This document provides an introduction to the theory of machines. It discusses key concepts such as kinematics, mechanisms, links, kinematic pairs, and degrees of freedom. Specifically:
- Kinematics is the study of relative motion between machine parts without considering forces or mass.
- A mechanism is an assembly of links that transmits and modifies motion. A machine adds the capability to transmit and modify power.
- Kinematic pairs constrain the relative motion between two links. Common pairs include sliding, turning, rolling, and spherical.
- A kinematic chain transmits defined motion through successive pairs. A mechanism is a kinematic chain with one fixed link.
- The degrees of freedom of a mechanism
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.
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
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-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.
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.
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.
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
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-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.
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.
CW RADAR, FMCW RADAR, FMCW ALTIMETER, AND THEIR PARAMETERSveerababupersonal22
It consists of cw radar and fmcw radar ,range measurement,if amplifier and fmcw altimeterThe CW radar operates using continuous wave transmission, while the FMCW radar employs frequency-modulated continuous wave technology. Range measurement is a crucial aspect of radar systems, providing information about the distance to a target. The IF amplifier plays a key role in signal processing, amplifying intermediate frequency signals for further analysis. The FMCW altimeter utilizes frequency-modulated continuous wave technology to accurately measure altitude above a reference point.
Welcome to WIPAC Monthly the magazine brought to you by the LinkedIn Group Water Industry Process Automation & Control.
In this month's edition, along with this month's industry news to celebrate the 13 years since the group was created we have articles including
A case study of the used of Advanced Process Control at the Wastewater Treatment works at Lleida in Spain
A look back on an article on smart wastewater networks in order to see how the industry has measured up in the interim around the adoption of Digital Transformation in the Water Industry.
Using recycled concrete aggregates (RCA) for pavements is crucial to achieving sustainability. Implementing RCA for new pavement can minimize carbon footprint, conserve natural resources, reduce harmful emissions, and lower life cycle costs. Compared to natural aggregate (NA), RCA pavement has fewer comprehensive studies and sustainability assessments.
Final project report on grocery store management system..pdfKamal Acharya
In today’s fast-changing business environment, it’s extremely important to be able to respond to client needs in the most effective and timely manner. If your customers wish to see your business online and have instant access to your products or services.
Online Grocery Store is an e-commerce website, which retails various grocery products. This project allows viewing various products available enables registered users to purchase desired products instantly using Paytm, UPI payment processor (Instant Pay) and also can place order by using Cash on Delivery (Pay Later) option. This project provides an easy access to Administrators and Managers to view orders placed using Pay Later and Instant Pay options.
In order to develop an e-commerce website, a number of Technologies must be studied and understood. These include multi-tiered architecture, server and client-side scripting techniques, implementation technologies, programming language (such as PHP, HTML, CSS, JavaScript) and MySQL relational databases. This is a project with the objective to develop a basic website where a consumer is provided with a shopping cart website and also to know about the technologies used to develop such a website.
This document will discuss each of the underlying technologies to create and implement an e- commerce website.
Industrial Training at Shahjalal Fertilizer Company Limited (SFCL)MdTanvirMahtab2
This presentation is about the working procedure of Shahjalal Fertilizer Company Limited (SFCL). A Govt. owned Company of Bangladesh Chemical Industries Corporation under Ministry of Industries.
Student information management system project report ii.pdfKamal Acharya
Our project explains about the student management. This project mainly explains the various actions related to student details. This project shows some ease in adding, editing and deleting the student details. It also provides a less time consuming process for viewing, adding, editing and deleting the marks of the students.
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.
Hierarchical Digital Twin of a Naval Power SystemKerry Sado
A hierarchical digital twin of a Naval DC power system has been developed and experimentally verified. Similar to other state-of-the-art digital twins, this technology creates a digital replica of the physical system executed in real-time or faster, which can modify hardware controls. However, its advantage stems from distributing computational efforts by utilizing a hierarchical structure composed of lower-level digital twin blocks and a higher-level system digital twin. Each digital twin block is associated with a physical subsystem of the hardware and communicates with a singular system digital twin, which creates a system-level response. By extracting information from each level of the hierarchy, power system controls of the hardware were reconfigured autonomously. This hierarchical digital twin development offers several advantages over other digital twins, particularly in the field of naval power systems. The hierarchical structure allows for greater computational efficiency and scalability while the ability to autonomously reconfigure hardware controls offers increased flexibility and responsiveness. The hierarchical decomposition and models utilized were well aligned with the physical twin, as indicated by the maximum deviations between the developed digital twin hierarchy and the hardware.
2. THEORY OF MACHINES
• The subject Theory of Machines may be
defined as the branch of science which deals
with the study of relative motion between the
various part of machine and the forces which
act on them.
