanism. So we

can obtain as many mechanisms as the number of links in a kinematic chain by fixing, in

turn, different links in a kinematic chain. This method of obtaining different mechanismsby fixing different links in a kinematic chain is known as inversion of the mechanism.

Types of Kinematic Chain:1) Four bar chain

2) Single slider chain

3) Double Slider chain

1) Four bar Chain:

The chain has four links and it looks like a cycle frame and hence it is

also called quadric cycle chain. It is shown in the figure. In this type of chain all four

pairs will be turning pairs.

Inversions of four bar chain mechanism:

There are three inversions:1) Beam Engine or Crank and lever mechanism.

2) Coupling rod of locomotive or double crank mechanism.

3) Watts straight line mechanism or double lever mechanism.


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1) Beam Engine:

When the crank AB rotates about A, the link CE pivoted at D makes verticalreciprocating motion at end E. This is used to convert rotary motion to reciprocating

motion and vice versa. It is also known as Crank and lever mechanism. This mechanism

is shown in the figure below.

2) Coupling rod of locomotive

In this mechanism the length of link AD = length of link C. Also length of linkAB = length of link CD. When AB rotates about A, the crank DC rotates about D. This

mechanism is used for coupling locomotive wheels. Since links AB and CD work as

cranks, this mechanism is also known as double crank mechanism. This is shown inthe figure below

3. Watts indicator mechanism (Double lever mechanism).A Watts indicator mechanism (also known as Watt's straight line mechanism or

double lever mechanism) which consists of four links is shown in Figure. The four linksare: fixed link at A, link A C, link CE and link BFD. It may be noted that BF and FD

form one link because these two parts have no relative motion between them. The links


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CE and BFD act as levers. The displacement of the link BFD is directly proportional to

the pressure of gas or steam which acts on the indicator plunger. On any smalldisplacement of the mechanism, the tracing point E at the end of the link CE traces out

approximately a straight line.

The initial position of the mechanism is shown in Figure by full lines whereas the

dotted lines show the position of the mechanism when the gas or steam pressure

In a four-bar linkage, we refer to the line segment between hinges on a given link as a bar

where: s = length of shortest bar l = length of longest bar p, q = lengths of intermediate bar

Grashof's theorem states that a four-bar mechanism has at leastone revolving link if

s + l


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A slotted link 1 is fixed. When the crank 2 rotates about O, the sliding piston 4

reciprocates in the slotted link 1. This mechanism is used in steam engine, pumps,

compressors, I.C. engines, etc.

2) Crank and slotted lever mechanism:

It is an application of second inversion.

The crank and slotted lever mechanism isshown in figure below.

In this mechanism link 3 is fixed. The slider (link 1) reciprocates in oscillatingslotted lever (link 4) and crank (link 2) rotates. Link 5 connects link 4 to the ram (link 6).

The ram with the cutting tool reciprocates perpendicular to the fixed link 3. The ram with

the tool reverses its direction of motion when link 2 is perpendicular to link 4. Thus thecutting stroke is executed during the rotation of the crank through angle and the return

stroke is executed when the crank rotates through angle or 360 . Therefore,

when the crank rotates uniformly, we get

Time of cutting = = .

Time of return 360

This mechanism is used in shaping machines, slotting machines and in rotary engines.

3) Whitworth quick return motion mechanism

Third inversion is obtained by fixing the crank i.e. link 2. Whitworth quick return

mechanism is an application of third inversion. This mechanism is shown in the figure

below. The crank OC is fixed and OQ rotates about O. The slider slides in the slottedlink and generates a circle of radius CP. Link 5 connects the extension OQ provided on

the opposite side of the link 1 to the ram (link 6). The rotary motion of P is


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taken to the ram R which reciprocates. The quick return motion mechanism is used in

shapers and slotting machines.

The angle covered during cutting stroke from P1 to P2 in counter clockwise direction is (or) 360 - 2. During the return stroke, the angle covered is 2 or .

Therefore,

Time to cutting = 360 - 2= 180 Time of return 2

= = .

360

4.Rotary internal combustion engine or Gnome engine.

Sometimes back, rotary internal combustion engines were used in aviation. Butnow-a-days gas turbines are used in its place. It consists of seven cylinders in one plane

and all revolves about fixed centre D, as shown in Figure, while the crank (link 2) is

fixed. In this mechanism, when the connecting rod (link 4) rotates, the piston (link 3)

reciprocates inside the cylinders forming link 1.

Ex: Rotary Engine


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5. Hand Pump

A pump device

The inversion of a mechanism does not change the motions of its links relative to each

other but does change their absolute motions.

6. Oscillating Cylinder Engine.

The arrangement of oscillating cylinder engine mechanism, as shown in Fig. 5.24,

is used to convert reciprocating motion into rotary motion. In this mechanism, the link 3

forming the turning pair is fixed. The link 3 corresponds to the connecting rod of a

reciprocating steam engine mechanism. When the crank (link 2) rotates, the piston

attached to piston rod (link 1) reciprocates and the cylinder (link 4) oscillates about a pin

pivoted to the fixed link atA.

