Kinematics of machinery
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Transcript of Kinematics of machinery
05/01/2023 By - T.S.SENTHILKUMAR/AP 1
KINEMATICS OF MACHINERY
05/01/2023 By - T.S.SENTHILKUMAR/AP 2
Mechanics
Dynamics
Kinetics Kinematics
Statics
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MECHANICS• The branch of scientific analysis that deals
with motions, time and forces is called mechanics.
• It is divided in to two parts statics and dynamics.
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CONT.…
STATICS• It deals with the analysis of stationary systems.
But time is not considered.DYNAMICS• It deals with the systems that change with
time.
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CONT.…
KINEMATICS• It is the study of motion, quite apart from the
forces which produce that motion.• It is the study of position, displacement,
rotation, speed, velocity and acceleration.KINETICS• It is the study of motion and its causes
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KINEMATICS
The subject matter which deals with this geometric constant of relative motion, without any reference to the cause of the motion that is the force is called kinematics.
For the study of kinematics, a machine may be referred to as a mechanism, which is a combination of inter connected rigid bodies capable of relative motion.
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MACHINERY Machinery is defined as a mechanical device or
the parts that keep something working. Machines or machine parts considered as a group. The working parts of a particular machine. An assemblage of machines. The parts of a machine collectively. An assemblage of machines or mechanical
apparatuses
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MECHANISM• It is defined as the combination of rigid or
resistance bodies assembled in such a way that the motion of one causes constrained and predictable motion to others is known as mechanism.
• If one of the links of a kinematic chain is fixed, then the chain is known as mechanism.
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MECHANISM An assembly of moving parts performing a complete
functional motion. A mechanism is a device designed to transform input
forces and movement into a desired set of output forces and movement.
Mechanisms generally consist of moving components such as gears and gear trains, belt and chain drives, cam and follower mechanisms, and linkages as well as friction devices such as brakes and clutches, and structural components such as the frame, fasteners, bearings, springs, lubricants and seals, as well as a variety of specialized machine elements such as splines, pins and keys.
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MACHINE• It is defined as a device which receives energy
and transforms it into some useful work.• If the mechanism is used to transmit power
(or) to do work, then it is known as machine.• The main function of the machine is to obtain
mechanical advantage.
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MACHINE
We can define machine as a device for transferring and transforming motion and force or power from the input that is, the source to the output that is the load.
The motion needs to be transformed as it is being transferred from the source to the load.
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KINEMATIC LINK, PAIR AND CHAIN
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KINEMATIC LINK
• It is a resistant body or assembly of resistant body of a machine connecting other parts of the machine with relative motion between them.
• There are three types of links available in order to transmit motion. They are as follows:
»Rigid link» Flexible link» Fluid link
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CONT.…Rigid linkA rigid link is one which does not undergo any deformation while transmitting motion. Practically rigid link does not exists. Ex : crank shaft, piston etc.,Flexible linkA flexible link is one which undergoes partial deformation without affecting the transfer motion. Ex : ropes, belts, chains, springs etc.,Fluid linkA fluid link is a link which has fluid inside the container and motion is transmitted through the fluid by pressure or compression. Ex: fluids used in hydraulic press, hydraulic jack, hydraulic crane etc.,
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Binary link, Ternary link, Quaternary link
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KINEMATIC PAIR
• A joint of two links that permits relative motion is called pair.
Types of kinematic pair1. Nature of relative motion between the links.2. Nature of contact between the links.3. Nature of mechanical arrangement.
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CONT.…Nature of relative motion
» Sliding pair» Turning pair» Cylindrical pair» Rolling pair» Spherical pair» Helical pair
Nature of contact» Lower pair» Higher pair
Nature of mechanical constraint» Closed pair» Unclosed pair
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Sliding pair
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Turning pair
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Cylindrical pair
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Rolling pair
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Spherical pair
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Helical pair or screw pair
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Lower pair
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Higher pair
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NATURE OF CONTACT
Closed pair• When two elements of a pair are held together
mechanically, they constitute a closed pair. Ex : All pair
Un closed pair• When two elements of a pair are not held
together mechanically, they constitute a unclosed pair.
Ex : cam and follower
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KINEMATIC CHAIN
• If the last link is joined to first link to transmit definite motion, then it is known as kinematic chain.
