unit-I-KOM

KINEMATICS OF MECHINERY:

24 July 2011 1 Kinematics of Machinery - Unit - I KINEMATICS OF MECHINERY

KINEMATICS OF MECHINERY:

24 July 2011 2 Kinematics of Machinery - Unit - I KINEMATICS OF MECHINERY Unit – I-Basics of Mechanism Unit – II – Kinematics Unit – III – Cams Unit – IV – Gears Unit – V - Friction

Unit – I-Basics of Mechanism:

24 July 2011 3 Kinematics of Machinery - Unit - I Unit – I-Basics of Mechanism 1.Terminologies Machine Mechanism Kinematic Pair Links Kinematic Chain 2.DOF Kutzhback Equation Grubler Equation 3.Grashoff Law 4.Mechanism Four Bar Single-Slider Crank Double-Slider 5.Inversion of Mechanism 6.Mechanical Advantage 7.Transmission Angle 8.Design of Mechanism

MECHANISM:

24 July 2011 4 Kinematics of Machinery - Unit - I MECHANISM Mechanism – Part of a machine, which transmit motion and power from input point to output point

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Example for Mechanism:

24 July 2011 6 Kinematics of Machinery - Unit - I Example for Mechanism

Example for Mechanism:

24 July 2011 7 Kinematics of Machinery - Unit - I Example for Mechanism

PLANAR MECHANISMS :

24 July 2011 8 Kinematics of Machinery - Unit - I 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.

MACHINE :

24 July 2011 9 Kinematics of Machinery - Unit - I MACHINE A machine is a mechanism or collection of mechanisms, which transmit force from the source of power to the resistance to be overcome.

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24 July 2011 10 Kinematics of Machinery - Unit - I Though all machines are mechanisms, all mechanisms are not machines

KINEMATICS:

24 July 2011 11 Kinematics of Machinery - Unit - I KINEMATICS

RELEVANCE OF KINEMATIC STUDY:

24 July 2011 12 Kinematics of Machinery - Unit - I RELEVANCE OF KINEMATIC STUDY Motion requirements Design requirements

MOTION STUDY:

24 July 2011 13 Kinematics of Machinery - Unit - I MOTION STUDY Study of position, displacement, velocity and acceleration of different elements of mechanism Given input Desired output

Motion requirement:

24 July 2011 14 Kinematics of Machinery - Unit - I Motion requirement

DESIGN REQUIREMENTS:

24 July 2011 15 Kinematics of Machinery - Unit - I DESIGN REQUIREMENTS Design: determination of shape and size Requires knowledge of material Requires knowledge of stress Requires knowledge of load acting (i) static load (ii) dynamic/inertia load

DYNAMIC/INERTIA LOAD:

24 July 2011 16 Kinematics of Machinery - Unit - I DYNAMIC/INERTIA LOAD Inertia load require acceleration

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LINK OR ELEMENT:

24 July 2011 20 Kinematics of Machinery - Unit - I LINK OR ELEMENT Any body (normally rigid) which has motion relative to another Binary link Ternary link Quaternary link

Examples of rigid links:

24 July 2011 21 Kinematics of Machinery - Unit - I Examples of rigid links

PAIRING ELEMENTS:

24 July 2011 22 Kinematics of Machinery - Unit - I PAIRING ELEMENTS Pairing elements: the geometrical forms by which two members of a mechanism are joined together, so that the relative motion between these two is consistent . Such a pair of links is called Kinematic Pair .

PAIRING ELEMENTS:

24 July 2011 23 Kinematics of Machinery - Unit - I PAIRING ELEMENTS

PAIRING ELEMENTS:

24 July 2011 24 Kinematics of Machinery - Unit - I PAIRING ELEMENTS

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KINEMATIC PAIRS:

24 July 2011 28 Kinematics of Machinery - Unit - I KINEMATIC PAIRS A mechanism has been defined as a combination so connected that each moves with respect to each other. A clue to the behavior lies in in the nature of connections, known as kinetic pairs. The degree of freedom of a kinetic pair is given by the number independent coordinates required to completely specify the relative movement.

TYPES OF KINEMATIC PAIRS :

24 July 2011 29 Kinematics of Machinery - Unit - I 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)PlanarPair

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24 July 2011 30 Kinematics of Machinery - Unit - I (ii) Higher pair: The contact between the pairing elements takes place at a point or along a line.

