This PPT is dedicated to circle properties with precise explanation and interesting figures. For more structured knowledge and quiz visit.
www.correcteducate.com
The document discusses calculating the area of a quadrilateral shape formed inside a circle. It defines the length of a chord in a circle and shows a diagram with a diameter AB and parallel chord PQ. It then finds the length of a perpendicular from the center C to the chord PQ, allowing the area of the quadrilateral PABQ to be determined using properties of chords, perpendiculars, radii, and the Pythagorean theorem.
This document contains the syllabus for an engineering graphics course. It covers curve constructions including conics, cycloids, and involutes. It also covers orthographic projection principles and projecting engineering components and objects from pictorial views to multiple views using first angle projection. Examples are provided on constructing a cycloid traced by a point on a rolling circle, drawing the involute of a square and circle, and projecting views of objects.
in this ppt Engineering Graphic's involute curve subjected.
INVOLUTE CURVE IS MORE USE IN EG SUBJECT OF ENGINEERING.
THANK YOU FOR WATCHING AND GIVING ME A CHANCE
This document provides definitions and examples of common engineering curves including involutes, cycloids, spirals, and helices. It begins by listing different types of involutes defined by the string length relative to the circle's circumference. Definitions are then given for cycloids based on whether the rolling circle is inside or outside the directing circle. Superior and inferior trochoids are distinguished based on this as well. Spirals are defined as curves generated by a point revolving around a fixed point while also moving toward it. Helices are curves generated by a point moving around a cylinder or cone surface while advancing axially. Examples are provided for drawing various curves along with methods for constructing tangents and normals.
The document discusses various conic sections and cycloidal curves. It defines conic sections as curves formed by the intersection of a plane with a right circular cone in different positions. The specific conic sections covered are circles, ellipses, parabolas, and hyperbolas. It also discusses the construction of these conic sections through diagrams. Additionally, it defines cycloidal curves as those generated by a point on a circle rolling along a straight line or circle, and provides examples of cycloids, epicycloids, and hypocycloids. It concludes by defining involutes as curves traced by a point on a string unwinding from or a line rolling around a circle or polygon.
The document provides instructions for performing various geometric constructions using drawing instruments. It covers constructing lines, angles, triangles, quadrilaterals, circles, ellipses, parabolas, hyperbolas and their tangents. The methods include using a compass, set squares, concentric circles and the distance squared rule. Instructions are given step-by-step with diagrams to divide lines into ratios, bisect angles, construct perpendiculars, inscribe and circumscribe shapes, draw tangents and join two points with a curve. The document also introduces graphic language components, drawing instruments and their use in technical drawing and sketching.
Conic sections are curves formed by the intersection of a plane and a cone. The type of conic section depends on the angle of the cutting plane:
- An ellipse results from a cutting plane parallel to the end generator.
- A parabola results from a cutting plane parallel to the axis.
- A hyperbola results from a cutting plane perpendicular to the axis.
The eccentricity defines the type of conic section, with eccentricity less than 1 for an ellipse, equal to 1 for a parabola, and greater than 1 for a hyperbola.
This PPT is dedicated to circle properties with precise explanation and interesting figures. For more structured knowledge and quiz visit.
www.correcteducate.com
The document discusses calculating the area of a quadrilateral shape formed inside a circle. It defines the length of a chord in a circle and shows a diagram with a diameter AB and parallel chord PQ. It then finds the length of a perpendicular from the center C to the chord PQ, allowing the area of the quadrilateral PABQ to be determined using properties of chords, perpendiculars, radii, and the Pythagorean theorem.
This document contains the syllabus for an engineering graphics course. It covers curve constructions including conics, cycloids, and involutes. It also covers orthographic projection principles and projecting engineering components and objects from pictorial views to multiple views using first angle projection. Examples are provided on constructing a cycloid traced by a point on a rolling circle, drawing the involute of a square and circle, and projecting views of objects.
in this ppt Engineering Graphic's involute curve subjected.
