The document provides information about various plane curves covered in the Engineering Graphics course GE8152 Unit 1. It includes definitions and methods for constructing conic sections like circles, ellipses, parabolas and hyperbolas on a plane. It also describes the construction of other curves like cycloids, epicycloids, hypocycloids, involutes of circles and squares. Detailed step-by-step processes are provided with diagrams to draw these curves using focus, directrix, radii and other geometric properties. The document serves as a reference for students to understand and construct different plane curves for applications in engineering graphics.
introduction of engineering graphics ,projection of points,lines,planes,solids,section of solids,development of surfaces,isometric projection,perspective projection
introduction of engineering graphics ,projection of points,lines,planes,solids,section of solids,development of surfaces,isometric projection,perspective projection
introduction of engineering graphics ,projection of points,lines,planes,solids,section of solids,development of surfaces,isometric projection,perspective projection
introduction of engineering graphics ,projection of points,lines,planes,solids,section of solids,development of surfaces,isometric projection,perspective projection
introduction of engineering graphics ,projection of points,lines,planes,solids,section of solids,development of surfaces,isometric projection,perspective projection
Mechanical Drafting Projection of solidsGaurav Mistry
Introduction and types of solids, Terms of solids and projections, Basics of projections, projection of solids to different planes, projection when different element of solids are resting on HP or VP, Different stages of projections.
introduction of engineering graphics ,projection of points,lines,planes,solids,section of solids,development of surfaces,isometric projection,perspective projection
introduction of engineering graphics ,projection of points,lines,planes,solids,section of solids,development of surfaces,isometric projection,perspective projection
introduction of engineering graphics ,projection of points,lines,planes,solids,section of solids,development of surfaces,isometric projection,perspective projection
introduction of engineering graphics ,projection of points,lines,planes,solids,section of solids,development of surfaces,isometric projection,perspective projection
introduction of engineering graphics ,projection of points,lines,planes,solids,section of solids,development of surfaces,isometric projection,perspective projection
Mechanical Drafting Projection of solidsGaurav Mistry
Introduction and types of solids, Terms of solids and projections, Basics of projections, projection of solids to different planes, projection when different element of solids are resting on HP or VP, Different stages of projections.
Curves2- THIS SLIDE CONTAINS WHOLE SYLLABUS OF ENGINEERING DRAWING/GRAPHICS. IT IS THE MOST SIMPLE AND INTERACTIVE WAY TO LEARN ENGINEERING DRAWING.SYLLABUS IS RELATED TO rajiv gandhi proudyogiki vishwavidyalaya / rajiv gandhi TECHNICAL UNIVERSITY ,BHOPAL.
CURVE 1- THIS SLIDE CONTAINS WHOLE SYLLABUS OF ENGINEERING DRAWING/GRAPHICS. IT IS THE MOST SIMPLE AND INTERACTIVE WAY TO LEARN ENGINEERING DRAWING.SYLLABUS IS RELATED TO rajiv gandhi proudyogiki vishwavidyalaya / rajiv gandhi TECHNICAL UNIVERSITY ,BHOPAL.
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.
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.
About
Indigenized remote control interface card suitable for MAFI system CCR equipment. Compatible for IDM8000 CCR. Backplane mounted serial and TCP/Ethernet communication module for CCR remote access. IDM 8000 CCR remote control on serial and TCP protocol.
• Remote control: Parallel or serial interface.
• Compatible with MAFI CCR system.
• Compatible with IDM8000 CCR.
• Compatible with Backplane mount serial communication.
• Compatible with commercial and Defence aviation CCR system.
• Remote control system for accessing CCR and allied system over serial or TCP.
• Indigenized local Support/presence in India.
• Easy in configuration using DIP switches.
Technical Specifications
Indigenized remote control interface card suitable for MAFI system CCR equipment. Compatible for IDM8000 CCR. Backplane mounted serial and TCP/Ethernet communication module for CCR remote access. IDM 8000 CCR remote control on serial and TCP protocol.
Key Features
Indigenized remote control interface card suitable for MAFI system CCR equipment. Compatible for IDM8000 CCR. Backplane mounted serial and TCP/Ethernet communication module for CCR remote access. IDM 8000 CCR remote control on serial and TCP protocol.
• Remote control: Parallel or serial interface
• Compatible with MAFI CCR system
• Copatiable with IDM8000 CCR
• Compatible with Backplane mount serial communication.
• Compatible with commercial and Defence aviation CCR system.
• Remote control system for accessing CCR and allied system over serial or TCP.
• Indigenized local Support/presence in India.
Application
• Remote control: Parallel or serial interface.
• Compatible with MAFI CCR system.
