Kom Unit1 Class Notes

Dept of MECH - MIET Engg College (Chapter 1) 7/23/2013

Class Lecture by S Renold Elsen 1

IntroductionIntroduction

Class Lecture Note by S Class Lecture Note by S RenoldRenold ElsenElsen11

RELEVANCE OF KINEMATIC STUDY RELEVANCE OF KINEMATIC STUDY

AnalysisAnalysis

Study of position, displacement, velocity and acceleration of different elements of mechanism

SynthesisSynthesis

Design: determination of shape and size

1. Requires knowledge of material

2. Requires knowledge of stress

3. Requires knowledge of load acting

(i) static load

(ii) dynamic/inertia load

Class Lecture Note by S Class Lecture Note by S RenoldRenold ElsenElsen 22

MachineMachine

• It is a device used transform/ transmit motion/work.


A machine is a mechanism or collection ofmechanisms, which transmit force fromthe source of power to the resistance tobe overcome.

StructureStructure

• It is an assemblage of a number of resistant bodies (known as members) having no relative motion between them.

• It is meant for carrying loads.

Class Lecture Note by S Renold Class Lecture Note by S Renold ElsenElsen 44



Diff b/w Machine and structureDiff b/w Machine and structureMachine structure

The parts of a machine move relative to one another .

The members of a structure do not move relative to one another.

A machine transforms the available energy into some useful work

No energy is transformed into useful work

The links of a machine transmit both power and motion

The members of a Structure transmit forces only. Class Lecture Note by S Renold Class Lecture Note by S Renold

ElsenElsen 55

LinkLinkA link or element need not to be a rigid body, but

it must be a resistant body.

1. Rigid link. A rigid link is one which does not undergo any deformation while transmitting motion.

2. Flexible link. A flexible link is one which is partly deformed in a manner not to affect the transmission of motion.

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


• Binary Link: - A link having two ends or joints is called Binary link.

• Ternary Link: - A link having three ends or joints is called as Ternary link.

• Quaternary Link: - A link having four ends or joints is called as Quaternary link.


Completely constrained motionCompletely constrained motion

• When the motion between a pair is limited to a definite direction irrespective of the direction of force applied.




Incompletely constrained motion. Incompletely constrained motion.

• When the motion between a pair can take place in more than one direction, then the motion is called an incompletely constrained motion


Successfully constrained motionSuccessfully constrained motion

• When the motion between the elements, forming a pair,is such that the constrained motion is not completed by itself, but by some other means, then the motion is said to be successfully constrained motion.


Kinematic PairKinematic Pair

• The two links or elements of a machine, when in contact with each other, are said to form 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.


Types of Kinematic Pairs Types of Kinematic Pairs

Kinematic pairs can be classified according to

• i) Nature of contact.

• ii) Nature of mechanical constraint.

• iii) Nature of relative motion.




Nature of ContactNature of Contact

Lower Pair: A pair of links having surface or area contact between the members.


Higher PairsHigher Pairs

• When a pair has a point or line contact between the links


Warping PairsWarping Pairs


Nature Of Mechanical ConstraintNature Of Mechanical Constraint

Form closed pair: When the elements of a pair are held together mechanically, it is known as a closed pair.

Force closed pair: When two links of a pair are in contact either due to force of gravity or some spring action, they constitute an unclosed pair.




The Prismatic JointThe Prismatic Joint

• Also known as a translational or sliding joint, has one translational degree of freedom between the two connected components.


Hinge JointHinge Joint

• Also known as a revolute joint, has one rotational degree of freedom between the two components.

• The two components are free to rotate relative to each other about the axis of the joint.


Screw Joint Screw Joint

• Relative displacement and the relative rotation, instead of being independent, are linearly related to each other.

• this joint effectively has only one degree of freedom.


Cylindrical JointCylindrical Joint

• It has one translational and one rotational degree of freedom between the two connected components.

• The components are free to slide and rotate relative to each other along the axis of joint.