INVOLUTE CURVE IS MORE USE IN EG SUBJECT OF ENGINEERING.
THANK YOU FOR WATCHING AND GIVING ME A CHANCE
This document provides definitions and examples of common engineering curves including involutes, cycloids, spirals, and helices. It begins by listing different types of involutes defined by the string length relative to the circle's circumference. Definitions are then given for cycloids based on whether the rolling circle is inside or outside the directing circle. Superior and inferior trochoids are distinguished based on this as well. Spirals are defined as curves generated by a point revolving around a fixed point while also moving toward it. Helices are curves generated by a point moving around a cylinder or cone surface while advancing axially. Examples are provided for drawing various curves along with methods for constructing tangents and normals.
The document discusses various conic sections and cycloidal curves. It defines conic sections as curves formed by the intersection of a plane with a right circular cone in different positions. The specific conic sections covered are circles, ellipses, parabolas, and hyperbolas. It also discusses the construction of these conic sections through diagrams. Additionally, it defines cycloidal curves as those generated by a point on a circle rolling along a straight line or circle, and provides examples of cycloids, epicycloids, and hypocycloids. It concludes by defining involutes as curves traced by a point on a string unwinding from or a line rolling around a circle or polygon.
The document provides instructions for performing various geometric constructions using drawing instruments. It covers constructing lines, angles, triangles, quadrilaterals, circles, ellipses, parabolas, hyperbolas and their tangents. The methods include using a compass, set squares, concentric circles and the distance squared rule. Instructions are given step-by-step with diagrams to divide lines into ratios, bisect angles, construct perpendiculars, inscribe and circumscribe shapes, draw tangents and join two points with a curve. The document also introduces graphic language components, drawing instruments and their use in technical drawing and sketching.
Conic sections are curves formed by the intersection of a plane and a cone. The type of conic section depends on the angle of the cutting plane:
- An ellipse results from a cutting plane parallel to the end generator.
- A parabola results from a cutting plane parallel to the axis.
- A hyperbola results from a cutting plane perpendicular to the axis.
The eccentricity defines the type of conic section, with eccentricity less than 1 for an ellipse, equal to 1 for a parabola, and greater than 1 for a hyperbola.
This document discusses engineering drawings and curves. It states that engineering drawings are the language used to communicate engineering ideas and execute work. Various types of curves are useful in engineering for understanding natural laws, manufacturing, design, analysis, and construction. Common engineering curves include conics, cycloids, involutes, spirals, and helices. Conics specifically include circles, ellipses, parabolas, and hyperbolas which are sections of a right circular cone cut by planes. The document provides definitions and examples of each type of conic section. It also discusses different methods for drawing ellipses like the arc of circles method.
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.
The document discusses various types of engineering curves including involutes, cycloids, spirals, and helices. It provides definitions for involutes, cycloids, epicycloids, hypotrochoids, spirals, and helices. Examples are given on how to draw involutes of circles, squares, and triangles. Methods for drawing tangents and normals to involutes, cycloids, and epicycloids are also described. Problems include drawing loci for points on circles rolling along straight or curved paths to form different types of cycloids.
The document discusses various geometric constructions including:
1. Dividing a line into equal parts and dividing a line in a given ratio.
2. Bisecting a given angle.
3. Inscribing a square in a given circle.
4. Drawing parabolas, cycloids, epicycloids, and hypocycloids by rolling and tracing circles.
Step-by-step methods are provided for each construction without mathematical proofs.
This document provides an overview of geometric construction concepts including:
- The principles of geometric construction using only a ruler and compass.
- Key terminology related to points, lines, angles, planes, circles, polygons and other basic geometric entities.
- Procedures for performing common geometric constructions such as bisecting lines, arcs and angles, constructing perpendiculars and parallels, dividing lines into equal parts, and constructing tangencies.