Kinematics of Machinery - B.K.Parrthipan 2
3. THEORY OF MACHINES -
BRANCHES
1. Statics.
It is that branch of Theory of Machines
which deals with the forces and their effects
while the machine parts are at rest. The mass
of the parts is assumed to be negligible.
2. Dynamics.
It is that branch of Theory of Machines
which deals with the forces and their effects,
while acting upon the machine parts in motion.
Kinematics of Machinery - B.K.Parrthipan 3
4. THEORY OF MACHINES -
BRANCHES
3. Kinematics.
It is that branch of Theory of Machines
which deals with the relative motion between
the various parts of the machines.
4. Kinetics.
It is that branch of Theory of Machines
which deals with the inertia forces which arise
from the combined effect of the mass and
motion of the machine parts.
Kinematics of Machinery - B.K.Parrthipan 4
5. MECHANISM
Mechanism:
• Mechanism is combinations of number of
bodies (usually rigid bodies) are assembled in
such a way that the motion of one causes
constrained and predictable motion to the
others.
• A mechanism transmits and modifies a motion.
6. MACHINE
Machine:
• A Machine is a mechanism or combination of
mechanisms imparting definite motions to the
parts.
• Also, it transmits and modifies the available
mechanical energy into desired (or useful)
work.
7. LINK
Link:
Each part of a machine, which moves relative
to some other part, is known as a kinematic
link (or simply link) or element.
7Kinematics of Machinery - B.K.Parrthipan
Binary link Ternary link Quaternary link
9. TYPES OF LINK
1. Rigid link.
A rigid link is one which does not undergo any
deformation while transmitting motion.
2. Flexible link.
A flexible link is one which is partly deformed in
a manner not to affect the transmission of motion.
3. Fluid link.
A fluid link is one in which the motion is
transmitted through the fluid by pressure or
compression.
9Kinematics of Machinery - B.K.Parrthipan
10. STRUCTURE
• It is an assemblage of a number of resistant
bodies (known as members) having no relative
motion between them and meant for carrying
loads having straining action.
• A railway bridge, a roof truss, machine frames
etc., are the examples of a structure.
• It differs from a machine.
10Kinematics of Machinery - B.K.Parrthipan
11. EXAMPLE OF A STRUCTURE
11Kinematics of Machinery - B.K.Parrthipan
12. DIFFERENCE BETWEEN
MACHINE AND STRUCTURE
• The parts of a machine move relative to one
another, whereas the members of a structure do
not move relative to one another.
• A machine transforms the available energy
into some useful work, whereas in a structure
no energy is transformed into useful work.
• The links of a machine may transmit both
power and motion, while the members of a
structure transmit forces only.`
12Kinematics of Machinery - B.K.Parrthipan
13. KINEMATIC PAIR
• 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.
13Kinematics of Machinery - B.K.Parrthipan
14. TYPES OF CONSTRAINED MOTIONS
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.
For example, the piston and cylinder (in a steam engine)
form a pair and the motion of the piston is limited to a
definite direction (i.e. it will only reciprocate) relative to the
cylinder irrespective of the direction of motion of the crank.
The motion of a square bar in a square hole and the motion of
a shaft with collars at each end in a circular hole are also
examples of completely constrained motion.
15. 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.
A circular bar or shaft in a circular hole, as shown in Fig, is an
example of an incompletely constrained motion as it may
either rotate or slide in a hole. These both motions have no
relationship with the other.
16. 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.
Consider a shaft in a foot-step bearing as shown in Fig. The
shaft may rotate in a bearing or it may move upwards. This is a
case of incompletely constrained motion. But if the load is
placed on the shaft to prevent axial upward movement of the
shaft, then the motion of the pair 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.
17. CLASSIFICATION
• According to the type of relative motion
between the elements
• According to the type of contact between the
elements
• According to the type of closure
17Kinematics of Machinery - B.K.Parrthipan
18. TYPE OF RELATIVE MOTION BETWEEN
THE ELEMENTS
(a) Sliding pair.
When the two elements of a pair are connected in such a way
that one can only slide relative to the other, the pair is known
as a sliding pair.
Eg: The piston and cylinder.
18Kinematics of Machinery - B.K.Parrthipan
19. TYPE OF RELATIVE MOTION BETWEEN
THE ELEMENTS
(b) Turning pair.
When the two elements of a pair are connected in such a way
that one can only turn or revolve about a fixed axis of another
link, the pair is known as turning pair.
Eg: Cycle wheels turning over their axle
19Kinematics of Machinery - B.K.Parrthipan
20. TYPE OF RELATIVE MOTION BETWEEN
THE ELEMENTS
(c) Rolling pair.
When the two elements of a pair are connected in such a way
that one rolls
over another fixed link, the pair is known as rolling pair.
Eg: Ball and roller bearings
20Kinematics of Machinery - B.K.Parrthipan
21. TYPE OF RELATIVE MOTION BETWEEN
THE ELEMENTS
(d) Screw pair.
