Mechanics of Machines Intro

Course Information Introduction Links Pairs Kinematic Diagrams Degrees of Freedom Four bar mechanism

MEC 203 MECHANICS OF MACHINESIntroduction

Dr. P. JEYARAJ

Assistant ProfessorDepartment of Mechanical Engineering

NITK Surathkal

August 14, 2013

Dr. P. Jeyaraj NIT Karnataka Surathkal


MEC 203 MECHANICS OF MACHINES

Objectives of the course

After undergoing the course the students will be able toCreate a structured problem denition and possible solutions for a givenunstructured problem statement in mechanism designAnalyze and explain the process of mechanism designCreate new mechanisms (synthesis mechanism) for a given purposeCalculate and analyze the position, velocity and acceleration of any pointon a link in a given mechanismAnalyze the static forces and dynamic forces in a given mechanism

Simulate simple mechanisms using Matlab /SCI lab / Working model 2D




Course coverage

Contents HrsIntroduction and denitions, Mobility , linkage type, Equivalents, Inversion 6

Position analysis , Velocity Analysis , Graphical and Analytical 7Acceleration analysis (including Coriolis acceleration) 6

Static Force analysis 7Dynamic Force Analysis 7Mechanism Synthesis 7

Total 40

Contents in red by Dr. K. V. Gangadharan and contents inblue by Dr. P. Jeyaraj




References

Robert L Norton ,Design of Machinery (621.815 N887) 2ndEdition, McGrawHill

Hamilton H Mabie and Charles F Reinholtz , Mechanismsand Dynamics of Machinery (621.81 M1121), 4th Edition,John Wiley and Sons

John J Uicker, Jr et. al Theory of Machines andMechanisms(621.81 U) ,3rd Edition, Oxford

Rattan S.S., Theory of Machines Tata McGraw HillPublishing Company Ltd., New Delhi, 2nd Edition, 2006

David H Myzska, Machines and Mechanisms, AppliedKinematic Analysis, 4th Edition, Prentice Hall, 2012.




Evaluation Plan

Component Percentage weightageEnd Semester Exam 50Mid Semester Exam 20

Quizzes and Assignments 15Mini Project 15

Total 100



Mechanics Classification

Mechanics



Kinematics Vs Kinetics

Kinematics Vs Kinetics

KINEMATICS - The study of motion without regard to forces

KINETICS - The study of forces on systems in motion

These two are really not physically separable, separated forinstructional/understanding reasons.

From Newtons second law, F = mawe need to know accelerations (a) in order to compute

dynamic forces (F) due to the motion of the systems mass (m)

So, understanding and analyzing the motion of a machinecomponent is very important



Kinematics

KinematicsOne principle aim of the kinematics is to create the desired motions of themachine component and then mathematically compute the positions, velocitiesand accelerations which those motions.

Since mass remains constant with time,dening the accelerations as a functionof time will dene the dynamic forces as a function of time.

In machinery which involves the largest forces encountered are often those dueto dynamics of the machine itself. These dynamic forces are proportional toacceleration, which brings us back to kinematics, the foundation of mechanicaldesign.

Very basic and early decisions in the design process involving kinematicprinciples can be crucial to the success of any mechanical design.

A design which has poor kinematics will prove troublesome and perform badly.



Need for Kinematic Analysis

Consider the design of an automotive windshield wiper system

First design task is to determine appropriate movements of the wiper.

Once the desired movement has been established, an assembly of componentsmust be congured to produce the wiper pattern.

Subsequent tasks include analyzing other motion issues such as timing of thewiper and wiping tendencies

So, understanding and analyzing the motion of the wiper system is necessary forproper operation


Kinematic Analysis

Kinematics is the study of motion without considering the forces which producethat motion.

More specically it is the study of position, displacement, velocity, and

acceleration.

Kinematic Analysis-Applications

Bicycle is a simple example of a kinematic system that contains a chain drive toprovide torque multiplication and simple cable operated linkages for braking

In an automobile - Steering system, wheel suspensions, and piston-engine

Construction equipment such as tractors, cranes and backhoes all use linkagesextensively

Exercise equipments

Terminology

MechanismA device which transforms motion to some desirable pattern

may contain linkages, cams, gears, belts and chain

typically develops very low forces and transmits little power

Examples

Umbrella , Folding chair and Adjustable desk lamp

DenitionA system of elements arranged to transmit motion in a pre determined fashion

Terminology

Machinetypically contains mechanisms

designed to provide signicant forces and transmit signicant power

Examples

Bulldozer, Robot,Engines

Denition

A system of elements arranged to transmit motion and energyin a pre determined fashion