The document provides information for an engineering class including the instructor's name and class details, assignments due dates and details, and content on surveying techniques and geometric constructions. Key points covered include potential errors in surveying, definitions of surveying, examples of historical errors, instructions for groups to practice drawing techniques, and methods for drawing various geometric shapes and their intersections.
Lecture4 Engineering Curves and Theory of projections.pptxKishorKumaar3
This document provides information about various types of plane curves generated by the motion of a circle or point rolling along another curve or line without slipping. It defines conic sections, which are curves formed by the intersection of a cone with a plane, including ellipses, parabolas, hyperbolas, and circles. It then discusses methods for constructing these conic sections geometrically using properties like eccentricity and foci. The document also covers roulettes like cycloids, epicycloids, hypocycloids, and trochoids formed by rolling motions, and provides examples of their geometric constructions.
The document discusses various conic sections and cycloidal curves. It defines conic sections as curves formed by the intersection of a plane with a right circular cone in different positions. Specific conic sections described include circles, ellipses, parabolas, and hyperbolas. Steps are provided to construct each of these conic sections graphically. Additionally, the document defines cycloidal curves as those generated by a point on a circle rolling along a straight line or circle. Specific cycloidal curves discussed include cycloids, epicycloids, and hypocycloids. Graphical construction steps are given for each.
The document discusses various conic sections and cycloidal curves. It defines conic sections as curves formed by the intersection of a plane with a right circular cone in different positions. Specific conic sections described include circles, ellipses, parabolas, and hyperbolas. Steps are provided to construct each of these conic sections geometrically. The document also discusses cycloidal curves generated by a point on a rolling circle, including cycloids, epicycloids, and hypocycloids. Steps are given for constructing these curves. Finally, the document defines involutes and provides methods for constructing involutes of squares and circles.
B.tech i eg u2 loci of point and projection of point and lineRai University
1. The document discusses different types of basic locus cases including points moving relative to geometric objects like lines and circles.
2. It also covers oscillating and rotating links, where a point slides along a link that is oscillating or rotating in a plane.
3. Examples and solutions are provided for different locus problems involving points moving to maintain a constant distance from objects like lines, circles, and other points. Diagrams clearly illustrate the solution steps and resulting loci.
The document discusses various methods of drawing conic sections such as ellipses, parabolas, and hyperbolas. It provides details on the concentric circle method, rectangle method, oblong method, arcs of circle method, and general locus method for drawing ellipses. For parabolas, it describes the rectangle method, tangent method, and basic locus method. The hyperbola can be drawn using the rectangular hyperbola method, basic locus method, and through a given point with its coordinates. The document also discusses how to draw tangents and normals to these conic section curves from a given point.
introduction of engineering graphics ,projection of points,lines,planes,solids,section of solids,development of surfaces,isometric projection,perspective projection
engineering curves :Engineering curves are fundamental shapes used in design, analysis, and visualization across various engineering fields. They include conic sections, polynomials, splines, Bezier curves, and NURBS. Represented by explicit, parametric, or implicit equations, they possess properties like curvature and tangents. Engineers use them in CAD, graphics, motion planning, curve fitting, and manufacturing for tasks like interpolation and approximation. Understanding these curves is vital for effective engineering design and problem-solving.
The document describes various types of engineering curves including involutes, cycloids, trochoids, epicycloids, hypocycloids, and spirals. It provides definitions and step-by-step solutions for drawing these curves based on different parameters such as the length of a string wound around a circular pole to form an involute, or the diameters of rolling and directing circles to form a cycloid. Examples are given of drawing these curves based on specific numerical values provided in word problems. Key terms defined include involute, cycloid, epicycloid, hypocycloid, and helix.
