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THEORY OF MACHINES AND MECHANISMS [ME-403]1Scheme and SyllabusThe Scheme of the course is - Scheme of IV Sem Grading System.pdf

The scheme of the course is - Syllabus-TOMM.docx2THEORY OF M/C AND MECHANISM [ME-403] SYLLABUS Unit I-Basics of Mechanism and MachinesUnit II KinematicsUnit III GearsUnit IV CamsUnit V - Gyroscopic Action in Machines3UNIT I-BASICS OF MECHANISM & MACHINES1.TerminologiesMachineMechanism LinksKinematic PairKinematic Chain Degree of freedom Inversion2. DOF for Mechanism Kutzhback Equation /Grubler Equation3. Grashoff Law4. Equivalent Linkages

4. Inversion of Kinematic Chains Four bar chain Slider crank chain5. Some Lower paired mechanisms Pantograph Straight line motion mechanisms Davis and Ackermanns steering mechanisms Hookes joint.Slotted Lever & Whitworth Q.R. mechanisms4THEORY OF MACHINES

Theory of Machine may be defined as that branch of Engineering - Science, which deals with the study of relative motion between the various parts of machine, and forces which act on them. Theory of Machine may be divided into Kinematics & Dynamics.5SUB-DIVISIONS OF THEORY OF MACHINES

Kinematics - It is that branch of Theory of Machines which deals with the relative motion between the various parts of the machines with out forces applying to it.Dynamics - It is that branch of Theory of Machines which deals with the forces and their effects, while acting upon the machine parts in motion. The forces may be either static or dynamic. Dynamics is further divided into Kinetics & Statics - Kinetics - It is that branch of Theory of Machines which deals with the inertia forces which arise from the combined effect of the mass and motion of the machine parts. - Statics - It is that branch of Theory of Machines which deals with the forces and their effects while the machine parts are at rest. The mass of the parts is assumed to be negligible

6DEFINITIONS Link - A resistant body which is connected to other such body such that a relative motion takes place between the two for transferring the motion.

Element Surface on link that decides its relative with respect to adjacent link.

Kinematic Pair - A combination of two links constitute a pair.

Kinematic Chain - A combination of different links to transfer motion from one place to another.

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DEFINITIONS Machine - is a mechanism or a collection of mechanisms which transmits force from the source of power to the resistance to be overcome, and thus perform a mechanical work.8Mechanism - is a combination of rigid bodies which are formed and connected together by some means, so that they are moved to perform some functions, such as the crank- connecting rod mechanism of the I.C. engines, steering mechanisms of automobiles. etcDefinitionsInversions - When different links of mechanism are fixed one by one , it results in different useful mechanisms . Each of this mechanism is called as Inversion.

Degree of Freedom-

For pairs : Number of relative motions between links

For mechanism : - No. of independent input motions required for operating the mechanism - No. of coordinates required to define the configuration of the mechanism.9Example of Mechanisms9

Lift platform

Front loader

Device to close the top flap of boxesExample of Mechanisms11

Moves packages from an assembly bench to a conveyor

Lift platform

Microwave carrier to assist people on wheelchairExample of Mechanisms12

Conceptual design for an exercise machine

Rowing type exercise machineClassification of linksAny body (normally rigid) which has motion relative to another

(a) Binary link (b) Ternary link

(c) Quaternary link13

CLASSIFICATION OF KINEMATIC PAIRS Four criteria :Type of relative motionRevolute pair Prismatic pairTwisting pairScrew pair Spherical pairRolling pair

Number of degree of freedom One degree of freedom Two degree of freedom

By type of closure between the links Open Pair Closed Pair

d) Type of contact between links Lower pair Higher Pair

14Based on relative motionRevolute pair

15A revolute allows only a relative rotation between elements 1 and 2, which can be expressed by a single coordinate angle 'theta.Based on relative motionPrismatic pairA prismatic pair allows only a relative translation between elements 1 and 2, which can be expressed by a single coordinate 'S'.