Terminology

Structuretypically contains rigidly connected non-movable members

designed to support or carry the loads

Examples

Table, bridges, buildings

Denition

A system of elements arranged to support the load


Machine Vs Mechanism Vs StructureMachine Mechanism Structure

relative motion exists relative motion exists no relative motion existsbetween its pair between its pair between its pair

it transforms available no energy It does not convertenergy into useful work transfer the available energy into workMembers are used to Members are used to structural members are used to

transfer both energy and motion transfer motion only carry loadsDynamo, Machine Tools, etc., Umbrella, Folding Chair Roof Trusses, Bridges

Positive dof Positive dof zero dof



Terminology

Frame: It is a reference for all other links. It is typically a part of machine ormechanism that exhibits no motion. Example: Bus body for wiper mechanism

Link: A member or combination of members of a mechanism, connecting othermembers and having motion relative to them

Pair: is a joint of two links having relative motion between them

Kinematic Chain: when kinematic pair are coupled in such a way that the lastlink is joined to the rst link to transmit motion, it is known as kinematic chain

Mechanism: when one link of a kinematic chain is xed it is known asmechanism.



Links

Types of Links

Binary Link: Link with two nodes

Ternary Link: Link with three nodes

Quaternary Link: Link with four nodes

node: point of attachment to the other links



Kinematic Pairs

Types of Kinematic Pairs

According to the nature of relative motion

According to the nature of contact

According to the nature of mechanical constraint



Kinematic Pairs


Revolute (or) Pin (or) Hinge Joint : It allows pure rotationbetween the two links that it connects

Sliding (or)prism (or) piston joint : It allows pure translationbetween the two links that it connects



Kinematic Pairs


Helical or helix or screw joint: The sliding and rotationalmotions are related by the helix angle of the thread. Themating surface is in form of helix

Cylindrical joint: The mating surface is plain and cylindrical inshape

These two pairs has both turning as well as sliding motionbetween them



Kinematic Pairs


Spherical or Globular joint: When one link in the form of asphere turns inside a xed link, spherical pair will form

Planar joint: The mating surface is plain and cylindrical inshape



Kinematic Pairs

According to the nature of contact

Lower pair: A pair of links having surface or area contactbetween the members is known as lower pair. The contactsurfaces of the two links are similar.Examples: Screw pair, Cylindrical pair, Prismatic pair

Higher pair: When a pair has a point or line contact betweenlinks, it is known as higher pair. The contact surfaces of thetwo links are dissimilar.Examples: Wheel rolling on a surface, Cam and follower pair,ball and roller bearings



Kinematic Pairs

Higher Pair Vs Lower Pair

A pin surrounded by a hole is an example for lower pair, where surface contactexists. However, if there is any clearance between pin and hole (as there mustbe for motion), so-called surface contact in the pin actually becomes linecontact, as the pin contacts only one side of the hole.

Likewise, at a microscopic level, a block sliding on a at surface actually hascontact only at discrete points, which are the tops of the surfaces asperities.

The main practical advantage of lower pairs over higher pais is their betterability to trap lubricant between their enveloping surfaces. This is especially truefor the rotating pin joint.

As a result, the pin joint is preferred for low wear and long life, compared to the

prismatic or slider joint.



Kinematic Pairs

According to the nature of mechanical constraint

Closed pair: When two links of a pair are held togethermechanically, it is known as a closed pair.

Unclosed pair: When two links of a pair in contact either dueto force of gravity or same spring action, it is known asunclosed pair.

Animation for classication of pairsDr. P. Jeyaraj NIT Karnataka Surathkal


Kinematic Diagrams

In analyzing the motion of a machine, it is often dicult to visualize themovement of the components in a full assembly drawing.

It is easier to represent the parts in skeleton form so that only the dimensionsthat inuence the motion of the mechanism are shown.

These stripped-down sketches of mechanisms are often referred to askinematic diagrams.



Kinematic Diagrams



Kinematic Diagrams

How to draw Kinematic Diagrams

A kinematic diagram should be drawn to a scale proportional to the actualmechanism.

For convenient reference, the links are numbered, starting with the frame as linknumber 1.

To avoid confusion, the joints should be lettered.

Consider a shearing press used to cut and trim electronic circuit board laminates



Kinematic Diagrams


Identify the FrameIn most of the cases the frame is rmly attached to the ground.

Its selection is important as all other links motion will be determined

relative to it.

Identify All Other LinksIdentify all the other links which are moving relative to the frame

In this problem, Handle (Link 2), Cutting blade (Link 3) and Bar that

connects the cutter with the handle (Link 3).

Identify the JointsIn this problem, Pin joint (A) connects Link 1 to Link 2; Pin joint (B)connects Link 2 to Link 3; Pin joint (C) connects Link 3 to Link 4

In addition, the cutter slides up and down, along the base. This sliding

joint (D) connects link 4 to 1

Identify any point of interest

Finally, the motion of the end of the handle is desired. Let it be X.