This document contains 12 theorems regarding circles:
1. Equal chords of a circle subtend equal angles at the centre.
2. If the angles subtended by the chords of a circle at the centre are equal, then the chords are equal.
3. The perpendicular from the centre of a circle to a chord bisects the chord.
The curve traced is an epicycloid, which is generated when a circle of radius 25 mm rolls around the outside of a larger circle of radius 150 mm without slipping. To draw the epicycloid: (1) Mark points around the smaller circle to divide it into 12 equal parts as it rolls, (2) Draw radii from the center of the large circle to these points to locate the centers of the smaller circle as it rolls, and (3) Draw arcs from these centers to trace the curve of the epicycloid. A tangent and normal are then drawn to the curve at a point 85 mm from the center of the large circle.
Conics Sections and its Applications.pptxKishorKumaar3
Conic sections are curves formed by the intersection of a cone with a plane. The type of conic section (triangle, circle, ellipse, parabola, hyperbola) depends on the position and orientation of the cutting plane relative to the cone's axis. Conic sections can be modeled and constructed using various methods that involve the focus, directrix, eccentricity, or arcs of circles. Roulettes are curves generated by the rolling contact of one curve on another without slipping, and include important types like cycloids, trochoids, and involutes that are used in engineering applications.
Mechatronics is a multidisciplinary field that refers to the skill sets needed in the contemporary, advanced automated manufacturing industry. At the intersection of mechanics, electronics, and computing, mechatronics specialists create simpler, smarter systems. Mechatronics is an essential foundation for the expected growth in automation and manufacturing.
Mechatronics deals with robotics, control systems, and electro-mechanical systems.
Contenu connexe
Similaire à Involute of a circle,Square, pentagon,HexagonInvolute_Engineering Drawing.pdf
This document discusses engineering drawings and curves. It states that engineering drawings are the language used to communicate engineering ideas and execute work. Various types of curves are useful in engineering for understanding natural laws, manufacturing, design, analysis, and construction. Common engineering curves include conics, cycloids, involutes, spirals, and helices. Conics specifically include circles, ellipses, parabolas, and hyperbolas which are sections of a right circular cone cut by planes. The document provides definitions and examples of each type of conic section. It also discusses different methods for drawing ellipses like the arc of circles method.
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.
The document discusses various types of engineering curves including involutes, cycloids, spirals, and helices. It provides definitions for involutes, cycloids, epicycloids, hypotrochoids, spirals, and helices. Examples are given on how to draw involutes of circles, squares, and triangles. Methods for drawing tangents and normals to involutes, cycloids, and epicycloids are also described. Problems include drawing loci for points on circles rolling along straight or curved paths to form different types of cycloids.
The document discusses various geometric constructions including:
1. Dividing a line into equal parts and dividing a line in a given ratio.
2. Bisecting a given angle.
3. Inscribing a square in a given circle.
4. Drawing parabolas, cycloids, epicycloids, and hypocycloids by rolling and tracing circles.
Step-by-step methods are provided for each construction without mathematical proofs.
This document provides an overview of geometric construction concepts including:
- The principles of geometric construction using only a ruler and compass.
- Key terminology related to points, lines, angles, planes, circles, polygons and other basic geometric entities.
- Procedures for performing common geometric constructions such as bisecting lines, arcs and angles, constructing perpendiculars and parallels, dividing lines into equal parts, and constructing tangencies.
The document provides information for an engineering class including the instructor's name and class details, assignments due dates and details, and content on surveying techniques and geometric constructions. Key points covered include potential errors in surveying, definitions of surveying, examples of historical errors, instructions for groups to practice drawing techniques, and methods for drawing various geometric shapes and their intersections.
Lecture4 Engineering Curves and Theory of projections.pptxKishorKumaar3
This document provides information about various types of plane curves generated by the motion of a circle or point rolling along another curve or line without slipping. It defines conic sections, which are curves formed by the intersection of a cone with a plane, including ellipses, parabolas, hyperbolas, and circles. It then discusses methods for constructing these conic sections geometrically using properties like eccentricity and foci. The document also covers roulettes like cycloids, epicycloids, hypocycloids, and trochoids formed by rolling motions, and provides examples of their geometric constructions.