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Based on relative motionScrew pairA screw pair allows only a relative movement between elements 1 and 2, which can be expressed by a single coordinate angle 'theta' or 'S'17

Based on relative motionCylindrical pairA cylindrical pair allows both rotation and translation between elements 1 and 2, which can be expressed as two independent coordinates angle 'theta' and 'S'18

Based on relative motionSpherical pairA spherical pair allows three degrees of freedom since the complete description of relative movement between the connected elements needs three independent coordinates.19

Based on relative motionFlat pairA planar pair allows three degrees of freedom. Two coordinates x and y describe the relative translation in the xy - plane and the third 'theta' describes the relative rotation about the z-axis.20

DEGREES OF FREEDOM (DOF)It is the number of independent motion (both translation & rotational) a body can have. 21

21DEGREES OF FREEDOM (For a planer link)The directions an object can move in. 2D Motion (3 DOF) - 2 translation & 1 rotation (2 lengths & 1 angle)

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How about 3D Space?In 2D plane22DEGREES OF FREEDOM (For a spatial link) 3D Motion (6 DOF) - 3 translation & 3 rotation (3 lengths & 3 angles)23

23Kinematic Pairs Based on type of closureOPEN KINEMATIC PAIR: is a joint for which contact between kinematic elements is maintained only for some possible positions of a mechanism.

CLOSED KINEMATIC PAIR: is a joint for which contact between kinematic elements is maintained within all possible positions of a mechanism.24

Types of kinematic pairs Based on nature of contact between elements

(i) Lower pair : The joint by which two members are connected has surface contact. A pair is said to be a lower pair when the connection between two elements are through the area of contact. Its 6 types are -

Revolute(Or)TurningPair Prismatic(Or)SlidingPair Screw(Or) HelicalPair

CylindricalPair Spherical (Or)GlobularPair Flat(or) PlanarPair25 Higher pair - is a joint for which the contact between the two kinematic elements is along a line or at a point.

Ball Bearing Cam with roller follower

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27 Types of kinematic pairs Based on degree of freedom Pairs with one DOF

Pairs with two DOF

Types of kinematic pairs Based on degree of freedom Pairs with three DOF

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Constrained motion 29 (a) Completely constrained motion

(b) Successfully constrained motion (c) Incompletely /Partially constrained motion 30

Degree of freedom for Mechanism Relation between Links, Pairs and JointsL=2P-4J=(3/2) L 2L => No of LinksP => No of PairsJ => No of JointsL.H.S > R.H.S => Locked chainL.H.S = R.H.S => Constrained Kinematic ChainL.H.S < R.H.S => Unconstrained Kinematic Chain31LOCKED CHAIN (Or) STRUCTURE Links connected in such a way that no relative motion is possible. L=3, J=3, P=3L.H.S>R.H.S32

KINEMATIC CHAIN MECHANISMSlider crank and four bar mechanisms L=4, J=4, P=4

L.H.S=R.H.S33

UNCONSTRAINED KINEMATIC CHAIN

L=5,P=5,J=5

L.H.S < R.H.S 34

DEGREES OF FREEDOM/MOBILITY OF A MECHANISM It is the number of inputs (number of independent coordinates) required to describe the configuration or position of all the links of the mechanism, with respect to the fixed link at any given instant. 35GRUBLERS CRITERION Number of degrees of freedom of a mechanism is given by F = 3(n-1)-2l-h. where,F = Degrees of freedomn = 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 pairs36A Few Examples DOF of Mechanisms

F = 3(n-1)-2l-hHere, n = 4, l = 4 & h = 0.F = 3(4-1)-2(4) = 1 (one input at one link will result in definite motion of all the links.37A Few Examples DOF of Mechanisms

F = 3(n-1)-2l-hHere, n = 5, l = 5 and h = 0.F = 3(5-1)-2(5) = 2 (two inputs to any two links are required to yield definite motions in all the links.)38A Few Examples DOF of Mechanisms

F = 3(n-1)-2l-hHere, 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

39A Few Examples DOF of Mechanisms

F = 3(n-1)-2l-hHere, 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) = 140DETERMINING DOF AND PAIRSNb=No of Binary LinksNt=No of Ternary LinksNo=No of Other LinksN=Total No of LinksL=No of LoopsP=No of PairsM=Mobility or DOFP=N+L-1M=N-(2L+1)

41DETERMINING DOF AND PAIRS

P=N+L-1M=N-(2L+1)Nb = 4,Nt=2, N0=0N=6, L=2Solution:P=6+2-1=7M=6-(2x2 +1)=1

42DETERMINING DOF AND PAIRS

P=N+L-1M=N-(2L+1)Nb = 5,Nt=1, N0=0N=6, L=2Sol:P=6+2-1=7M=6-(2x2 +1)=143Grashoffs law44For a four bar linkage planer, the sum of the shortest and longest link lengths must be less than or equal to the sum of the remaining two link lengths if there is to be continuous relative motion between the links