• To determine the given assemblage of links form the kinematic chain or not:• The two equations are:l = 2p – 4j = (3/2) * l – 2Where, l = number of linksp = number of pairsj = number of joints
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CONSTRAINED MOTIONS
Constrained Motions
Completely Constrained Motion
Uncompletely Constrained Motion
Successfully Constrained Motion
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TYPES OF JOINTS
JOINTSTernary
jointBinary joint Quaternary joint
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DEGREES OF FREEDOM The analysis of mechanism is the number of
degrees of freedom, also called the mobility of the device.
The mobility of a mechanism is defined as the number of input parameters which must be controlled independently in order to bring the device in to a particular position.
It is the number of independent coordinates required to describe the position of a body in space.
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DIFF. B/W MOVABILITY AND MOBILITY
Movability includes the six degrees of freedom of the device as a whole, as through the ground link were not fixed and thus applies to a kinematic chain.
Mobility neglects these and considers only the internal motions, thus applying to a mechanism.
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DESCRIPTION OF MOBILITY A link is to have ‘n’ degree of freedom if it has n
independent variables associated with its position in the plane.
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Then the number of degree of freedom of a mechanism (n) is given by,
n = 3 (l-1) – 2j – h
where, l = number of links j = number of binary joints h = number of higher pairs
This equation is called kutzbach criterion for the mobility of a mechanism.
If there is no higher pair, then h = 0. then kutzbach criterion, n = 3 (l-1) – 2j
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APPLICATION OF KUTZBACH CRITERION TO PLANE MECHANISM
• Mechanism with lower pairs– Three bar mechanism– Four bar mechanism– Five bar mechanism– Six bar mechanism
• Mechanism with higher pairs
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KUTZBACH CRITERION FOR SPATIAL MECHANISMS
n = 6(l-1) – 5P1 – 4P2 – 3P3 – 2P4 – 1P5
Where, n = Number of degree of freedom
l = Number of links
P1 = Number of pair having one degree of freedom
P2 = Number of pair having two degree of freedom
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GRUBLER’S CRITERION FOR PLANE MECHANISM
• Grubler’s mechanism is obtained by substituting n = 1 and h = 0 in Kutzbach criterion as below.
we know that, n = 3 (l-1) – 2j - h
l = 3 (l -1) – 2jor
3l – 2j – 4 = 0This equation is known as Grubler’s criterion for
plane mechanism
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GRUBLER’S CRITERION FOR SPATIAL MECHANISM
We know that Kutzbach criterion for spatial mechanism is
n = 6(l-1) – 5P1 – 4P2 – 3P3 – 2P4 – 1P5
substitute n = 1; P2, P3 , … P5 = 0
1 = 6(l-1) – 5P1 (or) 6l – 5P1 – 7 = 0This equation is known as Grubler’s equation forspatial mechanism.
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MECHANISM
• When one of the links of kinematic chain is fixed, then the chain is known as mechanism.
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TYPES OF MECHANISM
1. Simple mechanism2. Compound mechanism
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MACHINE
Kinematic Pair
When Connected As
Per Kutzbach’s Criterion
Kinematic Chain
When One Link Is FixedMechanism
When Forces And Couples
Are Transmitted
Machine
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INVERSION OF MECHANISM
The method of obtaining different mechanisms by fixing different links in a kinematic chain, is known as inversion of the mechanism.
