The document provides definitions and examples of common engineering curves including cycloids, involutes, spirals, and helices. It begins with definitions of these terms: a cycloid is the locus of a point on a circle rolling along a straight path; an involute is the locus of the end of a string wound around a circular pole; a spiral is a curve generated by a point revolving around a fixed point while moving toward it; and a helix is a curve generated by a point moving around a cylinder or cone while advancing in the axial direction. The document then provides examples and step-by-step solutions for drawing these curves based on given parameters such as string length, circle diameters, and rates of rotation/translation
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.
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.
This document provides information on engineering curves including involutes, cycloids, spirals, and helices. It defines each curve type and provides step-by-step solutions for drawing examples of each. For involutes, it shows how to draw the curve for different string lengths relative to the circle's circumference. It also demonstrates how to draw loci for rolling circles on both straight and curved paths to generate cycloids. Methods for drawing tangents and normals to involute curves are also illustrated.
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.
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.
This document provides definitions and methods for drawing various engineering curves including involutes, cycloids, spirals, and helices. It defines involutes as the locus of a point on the free end of a string wound around a circular pole. Cycloids are defined as the locus of a point on the edge of a circle rolling along a straight path. Spirals are curves generated by a point revolving around a fixed point while moving toward it. Helices are curves generated by a point moving around the surface of a cylinder or cone while advancing in the axial direction. The document also gives methods for drawing tangents and normals to these curves.
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.
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
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.
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.
This document provides information on engineering curves including involutes, cycloids, spirals, and helices. It defines each curve type and provides step-by-step solutions for drawing examples of each. For involutes, it shows how to draw the curve for different string lengths relative to the circle's circumference. It also demonstrates how to draw loci for rolling circles on both straight and curved paths to generate cycloids. Methods for drawing tangents and normals to involute curves are also illustrated.
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.
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.
This document provides definitions and methods for drawing various engineering curves including involutes, cycloids, spirals, and helices. It defines involutes as the locus of a point on the free end of a string wound around a circular pole. Cycloids are defined as the locus of a point on the edge of a circle rolling along a straight path. Spirals are curves generated by a point revolving around a fixed point while moving toward it. Helices are curves generated by a point moving around the surface of a cylinder or cone while advancing in the axial direction. The document also gives methods for drawing tangents and normals to these curves.
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.
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
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.
This document provides information on engineering curves and conic sections. It describes different methods for drawing ellipses, parabolas, and hyperbolas including the concentric circle method, rectangle method, oblong method, and arcs of circle method. It also discusses drawing tangents and normals to these curves. Conic sections such as ellipses, parabolas, and hyperbolas are formed by cutting a cone with different plane sections. The ratio of a point's distances from a fixed point and fixed line is used to define eccentricity for these curves.
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.
The document describes various engineering curves including conic sections like ellipses, parabolas, and hyperbolas. It provides different methods for constructing these curves, such as the concentric circle method, rectangle method, and directrix-focus method. It also discusses drawing tangents and normals to the curves. Other curves covered include involutes, cycloids, trochoids, spirals, and helices. The document contains examples demonstrating how to apply these construction techniques to draw the curves based on given parameters.
The document discusses various engineering curves including conic sections like ellipses, parabolas and hyperbolas. It provides definitions and methods of constructing these curves. Specifically, it outlines six methods of constructing ellipses including the concentric circle, rectangle, oblong, arcs of circle, rhombus and directrix-focus methods. It also describes three methods of constructing parabolas and hyperbolas including the rectangle method, method of tangents and directrix-focus method. Additionally, it discusses drawing tangents and normals to these curves.
This document provides an overview of topics related to engineering drawing and graphics. It covers scales, engineering curves, loci of points, orthographic projections, projections of points/lines/planes/solids, sections and developments, intersections of surfaces, and isometric projections. For each topic, it lists subsections that provide definitions, methods, and example problems. The document appears to be part of an online course or reference material for learning the principles and techniques of engineering drawing.
This document provides an overview of topics related to engineering graphics and geometric constructions. It covers scales, engineering curves, loci of points, orthographic projections, projections of geometric entities, sections and developments of solids, intersections of surfaces, and isometric projections. For each topic, it lists various subtopics and provides example problems and construction steps. The goal is to teach fundamental concepts and problem-solving techniques in engineering graphics.
Engineering drawing unit test soln sandes sigdelsigdelsandes
The document provides instructions for proportional division of a straight line and drawing common tangents to two circles using different methods. It also provides steps to draw various curves like ellipses, involutes, cycloids and helixes. Instructions are given on developments of various solids like prisms, pyramids, cones and truncated cones. Dimensioned drawings are included with clear labeling to illustrate each concept.
This document provides an overview of the contents of an engineering graphics course. It includes 17 sections covering topics like scales, engineering curves, orthographic projections, sections and developments, and isometric projections. For each section, it lists the subtopics that will be covered and provides example problems to solve. The document aims to introduce students to the key concepts and problem-solving techniques in engineering graphics.
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.
This document provides methods for drawing three common conic sections (ellipses, parabolas, and hyperbolas). It outlines six methods for drawing ellipses using concentric circles, rectangles, oblongs, arcs of circles, rhombi, and the directrix-focus definition. Two methods are given for drawing parabolas using rectangles and the directrix-focus definition. Hyperbolas can be drawn using rectangular hyperbolas based on coordinates or P-V diagrams, and the directrix-focus definition. The document also demonstrates how to draw tangents and normals to these curves from a given point using properties of their geometric definitions.
This document provides methods for drawing three common conic sections - ellipses, parabolas, and hyperbolas. It outlines six methods for drawing ellipses, including the concentric circle method, rectangle method, and directrix-focus method. Two methods are described for drawing parabolas: the rectangle method and directrix-focus method. Three hyperbola problems are also shown, demonstrating the rectangular hyperbola, P-V diagram, and directrix-focus definition. Examples are given for each conic section with step-by-step instructions to draw the curves using the different techniques.
This document provides methods for drawing three common conic sections (ellipses, parabolas, and hyperbolas). It outlines six methods for drawing ellipses using concentric circles, rectangles, oblongs, arcs of circles, rhombi, and the directrix-focus definition. Two methods are given for drawing parabolas using rectangles and the directrix-focus definition. Hyperbolas can be drawn using rectangular hyperbolas based on coordinates or P-V diagrams, and the directrix-focus definition. The document also demonstrates how to draw tangents and normals to these curves from a given point using properties of their geometric definitions.