Grashoffs law (a) Crank Rocker mechanism[Link adjacent to shorter link fixed]

(b) Crank Rocker mechanism[Link adjacent to shorter link fixed]

(c ) Crank Crank mechanism[Shortest link is fixed]

(d) Rocker Rocker mechanism[Link opposite to Shortest link is fixed]

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Inversions of mechanism A mechanism is one in which one of the links of a kinematic chain is fixed. Different mechanisms can be obtained by fixing different links of the same kinematic chain. Each of these mechanisms is called as inversion of the parent kinematic chain.

Four Bar Chain

Single Slider Crank

Double Slider Crank

46APPLICATIONLINK-1 FIXED CRANK-ROCKER MECHANISM OSCILLATORY MOTION

47Link 2 Fixed- DRAG LINK MECHANISM

48Locomotive Wheel DOUBLE CRANK MECHANISM

49Inversions of Slider Crank ChainSlider Crank Mechanism 50

Inversions of Slider Crank ChainCrank (Link 2) fixed

Crank (Link 2 fixed ) tua51

Actual Mechanism

Whitworth Quick Return Mechanism

Inversions of Slider Crank ChainCrank (Link 2) fixed Rotary Engine Mechanism52

Inversions of Slider Crank Chain Connecting rod (Link 3) fixed Slotted Lever Quick Return Mechanism53

Crank (Link 2) fixed(Verbatim mechanism)

Actual MechanismInversions of Slider Crank Chain Connecting rod (Link 3) fixedOscillating cylinder mechanism

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Inversions of Slider Crank ChainHand Pump Mechanism55

Slider (Link 4) is fixed

Inversions of Four Bar chainQuick return motion mechanismsDrag link mechanism56

Crank and slotted lever quick return motion mechanism57

Crank and slotted lever quick return motion mechanism

58Application of Crank and slotted lever quick return motion mechanism

59ApplicationInversion IV Link 4 Slider fixed Pendulum pump or bull engine60

3. DOUBLE SLIDER CRANK CHAIN It is a kinematic chain consisting of two turning pairs and two sliding pairs. Link 1 Frame Link 2 Slider -ILink 3 CouplerLink 4 Slider - II61Inversion I Frame FixedDouble slider crank mechanism

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Elliptical trammelAC = p and BC = q, then, x = q.cos and y = p.sin.Rearranging,

Inversion II Slider - I Fixed SCOTCH YOKE MECHANISM Turning pairs 1&2, 2&3; Sliding pairs 3&4, 4&1 63

Inversion III Coupler Fixed OLDHAM COUPLING

64Other Mechanisms1.Straight line motion mechanismsCondition for perfect steeringLocus of pt.C will be a straight line, to AE if, is constant.Proof:65

1.a) Peaucellier mechanism 66

1.b) Roberts mechanism67

1.c) Pantograph 68

2.Indexing Mechanism

Geneva wheel mechanism69

3.Ratchets and EscapementsRatchet and pawl mechanism70

Application of Ratchet Pawl mechanism71

4. Toggle mechanismConsidering the equilibrium condition of slider 6,

For small angles of , F is much smaller than P.

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5.Hookes joint73

Hookes joint74

6.Steering gear mechanismCondition for perfect steering75

Ackermann steering gear mechanism76

Mechanical AdvantageMechanical Advantage of the Mechanism at angle a2 = 00 or 1800

Extreme position of the linkage is known as toggle positions.

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Transmission Angle

= a1=Crank Angle = a2 =Angle between crank and Coupler = a3 =Transmission angleCosine Lawa2 + d2 -2ad cos =b2 + c2 -2 bc cos Where a=AD, b=CD,c=BC, d=ABDetermine .78Design of Mechanism1.Slider Crank MechanismLink Lengths, Stroke Length, Crank Angle specified. 2.Offset Quick Return MechanismLink Lengths, Stroke Length, Crank Angle, Time Ratio specified.3.Four Bar Mechanism Crank Rocker MechanismLink Lengths and Rocker angle Specified.

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