The document discusses various conic sections and cycloidal curves. It defines conic sections as curves formed by the intersection of a plane with a right circular cone in different positions. Specific conic sections described include circles, ellipses, parabolas, and hyperbolas. Steps are provided to construct each of these conic sections graphically. Additionally, the document defines cycloidal curves as those generated by a point on a circle rolling along a straight line or circle. Specific cycloidal curves discussed include cycloids, epicycloids, and hypocycloids. Graphical construction steps are given for each.
The document discusses various conic sections and cycloidal curves. It defines conic sections as curves formed by the intersection of a plane with a right circular cone in different positions. Specific conic sections described include circles, ellipses, parabolas, and hyperbolas. Steps are provided to construct each of these conic sections geometrically. The document also discusses cycloidal curves generated by a point on a rolling circle, including cycloids, epicycloids, and hypocycloids. Steps are given for constructing these curves. Finally, the document defines involutes and provides methods for constructing involutes of squares and circles.
B.tech i eg u2 loci of point and projection of point and lineRai University
1. The document discusses different types of basic locus cases including points moving relative to geometric objects like lines and circles.
2. It also covers oscillating and rotating links, where a point slides along a link that is oscillating or rotating in a plane.
3. Examples and solutions are provided for different locus problems involving points moving to maintain a constant distance from objects like lines, circles, and other points. Diagrams clearly illustrate the solution steps and resulting loci.
The document discusses various methods of drawing conic sections such as ellipses, parabolas, and hyperbolas. It provides details on the concentric circle method, rectangle method, oblong method, arcs of circle method, and general locus method for drawing ellipses. For parabolas, it describes the rectangle method, tangent method, and basic locus method. The hyperbola can be drawn using the rectangular hyperbola method, basic locus method, and through a given point with its coordinates. The document also discusses how to draw tangents and normals to these conic section curves from a given point.
introduction of engineering graphics ,projection of points,lines,planes,solids,section of solids,development of surfaces,isometric projection,perspective projection
engineering curves :Engineering curves are fundamental shapes used in design, analysis, and visualization across various engineering fields. They include conic sections, polynomials, splines, Bezier curves, and NURBS. Represented by explicit, parametric, or implicit equations, they possess properties like curvature and tangents. Engineers use them in CAD, graphics, motion planning, curve fitting, and manufacturing for tasks like interpolation and approximation. Understanding these curves is vital for effective engineering design and problem-solving.
The document describes various types of engineering curves including involutes, cycloids, trochoids, epicycloids, hypocycloids, and spirals. It provides definitions and step-by-step solutions for drawing these curves based on different parameters such as the length of a string wound around a circular pole to form an involute, or the diameters of rolling and directing circles to form a cycloid. Examples are given of drawing these curves based on specific numerical values provided in word problems. Key terms defined include involute, cycloid, epicycloid, hypocycloid, and helix.
This document contains 12 theorems regarding circles:
1. Equal chords of a circle subtend equal angles at the centre.
2. If the angles subtended by the chords of a circle at the centre are equal, then the chords are equal.
3. The perpendicular from the centre of a circle to a chord bisects the chord.
The curve traced is an epicycloid, which is generated when a circle of radius 25 mm rolls around the outside of a larger circle of radius 150 mm without slipping. To draw the epicycloid: (1) Mark points around the smaller circle to divide it into 12 equal parts as it rolls, (2) Draw radii from the center of the large circle to these points to locate the centers of the smaller circle as it rolls, and (3) Draw arcs from these centers to trace the curve of the epicycloid. A tangent and normal are then drawn to the curve at a point 85 mm from the center of the large circle.
Conics Sections and its Applications.pptxKishorKumaar3
Conic sections are curves formed by the intersection of a cone with a plane. The type of conic section (triangle, circle, ellipse, parabola, hyperbola) depends on the position and orientation of the cutting plane relative to the cone's axis. Conic sections can be modeled and constructed using various methods that involve the focus, directrix, eccentricity, or arcs of circles. Roulettes are curves generated by the rolling contact of one curve on another without slipping, and include important types like cycloids, trochoids, and involutes that are used in engineering applications.