Planar Joint Planar Joint

• The has two translational and one rotational degrees of freedom between the two components.

• Both components are free to translate relative to each other in a plane perpendicular to the axis of joint, and they are also free to rotate about this axis.


Ball JointBall Joint

• Also known as a spherical joint, has three rotational degrees of freedom between the two attached components


• Binary joint. When two links are joined at the same connection, the joint is known as binary joint.

• Ternary joint. When three links are joined at the same connection, the joint is known as ternary joint.

• Quaternary joint. When four links are joined at the same connection, the joint is called a quaternary joint.

Types of JointsTypes of Joints


PLANAR MECHANISMS

• When all the links of a mechanism have plane motion, it is called as a planar mechanism. All the links in a planar mechanism move in planes parallel to the reference plane.





KINEMATIC CHAIN

Group of links either joined together orarranged in a manner that permits them tomove relative to one another.

MECHANISM

• A mechanism is a constrained kinematic chain.

• Motion of any one link in the kinematic chainwill give a definite and predictable motionrelative to each of the others.

• Usually one of the links of the kinematic chainis fixed in a mechanism

Kinematic Chain

• Relation between Links, Pairs and Joints

L=2P-4

J=(3/2) L – 2

L => No of Links

P => No of Pairs

J => No of Joints

L.H.S > R.H.S => Locked chain

L.H.S = R.H.S => Constrained Kinematic Chain

L.H.S < R.H.S => Unconstrained Kinematic Chain


GRUBLER’S CRITERION Number of degrees of freedom of a mechanism is

given by F = 3(n-1)-2l-h.

F = Degrees of freedom n = Number of links in the mechanism. l = Number of lower pairs, which is obtained by

counting the number of joints.If more than two links are joined together at any

point, then, one additional lower pair is to be considered for every additional link.

h = Number of higher pairs


Examples - DOF

• F = 3(n-1)-2l-h

• Here, n = 6, l = 7 and h = 0.

• F = 3(6-1)-2(7) = 1

• I.e., one input to any one link will result in definite motion of all the links.




Examples Examples -- DOFDOF

• F = 3(n-1)-2l-h

• Here, n = 6, l = 7 (at the intersection of 2, 3 and 4, two lower pairs are to be considered) and h = 0.

• F = 3(6-1)-2(7) = 1


Grashoff Law

• The sum of the shortest and longest link length should not exceed the sum of the other two link lengths.


INVERSION OF 4INVERSION OF 4--BAR CHAINBAR CHAIN

1) BEAM ENGINE

2) COUPLING ROD OF LOCOMOTIVE

3) WATT’S INDICATOR MECHANISM

BEAM ENGINEBEAM ENGINE




COUPLING ROD OF LOCOMOTIVE


WATT’S INDICATOR MECHANISM


SINGLE SLIDER CRANK CHAINSINGLE SLIDER CRANK CHAIN


INVERSIONINVERSION OF SINGLE SLIDER CRANK CHAINOF SINGLE SLIDER CRANK CHAIN

• PENDULUM PUMP

• OSCILLATING CYLINDER ENGINE

• ROTARY I.C. ENGINE

• CRANK & SLOTTED QUICK RETURN MOTION MECHANISM

• WHITWORTH QUICK RETURN MOTION MECHANISM




PENDULUM PUMP (BULL ENGINE) PENDULUM PUMP (BULL ENGINE)


OSCILLATING CYLINDER ENGINEOSCILLATING CYLINDER ENGINE


ROTARY I.C. ENGINEROTARY I.C. ENGINE


CRANK & SLOTTED QUICK RETURN MOTION MECHANISMCRANK & SLOTTED QUICK RETURN MOTION MECHANISM




Crank and slotted lever quick return motion mechanism.

• This mechanism is mostly used in shaping machines, slotting machines and in rotary internal combustion engines.

• In this mechanism, the link AC (i.e. link 3) forming the turning pair is fixed.

• The driving crank CB revolves with uniform angular speed about the fixed centre C.