The document describes different types of engineering curves including involutes, cycloids, spirals, and helices. It provides definitions and examples of how to draw each type of curve. Specifically, it explains how to draw an involute by winding a string around a circular pole and marking the path of the free end. It also describes how to draw different types of cycloids by having a small circle roll along a straight or curved path, and marking the location of a point on the circle's perimeter. Methods for drawing spirals and helices are also mentioned.
The document discusses various types of engineering curves including involutes, cycloids, spirals, and helices. It provides definitions for each type of curve and examples of problems involving drawing them, specifically:
1. It defines an involute as the locus of a point on a string wound around a circular pole, a cycloid as the locus of a point on the circumference of a circle rolling along a straight line, and a spiral as a curve generated by a point revolving around a fixed point while moving toward it.
2. It provides problems and solutions for drawing involutes of shapes such as an equilateral triangle, square, and circle with string lengths both greater and less than the circumference.
3
engineering curves .
Definition of Engineering Curves
Definition of Engineering Curves – When a cone is cut by a cutting plane with different positions of the plane relative to the axis of cone, it gives various types of curves like Triangle, Circle, ellipse, parabola, and hyperbola. These curves are known as conic sections.
* Vertical white line shows axis of cone in above image.
** Green lines shows different positions of cutting planes
Different methods to have types of conic sections on a cone we need to cut a cone as per following:
To get Triangle:
We have to cut cone from apex to centre of the base (vertically)
To get Circle:
We have to cut cone by a cutting plan which should parallel to base or perpendicular to axis of cone.
To get Ellipse:
We have to cut cone in such a way that the cutting plane remains inclined to axis of cone and it cuts all generators of cone.
To get Parabola:
We have to cut a cone by a cutting plane which should inclined to axis of cone but remains parallel to one of the generators of cone.
To get Hyperbola:
We have to cut a cone by cutting plane which should parallel to axis of cone.
The document discusses various types of engineering curves including involutes, cycloids, spirals, and helices. It provides definitions for these curves and describes methods for drawing tangents and normals to the curves. It also includes example problems demonstrating how to construct some of these curves step-by-step, such as drawing the involute of a circle, drawing a cycloid by rolling a circle along a straight path, and drawing spirals with one and two convolutions.
A cylinder and square prism intersect with their axes bisecting each other. To find the curves of intersection:
1. Draw lines on the surface of one solid and transfer points of intersection to corresponding positions on the other views.
2. When one solid completely penetrates another, there will be two curves of intersection.
3. Maximum surface contact between intersecting solids provides the strongest and most leak-proof joint.
This document provides methods for drawing three common conic sections (curves): ellipses, parabolas, and hyperbolas. It outlines six different methods for constructing ellipses, including the concentric circle, rectangle, oblong, arcs of circles, rhombus, and directrix-focus methods. Two methods are described for drawing parabolas: the rectangle method and method of tangents. And three examples are given for hyperbolas: the rectangular hyperbola using coordinates, the P-V diagram, and the directrix-focus method. The document also explains how to draw tangents and normals to these curves from a given point.
This document provides methods for drawing three common conic sections (curves): ellipses, parabolas, and hyperbolas. It outlines six different methods for constructing ellipses, including the concentric circle, rectangle, oblong, arcs of circles, rhombus, and directrix-focus methods. Two methods are described for drawing parabolas: the rectangle method and method of tangents. And three examples are given for hyperbolas: the rectangular hyperbola using coordinates, the P-V diagram, and the directrix-focus method. The document also explains how to draw tangents and normals to these curves from a given point.
Comparative analysis between traditional aquaponics and reconstructed aquapon...bijceesjournal
The aquaponic system of planting is a method that does not require soil usage. It is a method that only needs water, fish, lava rocks (a substitute for soil), and plants. Aquaponic systems are sustainable and environmentally friendly. Its use not only helps to plant in small spaces but also helps reduce artificial chemical use and minimizes excess water use, as aquaponics consumes 90% less water than soil-based gardening. The study applied a descriptive and experimental design to assess and compare conventional and reconstructed aquaponic methods for reproducing tomatoes. The researchers created an observation checklist to determine the significant factors of the study. The study aims to determine the significant difference between traditional aquaponics and reconstructed aquaponics systems propagating tomatoes in terms of height, weight, girth, and number of fruits. The reconstructed aquaponics system’s higher growth yield results in a much more nourished crop than the traditional aquaponics system. It is superior in its number of fruits, height, weight, and girth measurement. Moreover, the reconstructed aquaponics system is proven to eliminate all the hindrances present in the traditional aquaponics system, which are overcrowding of fish, algae growth, pest problems, contaminated water, and dead fish.
Introduction- e - waste – definition - sources of e-waste– hazardous substances in e-waste - effects of e-waste on environment and human health- need for e-waste management– e-waste handling rules - waste minimization techniques for managing e-waste – recycling of e-waste - disposal treatment methods of e- waste – mechanism of extraction of precious metal from leaching solution-global Scenario of E-waste – E-waste in India- case studies.
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.
This document provides information on engineering curves and conic sections. It describes different methods for drawing ellipses, parabolas, and hyperbolas including the concentric circle method, rectangle method, oblong method, and arcs of circle method. It also discusses drawing tangents and normals to these curves. Conic sections such as ellipses, parabolas, and hyperbolas are formed by cutting a cone with different plane sections. The ratio of a point's distances from a fixed point and fixed line is used to define eccentricity for these curves.
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.
The document describes various engineering curves including conic sections like ellipses, parabolas, and hyperbolas. It provides different methods for constructing these curves, such as the concentric circle method, rectangle method, and directrix-focus method. It also discusses drawing tangents and normals to the curves. Other curves covered include involutes, cycloids, trochoids, spirals, and helices. The document contains examples demonstrating how to apply these construction techniques to draw the curves based on given parameters.
The document discusses various engineering curves including conic sections like ellipses, parabolas and hyperbolas. It provides definitions and methods of constructing these curves. Specifically, it outlines six methods of constructing ellipses including the concentric circle, rectangle, oblong, arcs of circle, rhombus and directrix-focus methods. It also describes three methods of constructing parabolas and hyperbolas including the rectangle method, method of tangents and directrix-focus method. Additionally, it discusses drawing tangents and normals to these curves.
This document provides an overview of topics related to engineering drawing and graphics. It covers scales, engineering curves, loci of points, orthographic projections, projections of points/lines/planes/solids, sections and developments, intersections of surfaces, and isometric projections. For each topic, it lists subsections that provide definitions, methods, and example problems. The document appears to be part of an online course or reference material for learning the principles and techniques of engineering drawing.
