This document provides an overview of kinematics of mechanisms and machines. It begins by defining kinematics and dynamics, and explaining that kinematics deals with motion without consideration of forces. It then defines mechanisms and machines, and explains that mechanisms transmit motion via links and joints, while machines transmit both motion and force. Common kinematic pairs and chains are described. Finally, methods for analyzing velocity and acceleration in mechanisms are discussed, including graphical construction of velocity vector diagrams.
Unit 1 – Basics of Mechanics
Topics to be covered – unit1
Basic kinematic concepts and definitions
Degree of freedom & Mobility
Kutzbach criterion & Gruebler’s criterion
Grashof’s Law
Kinematic inversions of four-bar-chain and slider crank chains – Limit positions
Mechanical advantage – Transmission Angle
Classification of mechanisms
Description of some common mechanisms
Unit-3 - Velocity and acceleration of mechanisms, Kinematics of machines of VTU Syllabus prepared by Hareesha N Gowda, Asst. Prof, Dayananda Sagar College of Engg, Blore. Please write to hareeshang@gmail.com for suggestions and criticisms.
This slide includes the following topics:
classification of mechanisms – Basic kinematic concepts and definitions – Degree of freedom, Mobility – Kutzbach criterion, Gruebler’s criterion – Grashof’s Law – Kinematic inversions of four-bar chain and slider crank chains – Limit positions – Mechanical advantage – Transmission Angle – Description of some common mechanisms – Quick return mechanisms, Straight line generators, Universal Joint.
Unit 7-gear trains, Kinematics of machines of VTU Syllabus prepared by Hareesha N Gowda, Asst. Prof, Dayananda Sagar College of Engg, Blore. Please write to hareeshang@gmail.com for suggestions and criticisms.
Unit 1 – Basics of Mechanics
Topics to be covered – unit1
Basic kinematic concepts and definitions
Degree of freedom & Mobility
Kutzbach criterion & Gruebler’s criterion
Grashof’s Law
Kinematic inversions of four-bar-chain and slider crank chains – Limit positions
Mechanical advantage – Transmission Angle
Classification of mechanisms
Description of some common mechanisms
Unit-3 - Velocity and acceleration of mechanisms, Kinematics of machines of VTU Syllabus prepared by Hareesha N Gowda, Asst. Prof, Dayananda Sagar College of Engg, Blore. Please write to hareeshang@gmail.com for suggestions and criticisms.
This slide includes the following topics:
classification of mechanisms – Basic kinematic concepts and definitions – Degree of freedom, Mobility – Kutzbach criterion, Gruebler’s criterion – Grashof’s Law – Kinematic inversions of four-bar chain and slider crank chains – Limit positions – Mechanical advantage – Transmission Angle – Description of some common mechanisms – Quick return mechanisms, Straight line generators, Universal Joint.
Unit 7-gear trains, Kinematics of machines of VTU Syllabus prepared by Hareesha N Gowda, Asst. Prof, Dayananda Sagar College of Engg, Blore. Please write to hareeshang@gmail.com for suggestions and criticisms.
Static force analysis, Unit-1 of Dynamics of machines of VTU Syllabus compiled by Hareesha N Gowda, Asst. Prof, Dayananda Sagar College of Engg, Blore. Please write to hareeshang@gmail.com for suggestions and criticisms.
Kinematic link, Types of links, Kinematic pair, Types of constrained motions, Types of Kinematic pairs, Kinematic chain, Types of joints, Mechanism, Machine, Degree of freedom, Mobility of Mechanism, Inversion, Grashoff’s law, Four-Bar Chain and its Inversions, Slider crank Chain and its Inversions, Double slider crank Chain and its Conversions, Mechanisms with Higher pairs, Equivalent Linkages and its Cases - Sliding Pairs in Place of Turning Pairs, Spring in Place of Turning Pairs, Cam Pair in Place of Turning Pairs
Unit-6: Gyroscope, of Dynamics of machines of VTU Syllabus prepared by Hareesha N Gowda, Asst. Prof, Dayananda Sagar College of Engg, Blore. Please write to hareeshang@gmail.com for suggestions and criticisms.
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Belt is a Flexible Mechanical element that transmit power from one shaft to another
Belt is a Flexible Mechanical element that transmit power from one shaft to another
Gear Train
Ex: Automobile, engines etc.
Chain Drive
Ex : Bi-cycle , Motor cycle etc.
Belt Drive
Ex: Rice mills, sewing machine etc.
