Common Mechanisms 2

M h iMechanisms

Commonly used Mechanisms

Pantograph:Pantograph:

Pantographs were traditionally used to scale drawings.

It can exactly magnify or reduce a drawing.

In the days before CAD packages, pantograph was a vital drawing tool.

Pantograph are also used in some sensors, to magnify a small motion.

B

Pantograph (6 links, 5 turning joints)

A

D

C

ED E

O

Tracing Drawingi t ( )

Magnifiedby the ratioOB/OAg

point point (pen)OB/OA

Simple pantograph

B

C

A

E

D

o (pen)

Here scaling ratio is 2 (i.e OB/OA)

B

Pantograph

A

D

C

ED E

O

Specifications:1. AB=AD=DC=BC (they must form a Parallelogram).

B

Pantograph

A

D

C

ED E

O

At any position of pantograph, triangle OAD is similar to OBE.Hence OB/OA =BE/AD.

The scaling ratio the Pantograph is OB/OA or BE/AD

Toggle Mechanism:

A device for producing large mechanical advantage.Used in applications such as stone crushers.

2F

α

α

tan2

2tan

PFP

=∴

=

Small force

L f

For small values of α,F << P .F

PLarge force

A small force F (obtained by turning the wheel) causes a large force P at the

P

A small force F (obtained by turning the wheel) causes a large force P at thecrushing end.

Various Straight Line Motion mechanisms:

These are mechanisms which have only turning joints, and produce a straight line motion at some point in a link (i.e.produce a straight line motion at some point in a link (i.e. coupler point).

The straight line may be exact or approximate, or only a small portion of the path traced by the point. But it is still useful.

Mechanisms with sliding joint also produce straight line motion, but get worn out soon. Hence they are not considered here.

Straight line producing mechanisms were historically important. BecauseBecause,

(a)Difficulty of producing exact straight lines using sliding parts (sliding joints have to be accurately machined first).( g j y )

(b) To guide certain machine parts to move in a straight line.

Using “synthesis of mechanisms” concept, four bar mechanisms can bedesigned to produce portions of straight lines.designed to produce portions of straight lines.

input

Level luffing crane.‘P’ traces approximatelya straight line.

Film advance mechanism in a camera

Approximate Straight Line Mechanisms

1. Watts Mechanism (4 links, 4 turning joints)( i i ll d t id th i t / lid i l t i )(originally used to guide the piston/slider in early steam engines)

ooA

P

BO1

For limited rotation of O, Point ‘P’ will trace an approximate vertical straight line.

Specification: PA.OA = PB.O1B


ooA

P

BO1


o

A

oP’

BP

O1


A

P

BO1


ooP’

P

O1A” P”

B”


oo

O1A” P”

B”

It co ld g ide the imperfectl made pistons of the old steam enginesIt could guide the imperfectly made pistons of the old steam enginesin a straight line.

Used in car suspensionsIt will restrain horizontal movements (i.e swaying)

Scott Russell Mechanism(exact straight line motion)

PP

θslider

BC

θ

A

P moves in a straight line when the slider C moves back and forth .1 U d t t h lifti t t P1. Used to operate hammers or lifting water at P.2. Also used in automobile suspensions (for arresting horz. motion)

Specification: AB = PB=BCSpecification: AB = PB=BC


PP

θslider

BC

θ

A


P’

θslider

B

Cθ

A

Grass Hopper Mechanism - A modification of Scot Russell Mechanismand is an Approximate Straight line motion mechanismand is an Approximate Straight line motion mechanism

P

B

A

C

θ C’ Instead of a slider at C, it

Q

,is coupled toa long link CQ

For small angles θ, the point P will follow an approximate straight line, when C moves in an approximate straight line.Specification: BC2=PB.AB

P

B

A

C

Q

CQ is the driving link

P

B’

P’ B

B’

C’A

Q

CQ is the driving link

Tchebicheffs Mechanism(4 links, 4 turning joints)( s, tu g jo ts)

P AB St i ht li t d b PAB Straight line traced by P

O O1

Specifications:Specifications:

It has crossed equal links OA and O1B.

P is mid point of AB.AB:OO1:OA=1:2:2.5

Tchebicheffs Mechanism(4 li k 4 t i j i t )(4 links, 4 turning joints)

P AB ABStraight line traced by P

O O1


P’

O O1


P”

O O1

Tchebicheffs Mechanism is used to guide Saw blades in wood mill

Only Horizontal motion

allowed

O O1O O1

Exact Straight Line Mechanisms

They produce exact straight line motion when another link is rotatedthrough a limited anglethrough a limited angle.