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TYPES OF KINEMATIC CHAIN
Kinematic chain
Four bar chain Slider crank chain
Double crank chain
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FOUR BAR CHAIN
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Inversion Of Four
Bar Chain
Beam Engine
Coupled Locomotive Wheels
Watt’s Indicator Mechanis
m
Pantograph
Ackermann
Mechanism
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INVERSION OF FOUR BAR CHAINFirst
inversionBeam
Engine
second Inversion
Coupling rod of
locomotive
Third Inversion
Watt’s Indicator Mechanism
Pantograph
Ackermann Steering
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FIRST INVERSIONBeam engine• Mechanism.Gif\inversion of four bar chain\beam-
engine-o.Gif
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SECOND INVERSION
Coupling rod of a locomotive
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THIRD INVERSION
Watt’s indicator mechanism
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Pantograph
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ACKERMANN STEERING
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SINGLE SLIDER CRANK CHAIN
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INVERSION OF SLIDER CRANK CHAIN
Sing
le sl
ider
cra
nk
chai
n
Reciprocating engine
Reciprocating compressor
Whitworth quick return mechanismRotary or Gnome
engineCrank and slotted lever mechanism
Oscillating cylinder engine
Bull engine
Pump engine
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First Inversion
Reciprocating engine
Reciprocating compressor
Second Inversion
Whitworth quick return mechanism
Rotary engine
Third Inversion
Oscillating cylinder engine
Crank and slotted lever mechanism
Fourth Inversion
Bull Engine
Hand Pump
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FIRST INVERSION
• Reciprocating engine
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• Reciprocating compressor
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SECOND INVERSION
• Whitworth Quick Return Mechanism
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• Rotary Engine
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THIRD INVERSION
• Oscillating Cylinder Engine
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• Crank and Slotted lever Quick return Mechanismbasic1_quickreturn.gif
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FOURTH INVERSION
• Pendulum pump or bull engine
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• Hand pump
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DOUBLE SLIDER CRANK CHAIN
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Double Slider Crank Chain
Elliptical Trammel
Scotch Yoke Mechanism
Oldham Coupling
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FIRST INVERSION
Elliptical Trammel
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SECOND INVERSION
Scotch Yoke Mechanism
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THIRD INVERSION
Oldham's Coupling
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• Oldham's Coupling
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CLASSIFICATION OF MECHANISMS
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SNAP AND ACTION
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LINEAR ACTUATORS
• Stationary screws with travelling nuts• Stationary nuts with travelling screws• Single and double acting hydraulic and
pneumatic cylinders.
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FINE ADJUSTMENT
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CLAMPING MECHANISM
• C-Clamp
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SWINGING OR ROCKING• This type of mechanism produces a swinging or rocking
motion of a link. The motion is generally less than 360o and is an oscillatory motion.
Toothed Rack System• This is simply a rotating arm (b) with a link fitted with a
toothed rack (c) which meshes with a gear (d) to produce a rocking motion of the gear.
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SWINGING OR ROCKING (CONT..)
Crank and Rocker Mechanism• This is simply a four bar linkage (the frame
provides the first link). The operating characteristics are dependent on the length of the links and the design of the frame setting the pivot points..Rotation of the arm (b) produces a rocking motion of arm (d).
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SWINGING OR ROCKING (CONT..)
Crank and Rocker Mechanism
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SWINGING OR ROCKING (CONT..)
Quick Return linkage• The arm (b) rotates and results in a rocking
motion of arm (d)via the slider (c). The action is a quick return action because the angle (b) rotates through in one direction ,assumed to be the forward direction, is greater than the angle which result in the return motion.
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SWINGING OR ROCKING (CONT..)
Quick Return linkage
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SWINGING OR ROCKING (CONT..)
Cam and Follower Mechanism• Rotation of the cam (c) produces a rocking
motion of the lever (d) via the sliding interface (b). The arrangement only identifies the principle involved. In practice some means would have to be provided to ensure the lever is maintained in contact with the lever.
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SWINGING OR ROCKING (CONT..)
Cam and Follower Mechanism
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RATCHETS AND ESCAPEMENTS
• This mechanism is for rectilinear motion
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• This mechanism is used to regulate the movement of clock.
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REVERSING MECHANISM
• When a mechanism is desired which is capable of delivering output rotation in the either direction, some form of reversing mechanism is required.
• Ex : gear shifting
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COUPLINGS AND CONNECTORS
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INDEXING MECHANISM
• C:\Users\senthil\Desktop\Geneva_mechanism_6spoke_animation.gif
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Application of the Geneva drive• One is movie projectors : the film does not run
continuously through the projector. Instead, the film is advanced frame by frame, each frame standing still in front of the lens for 1/24 of a second
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STRAIGHT LINE MECHANISM
• Peaucellier Mechanism
C:\Users\senthil\Desktop\Peaucellier_linkage_animation.gif
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• Robert’s Mechanism
C:\Users\senthil\Desktop\Roberts_linkage.gif
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• Chebychev Mechanism
C:\Users\senthil\Desktop\Chebyshev_linkage.gif
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SLIDING CONNECTORS
• This connectors are used when one slider is to drive another slider.
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STOP, PAUSE AND HESITATION MECHANISM
• In an automobile engine a valve must open, remain open for a period of time, and then close.
Ex : cam and follower
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CURVE GENERATORS
• The connecting rod of a planar four bar linkage may be imagined as an infinite plane extending in all directions but pin connected to the input and output links.
• Then, during motion of the linkage, any point attached to the plane of the coupler generates some path with respect to the fixed link, this path is called coupler curve.