Similaire à Involute of a circle,Square, pentagon,HexagonInvolute_Engineering Drawing.pdf (20)
Mechatronics is a multidisciplinary field that refers to the skill sets needed in the contemporary, advanced automated manufacturing industry. At the intersection of mechanics, electronics, and computing, mechatronics specialists create simpler, smarter systems. Mechatronics is an essential foundation for the expected growth in automation and manufacturing.
Mechatronics deals with robotics, control systems, and electro-mechanical systems.
Supermarket Management System Project Report.pdfKamal Acharya
Supermarket management is a stand-alone J2EE using Eclipse Juno program.
This project contains all the necessary required information about maintaining
the supermarket billing system.
The core idea of this project to minimize the paper work and centralize the
data. Here all the communication is taken in secure manner. That is, in this
application the information will be stored in client itself. For further security the
data base is stored in the back-end oracle and so no intruders can access it.
Discover the latest insights on Data Driven Maintenance with our comprehensive webinar presentation. Learn about traditional maintenance challenges, the right approach to utilizing data, and the benefits of adopting a Data Driven Maintenance strategy. Explore real-world examples, industry best practices, and innovative solutions like FMECA and the D3M model. This presentation, led by expert Jules Oudmans, is essential for asset owners looking to optimize their maintenance processes and leverage digital technologies for improved efficiency and performance. Download now to stay ahead in the evolving maintenance landscape.
Open Channel Flow: fluid flow with a free surfaceIndrajeet sahu
Open Channel Flow: This topic focuses on fluid flow with a free surface, such as in rivers, canals, and drainage ditches. Key concepts include the classification of flow types (steady vs. unsteady, uniform vs. non-uniform), hydraulic radius, flow resistance, Manning's equation, critical flow conditions, and energy and momentum principles. It also covers flow measurement techniques, gradually varied flow analysis, and the design of open channels. Understanding these principles is vital for effective water resource management and engineering applications.
Height and depth gauge linear metrology.pdfq30122000
Height gauges may also be used to measure the height of an object by using the underside of the scriber as the datum. The datum may be permanently fixed or the height gauge may have provision to adjust the scale, this is done by sliding the scale vertically along the body of the height gauge by turning a fine feed screw at the top of the gauge; then with the scriber set to the same level as the base, the scale can be matched to it. This adjustment allows different scribers or probes to be used, as well as adjusting for any errors in a damaged or resharpened probe.
Software Engineering and Project Management - Introduction, Modeling Concepts...Prakhyath Rai
Introduction, Modeling Concepts and Class Modeling: What is Object orientation? What is OO development? OO Themes; Evidence for usefulness of OO development; OO modeling history. Modeling
as Design technique: Modeling, abstraction, The Three models. Class Modeling: Object and Class Concept, Link and associations concepts, Generalization and Inheritance, A sample class model, Navigation of class models, and UML diagrams
Building the Analysis Models: Requirement Analysis, Analysis Model Approaches, Data modeling Concepts, Object Oriented Analysis, Scenario-Based Modeling, Flow-Oriented Modeling, class Based Modeling, Creating a Behavioral Model.
Prediction of Electrical Energy Efficiency Using Information on Consumer's Ac...PriyankaKilaniya
Energy efficiency has been important since the latter part of the last century. The main object of this survey is to determine the energy efficiency knowledge among consumers. Two separate districts in Bangladesh are selected to conduct the survey on households and showrooms about the energy and seller also. The survey uses the data to find some regression equations from which it is easy to predict energy efficiency knowledge. The data is analyzed and calculated based on five important criteria. The initial target was to find some factors that help predict a person's energy efficiency knowledge. From the survey, it is found that the energy efficiency awareness among the people of our country is very low. Relationships between household energy use behaviors are estimated using a unique dataset of about 40 households and 20 showrooms in Bangladesh's Chapainawabganj and Bagerhat districts. Knowledge of energy consumption and energy efficiency technology options is found to be associated with household use of energy conservation practices. Household characteristics also influence household energy use behavior. Younger household cohorts are more likely to adopt energy-efficient technologies and energy conservation practices and place primary importance on energy saving for environmental reasons. Education also influences attitudes toward energy conservation in Bangladesh. Low-education households indicate they primarily save electricity for the environment while high-education households indicate they are motivated by environmental concerns.