This document provides an overview of topics related to engineering graphics and geometric constructions. It covers scales, engineering curves, loci of points, orthographic projections, projections of geometric entities, sections and developments of solids, intersections of surfaces, and isometric projections. For each topic, it lists various subtopics and provides example problems and construction steps. The goal is to teach fundamental concepts and problem-solving techniques in engineering graphics.
Engineering drawing unit test soln sandes sigdelsigdelsandes
The document provides instructions for proportional division of a straight line and drawing common tangents to two circles using different methods. It also provides steps to draw various curves like ellipses, involutes, cycloids and helixes. Instructions are given on developments of various solids like prisms, pyramids, cones and truncated cones. Dimensioned drawings are included with clear labeling to illustrate each concept.
This document provides an overview of the contents of an engineering graphics course. It includes 17 sections covering topics like scales, engineering curves, orthographic projections, sections and developments, and isometric projections. For each section, it lists the subtopics that will be covered and provides example problems to solve. The document aims to introduce students to the key concepts and problem-solving techniques in engineering graphics.
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.
This document provides methods for drawing three common conic sections (ellipses, parabolas, and hyperbolas). It outlines six methods for drawing ellipses using concentric circles, rectangles, oblongs, arcs of circles, rhombi, and the directrix-focus definition. Two methods are given for drawing parabolas using rectangles and the directrix-focus definition. Hyperbolas can be drawn using rectangular hyperbolas based on coordinates or P-V diagrams, and the directrix-focus definition. The document also demonstrates how to draw tangents and normals to these curves from a given point using properties of their geometric definitions.
This document provides methods for drawing three common conic sections - ellipses, parabolas, and hyperbolas. It outlines six methods for drawing ellipses, including the concentric circle method, rectangle method, and directrix-focus method. Two methods are described for drawing parabolas: the rectangle method and directrix-focus method. Three hyperbola problems are also shown, demonstrating the rectangular hyperbola, P-V diagram, and directrix-focus definition. Examples are given for each conic section with step-by-step instructions to draw the curves using the different techniques.
This document provides methods for drawing three common conic sections (ellipses, parabolas, and hyperbolas). It outlines six methods for drawing ellipses using concentric circles, rectangles, oblongs, arcs of circles, rhombi, and the directrix-focus definition. Two methods are given for drawing parabolas using rectangles and the directrix-focus definition. Hyperbolas can be drawn using rectangular hyperbolas based on coordinates or P-V diagrams, and the directrix-focus definition. The document also demonstrates how to draw tangents and normals to these curves from a given point using properties of their geometric definitions.
The document describes different types of engineering curves including involutes, cycloids, spirals, and helices. It provides definitions and examples of how to draw each type of curve. Specifically, it explains how to draw an involute by winding a string around a circular pole and marking the path of the free end. It also describes how to draw different types of cycloids by having a small circle roll along a straight or curved path, and marking the location of a point on the circle's perimeter. Methods for drawing spirals and helices are also mentioned.
The document discusses various types of engineering curves including involutes, cycloids, spirals, and helices. It provides definitions for each type of curve and examples of problems involving drawing them, specifically:
1. It defines an involute as the locus of a point on a string wound around a circular pole, a cycloid as the locus of a point on the circumference of a circle rolling along a straight line, and a spiral as a curve generated by a point revolving around a fixed point while moving toward it.
2. It provides problems and solutions for drawing involutes of shapes such as an equilateral triangle, square, and circle with string lengths both greater and less than the circumference.
3
engineering curves .
Definition of Engineering Curves
Definition of Engineering Curves – When a cone is cut by a cutting plane with different positions of the plane relative to the axis of cone, it gives various types of curves like Triangle, Circle, ellipse, parabola, and hyperbola. These curves are known as conic sections.
* Vertical white line shows axis of cone in above image.
** Green lines shows different positions of cutting planes
Different methods to have types of conic sections on a cone we need to cut a cone as per following:
To get Triangle:
We have to cut cone from apex to centre of the base (vertically)
To get Circle:
We have to cut cone by a cutting plan which should parallel to base or perpendicular to axis of cone.
To get Ellipse:
We have to cut cone in such a way that the cutting plane remains inclined to axis of cone and it cuts all generators of cone.
To get Parabola:
We have to cut a cone by a cutting plane which should inclined to axis of cone but remains parallel to one of the generators of cone.
To get Hyperbola:
We have to cut a cone by cutting plane which should parallel to axis of cone.
The document discusses various types of engineering curves including involutes, cycloids, spirals, and helices. It provides definitions for these curves and describes methods for drawing tangents and normals to the curves. It also includes example problems demonstrating how to construct some of these curves step-by-step, such as drawing the involute of a circle, drawing a cycloid by rolling a circle along a straight path, and drawing spirals with one and two convolutions.
A cylinder and square prism intersect with their axes bisecting each other. To find the curves of intersection:
1. Draw lines on the surface of one solid and transfer points of intersection to corresponding positions on the other views.
2. When one solid completely penetrates another, there will be two curves of intersection.
3. Maximum surface contact between intersecting solids provides the strongest and most leak-proof joint.
This document provides methods for drawing three common conic sections (curves): ellipses, parabolas, and hyperbolas. It outlines six different methods for constructing ellipses, including the concentric circle, rectangle, oblong, arcs of circles, rhombus, and directrix-focus methods. Two methods are described for drawing parabolas: the rectangle method and method of tangents. And three examples are given for hyperbolas: the rectangular hyperbola using coordinates, the P-V diagram, and the directrix-focus method. The document also explains how to draw tangents and normals to these curves from a given point.
This document provides methods for drawing three common conic sections (curves): ellipses, parabolas, and hyperbolas. It outlines six different methods for constructing ellipses, including the concentric circle, rectangle, oblong, arcs of circles, rhombus, and directrix-focus methods. Two methods are described for drawing parabolas: the rectangle method and method of tangents. And three examples are given for hyperbolas: the rectangular hyperbola using coordinates, the P-V diagram, and the directrix-focus method. The document also explains how to draw tangents and normals to these curves from a given point.