• A sliding block attached to the crank pin at B slides along the slotted bar AP and thus causes AP to oscillate about the pivoted point A

•A short link PR transmits the motion from AP to the ram which carries the tool and reciprocates along the line of stroke R1 R2.

•The line of stroke of the ram (i.e. R1 R2) is perpendicular to AC produced.

41Class Lecture Note by S Renold ElsenClass Lecture Note by S Renold Class Lecture Note by S Renold

ElsenElsen 4141

• In the extreme positions, AP1 and AP2 are tangential to the circle and the cutting tool is at the end of the stroke.

• The forward or cutting stroke occurs when the crank rotates from the position CB 1 to CB2 (or through an angle ) in the clockwise direction.

• The return stroke occurs when the crank rotates from the position CB2 to CB1 (or through angle ) in the clockwise direction.

• Since the crank has uniform angular speed,

therefore,

• Since the tool travels a distance of R1 R2 during cutting and return stroke, therefore travel of the tool or length of stroke

42Class Lecture Note by S Renold ElsenClass Lecture Note by S Renold Class Lecture Note by S Renold

ElsenElsen 4242

WHITWORTH QUICK RETURN MOTION MECHANISMWHITWORTH QUICK RETURN MOTION MECHANISM

Class Lecture Note by S Class Lecture Note by S RenoldRenoldElsenElsen 4343

Whitworth quick return motion mechanism• This mechanism is mostly used in shaping and slotting machines.

• In this mechanism, the link CD (link 2) forming the turning pair is fixed, as

• shown in Fig.

• The link 2 corresponds to a crank in a reciprocating steam engine. Thedriving crank CA (link 3) rotates at a uniform angular speed.

• The slider (link 4) attached to the crank pin at A slides along the slotted barPA (link 1) which oscillates at a pivoted point D.

• The connecting rod PR carries the ram at R to which a cutting tool is fixed.

• The motion of the tool is constrained along the line RD produced, i.e. alonga line passing through D and perpendicular to CD.

07/22/13 44Class Lecture Note by S Renold ElsenClass Lecture Note by S Renold Class Lecture Note by S Renold

ElsenElsen 4444



• When the driving crank CA moves from the position CA1 to CA2 (or the link DP from the position DP1 to DP2) through an angle in the clockwise direction, the tool moves from the left hand end of its stroke to the right hand end through a distance 2PD.

• Now when the driving crank moves from the position CA2 to CA1 (or the link DP from DP2 to DP1 ) through an angle in the clockwise direction, the tool moves back from right hand end of its stroke to the left hand end.

• A little consideration will show that the time taken during the left to right movement of the ram (i.e. during forward or cutting stroke) will be equal to the time taken by the driving crank to move from CA1 to CA2.

07/22/13 45Lecture Note by S Renold Elsen


• Similarly, the time taken during the right to left movement of the ram (or during the idle or return stroke) will be equal to the time taken by the driving crank to move from CA2 to CA1.

• Since the crank link CA rotates at uniform angular velocity therefore time taken during the cutting stroke (or forward stroke) is more than the time taken during the return stroke.

• In other words, the mean speed of the ram during cutting stroke is less than the mean speed during the return stroke.

07/22/13 46Hareesha N G, Dept of Aero Engg,

DSCE, Blore


• The ratio between the time taken during the cutting and return strokes is given by

07/22/13 47Class Lecture Note by S Renold ElsenClass Lecture Note by S Renold Class Lecture Note by S Renold

ElsenElsen 4747

INVERSION OF DOUBLE SLIDER CRANK CHAININVERSION OF DOUBLE SLIDER CRANK CHAIN

•• ELLIPTICAL TRAMMELELLIPTICAL TRAMMEL

•• SCOTCH YOKE MECHANISMSCOTCH YOKE MECHANISM

•• OLDHAM’S COUPLINGOLDHAM’S COUPLING




ELLIPTICAL TRAMMELSELLIPTICAL TRAMMELS


SCOTCH YOKE MECHANISMSCOTCH YOKE MECHANISM


OLDHAM’S COUPLINGOLDHAM’S COUPLING


Forces Acting in a MechanismForces Acting in a MechanismInput work per unit time = Output work per unit timeInput work per unit time = Output work per unit time

Work supplied to the joint A = Work transmitted by the joint BWork supplied to the joint A = Work transmitted by the joint B




Mechanical AdvantageMechanical Advantage

•• It is defined as the ratio of the load to the It is defined as the ratio of the load to the effort.effort.

