Kinematics of machinery

05/01/2023 By - T.S.SENTHILKUMAR/AP 1

KINEMATICS OF MACHINERY


Mechanics

Dynamics

Kinetics Kinematics

Statics


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.


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.


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


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.


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


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.


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.


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.


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.


KINEMATIC LINK, PAIR AND CHAIN


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


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.,


Binary link, Ternary link, Quaternary link


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.


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


Sliding pair


Turning pair


Cylindrical pair


Rolling pair


Spherical pair


Helical pair or screw pair


Lower pair


Higher pair


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


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


CONSTRAINED MOTIONS

Constrained Motions

Completely Constrained Motion

Uncompletely Constrained Motion

Successfully Constrained Motion


TYPES OF JOINTS

JOINTSTernary

jointBinary joint Quaternary joint


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.



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.


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.


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


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


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


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


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.


MECHANISM

• When one of the links of kinematic chain is fixed, then the chain is known as mechanism.


TYPES OF MECHANISM

1. Simple mechanism2. Compound mechanism


MACHINE

Kinematic Pair

When Connected As

Per Kutzbach’s Criterion

Kinematic Chain

When One Link Is FixedMechanism

When Forces And Couples

Are Transmitted

Machine


INVERSION OF MECHANISM

The method of obtaining different mechanisms by fixing different links in a kinematic chain, is known as inversion of the mechanism.


TYPES OF KINEMATIC CHAIN

Kinematic chain

Four bar chain Slider crank chain

Double crank chain


FOUR BAR CHAIN


Inversion Of Four

Bar Chain

Beam Engine

Coupled Locomotive Wheels

Watt’s Indicator Mechanis

m

Pantograph

Ackermann

Mechanism


INVERSION OF FOUR BAR CHAINFirst

inversionBeam

Engine

second Inversion

Coupling rod of

locomotive

Third Inversion

Watt’s Indicator Mechanism

Pantograph

Ackermann Steering


FIRST INVERSIONBeam engine• Mechanism.Gif\inversion of four bar chain\beam-

engine-o.Gif


SECOND INVERSION

Coupling rod of a locomotive


THIRD INVERSION

Watt’s indicator mechanism


Pantograph


ACKERMANN STEERING


SINGLE SLIDER CRANK CHAIN


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


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


FIRST INVERSION

• Reciprocating engine


• Reciprocating compressor


SECOND INVERSION

• Whitworth Quick Return Mechanism


• Rotary Engine


THIRD INVERSION

• Oscillating Cylinder Engine


• Crank and Slotted lever Quick return Mechanismbasic1_quickreturn.gif


FOURTH INVERSION

• Pendulum pump or bull engine


• Hand pump


DOUBLE SLIDER CRANK CHAIN


Double Slider Crank Chain

Elliptical Trammel

Scotch Yoke Mechanism

Oldham Coupling


FIRST INVERSION

Elliptical Trammel


SECOND INVERSION

Scotch Yoke Mechanism


THIRD INVERSION

Oldham's Coupling


• Oldham's Coupling


CLASSIFICATION OF MECHANISMS


SNAP AND ACTION


LINEAR ACTUATORS

• Stationary screws with travelling nuts• Stationary nuts with travelling screws• Single and double acting hydraulic and

pneumatic cylinders.


FINE ADJUSTMENT


CLAMPING MECHANISM

• C-Clamp


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.


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).



Crank and Rocker Mechanism



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.



Quick Return linkage



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.



Cam and Follower Mechanism


RATCHETS AND ESCAPEMENTS

• This mechanism is for rectilinear motion


• This mechanism is used to regulate the movement of clock.




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


COUPLINGS AND CONNECTORS




INDEXING MECHANISM

• C:\Users\senthil\Desktop\Geneva_mechanism_6spoke_animation.gif


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



STRAIGHT LINE MECHANISM

• Peaucellier Mechanism

C:\Users\senthil\Desktop\Peaucellier_linkage_animation.gif


• Robert’s Mechanism

C:\Users\senthil\Desktop\Roberts_linkage.gif


• Chebychev Mechanism

C:\Users\senthil\Desktop\Chebyshev_linkage.gif


SLIDING CONNECTORS

• This connectors are used when one slider is to drive another slider.


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


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.

Engineering

Kinematics of machinery