When the two elements of a pair are connected in such a way
that one element can turn about the other by screw threads, the
pair is known as screw pair.
Eg: Bolt with a nut.
21Kinematics of Machinery - B.K.Parrthipan
22. TYPE OF RELATIVE MOTION BETWEEN
THE ELEMENTS
(e) Spherical pair.
When the two elements of a pair are connected in such a way
that one element (with spherical shape) turns or swivels about
the other fixed element, the pair formed is called a spherical
pair.
Eg: The ball and socket joint
22Kinematics of Machinery - B.K.Parrthipan
23. TYPE OF CONTACT BETWEEN THE
ELEMENTS
(a) 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.
Examples: Nut turning on a screw, shaft rotating in a
bearing, all pairs of a slider-crank mechanism, universal
joint, etc.
23Kinematics of Machinery - B.K.Parrthipan
24. TYPE OF CONTACT BETWEEN THE
ELEMENTS
(b) 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.
Examples:
Wheel rolling on a surface, cam and follower pair, tooth
gears, ball and roller bearings, etc.
24Kinematics of Machinery - B.K.Parrthipan
25. TYPE OF CLOSURE BETWEEN THE
ELEMENTS
(a) Self closed pair.
When the two elements of a
pair are connected together
mechanically in such a way
that only required kind of
relative motion occurs, it is
then known as self closed
pair. The lower pairs are self
closed pair.
(b) Force - closed pair.
When the two elements of a
pair are not connected
mechanically but are kept
in contact by the action of
external forces, the pair is
said to be a force-closed pair.
25Kinematics of Machinery - B.K.Parrthipan
26. KINEMATIC CHAIN
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.
Ex:
The crankshaft of an engine forms a kinematic pair with the bearings which
are fixed in a pair, the connecting rod with the crank forms a second
kinematic pair, the piston with the connecting rod forms a third pair and the
piston with the cylinder forms a fourth pair. The total combination of these
links is a kinematic chain.
26Kinematics of Machinery - B.K.Parrthipan
27. TYPES OF JOINTS IN A CHAIN
• Binary joint
• Ternary joint (2BJ)
• Quaternary joint (3BJ)
27Kinematics of Machinery - B.K.Parrthipan
28. MECHANISM
When one of the links of a kinematic chain is fixed, the chain
is known as mechanism.
Classification:
A. Based on no. of links
1. Simple Mechanism:
A mechanism with four links is known as simple
mechanism,
2. Compound Mechanism:
The mechanism with more than four links is known as
compound mechanism.
28Kinematics of Machinery - B.K.Parrthipan
29. MECHANISM
B. Based on mobility
1. Planar Mechanism
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.
2. Spherical Mechanism
3. Spatial Mechanism
Spatial Mechanism have special geometric characteristics in that
all revolute axes are parallel and perpendicular to the plane of
motion and all prism axes lie in the plane of motion.
Kinematics of Machinery - B.K.Parrthipan 29
30. DEGREES OF FREEDOM/ MOBILITY
• It is defined as the number of input parameters
(usually pair variables) which must be independently
controlled in order to bring the mechanism into a
useful engineering purpose.
• It is possible to determine the number of degrees of
freedom of a mechanism directly from the number of
links and the number and types of joints which it
includes
• It is denoted by n
30Kinematics of Machinery - B.K.Parrthipan
31. KUTZBACH CRITERION
n = 3 (l – 1) – 2 j – h
Where,
l = no. of link
j = no. of binary joints
h = no. of higher pair
31Kinematics of Machinery - B.K.Parrthipan
32. MECHANISMS WITH A HIGHER PAIR
32Kinematics of Machinery - B.K.Parrthipan
33. GRUEBLERS CRITERION
• The Grubler’s criterion applies to mechanisms
with only single degree of freedom joints
where the overall mobility of the mechanism is
unity.
33Kinematics of Machinery - B.K.Parrthipan
34. GRASHOFF’S LAW
This law states that the sum of lengths of
longest and shortest links should be less than
sum of the lengths of other two links
l + S < p + q
Class I mechanism - Obeys Grashoff Law
Class II mechnism - Violates Grashoff Law
34Kinematics of Machinery - B.K.Parrthipan
35. INVERSION OF A MECHANISM
• The method of obtaining different mechanisms by fixing
different links in a kinematic chain, is known as inversion of
the mechanism
35Kinematics of Machinery - B.K.Parrthipan
36. FOUR BAR CHAIN
Basic Kinematic Chain of a Four bar chain consists of
• Frame (AB)
• Crank (AD)
• Coupler (DC)
• Output link (BC)
36Kinematics of Machinery - B.K.Parrthipan
37. INVERSIONS OF FOUR BAR CHAIN
• Crank and Lever Mechanism (Beam Engine)
• Double Crank Mechanism (Coupling rod of a locomotive)
• Rocker rocker or double rocker or double lever mechanism
(Watts Indicator Mechanism)
37Kinematics of Machinery - B.K.Parrthipan
38. BEAM ENGINE
38Kinematics of Machinery - B.K.Parrthipan
• 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.