• Compatible with IDM8000 CCR.
• Compatible with Backplane mount serial communication.
• Compatible with commercial and Defence aviation CCR system.
• Remote control system for accessing CCR and allied system over serial or TCP.
• Indigenized local Support/presence in India.
• Easy in configuration using DIP switches.
Overview of the fundamental roles in Hydropower generation and the components involved in wider Electrical Engineering.
This paper presents the design and construction of hydroelectric dams from the hydrologist’s survey of the valley before construction, all aspects and involved disciplines, fluid dynamics, structural engineering, generation and mains frequency regulation to the very transmission of power through the network in the United Kingdom.
Author: Robbie Edward Sayers
Collaborators and co editors: Charlie Sims and Connor Healey.
(C) 2024 Robbie E. Sayers
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.
HEAP SORT ILLUSTRATED WITH HEAPIFY, BUILD HEAP FOR DYNAMIC ARRAYS.
Heap sort is a comparison-based sorting technique based on Binary Heap data structure. It is similar to the selection sort where we first find the minimum element and place the minimum element at the beginning. Repeat the same process for the remaining elements.
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.
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.
6th International Conference on Machine Learning & Applications (CMLA 2024)
EG UNIT 1PLANE CURVES.ppt
1. GE 8152 - ENGINEERING GRAPHICS
Dr.R.Ganesamoorthy.
Professor / Mechanical Engineering.
Chennai Institute of Technology.
GE8152- ENGINEERING GRAPHICS - UNIT-1 PLANE CURVES
UNIT -1 PLANE CURVES
2. CONIC SECTIONS
GE8152- ENGINEERING GRAPHICS - UNIT-1 PLANE CURVES
Definition:
The sections obtained by the intersection of a right circular cone by a cutting plane in different positions
are called conic sections or conics.
3. CONIC SECTIONS
GE8152- ENGINEERING GRAPHICS - UNIT-1 PLANE CURVES
CIRCLE:
When the cutting plane is parallel to the base or perpendicular to the axis,
then the true shape of the section is circle.
ELLIPSE:
When the cutting plane is inclined to the horizontal plane and perpendicular to the vertical plane, then the
true shape of the section is an ellipse.
4. GE8152- ENGINEERING GRAPHICS - UNIT-1 PLANE CURVES
Parabola:
When the cutting plane is inclined to the axis and is parallel to one of the generators, then the true shape
of the section is a parabola.
Hyperbola:
When the cutting plane is parallel to the axis of the cone, then the true shape of the section is a
rectangular hyperbola.
5. GE8152- ENGINEERING GRAPHICS - UNIT-1 PLANE CURVES
Focus & Directrix
Conic may be defined as the locus of a point moving in a plane in such a way that the ratio of its
distances from a fixed point, called focus and a fixed straight line called directrix.
Eccentricity
The ratio of shortest distance from the focus to the shortest distance from the directrix is called
eccentricity.
7. GE8152- ENGINEERING GRAPHICS - UNIT-1 PLANE CURVES
1.Draw the directrix AB and axis CC’
2.Mark F on CC’ such that CF = 80 mm.
3.Divide CF into 7 equal parts and
mark V at the fourth division from C.
4.Now, e = FV/ CV = 3/4.
5.At V, erect a perpendicular VB = VF. Join CB. Through F,
draw a line at 45° to meet CB produced at D. Through D,
drop a perpendicular DV’on CC’. Mark O at the midpoint of V– V’.
Draw an ellipse when the distance between the focus and directrix is 80mm
and eccentricity is ¾.
8. GE8152- ENGINEERING GRAPHICS - UNIT-1 PLANE CURVES
6.With F as a centre and radius = 1–1’, cut two arcs on the perpendicular through 1 to locate P1 and P1’.
Similarly, with F as centre and radii =2-2’, 3–3’, etc., cut arcs on the corresponding perpendiculars to
locate P2 and P2’, P3 and P3’, etc. Also, cut similar arcs on the perpendicular through O to locate V1
and V1’.
7. Draw a smooth closed curve passing through V,
P1, P/2, P/3,., V1, …,V’, …, V1’, … P/3’, P/2’, P1’.
8. Mark F’ on CC’ such that V’ F’ = VF.
9. GE8152- ENGINEERING GRAPHICS - UNIT-1 PLANE CURVES
Draw an ellipse when the distance between the focus and directrix is 50mm and eccentricity is 2/3. Also
draw the tangent and normal curve.
11. GE8152- ENGINEERING GRAPHICS - UNIT-1 PLANE CURVES
Construct a parabola when the distance of the Focus from the directrix is
60 mm. Note: Eccentricity, e = 1.