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24 July 2011 31 Kinematics of Machinery - Unit - I Based on relative motion between pairing elements (a) Siding pair [DOF = 1] (b) Turning pair (revolute pair) [DOF = 1]

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24 July 2011 32 Kinematics of Machinery - Unit - I Based on relative motion between pairing elements (c) Cylindrical pair [DOF = 2] (d) Rolling pair [DOF = 1]

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24 July 2011 33 Kinematics of Machinery - Unit - I Based on relative motion between pairing elements (e) Spherical pair [DOF = 3] (f) Helical pair or screw pair [DOF = 1]

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24 July 2011 34 Kinematics of Machinery - Unit - I Based on the nature of mechanical constraint (a) Closed pair (b) Unclosed or force closed pair

CONSTRAINED MOTION :

24 July 2011 35 Kinematics of Machinery - Unit - I CONSTRAINED MOTION one element has got only one definite motion relative to the other

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24 July 2011 36 Kinematics of Machinery - Unit - I (a) Completely constrained motion

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24 July 2011 37 Kinematics of Machinery - Unit - I (b) Successfully constrained motion

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24 July 2011 38 Kinematics of Machinery - Unit - I (c) Incompletely constrained motion

KINEMATIC CHAIN :

24 July 2011 39 Kinematics of Machinery - Unit - I KINEMATIC CHAIN Group of links either joined together or arranged in a manner that permits them to move relative to one another.

Kinematic Chain:

24 July 2011 40 Kinematics of Machinery - Unit - I 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

LOCKED CHAIN (Or) STRUCTURE :

24 July 2011 41 Kinematics of Machinery - Unit - I LOCKED CHAIN (Or) STRUCTURE Links connected in such a way that no relative motion is possible. L=3, J=3, P=3 L.H.S>R.H.S

Kinematic Chain Mechanism:

24 July 2011 42 Kinematics of Machinery - Unit - I Kinematic Chain Mechanism Slider crank and four bar mechanisms L=4, J=4, P=4 L.H.S=R.H.S

Working of slider crank mechanism:

24 July 2011 43 Kinematics of Machinery - Unit - I Working of slider crank mechanism

Unconstrained kinematic chain L=5,P=5,J=5 L.H.S < R.H.S :

24 July 2011 44 Kinematics of Machinery - Unit - I Unconstrained kinematic chain L=5,P=5,J=5 L.H.S < R.H.S

DEGREES OF FREEDOM (DOF): :

24 July 2011 45 Kinematics of Machinery - Unit - I DEGREES OF FREEDOM (DOF): It is the number of independent coordinates required to describe the position of a body.

Degrees of freedom/mobility of a mechanism :

24 July 2011 46 Kinematics of Machinery - Unit - I 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.

GRUBLER’S CRITERION :

24 July 2011 47 Kinematics of Machinery - Unit - I GRUBLER’S CRITERION Number of degrees of freedom of a mechanism is given by F = 3(n-1)-2l-h. Where, 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:

24 July 2011 48 Kinematics of Machinery - Unit - I Examples - DOF F = 3(n-1)-2l-h Here, n = 4, l = 4 & h = 0. F = 3(4-1)-2(4) = 1 I.e., one input to any one link will result in definite motion of all the links.

Examples - DOF:

24 July 2011 49 Kinematics of Machinery - Unit - I Examples - DOF F = 3(n-1)-2l-h Here, n = 5, l = 5 and h = 0. F = 3(5-1)-2(5) = 2 I.e., two inputs to any two links are required to yield definite motions in all the links.

Examples - DOF:

24 July 2011 50 Kinematics of Machinery - Unit - I 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 - DOF:

24 July 2011 51 Kinematics of Machinery - Unit - I Examples - DOF 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

Examples - DOF:

24 July 2011 52 Kinematics of Machinery - Unit - I Examples - DOF F = 3(n-1)-2l-h Here, n = 11, l = 15 (two lower pairs at the intersection of 3, 4, 6 ; 2, 4, 5 ; 5, 7, 8 ; 8, 10, 11 ) and h = 0. F = 3(11-1)-2(15) = 0

Examples - DOF:

24 July 2011 53 Kinematics of Machinery - Unit - I Examples - DOF (a) F = 3(n-1)-2l-h Here, n = 4, l = 5 and h = 0. F = 3(4-1)-2(5) = -1 I.e., it is a structure (b) F = 3(n-1)-2l-h Here, n = 3, l = 2 and h = 1. F = 3(3-1)-2(2)-1 = 1 (c) F = 3(n-1)-2l-h Here, n = 3, l = 2 and h = 1. F = 3(3-1)-2(2)-1 = 1

Determining DOF and Pairs:

24 July 2011 54 Kinematics of Machinery - Unit - I Determining DOF and Pairs N b =No of Binary Links N t =No of Ternary Links N o =No of Other Links N=Total No of Links L=No of Loops P=No of Pairs M=Mobility or DOF P=N+L-1 M=N-(2L+1)