Rope Drive
Ex: lift, crane etc
Unit 1-introduction to Mechanisms, Kinematics of machines of VTU Syllabus prepared by Hareesha N Gowda, Asst. Prof, Dayananda Sagar College of Engg, Blore. Please write to hareeshang@gmail.com for suggestions and criticisms.
Static force analysis, Unit-1 of Dynamics of machines of VTU Syllabus compiled by Hareesha N Gowda, Asst. Prof, Dayananda Sagar College of Engg, Blore. Please write to hareeshang@gmail.com for suggestions and criticisms.
Kinematic link, Types of links, Kinematic pair, Types of constrained motions, Types of Kinematic pairs, Kinematic chain, Types of joints, Mechanism, Machine, Degree of freedom, Mobility of Mechanism, Inversion, Grashoff’s law, Four-Bar Chain and its Inversions, Slider crank Chain and its Inversions, Double slider crank Chain and its Conversions, Mechanisms with Higher pairs, Equivalent Linkages and its Cases - Sliding Pairs in Place of Turning Pairs, Spring in Place of Turning Pairs, Cam Pair in Place of Turning Pairs
Unit-6: Gyroscope, of Dynamics of machines of VTU Syllabus prepared by Hareesha N Gowda, Asst. Prof, Dayananda Sagar College of Engg, Blore. Please write to hareeshang@gmail.com for suggestions and criticisms.
Like Comment and download
Belt is a Flexible Mechanical element that transmit power from one shaft to another
Belt is a Flexible Mechanical element that transmit power from one shaft to another
Gear Train
Ex: Automobile, engines etc.
Chain Drive
Ex : Bi-cycle , Motor cycle etc.
Belt Drive
Ex: Rice mills, sewing machine etc.
Rope Drive
Ex: lift, crane etc
Unit 1-introduction to Mechanisms, Kinematics of machines of VTU Syllabus prepared by Hareesha N Gowda, Asst. Prof, Dayananda Sagar College of Engg, Blore. Please write to hareeshang@gmail.com for suggestions and criticisms.
THEORY OF MACHINES FOR VTU, AMIE, DME STUDENTS..
The study of a mechanism involves its analysis as well as synthesis.
Analysis is the study of motions and forces concerning different parts
of an existing mechanism. Whereas Synthesis involves the design of its
different parts.
Mechanics: It is that branch of scientific analysis which deals with
motion, time and force.
Kinematics is the study of motion, without considering the forces
which produce that motion. Kinematics of machines deals with the
study of the relative motion of machine parts. It involves the study of
position, displacement, velocity and acceleration of machine parts.
Dynamics of machines involves the study of forces acting on the
machine parts and the motions resulting from these forces.
Plane motion: A body has plane motion, if all its points move in
planes which are parallel to some reference plane. A body with plane
motion will have only three degrees of freedom. i.e., linear along two
axes parallel to the reference plane and rotational/angular about the
axis perpendicular to the reference plane. (eg. linear along X and Z
and rotational about Y.)The reference plane is called plane of motion.
Plane motion can be of three types. 1) Translation 2) rotation and 3)
combination of translation and rotation.
Translation: A body has translation if it moves so that all straight
lines in the body move to parallel positions. Rectilinear translation is a
motion wherein all points of the body move in straight lie paths.
Eg. The slider in slider crank mechanism has rectilinear translation.
Theory Of Machines in Mechanical EngineeringMohammedAsman
The theory of machines is a branch of mechanical engineering that deals with the study of mechanisms and their applications in various systems. It encompasses the analysis, design, and optimization of mechanisms such as gears, linkages, cams, and mechanisms to transmit motion and forces. This field explores principles of kinematics, dynamics, and control to understand the behavior and performance of machines, aiding in the development of efficient and functional mechanical systems for various industries.
Online aptitude test management system project report.pdfKamal Acharya
The purpose of on-line aptitude test system is to take online test in an efficient manner and no time wasting for checking the paper. The main objective of on-line aptitude test system is to efficiently evaluate the candidate thoroughly through a fully automated system that not only saves lot of time but also gives fast results. For students they give papers according to their convenience and time and there is no need of using extra thing like paper, pen etc. This can be used in educational institutions as well as in corporate world. Can be used anywhere any time as it is a web based application (user Location doesn’t matter). No restriction that examiner has to be present when the candidate takes the test.