Comparative analysis between traditional aquaponics and reconstructed aquapon...bijceesjournal
The aquaponic system of planting is a method that does not require soil usage. It is a method that only needs water, fish, lava rocks (a substitute for soil), and plants. Aquaponic systems are sustainable and environmentally friendly. Its use not only helps to plant in small spaces but also helps reduce artificial chemical use and minimizes excess water use, as aquaponics consumes 90% less water than soil-based gardening. The study applied a descriptive and experimental design to assess and compare conventional and reconstructed aquaponic methods for reproducing tomatoes. The researchers created an observation checklist to determine the significant factors of the study. The study aims to determine the significant difference between traditional aquaponics and reconstructed aquaponics systems propagating tomatoes in terms of height, weight, girth, and number of fruits. The reconstructed aquaponics system’s higher growth yield results in a much more nourished crop than the traditional aquaponics system. It is superior in its number of fruits, height, weight, and girth measurement. Moreover, the reconstructed aquaponics system is proven to eliminate all the hindrances present in the traditional aquaponics system, which are overcrowding of fish, algae growth, pest problems, contaminated water, and dead fish.
Introduction- e - waste – definition - sources of e-waste– hazardous substances in e-waste - effects of e-waste on environment and human health- need for e-waste management– e-waste handling rules - waste minimization techniques for managing e-waste – recycling of e-waste - disposal treatment methods of e- waste – mechanism of extraction of precious metal from leaching solution-global Scenario of E-waste – E-waste in India- case studies.
Null Bangalore | Pentesters Approach to AWS IAMDivyanshu
#Abstract:
- Learn more about the real-world methods for auditing AWS IAM (Identity and Access Management) as a pentester. So let us proceed with a brief discussion of IAM as well as some typical misconfigurations and their potential exploits in order to reinforce the understanding of IAM security best practices.
- Gain actionable insights into AWS IAM policies and roles, using hands on approach.
#Prerequisites:
- Basic understanding of AWS services and architecture
- Familiarity with cloud security concepts
- Experience using the AWS Management Console or AWS CLI.
- For hands on lab create account on [killercoda.com](https://killercoda.com/cloudsecurity-scenario/)
# Scenario Covered:
- Basics of IAM in AWS
- Implementing IAM Policies with Least Privilege to Manage S3 Bucket
- Objective: Create an S3 bucket with least privilege IAM policy and validate access.
- Steps:
- Create S3 bucket.
- Attach least privilege policy to IAM user.
- Validate access.
- Exploiting IAM PassRole Misconfiguration
-Allows a user to pass a specific IAM role to an AWS service (ec2), typically used for service access delegation. Then exploit PassRole Misconfiguration granting unauthorized access to sensitive resources.
- Objective: Demonstrate how a PassRole misconfiguration can grant unauthorized access.
- Steps:
- Allow user to pass IAM role to EC2.
- Exploit misconfiguration for unauthorized access.
- Access sensitive resources.
- Exploiting IAM AssumeRole Misconfiguration with Overly Permissive Role
- An overly permissive IAM role configuration can lead to privilege escalation by creating a role with administrative privileges and allow a user to assume this role.
- Objective: Show how overly permissive IAM roles can lead to privilege escalation.
- Steps:
- Create role with administrative privileges.
- Allow user to assume the role.
- Perform administrative actions.
- Differentiation between PassRole vs AssumeRole
Try at [killercoda.com](https://killercoda.com/cloudsecurity-scenario/)
Embedded machine learning-based road conditions and driving behavior monitoringIJECEIAES
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Applications of artificial Intelligence in Mechanical Engineering.pdf
CURVES2.ppt
1. INVOLUTE CYCLOID SPIRAL HELIX
ENGINEERING CURVES
Part-II
(Point undergoing two types of displacements)
1. Involute of a circle
a)String Length = D
b)String Length > D
c)String Length < D
2. Pole having Composite
shape.
3. Rod Rolling over
a Semicircular Pole.
1. General Cycloid
2. Trochoid
( superior)
3. Trochoid
( Inferior)
4. Epi-Cycloid
5. Hypo-Cycloid
1. Spiral of
One Convolution.
2. Spiral of
Two Convolutions.
1. On Cylinder
2. On a Cone
Methods of Drawing
Tangents & Normals
To These Curves.
AND
2. CYCLOID:
IT IS A LOCUS OF A POINT ON THE
PERIPHERY OF A CIRCLE WHICH
ROLLS ON A STRAIGHT LINE PATH.
INVOLUTE:
IT IS A LOCUS OF A FREE END OF A STRING
WHEN IT IS WOUND ROUND A CIRCULAR POLE
SPIRAL:
IT IS A CURVE GENERATED BY A POINT
WHICH REVOLVES AROUND A FIXED POINT
AND AT THE SAME MOVES TOWARDS IT.
HELIX:
IT IS A CURVE GENERATED BY A POINT WHICH
MOVES AROUND THE SURFACE OF A RIGHT CIRCULAR
CYLINDER / CONE AND AT THE SAME TIME ADVANCES IN AXIAL DIRECTION
AT A SPEED BEARING A CONSTANT RATIO TO THE SPPED OF ROTATION.
( for problems refer topic Development of surfaces)
DEFINITIONS
SUPERIORTROCHOID:
IF THE POINT IN THE DEFINATION
OF CYCLOID IS OUTSIDE THE CIRCLE
INFERIOR TROCHOID.:
IF IT IS INSIDE THE CIRCLE
EPI-CYCLOID
IF THE CIRCLE IS ROLLING ON
ANOTHER CIRCLE FROM OUTSIDE
HYPO-CYCLOID.
IF THE CIRCLE IS ROLLING FROM
INSIDE THE OTHER CIRCLE,
3. INVOLUTE OF A CIRCLE
Problem no 17: Draw Involute of a circle.
String length is equal to the circumference of circle.
1 2 3 4 5 6 7 8
P
P8
1
2
3
4
5
6
7
8
P3
P4
4 to p
P5
P7
P6
P2
P1
D
A
Solution Steps:
1) Point or end P of string AP is
exactly D distance away from A.
Means if this string is wound round
the circle, it will completely cover
given circle. B will meet A after
winding.
2) Divide D (AP) distance into 8
number of equal parts.
3) Divide circle also into 8 number
of equal parts.
4) Name after A, 1, 2, 3, 4, etc. up
to 8 on D line AP as well as on
circle (in anticlockwise direction).
5) To radius C-1, C-2, C-3 up to C-8
draw tangents (from 1,2,3,4,etc to
circle).
6) Take distance 1 to P in compass
and mark it on tangent from point 1
on circle (means one division less
than distance AP).
7) Name this point P1
8) Take 2-B distance in compass
and mark it on the tangent from
point 2. Name it point P2.