1.Draw directrix AB and axis CC’ as shown.
2.Mark F on CC’ such that CF = 60 mm.
3.Mark V at the midpoint of CF. Therefore, e = VF/ VC = 1.
At V, erect a perpendicular VB = VF. Join CB.
4.Mark a few points, say, 1, 2, 3, … on VC’ and erect
perpendiculars through them meeting CB produced at 1’,2’, 3’…
5.With F as a centre and radius = 1–1’, cut two arcs on the
perpendicular through 1 to locate P1 and P1’. Similarly, with F as
a centre and radii = 2–2’, 3–3’, etc., cut arcs on the
corresponding perpendiculars to locate P2 and P2’,P3 and P3’ etc.
6.Draw a smooth curve passing through V, P1,P2,P3 …P3’,P2’,P1’.
12. GE8152- ENGINEERING GRAPHICS - UNIT-1 PLANE CURVES
Construct a parabola when the distance of the Focus from the directrix is 50 mm. Also
draw tangent and normal curve at any point.
13. GE8152- ENGINEERING GRAPHICS - UNIT-1 PLANE CURVES
Construction of Hyperbola:
Hyperbolic shapes finds large number of industrial applications like the shape of cooling towers, mirrors
Used for long distance telescopes, etc.
14. GE8152- ENGINEERING GRAPHICS - UNIT-1 PLANE CURVES
Draw a hyperbola when the distance of the focus from the directrix is 55 mm and eccentricity is
3/2.
1. Draw a perpendicular line AB (directrix) and a horizontal line CC’ (axis).
2. Mark the focus point F on the axis line 55 mm from the directrix.
3. Divide the CF in to 5 equal parts.
4. As per the eccentricity mark the vertex V, in the third division of CF
5. Draw a perpendicular line from vertex V, and mark the point B,
6. with the distance VF.
7. Join the points C& B and extend the line.
15. GE8152- ENGINEERING GRAPHICS - UNIT-1 PLANE CURVES
7. Draw number of smooth vertical lines 1,2,3,4,5,6,etc., as shown in figure.
8. Now mark the points 1′, 2′, 3′, 4′, 5′…
9. Take the vertical distance of 11′ and with F as centre
draw an arc cutting the vertical line 11′ above and below the axis.
10. Similarly draw the arcs in all the vertical lines (22′, 33′, 44′…)
11. Draw a smooth curve through the cutting points to get the required
hyperbola by free hand.
16. GE8152- ENGINEERING GRAPHICS - UNIT-1 PLANE CURVES
Draw a hyperbola when the distance of the focus from the directrix is 50 mm and eccentricity is 3/2. Also
draw tangent and normal curve at any point.
17. GE8152- ENGINEERING GRAPHICS - UNIT-1 PLANE CURVES
Cycloidal curves
Cycloidal curves are generated by a fixed point on the circumference of a circle, which rolls without
slipping along a fixed straight line or a circle.
In engineering drawing some special Curves ( Cycloidal curves) are used in the profile of teeth of gear
wheels.
The rolling circle is called generating circle. The fixed straight line or circle is called directing line or
directing circle.
18. GE8152- ENGINEERING GRAPHICS - UNIT-1 PLANE CURVES
1. Cycloid is a curve generated by a point on the circumference of a circle which rolls along a straight line.
2. Draw a circle with diameter 50mm and mark the centre O.
3. Divide the circle in to 12 equal parts as1,2,3…12.
4. Draw horizontal line from the bottom points of the circle, with the distance equal to the circumference of
the circle (ПD) and mark the other end point B.
5. Divide the line AB in to 12 equal parts. (1′, 2′, 3′…12′)
6. Draw a horizontal line from O to and mark the equal distance point O1, O2,O3…O12.
7. Draw smooth horizontal lines from the points 1,2,3…12.
19. GE8152- ENGINEERING GRAPHICS - UNIT-1 PLANE CURVES
8. When the circle starts rolling towards right hand side, the point 1 coincides with 1′ at the same time the
centreO moves to O1. Take OA as radius, O1 as center draw an arc to cut the horizontal line 1 to mark
the point a1.
9. Similarly O2 as center and with same radius OA draw an arc to cut the horizontal line 2 to mark the
point a2. Similarly mark a3, a4…a11.
10. Draw a smooth curve through the points a1, a2, a3,…. a11, B by free hand.
11. The obtained curve is a cycloid
20. GE8152- ENGINEERING GRAPHICS - UNIT-1 PLANE CURVES
A circle of 72mm dia rolls along a straight line without slipping. Draw the curve traced out by a point P on
the circumference, for complete one revolution. Name the curve, also draw the tangent and normal curve
at a point 62 mm from the straight line.