Every time when lecturers/professors need to conduct examinations they have to sit down think about the questions and then create a whole new set of questions for each and every exam. In some cases the professor may want to give an open book online exam that is the student can take the exam any time anywhere, but the student might have to answer the questions in a limited time period. The professor may want to change the sequence of questions for every student. The problem that a student has is whenever a date for the exam is declared the student has to take it and there is no way he can take it at some other time. This project will create an interface for the examiner to create and store questions in a repository. It will also create an interface for the student to take examinations at his convenience and the questions and/or exams may be timed. Thereby creating an application which can be used by examiners and examinee’s simultaneously.
Examination System is very useful for Teachers/Professors. As in the teaching profession, you are responsible for writing question papers. In the conventional method, you write the question paper on paper, keep question papers separate from answers and all this information you have to keep in a locker to avoid unauthorized access. Using the Examination System you can create a question paper and everything will be written to a single exam file in encrypted format. You can set the General and Administrator password to avoid unauthorized access to your question paper. Every time you start the examination, the program shuffles all the questions and selects them randomly from the database, which reduces the chances of memorizing the questions.
Hybrid optimization of pumped hydro system and solar- Engr. Abdul-Azeez.pdffxintegritypublishin
Advancements in technology unveil a myriad of electrical and electronic breakthroughs geared towards efficiently harnessing limited resources to meet human energy demands. The optimization of hybrid solar PV panels and pumped hydro energy supply systems plays a pivotal role in utilizing natural resources effectively. This initiative not only benefits humanity but also fosters environmental sustainability. The study investigated the design optimization of these hybrid systems, focusing on understanding solar radiation patterns, identifying geographical influences on solar radiation, formulating a mathematical model for system optimization, and determining the optimal configuration of PV panels and pumped hydro storage. Through a comparative analysis approach and eight weeks of data collection, the study addressed key research questions related to solar radiation patterns and optimal system design. The findings highlighted regions with heightened solar radiation levels, showcasing substantial potential for power generation and emphasizing the system's efficiency. Optimizing system design significantly boosted power generation, promoted renewable energy utilization, and enhanced energy storage capacity. The study underscored the benefits of optimizing hybrid solar PV panels and pumped hydro energy supply systems for sustainable energy usage. Optimizing the design of solar PV panels and pumped hydro energy supply systems as examined across diverse climatic conditions in a developing country, not only enhances power generation but also improves the integration of renewable energy sources and boosts energy storage capacities, particularly beneficial for less economically prosperous regions. Additionally, the study provides valuable insights for advancing energy research in economically viable areas. Recommendations included conducting site-specific assessments, utilizing advanced modeling tools, implementing regular maintenance protocols, and enhancing communication among system components.
Sachpazis:Terzaghi Bearing Capacity Estimation in simple terms with Calculati...Dr.Costas Sachpazis
Terzaghi's soil bearing capacity theory, developed by Karl Terzaghi, is a fundamental principle in geotechnical engineering used to determine the bearing capacity of shallow foundations. This theory provides a method to calculate the ultimate bearing capacity of soil, which is the maximum load per unit area that the soil can support without undergoing shear failure. The Calculation HTML Code included.
An Approach to Detecting Writing Styles Based on Clustering Techniquesambekarshweta25
An Approach to Detecting Writing Styles Based on Clustering Techniques
Authors:
-Devkinandan Jagtap
-Shweta Ambekar
-Harshit Singh
-Nakul Sharma (Assistant Professor)
Institution:
VIIT Pune, India
Abstract:
This paper proposes a system to differentiate between human-generated and AI-generated texts using stylometric analysis. The system analyzes text files and classifies writing styles by employing various clustering algorithms, such as k-means, k-means++, hierarchical, and DBSCAN. The effectiveness of these algorithms is measured using silhouette scores. The system successfully identifies distinct writing styles within documents, demonstrating its potential for plagiarism detection.
Introduction:
Stylometry, the study of linguistic and structural features in texts, is used for tasks like plagiarism detection, genre separation, and author verification. This paper leverages stylometric analysis to identify different writing styles and improve plagiarism detection methods.
Methodology:
The system includes data collection, preprocessing, feature extraction, dimensional reduction, machine learning models for clustering, and performance comparison using silhouette scores. Feature extraction focuses on lexical features, vocabulary richness, and readability scores. The study uses a small dataset of texts from various authors and employs algorithms like k-means, k-means++, hierarchical clustering, and DBSCAN for clustering.
Results:
Experiments show that the system effectively identifies writing styles, with silhouette scores indicating reasonable to strong clustering when k=2. As the number of clusters increases, the silhouette scores decrease, indicating a drop in accuracy. K-means and k-means++ perform similarly, while hierarchical clustering is less optimized.