Digital Twins Computer Networking Paper Presentation.pptxaryanpankaj78
A Digital Twin in computer networking is a virtual representation of a physical network, used to simulate, analyze, and optimize network performance and reliability. It leverages real-time data to enhance network management, predict issues, and improve decision-making processes.
Involute of a circle,Square, pentagon,HexagonInvolute_Engineering Drawing.pdf
1. An involute 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.
2. C
To draw an involute of a given Triangle
AB=30MM
B
A
3. A as center AB as the radius draw the arc
,then increase the AC Line .
A
C
B
P1
R
1
=
3
0
4. C as the center CP1 as the radius draw the
arc ,then increase the BC Line upto P2.
A
C
B
P1
R
1
=
3
0
P2
R2=CP1=60
5. B as the center BP2 as the radius draw the
arc ,then increase the AB Line upto P3.
A
C
B
P1
R
1
=
3
0
P2
R2=CP1=60
P3
R
3
=
B
P
3
=
9
0
6. FOR Tangent and normal Line mark M at any point on the ARC
A
C
B
P1
R
1
=
3
0
P2
R2=CP1=60
P3
R
3
=
B
P
3
=
9
0
M
7. Now join the point M and B and then increse the line uppto N
A
C
B
P1
R
1
=
3
0
P2
R2=CP1=60
P3
R
3
=
B
P
3
=
9
0
M
N
8. Now draw the Line through the point M perpendicular to MN Line .
A
C
B
P1
R
1
=
3
0
P2
R2=CP1=60
P3
R
3
=
B
P
3
=
9
0
M
N
N
N
9. An involute 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.
10. To draw an involute of a given square.
A
B
C D
11. Taking A as the starting point, with centre B and radius BA=40MM
draw an arc to intersect the line CB produced at P1.
A
B
C D
12. Taking A as the starting point, with centre B and radius BA=40MM
draw an arc to intersect the line CB produced at P1.
A
B
C D
P1
R
1
=
A
B
=
4
0
13. P2
With Centre C and radius CP 1 =2*40=80, draw on
arc to intersect the line DC produced at P 2.
R2=CP1=80
A
B
C D
P1
R
1
=
A
B
=
4
0
14. R
3
=
D
P
2
=
1
2
0
With Centre D and radius DP 2 =3*40=120,
draw on arc to intersect the line AD produced
at P3.
P2
P3
R2=CP1=80
A
B
C D
P1
R
1
=
A
B
=
4
0
15. R
4
=
A
P
3
=
1
6
0
R
3
=
D
P
2
=
1
2
0
With Centre A and radius
AP3 =4*40=160, draw on
arc to intersect the line
AB produced at P4.