Class Lecture Note by S Renold ElsenClass Lecture Note by S Renold Elsen 5353

Pantograph Pantograph

Class Lecture Note by S Renold Class Lecture Note by S Renold ElsenElsen

Class Lecture Note by S Renold Elsen

5454

Straight Line MechanismStraight Line Mechanism


PeaucellierPeaucellier mechanismmechanism

It consists of a fixed link OO1.links O1A, OC, OD, AD, DB, BC and CA are connected

by turning pairs at their intersections.AC = CB = BD = DA ; OC = OD ; and OO1 = O1AOC2 = OR2 + RC2 ...(i)BC2 = RB2 + RC2 ...(ii)Subtracting equation (ii) from (i), OC2 – BC2 = OR2 – RB2

= (OR + RB) (OR – RB)= OB × OA




Watt’s mechanismWatt’s mechanism


Watt’s mechanismWatt’s mechanism

• OBAO1 is a crossed four bar chain in which O and O1 are fixed.

• In the mean position of the mechanism, links OB and O1A are parallel and the coupling rod AB is perpendicular to O1A and OB.

• The tracing point P traces out an approximate straight line over certain positions of its movement, if PB/PA = O1A/OB.

• In the initial mean position of the mechanism, the instantaneous centre of the link BA lies at infinity. Therefore the motion of the point P is along the vertical line BA .


• Let OB′ A′O1 be the new position of the mechanism after the links OB and O1A are displaced through an angle θ and φ respectively.

• The instantaneous centre now lies at I. Since the angles θ and φ are very small

arc B B′ = arc A A′ or OB × θ = O1A × φ

OB / O1 A = φ / θ

A′P′ = IP′ × φ, and B′P′ = IP′ × θ

A′P′ / B′P′ = φ / θ

OB/ O1A=A′P′/B′P′=AP/BP


Steering Gear MechanismSteering Gear Mechanism• The steering gear mechanism is used for changing the

direction of two or more of the wheel axles with reference to the chassis.

• The front wheels are placed over the front axles, which are pivoted at the points A and B.

• When the vehicle takes a turn, the front wheels along with the respective axles turn about the respective pivoted points.

• The back wheels remain straight and do not turn..




• The two front wheels must turn about the same instantaneous centre I which lies on the axis of the back wheels to avoid skidding.

• The axis of the inner wheel makes a larger turning angle θ than the angle φ subtended by the axis of outer wheel.

a = Wheel track,

b = Wheel base, and

c = Distance between the pivots A and B of the front axle.

Now from triangle IBP from triangle IAP

cot θ= BP/IP cot φ = AP/IP= (AB+BP)/IP=

(AB/IP)+(BP/IP)= c/b + cot θ

This is the fundamental equation for correct steering.Class Lecture Note by S Renold Class Lecture Note by S Renold

ElsenElsen 6161

Davis Steering GearDavis Steering Gear


Davis Steering GearDavis Steering Gear

• It is an exact steering gear mechanism.

• The slotted links AM and BH are attached to the front wheel axle, which turn on pivots A and B respectively.

• The rod CD is constrained to move in the direction of its length, by the sliding members at P and Q.

• These constraints are connected to the slotted link AM and BH by a sliding and a turning pair at each end.


•• The steering is affected by moving CD to the right or left of The steering is affected by moving CD to the right or left of its normal position.its normal position.

triangle AA′ C′ triangle AA′C

triangle BB′D′




for correct steering


Ackerman Steering Gear SimulationAckerman Steering Gear Simulation


1. The whole mechanism of the Ackerman steering gear is on back of the front wheels; whereas in Davis steering gear, it is in front of the wheels.