Conclusion and Future Work:
The system works well for distinguishing writing styles with two clusters but becomes less accurate as the number of clusters increases. Future research could focus on adding more parameters and optimizing the methodology to improve accuracy with higher cluster values. This system can enhance existing plagiarism detection tools, especially in academic settings.
Water billing management system project report.pdfKamal Acharya
Our project entitled “Water Billing Management System” aims is to generate Water bill with all the charges and penalty. Manual system that is employed is extremely laborious and quite inadequate. It only makes the process more difficult and hard.
The aim of our project is to develop a system that is meant to partially computerize the work performed in the Water Board like generating monthly Water bill, record of consuming unit of water, store record of the customer and previous unpaid record.
We used HTML/PHP as front end and MYSQL as back end for developing our project. HTML is primarily a visual design environment. We can create a android application by designing the form and that make up the user interface. Adding android application code to the form and the objects such as buttons and text boxes on them and adding any required support code in additional modular.
MySQL is free open source database that facilitates the effective management of the databases by connecting them to the software. It is a stable ,reliable and the powerful solution with the advanced features and advantages which are as follows: Data Security.MySQL is free open source database that facilitates the effective management of the databases by connecting them to the software.
Saudi Arabia stands as a titan in the global energy landscape, renowned for its abundant oil and gas resources. It's the largest exporter of petroleum and holds some of the world's most significant reserves. Let's delve into the top 10 oil and gas projects shaping Saudi Arabia's energy future in 2024.
We have compiled the most important slides from each speaker's presentation. This year’s compilation, available for free, captures the key insights and contributions shared during the DfMAy 2024 conference.
Cosmetic shop management system project report.pdfKamal Acharya
Buying new cosmetic products is difficult. It can even be scary for those who have sensitive skin and are prone to skin trouble. The information needed to alleviate this problem is on the back of each product, but it's thought to interpret those ingredient lists unless you have a background in chemistry.
Instead of buying and hoping for the best, we can use data science to help us predict which products may be good fits for us. It includes various function programs to do the above mentioned tasks.
Data file handling has been effectively used in the program.
The automated cosmetic shop management system should deal with the automation of general workflow and administration process of the shop. The main processes of the system focus on customer's request where the system is able to search the most appropriate products and deliver it to the customers. It should help the employees to quickly identify the list of cosmetic product that have reached the minimum quantity and also keep a track of expired date for each cosmetic product. It should help the employees to find the rack number in which the product is placed.It is also Faster and more efficient way.
6th International Conference on Machine Learning & Applications (CMLA 2024)ClaraZara1
6th International Conference on Machine Learning & Applications (CMLA 2024) will provide an excellent international forum for sharing knowledge and results in theory, methodology and applications of on Machine Learning & Applications.
Literature Review Basics and Understanding Reference Management.pptxDr Ramhari Poudyal
Three-day training on academic research focuses on analytical tools at United Technical College, supported by the University Grant Commission, Nepal. 24-26 May 2024
3. 10-06-2017Jahangirabad Institute of Technology 3
In the starting of Kinematics of Machines we need to
understand the concepts of ‘Kinematics’ and ‘Dynamics’.
Kinematics of mechanisms is concerned with the motion
of the parts without considering how the influencing
factors (force and mass) affect the motion. Therefore,
kinematics deals with the fundamental concepts.
Kinetics deals with action of forces on bodies.
Dynamics is the combination of kinematics and kinetics.
Dynamics of mechanisms concerns the forces that act on
the parts -- both balanced and unbalanced forces, taking
into account the masses and accelerations of the parts as
well as the external forces.
4. 10-06-2017Jahangirabad Institute of Technology 4
The basic of KOM is include “Mechanisms” and “Machines”.
The word Mechanism has many meanings. In kinematics, a
mechanism is a means of transmitting, controlling, or
constraining relative movement .
Movements which are electrically, magnetically,
pneumatically operated are excluded from the concept of
mechanism.
The central theme for mechanisms is rigid bodies connected
together by joints.
5. 10-06-2017Jahangirabad Institute of Technology 5
A machine is a combination of rigid or resistant
bodies, formed and connected do that they move with
definite relative motions and transmit force from the
source of power to the resistance to be overcome.
A machine has two functions: transmitting definite
relative motion and transmitting force. These
functions require strength and rigidity to transmit the
forces.
6. 10-06-2017Jahangirabad Institute of Technology 6
Mechanisms can be divided into planar mechanisms and
spatial mechanisms, according to the relative motion of the
rigid bodies.