The two well known devices are,

1. Peaucellier Mechanism2. Harts Mechanism

They are used where precise linear motion is needed. Eg. Mechatronics applications, Cameras etc

Peaucellier Mechanism (8 links, 6 turning joints)

Was invented in 1864 by Peaucellier and was considered a milestone at that time.

P

C OQ is the rotating link.

Then P will move in a

Q

B

straight line perpendicular to OA.

OA

B

Specifications:1. OQ=OA2. AB=AC3. PBQC is a parallelogram (i.e links are equal)


P

C

Q

B

OA

B


P’

OA


P”OA

Harts Mechanism

AC

PPE (pivoted to the ground)

O

crank

BD

Needs 6 links and 7 turning joints.More compact than Peaucellier Mechanism.

Specifications: It is basically a crossed paralellogram. So CD=AB and AD=BC.

OP is the crank. Link AB is pivoted to the pground at E.

Also, OP=OE.

AC

PPE

O

crank

BD

Draw lines through AC and DB.They will be always parallel to each other.

AC

PQ P

O

Q Ecrank

BD

Now locate the point Q (on BC) by drawing a parallel line thru P.

This is the straight line generation point.

AC

PQ P

O

Q

900

E

BD900

It can be shown that, when the crank OP rotates, Q will move in a t i ht li di l t OEstraight line perpendicular to OE .

Some other important Mechanisms

1. Hookes Joint (Universal Joint)

This is used when two shafts have a misalignment between themThis is used when two shafts have a misalignment between them.

Motor (driving unit)Pump (driven)

Driven shaft - Driving shaft -ω1, θω2

α=angle between shafts

Hookes joint

When the driving shaft makes one revolution at constant ω1, driven shaft also makes one revolution.

But ω2 is not constant during the revolution. It varies as a function of θ.

E en if dri ing shaft r ns at constant ill fl ct ate abo eEven if driving shaft runs at constant ω1 , ω2 will fluctuate above and below ω1 .

Hookes Joint

Cross piece

Forked ends of shaft

Shaft-1

Hookes Joint

ω1, θ1

α Shaft-1(Driving)

ω2

How does ω2 fluctuate with ω1 ?

It can be shown that,

cosα⎛ ⎞2 1 2 2

2 1

cos1 sin cos

when 0 (shafts are perfectly aligned) then .

αω ωα θ

α ω ω

⎛ ⎞= ⎜ ⎟−⎝ ⎠

→ →2 1

02Also it can be summarized that in a 360 rotation will fluctuate ω

2 max 1 2 min 1

between, . / cos and . cos .ω ω α ω ω α= =

Usuall 2 10

y the speed fluctuation of must be kept within 5% of .

H it i t k ll ibl ( <15 )

ω ω±0Hence it is necessary to keep as small as possible (say <15 )α

Double Hooke’s Joint(used in old cars with rear wheel drive)(used in old cars with rear wheel drive)

α1

EngineRear Wheel

1

Driving shaftα2

Driving shaft(ω1)Driven shaft

(ω2)

Here the speed (ω2) of driving shaft depends on α1 and α2.

If α1 = α2 and all shafts are in the same plane, it can be 1 2 p ,shown that ω2= ω1.

Oldhams coupling

Used to connect two misaligned shafts, but parallel to each other.

poss

ible

mot

ion

p

Flange 1 Flange 2Intermediatepiece

Intermediate piece

The intermediate piece ill co ple the t o flanges It has an eccentricThe intermediate piece will couple the two flanges. It has an eccentricmotion as the shafts rotate.

The angular velocities of the driving and driven shafts are sameThe angular velocities of the driving and driven shafts are same.

Geneva MechanismThis is used to convert uniform rotary input to intermittent rotarys s used to co e t u o ota y put to te tte t ota youtput.

It has many applications where intermittent motion is needed:Eg. movie projector film advance, assembly lines.

Uniformly rotating li klink Intermittently

rotating Geneva wheel.

90 0o (rotate thru 900

Idle for 2700)

Basic Geneva Mechanism

aa

ob

Basic Geneva Mechanism

The actual Geneva mechanism has some refinementsfor locking of Geneva wheelfor locking of Geneva wheel.