P2
P3
R2=CP1=80
A
B
C D
P1
R
1
=
A
B
=
4
0
4*AB=120 (equal to the perimeter of the square)
22. E
D
C
A
C as the center CP1 as the Radius Draw the arc
R
1
=
A
B
=
3
0
M
M
P1
P2
R
2
=
C
P
1
=
6
0
B
23. E
D
C
A
D as the center DP2 as the Radius Draw the arc upto P3
R
1
=
A
B
=
3
0
M
M
P1
P2
R
2
=
C
P
1
=
6
0
P3
R3=DP2=90
B
24. E
D
C
A
D as the center DP2 as the Radius Draw the arc upto P3
R
1
=
A
B
=
3
0
M
M
P1
P2
R
2
=
C
P
1
=
6
0
P3
R3=DP2=90
B
25. E
D
C
A
E as the center EP3 as the Radius Draw the arc upto P4
R
1
=
A
B
=
3
0
M
M
P1
P2
R
2
=
C
P
1
=
6
0
P3
R3=DP2=90
P4
R
4
=
E
P
4
=
1
2
0
B
26. E
D
C
A
A as the center AP4 as the Radius Draw the arc upto P5
R
1
=
A
B
=
3
0
M
M
P1
P2
R
2
=
C
P
1
=
6
0
P3
R3=DP2=90
P4
R
4
=
E
P
4
=
1
2
0
P5
R
5
=
A
P
5
=
1
5
0
5*AB=150
B
27. Draw the Involute of a hexagon of side AB=25MM
Draw the hexagon of side AB=25MM By using any Method
A
B
C
D E
F
28. A
B
C
D E
F
B as the Center BA as the Radius Draw the arc P1=AB=25MM
P1
R1=AB=25MM
29. A
B
C
D E
F
C as the Center CP1 as the Radius Draw the arc P2=50MM
P1
R1=AB=25MM
P2
R
2
=
C
P
1
=
5
0
M
M
30. A
B
C
D E
F
D as the Center DP2 as the Radius Draw the arc Upto P3=75MM
P1
R1=AB=25MM
P2
R
2
=
C
P
1
=
5
0
M
M
P3
R3=DP2=75MM
31. A
B
C
D E
F
E as the Center EP3 as the Radius Draw the arc Upto P4=100MM
P1
R1=AB=25MM
P2
R
2
=
C
P
1
=
5
0
M
M
P3
R3=DP2=75MM
P4
R4=EP4=100MM
32. A
B
C
D E
F
F as the Center FP4 as the Radius Draw the arc Upto P5=125MM
P1
R1=AB=25MM
P2
R
2
=
C
P
1
=
5
0
M
M
P3
R3=DP2=75MM
P4
R4=EP4=100MM
P5
R
5
=
1
2
5
P6
R
6
=
1
5
0
6*AB=150
33. To draw an involute of a given circle of radus R
1. With 0 as centre and radius R, draw the given circle.
2. Taking P as the starting point, draw the tangent PA equal in length to the circumference of the
circle.
3. Divide the line PA and the circle into the same number of equal pats and number the points.
4. Draw tangents to the circle at the points 1,2,3 etc., and locate the points PI' P2 , P3 etc., such
that !PI = PI 1, 2P2 = P21 etc. A smooth curve through the points P, PI' P 2 etc., is the required
involute.
Note: 1. The tangent to the circle is a normal to the involute. Hence, to draw a normal and tangent
at a point M on it, first draw the tangent BMN to the circle. This is the normal to the curve and.
a line IT drawn through M and perpendicular to BM is the tangent to the curve.
34. 1. With 0 as centre and radius R=25MM, draw the given circle.
O
R=25MM
35. P1
Divide the circle into 8 parts 360/8=45
Then draw the Tangent through the point 1 according to the figure
36. P1
P2
Then draw the Tangent through the point 2 according to the
figure and draw the arc 2 as the center 2P1 as the radius
37. P1
P2
P3
Then draw the Tangent through the point 3
according to the figure and draw the arc 3 as
the center 3P3 as the radius
38. P1
P2
P3
P4
Then draw the Tangent through the point 4 according to
the figure and draw the arc 4 as the center 4P3 as the
radius
39. P1
P2
P3
P4
P5
Then draw the Tangent through the point 5
according to the figure and draw the arc 5 as
the center 5P4 as the radius
40. P1
P2
P3
P4
P5
P6
Then draw the Tangent through the point 6 according to the figure and draw the arc 6
as the center 6P5 as the radius
41. P1
P2
P3
P4
P5
P6
P7
Then draw the Tangent through the point 7 according to the figure and draw the arc
7 as the center 7P6 as the radius