In a planar mechanisms, all of the relative motions of the
rigid bodies are in one plane or in parallel(2D) planes.
If there is any relative motion that is not in the same plane
or in parallel planes(3D), the mechanism is called the
spatial mechanism.
In other words, planar mechanisms are essentially two
dimensional while spatial mechanisms are three
dimensional.
7. 10-06-2017Jahangirabad Institute of Technology 7
Each part of a machine, which moves relative to
some other part, is known as a kinematic link (or
simply link) or element.
A link may consist of several parts, which are
rigidly fastened together, so that they do not move
relative to one another.
8. 10-06-2017Jahangirabad Institute of Technology 8
Rigid link.
A rigid link is one which does not undergo any deformation while
transmitting motion. Strictly speaking, rigid links do not exist.
However, as the deformation of a connecting rod, crank etc. of a
reciprocating steam engine is not appreciable, they can be
considered as rigid links.
Flexible link.
A flexible link is one which is partly deformed in a manner not to
affect the transmission of motion. For example, belts, ropes, chains
and wires are flexible links and transmit tensile forces only.
Fluid link.
A fluid link is one which is formed by having a fluid in a receptacle
and the motion is transmitted through the fluid by pressure or
compression only, as in the case of hydraulic presses, jacks and
brakes.
9. 10-06-2017Jahangirabad Institute of Technology 9
The two links or elements of a machine, when in
contact with each other, are said to form a pair. If the
relative motion between them is completely or
successfully constrained (i.e. in a definite direction),
the pair is known as kinematic pair.
11. 10-06-2017Jahangirabad Institute of Technology 11
Lower pair
When the two elements of a pair have a surface contact
when relative motion takes place and the surface of one
element slides over the surface of the other, the pair
formed is known as lower pair. It will be seen that sliding
pairs, turning pairs and screw pairs form lower pairs.
12. 10-06-2017Jahangirabad Institute of Technology 12
Higher pair
When the two elements of a
pair have a line or point
contact when relative motion
takes place and the motion
between the two elements is
partly turning and partly
sliding, then the pair is
known as higher pair.
A pair of friction discs,
toothed gearing, belt and
rope drives, ball and roller
bearings and cam and
follower are the examples of
higher pairs.
13. 10-06-2017Jahangirabad Institute of Technology 13
1.Completely constrained
motion
When the motion between a
pair is limited to a definite
direction irrespective of the
direction of force applied,
then the motion is said to
be a completely constrained
motion.
The motion of a square bar
in a square hole, as shown
in Fig. 2, and the motion of
a shaft with collars at each
end in a circular hole, as
shown in Fig.
14. 10-06-2017Jahangirabad Institute of Technology 14
2.Incompletely constrained
motion
When the motion between
a pair can take place in
more than one direction,
then the motion is called
an incompletely
constrained motion.
The change in the direction
of impressed force may
alter the direction of
relative motion between
the pair.
15. 10-06-2017Jahangirabad Institute of Technology 15
3.Successfully constrained
motion
When the motion between the
elements, forming a pair, is
such that the constrained
motion is not completed by
itself, but by some other
means, then the motion is
said to be successfully
constrained motion.
The motion of an I.C. engine
valve and the piston
reciprocating inside an
engine cylinder are also the
examples of successfully
constrained motion.
16. 10-06-2017Jahangirabad Institute of Technology 16
When the kinematic pairs are coupled in such a way that
the last link is joined to the first link to transmit definite
motion (i.e. completely or successfully constrained
motion), it is called a kinematic chain.
In other words, a kinematic chain may be defined as a
combination of kinematic pairs, joined in such a way that
each link forms a part of two pairs and the relative motion
between the links or elements is completely or successfully
constrained.
17. 10-06-2017Jahangirabad Institute of Technology 17
If each link is assumed to form two pairs with two adjacent links, then the
relation between the number of pairs ( p ) forming a kinematic chain and the
number of links ( l ) may be expressed in the form of an equation :
Since in a kinematic chain each link forms a part of two pairs, therefore there
will be as many links as the number of pairs.
Another relation between the number of links (l) and the number of joints ( j )
which constitute a kinematic chain is given by the expression :
If in the example
L.H.S>R.H.S That’ll be considered as “Locked Chain”.
L.H.S=R.H.S That’ll be considered as “One D.O.F”.
L.H.S<R.H.S That’ll be considered as “Unconstrained Chain”.