Determining DOF and Pairs:

24 July 2011 55 Kinematics of Machinery - Unit - I Determining DOF and Pairs P=N+L-1 M=N-(2L+1) N b = 4,N t =2, N 0 =0 N=6, L=2 Sol: P=6+2-1=7 M=6-(2x2 +1)=1

Determining DOF and Pairs:

24 July 2011 56 Kinematics of Machinery - Unit - I Determining DOF and Pairs P=N+L-1 M=N-(2L+1) N b = 5,N t =1, N 0 =0 N=6, L=2 Sol: P=6+2-1=7 M=6-(2x2 +1)=1

Determining DOF and Pairs:

24 July 2011 57 Kinematics of Machinery - Unit - I Determining DOF and Pairs P=N+L-1 M=N-(2L+1) N b = 9,N t =0, N 0 =2 N=11, L=5 Sol: P=11+5-1=15 M=11-(2x5 +1)=0

Grashoff Law:

24 July 2011 58 Kinematics of Machinery - Unit - I Grashoff Law The sum of the shortest and longest link length should not exceed the sum of the other two link lengths. s+l < p+q (e.x) (1+2) < (3+4)

INVERSIONS OF MECHANISM :

24 July 2011 59 Kinematics of Machinery - Unit - I 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. These are called as inversions of the mechanism.

INVERSIONS OF MECHANISM:

24 July 2011 60 Kinematics of Machinery - Unit - I INVERSIONS OF MECHANISM 1.Four Bar Chain 2.Single Slider Crank 3.Double Slider Crank

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1. FOUR BAR CHAIN :

24 July 2011 64 Kinematics of Machinery - Unit - I 1. FOUR BAR CHAIN (link 1) frame (link 2) crank (link 3) coupler (link 4) rocker

INVERSIONS OF FOUR BAR CHAIN:

24 July 2011 65 Kinematics of Machinery - Unit - I INVERSIONS OF FOUR BAR CHAIN Fix link 1& 3. Crank-rocker or Crank-Lever mechanism Fix link 2. Drag link or Double Crank mechanism Fix link 4. Double rocker mechanism Pantograph

APPLICATION link-1 fixed- CRANK-ROCKER MECHANISM OSCILLATORY MOTION:

24 July 2011 66 Kinematics of Machinery - Unit - I APPLICATION link-1 fixed- CRANK-ROCKER MECHANISM OSCILLATORY MOTION

CRANK-ROCKER MECHANISM:

24 July 2011 Kinematics of Machinery - Unit - I 67 CRANK-ROCKER MECHANISM

Link 2 Fixed- DRAG LINK MECHANISM :

24 July 2011 68 Kinematics of Machinery - Unit - I Link 2 Fixed- DRAG LINK MECHANISM

Locomotive Wheel - DOUBLE CRANK MECHANISM :

24 July 2011 69 Kinematics of Machinery - Unit - I Locomotive Wheel - DOUBLE CRANK MECHANISM

2.SLIDER CRANK CHAIN Link1=Ground Link2=Crank Link3=ConnectingRod Link4=Slider :

24 July 2011 70 Kinematics of Machinery - Unit - I 2.SLIDER CRANK CHAIN Link1=Ground Link2=Crank Link3=ConnectingRod Link4=Slider

lnversions of slider crank chain :

24 July 2011 71 Kinematics of Machinery - Unit - I lnversions of slider crank chain crank fixed (b) connecting rod fixed (c) slider fixed Link 2 fixed Link 3 fixed Link 4 fixed

Application Inversion II – Link 2 Crank fixed Whitworth quick return motion mechanism:

24 July 2011 72 Kinematics of Machinery - Unit - I Application Inversion II – Link 2 Crank fixed Whitworth quick return motion mechanism

Quick return motion mechanisms:

24 July 2011 73 Kinematics of Machinery - Unit - I Quick return motion mechanisms Drag link mechanism

Rotary engine– II inversion of slider crank mechanism. (crank fixed):

24 July 2011 74 Kinematics of Machinery - Unit - I Rotary engine– II inversion of slider crank mechanism. (crank fixed)

Application Inversion III -Link 3 Connecting rod fixed Crank and slotted lever quick return mechanism:

24 July 2011 75 Kinematics of Machinery - Unit - I Application Inversion III -Link 3 Connecting rod fixed Crank and slotted lever quick return mechanism

Crank and slotted lever quick return motion mechanism:

24 July 2011 Kinematics of Machinery - Unit - I 76 Crank and slotted lever quick return motion mechanism

Crank and slotted lever quick return motion mechanism:

24 July 2011 77 Kinematics of Machinery - Unit - I Crank and slotted lever quick return motion mechanism

Application of Crank and slotted lever quick return motion mechanism:

24 July 2011 78 Kinematics of Machinery - Unit - I Application of Crank and slotted lever quick return motion mechanism

Oscillating cylinder engine–III inversion of slider crank mechanism (connecting rod fixed) :

24 July 2011 79 Kinematics of Machinery - Unit - I Oscillating cylinder engine–III inversion of slider crank mechanism (connecting rod fixed)

Application Inversion IV – Link 4 Slider fixed Pendulum pump or bull engine:

24 July 2011 80 Kinematics of Machinery - Unit - I Application Inversion IV – Link 4 Slider fixed Pendulum pump or bull engine

3. DOUBLE SLIDER CRANK CHAIN :

24 July 2011 81 Kinematics of Machinery - Unit - I 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 -I Link 3 Coupler Link 4 Slider - II

Inversion I – Frame Fixed Double slider crank mechanism:

24 July 2011 82 Kinematics of Machinery - Unit - I Inversion I – Frame Fixed Double slider crank mechanism Elliptical trammel AC = p and BC = q, then, x = q.cosθ and y = p.sinθ. Rearranging,

Inversion II – Slider - I Fixed SCOTCH –YOKE MECHANISM :

24 July 2011 83 Kinematics of Machinery - Unit - I Inversion II – Slider - I Fixed SCOTCH –YOKE MECHANISM Turning pairs –1&2, 2&3; Sliding pairs – 3&4, 4&1

Inversion III – Coupler Fixed OLDHAM COUPLING :

24 July 2011 84 Kinematics of Machinery - Unit - I Inversion III – Coupler Fixed OLDHAM COUPLING

Other Mechanisms 1.Straight line motion mechanisms:

24 July 2011 85 Kinematics of Machinery - Unit - I Other Mechanisms 1.Straight line motion mechanisms Condition for perfect steering Locus of pt.C will be a straight line, ┴ to AE if, is constant. Proof:

1.a) Peaucellier mechanism:

24 July 2011 86 Kinematics of Machinery - Unit - I 1.a) Peaucellier mechanism

1.b) Robert’s mechanism:

24 July 2011 87 Kinematics of Machinery - Unit - I 1.b) Robert’s mechanism

1.c) Pantograph:

24 July 2011 88 Kinematics of Machinery - Unit - I 1.c) Pantograph

2.Indexing Mechanism :

24 July 2011 89 Kinematics of Machinery - Unit - I 2.Indexing Mechanism Geneva wheel mechanism

3.Ratchets and Escapements:

24 July 2011 90 Kinematics of Machinery - Unit - I 3.Ratchets and Escapements Ratchet and pawl mechanism

Application of Ratchet Pawl mechanism:

24 July 2011 91 Kinematics of Machinery - Unit - I Application of Ratchet Pawl mechanism

4. Toggle mechanism:

24 July 2011 92 Kinematics of Machinery - Unit - I 4. Toggle mechanism Considering the equilibrium condition of slider 6, For small angles of α , F is much smaller than P.

5.Hooke’s joint:

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Hooke’s joint:

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6.Steering gear mechanism:

24 July 2011 95 Kinematics of Machinery - Unit - I 6.Steering gear mechanism Condition for perfect steering

Ackermann steering gear mechanism:

24 July 2011 96 Kinematics of Machinery - Unit - I Ackermann steering gear mechanism

Mechanical Advantage:

24 July 2011 97 Kinematics of Machinery - Unit - I Mechanical Advantage Mechanical Advantage of the Mechanism at angle a2 = 0 0 or 180 0 Extreme position of the linkage is known as toggle positions.

Transmission Angle:

24 July 2011 98 Kinematics of Machinery - Unit - I Transmission Angle θ = a1=Crank Angle γ = a2 =Angle between crank and Coupler μ = a3 =Transmission angle Cosine Law a 2 + d 2 -2ad cos θ = b 2 + c 2 -2 bc cos μ Where a=AD, b=CD, c=BC, d=AB Determine μ .

Design of Mechanism:

24 July 2011 99 Kinematics of Machinery - Unit - I Design of Mechanism 1.Slider – Crank Mechanism Link Lengths, Stroke Length, Crank Angle specified. 2.Offset Quick Return Mechanism Link Lengths, Stroke Length, Crank Angle, Time Ratio specified. 3.Four Bar Mechanism – Crank Rocker Mechanism Link Lengths and Rocker angle Specified.

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