9) Similarly take 3 to P, 4 to P, 5 to
P up to 7 to P distance in compass
and mark on respective tangents
and locate P3, P4, P5 up to P8 (i.e.
A) points and join them in smooth
curve it is an INVOLUTE of a given
circle.
4. INVOLUTE OFA CIRCLE
String length MORE than D
1 2 3 4 5 6 7 8
P
1
2
3
4
5
6
7
8
P3
P4
4 to p
P5
P7
P6
P2
P1
165 mm
(more than D)
D
p8
Solution Steps:
In this case string length is more
than D.
But remember!
Whatever may be the length of
string, mark D distance
horizontal i.e.along the string
and divide it in 8 number of
equal parts, and not any other
distance. Rest all steps are same
as previous INVOLUTE. Draw
the curve completely.
Problem 18: Draw Involute of a circle.
String length is MORE than the circumference of circle.
5. 1 2 3 4 5 6 7 8
P
1
2
3
4
5
6
7
8
P3
P4
4 to p
P5
P7
P6
P2
P1
150 mm
(Less than D)
D
INVOLUTE OFA CIRCLE
String length LESS than D
Problem 19: Draw Involute of a circle.
String length is LESS than the circumference of circle.
Solution Steps:
In this case string length is Less
than D.
But remember!
Whatever may be the length of
string, mark D distance
horizontal i.e.along the string
and divide it in 8 number of
equal parts, and not any other
distance. Rest all steps are same
as previous INVOLUTE. Draw
the curve completely.
6. 1
2
3
4
5
6
1 2 3 4 5 6
A
P
D/2
P1
1
to
P
P2
P3
3 to P
P4
P
P5
P6
INVOLUTE
OF
COMPOSIT SHAPED POLE
PROBLEM 20 : A POLE IS OF A SHAPE OF HALF HEXABON AND SEMICIRCLE.
ASTRING IS TO BE WOUND HAVING LENGTH EQUAL TO THE POLE PERIMETER
DRAW PATH OF FREE END P OF STRING WHEN WOUND COMPLETELY.
(Take hex 30 mm sides and semicircle of 60 mm diameter.)
SOLUTION STEPS:
Draw pole shape as per
dimensions.
Divide semicircle in 4
parts and name those
along with corners of
hexagon.
Calculate perimeter
length.
Show it as string AP.
On this line mark 30mm
from A
Mark and name it 1
Mark D/2 distance on it
from 1
And dividing it in 4 parts
name 2,3,4,5.
Mark point 6 on line 30
mm from 5
Now draw tangents from
all points of pole
and proper lengths as
done in all previous
involute’s problems and
complete the curve.
7. 1
2
3
4
D
1
2
3
4
A
B
A1
B1
A2 B2
A3
B3
A4
B4
PROBLEM 21 : Rod AB 85 mm long rolls
over a semicircular pole without slipping
from it’s initially vertical position till it
becomes up-side-down vertical.
Draw locus of both ends A & B.
Solution Steps?
If you have studied previous problems
properly, you can surely solve this also.
Simply remember that this being a rod,
it will roll over the surface of pole.
Means when one end is approaching,
other end will move away from poll.
OBSERVE ILLUSTRATION CAREFULLY!
8. P
C1 C2 C3 C4 C5 C6 C7 C8 C9 C10 C11 C12
p1
p2
p3
p4
p5
p6
p7
p8
D
CYCLOID
PROBLEM 22: DRAW LOCUS OF A POINT ON THE PERIPHERY OF A CIRCLE
WHICH ROLLS ON STRAIGHT LINE PATH. Take Circle diameter as 50 mm
Solution Steps:
1) From center C draw a horizontal line equal to D distance.
2) Divide D distance into 12 number of equal parts and name them C1, C2, C3__ etc.
3) Divide the circle also into 12 number of equal parts and in clock wise direction, after P name 1, 2, 3 up to 12.
4) From all these points on circle draw horizontal lines. (parallel to locus of C)
5) With a fixed distance C-P in compass, C1 as center, mark a point on horizontal line from 1. Name it P.
6) Repeat this procedure from C2, C3, C4 upto C12 as centers. Mark points P2, P3, P4, P5 up to P8 on the
horizontal lines drawn from 1,2, 3, 4, 5, 6, 7 respectively.
7) Join all these points by curve. It is Cycloid.
p9
p10
p11
p12
1
2
3
5
4
6
7
8
9
10
11
12
9. C1 C2 C3 C4 C5 C6 C7 C8
p1
p2
p3
p4
p5
p6
p7
p8
1
2
3
4
5
6
7
C
D
SUPERIOR TROCHOID
P
PROBLEM 23: DRAW LOCUS OF A POINT , 5 MM AWAY FROM THE PERIPHERY OF A
CIRCLE WHICH ROLLS ON STRAIGHT LINE PATH. Take Circle diameter as 50 mm
Solution Steps:
1) Draw circle of given diameter and draw a horizontal line from it’s center C of length D and divide it
in 8 number of equal parts and name them C1, C2, C3, up to C8.
2) Draw circle by CP radius, as in this case CP is larger than radius of circle.
3) Now repeat steps as per the previous problem of cycloid, by dividing this new circle into 8 number of
equal parts and drawing lines from all these points parallel to locus of C and taking CP radius wit
different positions of C as centers, cut these lines and get different positions of P and join
4) This curve is called Superior Trochoid.
10. P
C1 C2 C3 C4 C5 C6 C7 C8
p1
p2
p
3
p4
p5
p6
p7
p8
1
2
3
4
5
6
7
C
D
INFERIOR TROCHOID
PROBLEM 24: DRAW LOCUS OF A POINT , 5 MM INSIDE THE PERIPHERY OF A
CIRCLE WHICH ROLLS ON STRAIGHT LINE PATH. Take Circle diameter as 50 mm
Solution Steps:
1) Draw circle of given diameter and draw a horizontal line from it’s center C of length D and divide it
in 8 number of equal parts and name them C1, C2, C3, up to C8.
2) Draw circle by CP radius, as in this case CP is SHORTER than radius of circle.
3) Now repeat steps as per the previous problem of cycloid, by dividing this new circle into 8 number
of equal parts and drawing lines from all these points parallel to locus of C and taking CP radius
with different positions of C as centers, cut these lines and get different positions of P and join
those in curvature.
4) This curve is called Inferior Trochoid.