42 pl
2
2
3
lj
19. 10-06-2017Jahangirabad Institute of Technology 19
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 equation:
hjln 2)1(3
21. 10-06-2017Jahangirabad Institute of Technology 21
When one of links is fixed in a kinematic chain, its
called mechanism. So we can obtain many mechanism
by fixing, in turn, different links in kinematic chain.
This method is known as “inversion of mechanism”.
23. 10-06-2017Jahangirabad Institute of Technology 23
Beam engine (crank and lever mechanism)
A part of the mechanism of a beam engine (also known as crank and
lever mechanism) which consists of four links, is shown in Fig.
In this mechanism, when the crank rotates about the fixed centre A,
the lever oscillates about a fixed centre D.
The end E of the lever CDE is connected to a piston rod which reciprocates
due to the rotation of the crank.
In other words, the purpose of this mechanism is to convert rotary motion
into reciprocating motion.
24. 10-06-2017Jahangirabad Institute of Technology 24
Coupling rod of a locomotive (Double crank
mechanism).
Watt’s indicator mechanism (Double lever
mechanism).
26. 10-06-2017Jahangirabad Institute of Technology
A single slider crank chain is a modification of the
basic four bar chain.
It consist of one sliding pair and three turning pairs. It
is, usually, found in reciprocating steam engine
mechanism.
This type of mechanism converts rotary motion into
reciprocating motion and vice versa.
27. 10-06-2017Jahangirabad Institute of Technology 27
1. Pendulum pump or Bull
engine.
2. Oscillating cylinder
engine
3. Rotary internal
combustion engine
4. Crank and slotted lever
quick return motion
mechanism.
5. Whitworth quick return
motion mechanism.
34. Velocity analysis of any mechanism can be carried out by
various methods.
1. By graphical method
2. By relative velocity method
3. By instantaneous method
10-06-2017Jahangirabad Institute of Technology 34
35. By Graphical Method
The following points are to be considered while solving problems
by this method.
1. Draw the configuration design to a suitable scale.
2. Locate all fixed point in a mechanism as a common point in
velocity diagram.
3. Choose a suitable scale for the vector diagram velocity.
10-06-2017Jahangirabad Institute of Technology 35
36. 4. The velocity vector of each rotating link is r
to the link.
5. Velocity of each link in mechanism has both magnitude and
direction. Start from a point whose magnitude and direction is
known.
6. The points of the velocity diagram are indicated by small letters.
10-06-2017Jahangirabad Institute of Technology 36
37. To explain the method let us take a few
specific examples.
1. Four – Bar Mechanism:
In a four bar chain ABCD link AD is fixed
and in 15 cm long. The crank AB is 4 cm
long rotates at 180 rpm (cw) while link CD
rotates about D is 8 cm long BC = AD and
BAD| = 60o
. Find angular velocity of link
CD.
Configuration Diagram
60o
wBA
A D
B
C
15 cm
15 cm
8 cm
10-06-2017Jahangirabad Institute of Technology 37
38. Velocity vector diagram
Vb = r = ba x AB = 4x
60
120x2π
= 50.24 cm/sec
Choose a suitable scale
1 cm = 20 m/s = ab
r
to CD
r
to BC
r
to AB
a, d
b
C Vcb
10-06-2017Jahangirabad Institute of Technology 38
39. Vcb = bc
Vc = dc = 38 cm/s = Vcd
We know that V = ωR
Vcd = cD x CD
WcD = 75.4
8
38Vcd
CD
rad/s (cw)
10-06-2017Jahangirabad Institute of Technology 39
40. Learning Outcomes:
• This session deals with velocity vector diagrams for
determining the velocity at different points in
different mechanisms like IC engine Mechanism and
Crank and slotted Lever Mechanism.
10-06-2017Jahangirabad Institute of Technology 40
41. 10-06-2017Jahangirabad Institute of Technology 41
• Introduction.
• Definition of Displacement, Velocity and
Acceleration.
• Difference between absolute Velocity and
Relative Velocity.
• Steps to construct Velocity Vector diagram.
• Velocity Vector diagram for a Four Bar
Mechanism
42. 1. Slider Crank Mechanism:
In a crank and slotted lover mechanism crank rotates
of 300 rpm in a counter clockwise direction. Find
(i) Angular velocity of connecting rod and
(ii) Velocity of slider.
