session 1 introduction to kinematics

8/12/2019 Session 1 Introduction to Kinematics

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M.S. Ramaiah School of Advanced Studies, Bengaluru

PEMP

MMD2509

Introduction to Kinematics

Session delivered by:

Dr. Arun R. Rao


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Session Objectives

At the end of the session, the students would have understood

about Fundamentals of kinematics

Types of motion,

Links, Joints

Kinematic-chains,

Mechanisms, Structure, Linkage transformation

Intermittent motion Inversions,

Four bar linkage and Inversions

Slider Crank Mechanism and Inversions

Straight-line Motion Mechanisms


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Engineering mechanics

Engineering mechanics is a branch of the physical

sciences which looks to understand the actions andreactions of bodies at rest or in motion.

Much of modern engineering mechanics is based onIsaac Newton's laws of motion while the modern

practice of their application can be traced back toTimoshenko, who is said to be the father of modernengineering mechanics.

Engineering mechanics can be subdivided into statics,strength of materials, dynamics, deformable bodies andfluid mechanics.


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Mechanics


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Statics:

Statics deals with the analysis of stationary systems, that is, those inwhich time is not a factor

Dynamics:deals with systems that change with time.

Kinematics

Kinematics is the branch of dynamics that consists of the study ofmotion without the reference to the forces that cause, or aredeveloped by, the motion. It is the study of motion, quite apart fromthe forces which produce that motion. More particularly,kinematics is the study of position, displacement, rotation, speed,velocity, and acceleration

Kinetics

It is the study of force on system during motion where the effectsof the forces on the body is considered..


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Machine

It is a combination of resistant bodies

so arranged that by their means themechanical forces of nature can be

compelled to do work accompanied

by certain determinate motion

Structure

It is also a combination of resistant

bodies connected by joints, but its

purpose is not to do work or totransform motion. A structure is

intended to be rigid


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Machine

A machine is a mechanism or group of mechanism used toperform useful work. Its chief function is to adopt a source of

power to some specific work requirement


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MechanismsA mechanism is a constrained kinematic chain. Motion of any one link in the

kinematic chain will give a definite and predictable motion relative to each of the

others. Usually one of the links of the kinematic chain is fixed in a mechanismPlanar 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.

Water Pumping Mechanism Hydraulic Door retracting Mechanism


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Mechanisms Mechanisms are the mechanical

portion of machines that have

the function of transferring

motion and forces from a power

source (motor) to an output

A mechanism may, in general,

be considered a collection ofparts that are arranged and

connected so that they produce

the desired motion of the

machine

The primary purpose of mostmechanisms analyses is to

ensure that the device will

exhibit motion that will

accomplish the desired purpose

of the machine


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MECHANISMS AND STRUCTURES

The degree of freedom of an assembly of links completely predicts its character.

There are only three possibilities. If the DOF is positive, it will be a mechanism, and the link will have relativemotion.

If the DOF is exactly zero, then it will be a structure, and n motion is possible.

If the DOF is negative, then it is a preloaded structure, which means that nomotion is possible and some stresses may also be present at the time of assemblyFigure shows examples of these three cases. One link is grounded in each case.


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Element or Link Each part of a machine which has motion relative to some other

parts is termed an element or link

A link need not necessarily be rigid body, but it must be a resistant

body

E.g: incompressible fluids, belt, rope, chain etc

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Kinematic Pairs

Kinematic pairs may be classified as higherand lower pairs

Higher pair are the ones consisting ofline or point contact

while in motion as in the case of a roller or ball bearing

Lower pair are the ones consisting of surface contact

between two links as in pin joint or a slider

Lower Pairs may be classified as turning pairs, sliding pairs,

spherical pairs, screw or helical pairs and rolling pairs

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Based on nature of contact between elements

Lower pair

The joint by which two members are connected has surface contact.

Higher pair

The contact between the pairing elements takes place at a point or along a line.

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Kinematic Pairs

Sliding Pair Two elements are so connected that one is

constrained to have a sliding motion relative to the other

Screw Pair When one element turns about the other element by

means of threads, it forms a screw or helical pair

E.g.. Bolt and nut

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Kinematic Pairs

Turing Pair when two element are so connected that one

is constrained to turn about a fixed axis of other it forms aturning pair

E.g.. Crank Shaft turning in a bearing

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Spherical Pair- when one element is in the form of sphere turns

about the other fixed element it forms a spherical pair

E.g.. Ball and Socket joint

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Rolling Pair when two elements are so connected that one is

constrained to roll in other fixed element it forms a rolling pair

E.g.. Ball and roller bearing

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Lower Pairs

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Lower Pairs


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Higher Pairs

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Planar Mechanism

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Spherical Mechanisms

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Spatial Mechanisms

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Constrained Motion

one element has got only one definite motion relative to the other

Completely constrained motion

Successfully constrained motion

Incompletely

constrained motion

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Kinematic Chain A Kinematic chain is any group of links connected together for the

purpose of transmitting forces or motions

Locked Kinematic chain is an arrangement of links such that no link canmove relative to the other links in the chain

Constrained Kinematic Chain is an arrangement of links such that amovement of one link causes a definite predictable movement of the otherlinks

Unconstrained Kinematic Chain is an arrangement of links such that a

movement of one link does not cause a predictable movement of the otherlinks

InversionsBy making a different link in a kinematic chain the fixed member, weobtain a different mechanism. Thus any one of the links may be arbitrarilyselected as the fixed link, and each arrangement is an inversion of the

othersInversion of a kinematic linkage or mechanism is observing the motion ofthe members of the mechanism with fixing different links as referenceframe. Each time when a different link is chose as the frame link themechanism shows different characteristics of the motion.