11. C2
EPI CYCLOID :
P
O
r = CP
r
R
3600
=
1
2
3
4 5
6
7
Generating/
Rolling Circle
Directing Circle
PROBLEM 25: DRAW LOCUS OF A POINT ON THE PERIPHERY OF A CIRCLE
WHICH ROLLS ON A CURVED PATH. Take diameter of rolling Circle 50 mm
And radius of directing circle i.e. curved path, 75 mm.
Solution Steps:
1) When smaller circle will roll on
larger circle for one revolution it will
cover D distance on arc and it will
be decided by included arc angle .
2) Calculate by formula = (r/R) x
3600.
3) Construct angle with radius OC
and draw an arc by taking O as center
OC as radius and form sector of angle
.
4) Divide this sector into 8 number of
equal angular parts. And from C
onward name them C1, C2, C3 up to
C8.
5) Divide smaller circle (Generating
circle) also in 8 number of equal parts.
And next to P in clockwise direction
name those 1, 2, 3, up to 8.
6) With O as center, O-1 as radius
draw an arc in the sector. Take O-2, O-
3, O-4, O-5 up to O-8 distances with
center O, draw all concentric arcs in
sector. Take fixed distance C-P in
compass, C1 center, cut arc of 1 at P1.
Repeat procedure and locate P2, P3,
P4, P5 unto P8 (as in cycloid) and join
them by smooth curve. This is EPI –
CYCLOID.
13. HYPO CYCLOID
P1
P2
P3
P4
P5
P6 P7
P8
P
1
2
3
6
5
7
4
O
OC = R ( Radius of Directing Circle)
CP = r (Radius of Generating Circle)
r
R
3600
=
PROBLEM 26: DRAW LOCUS OF A POINT ON THE PERIPHERY OF A CIRCLE
WHICH ROLLS FROM THE INSIDE OF A CURVED PATH. Take diameter of
rolling circle 50 mm and radius of directing circle (curved path) 75 mm.
Solution Steps:
1) Smaller circle is rolling
here, inside the larger
circle. It has to rotate
anticlockwise to move
ahead.
2) Same steps should be
taken as in case of EPI –
CYCLOID. Only change is
in numbering direction of
8 number of equal parts
on the smaller circle.
3) From next to P in
anticlockwise direction,
name 1,2,3,4,5,6,7,8.
4) Further all steps are
that of epi – cycloid. This
is called
HYPO – CYCLOID.
15. 7 6 5 4 3 2 1
P
1
2
3
4
5
6
7
P2
P6
P1
P3
P5
P7
P4 O
SPIRAL
Problem 27: Draw a spiral of one convolution. Take distance PO 40 mm.
Solution Steps
1. With PO radius draw a circle
and divide it in EIGHT parts.
Name those 1,2,3,4, etc. up to 8
2 .Similarly divided line PO also in
EIGHT parts and name those
1,2,3,-- as shown.
3. Take o-1 distance from op line
and draw an arc up to O1 radius
vector. Name the point P1
4. Similarly mark points P2, P3, P4
up to P8
And join those in a smooth curve.
It is a SPIRAL of one convolution.
IMPORTANT APPROACH FOR CONSTRUCTION!
FIND TOTAL ANGULAR AND TOTAL LINEAR DISPLACEMENT
AND DIVIDE BOTH IN TO SAME NUMBER OF EQUAL PARTS.
16. 16 13 10 8 7 6 5 4 3 2 1 P
1,9
2,10
3,11
4,12
5,13
6,14
7,15
8,16
P1
P2
P3
P4
P5
P6
P7
P8
P9
P10
P11
P12
P13 P14
P15
SPIRAL
of
two convolutions
Problem 28
Point P is 80 mm from point O. It starts moving towards O and reaches it in two
revolutions around.it Draw locus of point P (To draw a Spiral of TWO convolutions).
IMPORTANT APPROACH FOR CONSTRUCTION!
FIND TOTAL ANGULAR AND TOTAL LINEAR DISPLACEMENT
AND DIVIDE BOTH IN TO SAME NUMBER OF EQUAL PARTS.
SOLUTION STEPS:
Total angular displacement here
is two revolutions And
Total Linear displacement here
is distance PO.
Just divide both in same parts i.e.
Circle in EIGHT parts.
( means total angular displacement
in SIXTEEN parts)
Divide PO also in SIXTEEN parts.
Rest steps are similar to the previous
problem.
17. 1
2
3
4
5
6
7
8
P
P1
P
P2
P3
P4
P5
P6
P7
P8
1
2
3
4
5
6
7
HELIX
(UPON A CYLINDER)
PROBLEM: Draw a helix of one convolution, upon a cylinder.
Given 80 mm pitch and 50 mm diameter of a cylinder.
(The axial advance during one complete revolution is called
The pitch of the helix)
SOLUTION:
Draw projections of a cylinder.
Divide circle and axis in to same no. of equal parts. ( 8 )
Name those as shown.
Mark initial position of point ‘P’
Mark various positions of P as shown in animation.
Join all points by smooth possible curve.
Make upper half dotted, as it is going behind the solid
and hence will not be seen from front side.
18. P
1
2
3
4
5
6
7
P
P1
P2
P3
P4
P5
P6
P7
P8
P1
P2
P3
P4
P5
P6
P7
P8
X Y
HELIX
(UPON A CONE)
PROBLEM: Draw a helix of one convolution, upon a cone,
diameter of base 70 mm, axis 90 mm and 90 mm pitch.
(The axial advance during one complete revolution is called
The pitch of the helix)
SOLUTION:
Draw projections of a cone
Divide circle and axis in to same no. of equal parts. ( 8 )
Name those as shown.
Mark initial position of point ‘P’
Mark various positions of P as shown in animation.
Join all points by smooth possible curve.
Make upper half dotted, as it is going behind the solid
and hence will not be seen from front side.
19. Q
Involute
Method of Drawing
Tangent & Normal
STEPS:
DRAW INVOLUTE AS USUAL.
MARK POINT Q ON IT AS DIRECTED.
JOIN Q TO THE CENTER OF CIRCLE C.
CONSIDERING CQ DIAMETER, DRAW
A SEMICIRCLE AS SHOWN.
MARK POINT OF INTERSECTION OF
THIS SEMICIRCLE AND POLE CIRCLE
AND JOIN IT TO Q.
THIS WILL BE NORMAL TO INVOLUTE.
DRAW A LINE AT RIGHT ANGLE TO
THIS LINE FROM Q.
IT WILL BE TANGENT TO INVOLUTE.