Configuration diagram
60 mm
45o
A
B
150 mm
10-06-2017Jahangirabad Institute of Technology 42
43. Step 1: Determine the magnitude and velocity of
point A with respect to 0,
VA = O1A x O2A = 60x
60
300x2
= 600 mm/sec
Step 2: Choose a suitable scale to draw velocity vector diagram.
Velocity vector diagram
O
Vaa
b
r
to AB r
to OA
Along sides B
Vab = ab
ba =
150BA
Vba
r/s
Vb = ob velocity of slider
Note: Velocity of slider is along
the line of sliding.
10-06-2017Jahangirabad Institute of Technology 43
44. 3. Shaper Mechanism:
In a crank and slotted lever mechanisms crank O2A rotates
at r/s in CCW direction. Determine the velocity of slider.
Configuration diagram
4
O1
O2
C
B
3
2
W
5
6
D Scale 1 cm = x m/s
10-06-2017Jahangirabad Institute of Technology 44
45. Velocity vector diagram
Va = 2 x O2A
CO
cO
BO
bO
1
1
1
1
To locate point C
BO
CO
bOcO
1
1
11
Scale 1 cm = x m/s
d O1O2
VDC
c
a
b
VBA
VAO2 = VA
VBO1
10-06-2017Jahangirabad Institute of Technology 45
46. To Determine Velocity of Rubbing
Two links of a mechanism having turning point will be connected
by pins. When the links are motion they rub against pin surface.
The velocity of rubbing of pins depends on the angular velocity of
links relative to each other as well as direction.
10-06-2017Jahangirabad Institute of Technology 46
47. For example: In a four bar mechanism we have
pins at points A, B, C and D.
Vra = ab x ratios of pin A (rpa)
+ sign is used ab is CW and Wbc is CCW i.e. when angular
velocities are in opposite directions use + sign when angular
velocities are in some directions use - ve sign.
VrC = (bc + cd) radius r
VrD = cd rpd
Problems on velocity by velocity vector method (Graphical
10-06-2017Jahangirabad Institute of Technology 47
48. Problems on velocity by velocity vector
method (Graphical solutions)
Problem 1:
In a four bar mechanism, the dimensions of the links are as given
below:
AB = 50 mm, BC = 66 mm
CD = 56 mm and AD = 100 mm
At a given instant when o
60DAB| the angular velocity of link
AB is 10.5 r/s in CCW direction.
10-06-2017Jahangirabad Institute of Technology 48
49. Determine,
i) Velocity of point C
ii) Velocity of point E on link BC when BE = 40 mm
iii) The angular velocity of link BC and CD
iv) The velocity of an offset point F on link BC, if BF = 45 mm, CF
= 30 mm and BCF is read clockwise.
v) The velocity of an offset point G on link CD, if CG = 24 mm,
DG = 44 mm and DCG is read clockwise.
vi) The velocity of rubbing of pins A, B, C and D. The ratio of the
pins are 30 mm, 40 mm, 25 mm and 35 mm respectively.
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50. Solution:
Step -1: Construct the configuration diagram
selecting a suitable scale.
60o
A D
B
C
F
G
Scale: 1 cm = 20 mm
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51. Step – 2: Given the angular velocity of link AB and its direction of
rotation determine velocity of point with respect to A (A is fixed
hence, it is zero velocity point).
Vba = BA x BA
= 10.5 x 0.05 = 0.525 m/s
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52. Step – 3: To draw velocity vector diagram
choose a suitable scale, say 1 cm = 0.2 m/s.
First locate zero velocity points.
Draw a line r
to link AB in the direction of rotation of link AB
(CCW) equal to 0.525 m/s.
C
f
Ved
a, d
e, g
Vba = 0.525 m/s
b
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53. From b draw a line r
to BC and from d. Draw d line r
to CD
to interest at C.
Vcb is given vector bc Vbc = 0.44 m/s
Vcd is given vector dc Vcd = 0.39 m/s
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54. Step – 4: To determine velocity of point E (Absolute
velocity) on link BC, first locate the position of point E
on velocity vector diagram. This can be done by taking
corresponding ratios of lengths of links to vector
distance i.e.
BC
BE
bc
be
be =
BC
BE
x Vcb =
066.0
04.0
x 0.44 = 0.24 m/s
Join e on velocity vector diagram to zero velocity points a, d
vector de = Ve = 0.415 m/s.
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55. Step 5: To determine angular velocity of links BC and CD, we
know Vbc and Vcd.
Vbc = WBC x BC
WBC = )(.sec/6.6
066.0
44.0
cwrad
BC
Vbc
Similarly, Vcd = WCD x CD
WCD = s/r96.6
056.0
39.0
CD
Vcd
(CCW)
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56. Step – 6: To determine velocity of an offset point F
Draw a line r
to CF from C on velocity vector diagram.