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Quadratic Chain

Quadratic chain is a four links kinematic chain

Four bar chain and its inversion

A four bar mechanism is a mechanism having four rigid linkswith one link fixed, the chain consists of four turning pairs

The fixed link is referred to as the frame

The rotating link is called the driver or crank

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Quadratic Chain

The other rotating link is called the follower or rocker

The floating link is called the connecting rod

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Four Bar Chain Mechanism

The four-bar mechanism is called as a kinematic chain. In this

planar mechanism, four links are constrained by four cylindricaljoints. When one link is fixed or grounded, the motion of a second

link determines the motion of the third and fourth links

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Inversions of 4-bar Chain mechanism

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Inversions of 4-bar chain mechanism

CRANK-ROCKER MECHANISM DRAG LINK MECHANISM

DOUBLE CRANK MECHANISM

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Applications of 4-bar chain Mechanism

Brake of a Wheelchair Folding sofaBackhoe Excavator

Door MechanismSheet Metal Shear (Mechanical Workshop)

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Linkages of more than 4 bars

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More than 4 Link Mechanisms

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Slider Crank Mechanism

x

Connecting rod

Piston

Crank

arm

Crank pin

Cylinder

Crankshaft

Gudgeonpin

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Single slider crank Mechanism

The function of the reciprocating engine is to convert thereciprocating motion into rotary motion. It is a simplest from ofsingle slider crank chain mechanism. In reciprocating engine there

is one sliding pair and three turning pairs. In figure there are threeturning pairs and the sliding pair is formed between the cross headand the guides. Link 1 is fixed (frame). Link 2 will act as a crank,which rotates. Link 3 is a connecting rod and link 4 is a crosshead.

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lnversions of slider crank chain

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Multi-cylinder Engine- an inversion of slider crank

mechanism

Crankshaft piston

assembly

Pistons

Fuel

and air

Compressed

fuel and air

Spark plug

Crank armsCrank shaft

Connecting rods

Inlet & outletvalves

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Pendulum pump or bull engineIII inversion of slider crank mechanism (slider fixed)

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Oscillating Cylinder Engine

Inversion is obtained by fixing the link CD as shown in fig

As the crank rotates about C the slotted link AB slides over

the die block which is pivoted to the fixed link at D

The mechanism of oscillating cylinder engine is based

upon it

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Oscillating Cylinder Engine

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Whitworth Quick Return Mechanism The inversion is obtained by fixing the link BC. It is used in a number of applications

such as slotting and shaping machines

The crank CD rotates at uniform speed. The die block D slides along the slotted link

AB and causes this to revolute about B with variable speed

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Crank and slotted lever quick return motion mechanism

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Double Slider Crank Chain and its

Inversions The kinematic chain consists of two turning and two

sliding pair

Two slide block A and B slide along slots in a frame S and

the pins A and B on the slide blocks are connected by the

link AB as shown Such a Kinematic chain has three inversions

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Elliptical Trammel

It is an instrument for drawing ellipses. The slotted frame S is fixed. Any

point, such as P on the link AB except the midpoint of AB will trace an ellipseas the slide blocks A and B slide along their respective slots

The equation of an ellipse with centre at O is given by

sin2 + cos2 = x2 / a2 + y2/ b2 = 1

AC = p and BC = q,

then, x = q.cos and y = p.sin.

Rearranging,

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Oldhams Coupling

Second inversion is obtained by fixing the link AB as

shown

For a given angular displacement of any one of the slide

block, the frame and other block will turn through the same

angular displacement

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Scotch Yoke Mechanism

Third inversion isobtained by fixing any

one of the two blocks

A or B as shown in fig.

The link AB can rotate

about A as centre and

thus cause the frame to

reciprocate


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Straight line motion mechanisms

Condition for perfect steering Locus of pt.C will be a straight

line,to AE if,

is constant.Proof:

ACAB

..,

.

constACifABconstAE

constbutAD

AD

ACAB

AE

AE

AB

AC

AD

ABDAEC

==

=

=

=

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Peaucellier mechanism Roberts mechanism

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Pantograph

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Watts MechanismDrafter Mechanism

Tongs Mechanism

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Toggle mechanism

Considering the

equilibrium condition ofslider 6,

For small angles of, F i s

much smaller than P.

tan2

2tan

PF

P

F

=

=

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Intermittent Motion Mechanisms

Geneva Mechanism

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Ratchet and pawl mechanism

Application of Ratchet Pawl

mechanism

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Ratchet and pawl mechanism

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Other Intermittent Motion Mechanism

Mutilated Gear Elliptical GearsEscapement


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session 1 introduction to kinematics

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