40. COUPLING ROD OF LOCOMOTIVE
• In this mechanism, the links AD and BC (having equal length)
act as cranks and are connected to the respective wheels.
• The link CD acts as a coupling rod and the link AB is fixed in
order to maintain a constant centre to centre distance between
them.
• This mechanism is meant for transmitting rotary motion from
one wheel to the other wheel.
41. WATT’S INDICATOR DIAGRAM
41
A Watt’s indicator mechanism (also known as Watt's straight line
mechanism or double lever mechanism) which consists of four links,
is shown in Fig.
• The four links are : fixed link at A, link AC, link CE and link BFD.
It may be noted that BF and FD form one link because these two
parts have no relative motion between them. The links CE and BFD
act as levers.
• The displacement of the link BFD is directly proportional to the
pressure of gas or steam which acts on the indicator plunger.
• On any small displacement of the mechanism, the
tracing point E at the end of the link CE traces out
approximately a straight line.
• The initial position of the mechanism is shown in
Fig. by full lines whereas the dotted lines show
the position of the mechanism when the gas or
steam pressure acts on the indicator plunger.
43. MECHANICALADVANTAGE
• It is defined as the ratio of output torque to the input torque.
• It is also defined as the ratio of load to effort.
43Kinematics of Machinery - B.K.Parrthipan
44. TRANSMISSION ANGLE
• It is defined as the angle between the coupler and the follower
and it is denoted by
Kinematics of Machinery - B.K.Parrthipan 44
45. SINGLE SLIDER CRANK CHAIN
• Frame
• Crank
• Connecting Rod
• Cross Head – Slider
45Kinematics of Machinery - B.K.Parrthipan
46. INVERSIONS
• Pendulum Pump or Bull Engine
• Oscillating Cylinder Engine
• Rotary IC Engine or Gnome Engine
• Crank and Slotted Lever Mechanism
• Whitworth Quick Return Mechanism
46Kinematics of Machinery - B.K.Parrthipan
53. 1. Elliptical trammels.
• It is an instrument used for drawing ellipses. This inversion is obtained by fixing the
slotted plate (link 4), as shown in Fig.
• The fixed plate or link 4 has two straight grooves cut in it, at right angles to each
other.
• The link 1 and link 3, are known as sliders and form sliding pairs with link 4. The
link AB (link 2) is a bar which forms turning pair with links 1 and 3.
• When the links 1 and 3 slide along their respective grooves, any point on the link 2
such as P traces out an ellipse on the surface of link 4, as shown in Fig. A little
consideration will show that AP and BP are the semi-major axis and semi-minor axis
of the ellipse respectively.
53
55. 2. Scotch yoke mechanism.
• The Scotch yoke is a mechanism for converting the linear motion of a
slider into rotational motion or vice-versa. The piston or other reciprocating
part is directly coupled to a sliding yoke with a slot that engages a pin on
the rotating part.
• This mechanism is used for converting rotary motion into a reciprocating
motion. The inversion is obtained by fixing either the link 1 or link 3. In
Fig. link 1 is fixed.
• In this mechanism, when the link 2 (which corresponds to crank) rotates
about B as centre, the link 4 (which corresponds to a frame) reciprocates.
• The fixed link 1 guides the frame.
55
56. 3. Oldham’s coupling.
• An oldham's coupling is used for connecting two parallel shafts whose axes are at a
small distance apart. The shafts are coupled in such a way that if one shaft rotates,
the other shaft also rotates at the same speed.
• This inversion is obtained by fixing the link 2, as shown in Fig (a).
• The shafts to be connected have two flanges (link 1 and link 3) rigidly fastened at
their ends by forging.
• The link 1 and link 3 form turning pairs with link 2.
• These flanges have diametrical slots cut in their inner faces, as shown in Fig.(b).
• The intermediate piece (link 4) which is a circular disc, have two tongues (i.e.
diametrical projections) T1 and T2 on each face at right angles to each other, as
shown in Fig. (c).
• The tongues on the link 4 closely fit into the slots in the two flanges (link 1 and link
3). The link 4 can slide or reciprocate in the slots in the flanges.
56
58. Straight Line Generating Mechanism
• Two types
• only turning pairs are used
• only sliding pairs are used
• Also Classified as
• Exact Straight line mechanism
• Approximate straight line mechanism
58Kinematics of Machinery - B.K.Parrthipan
59. Exact Straight line Mechanism
• Peaucellier Mechanism
59Kinematics of Machinery - B.K.Parrthipan