Draw a line r
to BF from b on velocity vector diagram to
intersect the previously drawn line at ‘f’.
From the point f to zero velocity point a, d and measure
vector fa/fd to get Vf = 0.495 m/s.
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57. Step – 7: To determine velocity of an offset point.
Draw a line r
to GC from C on velocity vector diagram.
Draw a line r
to DG from d on velocity vector diagram to
intersect previously drawn line at g.
Measure vector dg to get velocity of point G.
Vg = s/m305.0dg
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58. Step – 8: To determine rubbing velocity at pins
Rubbing velocity at pin A will be
Vpa = ab x rad of pin A = 10.5 x 0.03 = 0.315 m/s
Rubbing velocity at pin B will be
Vpb = (ab + cb) x rad of point at B.
[ab CCW and cbCW]
Vpb = (10.5 + 6.6) x 0.04 = 0.684 m/s.
Rubbing velocity at point D will be
cd x rpd of pin D
= 6.96 x 0.035 = 0.244 m/s
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61. 10-06-2017Jahangirabad Institute of Technology 61
Cams convert rotary
oscillating or linear
motion into a linear or
reciprocating action to
carry out useful work.
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Plate cam
Sometimes called a disc,
radial or edge cam.
Made up of a flat plate or
disc with an edge profile to
transmit motion.
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Cylindrical cam
Sometimes called a barrel
cam. It’s curved surface has
a groove machined, within
which a follower is
contained. The movement
is parallel to cam axis.
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Face cam
In its flat surface, this
rotary cam has a groove cut
within which a constrained
follower moves. The groove
ensures no need for a
return spring.
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Wedge or Knife type
This has the advantage that it
can follow complicated
profiles. However, it is not
often used as it wears rapidly,
due to the high frictional
forces. It can also track
profiles in both directions.
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Roller
This has the advantage that wear is
minimised, due to the roller action.
However, the profile of the cam and
roller radius must not conflict. If the
profile is smaller than the radius of
the roller then the roller will follow
the incorrect path.
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Flat ended
This cannot be used for concave
profiles. It wears slower than a
knife-edge follower, since the
points of contact move across
the surface of the follower. These
are often offset and allowed to
spin.
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• List three applications of different
types of cams.
• What could be used today instead of
cams? (Think of CNC machines.)
• What materials could be used for
cams?
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The motion of the cam follower
depends upon the profile or
shape of the cam. Therefore the
profile determines the resultant
action.
Cams are expensive to make and
therefore the cam follower is
normally sacrificial - allowed to
wear.
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Draw a cam displacement diagram for the following cam:
This cam needs to rise for 50 mm and fall 50mm due to uniform velocity.
87. 10-06-2017Jahangirabad Institute of Technology 87
Draw a cam displacement diagram for the following cam:
This cam needs to rise for 50 mm and fall 50mm due to uniform velocity.
Repeat this cam but rise due to SHM and fall using uniform acceleration
and retardation
88. 10-06-2017Jahangirabad Institute of Technology 88
Homework Questions?
Name 3 types of cam
Name 2 types of follower
Describe uniform acceleration
and retardation.
Name the other types of
profile
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Power transmission is the movement of energy from its
place of generation to a location where it is applied to
performing useful work
A gear is a component within a transmission device that
transmits rotational force to another gear or device
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1. According to the position of axes of the shafts.
a. Parallel
1.Spur Gear
2.Helical Gear
3.Rack and Pinion
b. Intersecting
Bevel Gear
c. Non-intersecting and Non-parallel
worm and worm gears
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Teeth is parallel to axis of
rotation
Transmit power from one
shaft to another parallel shaft
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Rack and pinion gears are
used to convert rotation (From
the pinion) into linear motion
(of the rack)
A perfect example of this is the
steering system on many cars
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Simple gear train
Compound gear train
Planetary gear train
Simple Gear Train
The most common of the gear train is the gear pair
connecting parallel shafts. The teeth of this type can
be spur, helical or herringbone.
Only one gear may rotate about a single axis
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For large velocities,
compound
arrangement is
preferred
Two or more gears
may rotate about a
single axis
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They have higher gear ratios.
They are popular for automatic transmissions in
automobiles.
They are also used in bicycles for controlling power of
pedaling automatically or manually.
They are also used for power train between internal
combustion engine and an electric motor