1 2 3 4 5 6 7 8
P
P8
1
2
3
4
5
6
7
8
INVOLUTE OFA CIRCLE
D
C
20. Q
N
CYCLOID
Method of Drawing
Tangent & Normal
STEPS:
DRAW CYCLOID AS USUAL.
MARK POINT Q ON IT AS DIRECTED.
WITH CP DISTANCE, FROM Q. CUT THE
POINT ON LOCUS OF C AND JOIN IT TO Q.
FROM THIS POINT DROP A PERPENDICULAR
ON GROUND LINE AND NAME IT N
JOIN N WITH Q.THIS WILL BE NORMAL TO
CYCLOID.
DRAW A LINE AT RIGHT ANGLE TO
THIS LINE FROM Q.
IT WILL BE TANGENT TO CYCLOID.
P
C1 C2 C3 C4 C5 C6 C7 C8
D
CYCLOID
C
21. 7 6 5 4 3 2 1
P
1
2
3
4
5
6
7
P2
P6
P1
P3
P5
P7
P4 O
SPIRAL (ONE CONVOLUSION.)
Q
Spiral.
Method of Drawing
Tangent & Normal
Constant of the Curve =
Difference in length of any radius vectors
Angle between the corresponding
radius vector in radian.
OP – OP2
/2
OP – OP2
1.57
= 3.185 m.m.
=
=
STEPS:
*DRAW SPIRAL AS USUAL.
DRAW A SMALL CIRCLE OF RADIUS EQUAL TO THE
CONSTANT OF CURVE CALCULATED ABOVE.
* LOCATE POINT Q AS DISCRIBED IN PROBLEM AND
THROUGH IT DRAW A TANGENTTO THIS SMALLER
CIRCLE.THIS IS A NORMAL TO THE SPIRAL.
*DRAW A LINE AT RIGHT ANGLE
*TO THIS LINE FROM Q.
IT WILL BE TANGENT TO CYCLOID.
22. LOCUS
It is a path traced out by a point moving in a plane,
in a particular manner, for one cycle of operation.
The cases are classified in THREE categories for easy understanding.
A} Basic Locus Cases.
B} Oscillating Link……
C} Rotating Link………
Basic Locus Cases:
Here some geometrical objects like point, line, circle will be described with there relative
Positions. Then one point will be allowed to move in a plane maintaining specific relation
with above objects. And studying situation carefully you will be asked to draw it’s locus.
Oscillating & Rotating Link:
Here a link oscillating from one end or rotating around it’s center will be described.
Then a point will be allowed to slide along the link in specific manner. And now studying
the situation carefully you will be asked to draw it’s locus.
STUDY TEN CASES GIVEN ON NEXT PAGES
23. A
B
p
4 3 2 1
F
1 2 3 4
SOLUTION STEPS:
1.Locate center of line, perpendicular to
AB from point F. This will be initial
point P.
2.Mark 5 mm distance to its right side,
name those points 1,2,3,4 and from those
draw lines parallel to AB.
3.Mark 5 mm distance to its left of P and
name it 1.
4.Take F-1 distance as radius and F as
center draw an arc
cutting first parallel line to AB. Name
upper point P1 and lower point P2.
5.Similarly repeat this process by taking
again 5mm to right and left and locate
P3P4.
6.Join all these points in smooth curve.
It will be the locus of P equidistance
from line AB and fixed point F.
P1
P2
P3
P4
P5
P6
P7
P8
PROBLEM 1.: Point F is 50 mm from a vertical straight line AB.
Draw locus of point P, moving in a plane such that
it always remains equidistant from point F and line AB.
Basic Locus Cases:
24. A
B
p
4 3 2 1 1 2 3 4
P1
P2
P3
P4
P5
P6
P7
P8
C
SOLUTION STEPS:
1.Locate center of line, perpendicular to
AB from the periphery of circle. This
will be initial point P.
2.Mark 5 mm distance to its right side,
name those points 1,2,3,4 and from those
draw lines parallel to AB.
3.Mark 5 mm distance to its left of P and
name it 1,2,3,4.
4.Take C-1 distance as radius and C as
center draw an arc cutting first parallel
line to AB. Name upper point P1 and
lower point P2.
5.Similarly repeat this process by taking
again 5mm to right and left and locate
P3P4.
6.Join all these points in smooth curve.
It will be the locus of P equidistance
from line AB and given circle.
50 D
75 mm
PROBLEM 2 :
A circle of 50 mm diameter has it’s center 75 mm from a vertical
line AB.. Draw locus of point P, moving in a plane such that
it always remains equidistant from given circle and line AB.
Basic Locus Cases:
25. 95 mm
30 D
60 D
p
4 3 2 1 1 2 3 4
C2
C1
P1
P2
P3
P4
P5
P6
P7
P8
PROBLEM 3 :
Center of a circle of 30 mm diameter is 90 mm away from center of another circle of 60 mm diameter.
Draw locus of point P, moving in a plane such that it always remains equidistant from given two circles.
SOLUTION STEPS:
1.Locate center of line,joining two
centers but part in between periphery
of two circles.Name it P. This will be
initial point P.
2.Mark 5 mm distance to its right
side, name those points 1,2,3,4 and
from those draw arcs from C1
As center.
3. Mark 5 mm distance to its right
side, name those points 1,2,3,4 and
from those draw arcs from C2 As
center.
4.Mark various positions of P as per
previous problems and name those
similarly.
5.Join all these points in smooth
curve.
It will be the locus of P
equidistance from given two circles.
Basic Locus Cases:
26. 2
C
C1
30 D
60 D
350
C1
Solution Steps:
1) Here consider two pairs,
one is a case of two circles
with centres C1 and C2 and
draw locus of point P
equidistance from
them.(As per solution of
case D above).
2) Consider second case
that of fixed circle (C1)
and fixed line AB and
draw locus of point P
equidistance from them.
(as per solution of case B
above).
3) Locate the point where
these two loci intersect
each other. Name it x. It
will be the point
equidistance from given
two circles and line AB.
4) Take x as centre and its
perpendicular distance on
AB as radius, draw a circle
which will touch given two
circles and line AB.
Problem 4:In the given situation there are two circles of
different diameters and one inclined line AB, as shown.
Draw one circle touching these three objects.
Basic Locus Cases:
27. P
A B
4 3 2 1 1 2 3 4
70 mm 30 mm
p1
p2
p3
p4
p5
p6
p7
p8
Problem 5:-Two points A and B are 100 mm apart.