2. The Ackerman steering gear consists of turning pairs, whereas Davis steering gear consists of sliding members.

Ackerman Steering GearAckerman Steering Gear

•In Ackerman steering gear, the mechanism ABCD is a four bar crank chain.•The shorter links BC and AD are of equal length and are connected by hinge joints with front wheel axles. •The longer links AB and CD are of unequal length.Class Lecture Note by S Renold Class Lecture Note by S Renold

ElsenElsen 6767

1. When the vehicle moves along a straight path, 1. When the vehicle moves along a straight path, the longer links AB and CD are parallel and the the longer links AB and CD are parallel and the shorter links BC and AD are equally inclined to the shorter links BC and AD are equally inclined to the longitudinal axis of the vehiclelongitudinal axis of the vehicle

2. When the vehicle is steering to the left, the 2. When the vehicle is steering to the left, the position of the gear is shown by dotted lines in . position of the gear is shown by dotted lines in . In this position, the lines of the front wheel axle In this position, the lines of the front wheel axle intersect on the back wheel axle at I, for correct intersect on the back wheel axle at I, for correct steering.steering.

3. When the vehicle is steering to the right, the 3. When the vehicle is steering to the right, the similar position may be obtained.similar position may be obtained.

Three positions steering.




Steering Mechanism WorkingSteering Mechanism Working


Universal or Hooke’s JointUniversal or Hooke’s Joint


Universal or Hooke’s JointUniversal or Hooke’s Joint

• A *Hooke’s joint is used to connect two shafts, which are intersecting at a small angle.

• The end of each shaft is forked to U-type and each fork provides two bearings for the arms of a cross.

• The arms of the cross are perpendicular to each other. The motion is transmitted from the driving shaft to driven shaft through a cross.

• The inclination of the two shafts may be constant, but in actual practice it varies, when the motion is transmitted.

• The main application of the Universal or Hooke’s joint is found in the transmission from the gear box to the differential or back axle of the automobiles.

• It is also used as a knee joint in milling machines.Class Lecture Note by S Renold Class Lecture Note by S Renold

ElsenElsen 7171

Intermittent Motion Mechanism

• Intermittent motion means that the motion is not continuous, but it ceases after definite intervals.

• Intermittent rotary motion is required generally in machine tools where work table, hexagonal turret, and spindle are to be indexed.




Ratchet and Pawl Mechanism• This mechanism is used to produce intermittent circular

motion from an oscillating or reciprocating member.

• Figure shows the details of a pawl and ratchet mechanism.

• Wheel 4 is given intermittent circular motion by means of arm 2 and driving pawl 3.

• A second pawl 5 prevents 4 from turning backward when 2 is rotated clockwise in preparation for another stroke.

• The line of action PN of the driving pawl and tooth must pass between centres O and A in order to have pawl 3 remain in contact with the tooth.

07/22/13 73Class Lecture Note by S Class Lecture Note by S RenoldRenoldElsenElsen

7373

Escapement Escapement • An device in mechanical watches and clocks that transfers

energy to the time keeping element and allows the number of its oscillations to be counted .

• The escapement is driven by force from a coiled spring or a suspended weight, transmitted through the timepiece's gear train.

• The escapement releases the tooth of a gear, which therefore changes from a "locked" state to a "drive" state until the opposite arm strikes another tooth on the gear, which locks the gear again


Indexing MechanismIndexing Mechanism


Geneva Mechanism• Geneva wheel mechanism which consists of a driving wheel 1.

• It rotates continuously, and carries a pin P that engages in a slot in die driven member 2.

• The follower or driven member 2 is turned 1/4th of a revolution for each revolution of plate 1.

07/22/13 76Hareesha N G, Dept of Aero Engg,

DSCE, Blore


Documents

Kom Unit1 Class Notes