Uniformly rotating link “oa”is fashioned with a circular portion

op

ω

p

ra

r

oa= r; Also there is a circle of radius ‘p’ (p<r)

GGeneva Wheel

pp

p

Geneva Wheel

pp

prr√2 r

This is the center distance for

Geneva Wheel

This is the center distance for Geneva wheel with 4 slots

Assembled Geneva Wheel

ω Uniform Rotation

Intermittent Rotation

Geneva is Locked because of the radiusbecause of the radius

Plug enters the next Genevawheel slot, forcing it to rotate.

Applications:Applications:

Movie projectors: Each film has to pause 1/24 sec inMovie projectors: Each film has to pause 1/24 sec infront of the projection lens. The film roll has to be rotated intermittently.

The film roll is advanced through a Geneva Mechanism.

The Geneva Mechanism is driven by a motor with uniform RPM.e Ge e a ec a s s d e by a oto t u o

Automobile Steering Mechanism

Simplified representation of Automobile Steering.

Front wheels, axis can beswivelled.swivelled.

Chassis

Rear Wheels, axle direction is fixed

Automobile Steering Mechanism

V

Instantaneous Center

For the vehicle to turn smoothly, all wheels must turnabout a common instantaneous center.

θ

Front wheels have to be swivelled thru different angles.

θ

Φ

VΦ

θ


Φ

Steering Mechanism must turn Inner wheel thru θ andouter wheel thru Φ .

θθ

Φ

VΦ

θ


Φ

Condition for correct steering :From the geometry it can be shown that,

θ

From the geometry it can be shown that,cot Φ – cot θ = (W/H) .

θ

Φ

H (wheel base)

Φθ

H (wheel base)

Φ

W (track width)

Davis Steering Gear:Obeys the law of steering, cot Φ – cot θ = (W/H), y g, ( ),

(for all angles)

Two slotted bell crank leverscrank levers


(for all angles)

Slider bar is movedl ft i htleft or right


(for all angles)α

b

hh

tan α = W / (2H)= Track width 2 x Wheel base

Then chose b and h such that;tan α = b/h


(for all angles)


(for all angles)

θΦ

θ

θ > Φθ Φ

Davis Steering Gear

Advantage: Obeys law of steering

Disadvantage: Due to sliding joints, the mechanism gets worn outafter a period of use. There will be slackness (‘play’)d i t iduring steering.

Ackermans Steering Gear:Ackermans Steering Gear:

It is a steering gear with all turning joints.

Only approximately follows law of steering.

It is extensively used as steering gear for most modern vehicles.

It is a compromise between law of steering and practicality.

Ackermans mechanism is set behind the front wheels

B C

A D

Steering bar is movedleft or right

B C

A D

αα

A D

αUsually, the center lines ofLinks CD and AB are designed to meet the rearare designed to meet the rear axle center.

Ackerman steering gear willsatisfy “law of steering” foronly one steering position on each side.

Thi i ll t thThis is usually set as thesmallest turning radius.

For larger turning radiusthe front wheel inst. centerswill intersect above the rearaxle.

But the effect of this error is less for large turning radius

SLIP:

If all the instantaneous centres of all tyres perfectly coincide the tyresIf all the instantaneous centres of all tyres perfectly coincide, the tyrespoint in the direction of motion of the vehicle (i.e concentric circular arcs) -No Slip.

If the instantaneous centres do not coincide there is mismatch betweenwhere each tyre is pointed and the general direction of motion of the vehicle.

This is the slip angle of each tyre, and it must be kept to a minimum. Because of slip angle sidewise forces occur, which force the vehicleoff from its path.

Front wheel Independent suspension for Automobiles

‐Mac Pherson strut (since 1945)

The front wheels need independent suspensions since they yneed to be steeredthrough different angles.

Mac Pherson strut is an inversion of Slider Crank( i i C k d Sl tt d l(same inversion as Crank and Slotted leverQuick return mechanism)

Planar representation ofMac Pherson suspension

Mac Pherson suspension has to be modified for

ti lpractical use1. provision for steering.2. Spring suspension

Spring+viscous damper

Swivel joint for steering .(Steering arm not shown)

Actual Mac Pherson suspension in 3 D

Spring+viscous damper

Steering rod

Swivel joint for steering .

Common Mechanisms 2

Documents

Transcript of Common Mechanisms 2