There is a point P, moving in a plane such that the
difference of it’s distances from A and B always
remains constant and equals to 40 mm.
Draw locus of point P.
Basic Locus Cases:
Solution Steps:
1.Locate A & B points 100 mm apart.
2.Locate point P on AB line,
70 mm from A and 30 mm from B
As PA-PB=40 ( AB = 100 mm )
3.On both sides of P mark points 5
mm apart. Name those 1,2,3,4 as usual.
4.Now similar to steps of Problem 2,
Draw different arcs taking A & B centers
and A-1, B-1, A-2, B-2 etc as radius.
5. Mark various positions of p i.e. and join
them in smooth possible curve.
It will be locus of P
28. 1) Mark lower most
position of M on extension
of AB (downward) by taking
distance MN (40 mm) from
point B (because N can
not go beyond B ).
2) Divide line (M initial
and M lower most ) into
eight to ten parts and mark
them M1, M2, M3 up to the
last position of M .
3) Now take MN (40 mm)
as fixed distance in compass,
M1 center cut line CB in N1.
4) Mark point P1 on M1N1
with same distance of MP
from M1.
5) Similarly locate M2P2,
M3P3, M4P4 and join all P
points.
It will be locus of P.
Solution Steps:
600
M
N
N1
N2
N3
N4
N5
N6
N7
N8
N9
N10
N11
N12
A
B
C
D
M1
M2
M3
M4
M5
M7
M8
M9
M10
M11
M6
M12
M13
N13
p
p1
p2
p3
p4
p5
p6
p7
p8
p9
p10
p13
p11
p12
Problem 6:-Two points A and B are 100 mm apart.
There is a point P, moving in a plane such that the
difference of it’s distances from A and B always
remains constant and equals to 40 mm.
Draw locus of point P.
FORK & SLIDER
29. 1
2
3
4
5
6
7
8
p
p1
p2
p3
p4
p5
p6
p7
p8
O
A A1
A2
A3
A4
A5
A6
A7
A8
Problem No.7:
A Link OA, 80 mm long oscillates around O,
600 to right side and returns to it’s initial vertical
Position with uniform velocity.Mean while point
P initially on O starts sliding downwards and
reaches end A with uniform velocity.
Draw locus of point P
Solution Steps:
Point P- Reaches End A (Downwards)
1) Divide OA in EIGHT equal parts and from O to A after O
name 1, 2, 3, 4 up to 8. (i.e. up to point A).
2) Divide 600 angle into four parts (150 each) and mark each
point by A1, A2, A3, A4 and for return A5, A6, A7 andA8.
(Initial A point).
3) Take center O, distance in compass O-1 draw an arc upto
OA1. Name this point as P1.
1) Similarly O center O-2 distance mark P2 on line O-A2.
2) This way locate P3, P4, P5, P6, P7 and P8 and join them.
( It will be thw desired locus of P )
OSCILLATING LINK
30. p
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
O
A
Problem No 8:
A Link OA, 80 mm long oscillates around O,
600 to right side, 1200 to left and returns to it’s initial
vertical Position with uniform velocity.Mean while point
P initially on O starts sliding downwards, reaches end A
and returns to O again with uniform velocity.
Draw locus of point P
Solution Steps:
( P reaches A i.e. moving downwards.
& returns to O again i.e.moves upwards )
1.Here distance traveled by point P is PA.plus
AP.Hence divide it into eight equal parts.( so
total linear displacement gets divided in 16
parts) Name those as shown.
2.Link OA goes 600 to right, comes back to
original (Vertical) position, goes 600 to left
and returns to original vertical position. Hence
total angular displacement is 2400.
Divide this also in 16 parts. (150 each.)
Name as per previous problem.(A, A1 A2 etc)
3.Mark different positions of P as per the
procedure adopted in previous case.
and complete the problem.
A2
A1
A3
A4
A5
A6
A7
A8
A9
A10
A11
A12
A13
A14
A15
A16
p8
p
5
p6
p7
p2
p4
p1
p3
OSCILLATING LINK
31. A B
A1
A2
A4
A5
A3
A6
A7
P
p1 p2
p3
p4
p5
p6
p7
p8
1 2 3
4 5 6 7
Problem 9:
Rod AB, 100 mm long, revolves in clockwise direction for one revolution.
Meanwhile point P, initially on A starts moving towards B and reaches B.
Draw locus of point P.
ROTATING LINK
1) AB Rod revolves around
center O for one revolution and
point P slides along AB rod and
reaches end B in one
revolution.
2) Divide circle in 8 number of
equal parts and name in arrow
direction after A-A1, A2, A3, up
to A8.
3) Distance traveled by point P
is AB mm. Divide this also into 8
number of equal parts.
4) Initially P is on end A. When
A moves to A1, point P goes
one linear division (part) away
from A1. Mark it from A1 and
name the point P1.
5) When A moves to A2, P will
be two parts away from A2
(Name it P2 ). Mark it as above
from A2.
6) From A3 mark P3 three
parts away from P3.
7) Similarly locate P4, P5, P6,
P7 and P8 which will be eight
parts away from A8. [Means P
has reached B].
8) Join all P points by smooth
curve. It will be locus of P
32. A B
A1
A2
A4
A5
A3
A6
A7
P
p1
p2
p3
p4
p5
p6
p7
p8
1 2 3 4
5
6
7
Problem 10 :
Rod AB, 100 mm long, revolves in clockwise direction for one revolution.
Meanwhile point P, initially on A starts moving towards B, reaches B
And returns to A in one revolution of rod.
Draw locus of point P.
Solution Steps
+ + + +
ROTATING LINK
1) AB Rod revolves around center O
for one revolution and point P slides
along rod AB reaches end B and
returns to A.
2) Divide circle in 8 number of equal
parts and name in arrow direction
after A-A1, A2, A3, up to A8.
3) Distance traveled by point P is AB
plus AB mm. Divide AB in 4 parts so
those will be 8 equal parts on return.
4) Initially P is on end A. When A
moves to A1, point P goes one
linear division (part) away from A1.
Mark it from A1 and name the point
P1.
5) When A moves to A2, P will be
two parts away from A2 (Name it P2
). Mark it as above from A2.
6) From A3 mark P3 three parts
away from P3.
7) Similarly locate P4, P5, P6, P7
and P8 which will be eight parts away
from A8. [Means P has reached B].
8) Join all P points by smooth curve.
It will be locus of P
The Locus will follow the loop
path two times in one revolution.