Kinematic Diagrams




Degrees of Freedom or Mobility of Mechanisms

The systems DOF is equal to the number of independent parameters that areneeded to uniquely define its position in space at any instant of time.

Figure shows a pencil lying on a at piece of paper with an x, y coordinatesystem added

Three parameters (DOF) are required to completely dene the position of thepencil on the paper, two linear coordinates (x,y) to dene the position of anyone point on the pencil and one angular coordinate () to dene the angle ofthe pencil with respect to the axes.

This system of pencil in a plane has three DOF.



Grueblers CriterionAny link in a plane has 3 DOF. Therefore, a system of N unconnected links inthe same will have 3N DOF

When any link is grounded or attached to the reference frame, all three of itsDOF will be removed. Now the total DOF is 3N-3

When a pair having one DOF is formed between two links, then two DOF foreach pair will be reduced. Now the total DOF is 3N-3-2P1, where P1 is numberof pairs having one DOF

Similarly for a pair having two DOF, one DOF for each pair will be reduced.Now total DOF of the mechanism is 3N-3-2P1-1P2, where P2 is number ofpairs having two DOF

So, for planar mechanisms, DOF=3(N-1)-2P1-1P2.

This is known as Grueblers criterion for degrees of freedom of planemechanisms in which each movable link possesses three degrees of freedom

Kutzhachs criterion DOF=3(N-1)-2P1



Problems on DOF

Find mobility of the mechanisms given



Four bar mechanismIt is the most fundamental of the plane kinematic mechanism.

It consists of four rigid links which are connected in the form of a quadrilateralby four pin joints.

It has one degrees of freedom and fully operated by one driver. The pivoted linkconnected to the driver or power source is called as input link.

The xed link is known as GROUND or FRAME, the output link is known asFOLLOWER and the link which connects input and output links is known asCOUPLER.

A link that makes complete revolution is called as CRANK which is mostly inputlink and a link which oscillates is called as ROCKER

Four bar mechanism animationDr. P. Jeyaraj NIT Karnataka Surathkal


The Grashof Condition

It is a very simple relationship which predicts the rotationbehavior or rotatability of a four bar linkage based only on thelink lengths.

Let S = length of the shortest link, L = length of the longestlink, P = length of one remaining link, and Q = length of theother remaining link.

If S+L P+Q, then linkage is Grashof and at least one linkwill be capable of making a full revolution with respect to theground.

If the inequality is not true, then the linkage is non-Grashofand no link will be capable of a complete revolution relative toany other link.



Inversion of a kinematic chain

The method of obtaining dierent mechanisms by xingdierent links of a kinematic chain is known as inversion.

Thus there are as many inversions of a given linkage as it haslinks.

The motions resulting from each inversion can be quitedierent, but some inversions of a linkage may yield motionssimilar to other inversions of the same linkage.

In these cases only some of the inversions may have distinctlydierent motions. We will denote the inversions which havedistinctly dierent motions as distinct inversions.



Inversion of a four bar chain

Four dierent inversions of four bar chain are



Inversion of a four bar chain

Applications of four bar inversions are



Inversion of single slider chain




Inversion of single slider chain

Applications of single slider crank chain are



Quick Return Mechanisms

Need for Quick Return MechanismsDuring the cutting stroke there is a limit of speed imposed to the cuttingtool due to various reasons like, heat dissipation, life of tool bits, etc.,

But no speed limit exists for the return stroke or idle stroke.

Applications of Quick Return MechanismsPushing the parts along assembly lineClamping parts together while they are welded

Folding cardboard boxes in an automated packaging machine



Crank and Slotted MechanismIt will be easily seen from the gure that the stroke of the cutting tool startsfrom E when the link2 is at right angles to the lever4. Also lever4 is tangentialto the crank radius circle at point A.

Time ratio = timeofcuttingtimeofreturn

=



Whitworth MechanismThe extreme positions of the arm correspond to the positions AD and AD i.e.,the position of the pin at D and D. This will happen when the pin C occupiespositions C and C repectively.



Comparison

Whitworth Crank and Slotted lever

crank is xed connecting rod is xed

slotted lever revolves slotted lever oscillatesline of stroke passes through line of stroke passes throughthe pivot point of slotted lever some distance away from the pivot point



Inversion of double slider chain



Course InformationIntroductionKinematics Vs KineticsMachine, Mechanism and Structure

LinksPairsKinematic DiagramsDegrees of FreedomFour bar mechanismInversion of four bar chainInversions of single slider chainQuick Return MechanismsInversions of double slider chain

Mechanics of Machines Intro

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