Transmission Angle

In Figure, ifAB is the input link, the force applied to the output link, CD, istransmitted through the coupler linkBC. (That is, pushing on the linkCD imposes a force

on the linkAB, which is transmitted through the linkBC.) For sufficiently slow motions


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(negligible inertia forces), the force in the coupler link is pure tension or compression

(negligible bending action) and is directed alongBC. For a given force in the couplerlink, the torque transmitted to the output bar (about pointD) is maximum when the angle

between coupler barBCand output bar CD is /2. Therefore, angle BCD is called

transmission angle.

When the transmission angle deviates significantly from /2, the torque on the

output bar decreases and may not be sufficient to overcome the friction in the system. Forthis reason, the deviation angle =| /2- | should not be too great. In practice, there is no

definite upper limit for , because the existence of the inertia forces may eliminate the

undesirable force relationship that is present under static conditions. Nevertheless, thefollowing criterion can be followed.

Mechanisms:

i) Quick return motion mechanisms:

Many a times mechanisms are designed to perform repetitive operations. During these

operations for a certain period the mechanisms will be under load known asworking stroke and the remaining period is known as the return stroke, the

mechanism returns to repeat the operation without load. The ratio of time of working

stroke to that of the return stroke is known a time ratio. Quick return mechanisms areused in machine tools to give a slow cutting stroke and a quick return stroke.

The various quick return mechanisms commonly used are

i) Whitworthii) Drag linkiii) Crank and slotted lever mechanism

Withworth quick-return mechanism & Crank and slotted lever mechanism have

already discussed in the previous chapter (Inversion of Slider Crank Mechanism)


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Drag link mechanism

This is four bar mechanism with double crank in which the shortest link is fixed.

If the crank AB rotates at a uniform speed, the crank CD rotate at a non-uniform speed.

This rotation of link CD is transformed to quick return reciprocatory motion of the

ram E by the link CE as shown in figure. When the crank AB rotates through an

angle in Counter clockwise direction during working stroke, the link CD rotates

through 180o. We can observe that / > / . Hence time of working stroke is /

times more or the return stroke is / times quicker.

Shortest link is always stationary link. Sum of the shortest and the longest links of

the four links 1, 2, 3 and 4 are less than the sum of the other two. It is the necessary

condition for the drag link quick return mechanism.


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Application1. Profile Grinding (in which the part obtains its form from a greatly enlarged

pattern)

2. In engraving machine3. In guiding cutting torch to generate contour similar to template4. Used as an indicator rig (reproduce to a smaller scale the displacement of cross-

head and piston of the reciprocating engine)

5. In pencile mechanisms of engine indicators (pressure inside the cylinder, isreproduced to an enlarged scale)


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Straight Line Motion Mechanisms


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Exact Straight Line Motion Mechanisms


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Ratchet and Pawl mechanismThis mechanism is used in producing intermittent rotary Motion member. A

ratchet and Pawl mechanism consists of a ratchet wheel 2 and a pawl 3 as shown in thefigure. When the lever 4 carrying pawl is raised, the ratchet wheel rotates in the counter

clock wise direction (driven by pawl). As the pawl lever is lowered the pawl slides over

the ratchet teeth. One more pawl 5 is used to prevent the ratchet from reversing. Ratchetsare used in feed mechanisms, lifting jacks, clocks, watches and counting devices.


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The ratchet can be used to move a toothed wheel one tooth at a time. The partused to move the ratchet is known as the pawl. The ratchet can be used as a way of

gearing down motion. By its nature motion created by a ratchet is intermittent. By using

two pawls simultaneously this intermittent effect can be almost, but not quite, removed.Ratchets are also used to ensure that motion only occurs in only one direction,

useful for winding gear which must not be allowed to drop. Ratchets are also used in the

freewheel mechanism of a bicycle.


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Geneva mechanismGeneva mechanism is an intermittent motion mechanism. It consists of a driving

wheel D carrying a pin P which engages in a slot of follower F as shown in figure.

During one quarter revolution of the driving plate, the Pin and follower remain in

contact and hence the follower is turned by one quarter of a turn. During the remaining

time of one revolution of the driver, the follower remains in rest locked in positionby the circular arc.

The Geneva stop is named after the Geneva cross, a similar shape to themain part of the mechanism.

The Geneva stop is used to provide intermittent motion, the orange wheel turnscontinuously, the dark blue pin then turns the blue cross quarter of a turn for each

revolution of the drive wheel. The crescent shaped cut out in dark orange section lets the points of the cross past,

and then locks the wheel in place when it is stationary.

The Geneva stop mechanism is used commonly in film.


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Example Problems:


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Unit-i Basics of Machines