21. GE8152- ENGINEERING GRAPHICS - UNIT-1 PLANE CURVES
Epicycloid is the curve generated by a point on the circumference of a circle which rolls without slipping
along another circle outside it.
22. GE8152- ENGINEERING GRAPHICS - UNIT-1 PLANE CURVES
1. With O as centre and radius OP (base circle radius), draw an arc PQ.
2. The included angle θ = (r/R) x 360°.
3. With O as centre and OC as radius, draw an arc to represent locus of centre.
4. Divide arc PQ in to 12 equal parts and name them as 1’, 2’, …., 12’.
5. Join O1’, O2’, … and produce them to cut the locus of centres at C1, C2, ….C12. Taking C1 as
centre,
6. and radius equal to r, draw an arc cutting the arc through 1 at P1.
7. Taking C2 as centre and with the same radius, draw an arc cutting the arc through 2 at P2 Similarly
obtain points P3, P3, …., P12.
8. Draw a smooth curve passing through P1, P2….. , P12, which is the required epiclycloid.
24. GE8152- ENGINEERING GRAPHICS - UNIT-1 PLANE CURVES
Construct a epi-cycloid rolling circle 60mm
diameter and directing circle 122mm radius.
Draw also the tangent and normal at M,
which on the curve.
1. With O as centre and radius OP (base circle radius), draw an arc
PQ.
2. The included angle θ = (r/R) x 360°.
3. With O as centre and OC as radius, draw an arc to represent
locus of centre.
4. Divide arc PQ in to 12 equal parts and name them as 1’, 2’, ….,
12’.
5. Join O1’, O2’, … and produce them to cut the locus of centres at
C1, C2, ….C12. Taking C1 as centre,
6. and radius equal to r, draw an arc cutting the arc through 1 at P1.
7. Taking C2 as centre and with the same radius, draw an arc
cutting the arc through 2 at P2 Similarly obtain points P3, P3, ….,
P12.
8. Draw a smooth curve passing through P1, P2….. , P12, which is
the required epiclycloid.
25. GE8152- ENGINEERING GRAPHICS - UNIT-1 PLANE CURVES
Hypocycloid is the curve generated by a point on the circumference of a circle which rolls without slipping
inside another circle.
26. GE8152- ENGINEERING GRAPHICS - UNIT-1 PLANE CURVES
1.With O as centre and radius OB (base circle radius), draw an arc BA.
2.The included angle θ = (r/R) x 360°. With O as centre and OB as radius, draw an arc to represent locus
of centre.
3.Divide arc AB in to 12 equal parts and name them as 1’, 2’, …., 12’. Join O1’, O2’, …, O12’ so as to
cut the locus of centres at C1, C2,….C12.
4.Taking C1 as centre, and radius equal to r, draw an arc cutting the arc through 1 at P1. Taking C2 as
centre and with the same radius, draw an arc cutting the arc through 2 at P2.
5.Similarly obtain points P3, P3, …., P12.
6.Draw a smooth curve passing through P1, P2….. , P12, which is the required hypocycloid.
28. GE8152- ENGINEERING GRAPHICS - UNIT-1 PLANE CURVES
INVOLUTES:
An involutes is a curve traced by a point on a perfectly flexible string, while unwinding from around a
circle or polygon the string being kept taut (tight). It is also a curve traced by a point on a straight line
while the line is rolling around a circle or polygon without slipping.
29. GE8152- ENGINEERING GRAPHICS - UNIT-1 PLANE CURVES
Draw an involutes of a given square.
1. Draw the given square ABCD of side a.(a=30mm)
2. Taking D as the starting point, with centre A and radius
DA=a, draw an arc to intersect the line BA produced at P1.
3. With Centre B and radius BP1 = 2 a, draw on arc to
intersect the line CB produced at P2.
4. Similarly, locate the points P3 and P4.
5. The curve through D, PI' P2, P3 and P4 is the
required involutes.
6. DP 4 is equal to the perimeter of the square.
30. GE8152- ENGINEERING GRAPHICS - UNIT-1 PLANE CURVES
Construction of Involutes of circle
1. Draw the circle with O as centre and OA as radius.(20mm).
2. Draw line P-P12 = 2π D, tangent to the circle at P
3. Divide the circle into 12 equal parts. Number them as1, 2…
4. Divide the line PQ into 12 equal parts and number as1΄,2΄…..
5. Draw tangents to the circle at 1, 2,3….
6. Locate points P1, P2 such that 1-P1 = P1΄,
2-P2 = P2΄ Join P, P1,P2...
7.The tangent to the circle at any point on it is
always normal to the its involutes.