The document discusses the procedure for solving problems involving the projections of plane figures. It explains that there are three steps: 1) assume an initial position and draw front and top views, 2) consider surface inclination and draw updated views, and 3) consider side/edge inclination and draw final views. It provides examples of applying this procedure to problems involving rectangles, triangles, pentagons, and circles with different surface and edge inclinations. The key is to start with the true shape view based on the initial positioning assumptions and update the views with each additional piece of inclination information provided.
Ist year engineering-graphics-ed-for-be-students (1) (1)Vivek Sricharan
1. The document discusses the procedure for solving problems involving the projections of plane figures.
2. It involves a 3 step process of drawing initial projections assuming a position, then adjusting for surface inclination, and finally adjusting for side/edge inclination.
3. Key assumptions are made for the initial position based on whether the surface is parallel or inclined to the horizontal or vertical planes.
1. The document discusses various methods for projecting plane figures including rectangles, triangles, pentagons, hexagons, circles, and freely suspended shapes.
2. Key steps involve determining the figure's position and orientation relative to reference planes, making assumptions for the initial position, and then applying successive surface and edge inclinations.
3. Examples demonstrate how to identify relevant details, apply the three-step projection process, and note differences in problems involving different geometric shapes or inclination descriptions.
Engineering Drawing Notes For 1st and 2nd sem (Engineering)Saroj Kumar
The document discusses the process for drawing projections of plane figures. It explains that problems will provide the description and position of the plane figure relative to the horizontal and vertical planes. The position is described by the inclination of the surface to one reference plane and the inclination of an edge to the other plane. The document outlines a three-step process for solving these problems: 1) Draw front and top views assuming an initial position, 2) Consider surface inclination and redraw views, 3) Consider edge inclination and draw final views. It provides examples of applying this process to rectangles, triangles, and other shapes with given surface and edge inclinations.
B.tech i eg u3 projection of planes, solid and development of surfacesRai University
This document provides information on projections of planes and surfaces in engineering graphics. It begins with definitions of key terms like true shape, apparent shape, and reduced shape as they relate to projections. It then presents examples of how to draw projections of different plane figures in different orientations, such as when the surface is parallel to or inclined to the horizontal or vertical planes. It provides pictorial representations and orthographic projections for various cases including rectangles, pentagons, hexagons, and circles oriented in different ways. The document concludes with example problems demonstrating how to apply the concepts.
The document discusses the process of determining the true shape of a plane figure given its projections. It describes using an auxiliary plane method with the following steps:
1. Draw the given front and top views.
2. Select a line in the views representing true length and draw a plane perpendicular to it.
3. Project one view onto the auxiliary plane.
4. Draw a second plane parallel to the projected view and project the other view onto it.
5. The projected view on the second plane represents the true shape of the object.
The method converts one inclined view to a line view using an auxiliary plane, then projects the other view onto a parallel plane to obtain the true shape.
The document provides information on the projection of plane figures:
1) It explains the basics of plane projection problems, including what is typically given (projections of the plane) and asked for (its position relative to reference planes).
2) Plane figures can have their surface parallel or inclined to the horizontal or vertical planes, and edges parallel or inclined to the other reference plane. The document demonstrates solving problems through 3 steps of initial positioning, surface inclination, and edge inclination.
3) Several example problems are worked through step-by-step to show determining the front, top, and side views of planes in different orientations, such as a pentagon inclined to the horizontal plane and a side to the vertical plane
Here are the steps to solve this problem:
1. Draw the top view of the rhombus with the longer diagonal horizontal at 100 mm.
2. This top view represents the true shape and size of the square in its top view.
3. Since the top view shows the true shape, the surface of the square must be parallel to the VP.
4. Draw the front view of the square below the top view, with the sides parallel to the XY line and of length 100 mm each.
5. The front view will also show the true shape and size of the square since its surface is parallel to the VP.
Therefore, the front view of the square is another square of side 100 mm, drawn
Ist year engineering-graphics-ed-for-be-students (1) (1)Vivek Sricharan
1. The document discusses the procedure for solving problems involving the projections of plane figures.
2. It involves a 3 step process of drawing initial projections assuming a position, then adjusting for surface inclination, and finally adjusting for side/edge inclination.
3. Key assumptions are made for the initial position based on whether the surface is parallel or inclined to the horizontal or vertical planes.
1. The document discusses various methods for projecting plane figures including rectangles, triangles, pentagons, hexagons, circles, and freely suspended shapes.
2. Key steps involve determining the figure's position and orientation relative to reference planes, making assumptions for the initial position, and then applying successive surface and edge inclinations.
3. Examples demonstrate how to identify relevant details, apply the three-step projection process, and note differences in problems involving different geometric shapes or inclination descriptions.
Engineering Drawing Notes For 1st and 2nd sem (Engineering)Saroj Kumar
The document discusses the process for drawing projections of plane figures. It explains that problems will provide the description and position of the plane figure relative to the horizontal and vertical planes. The position is described by the inclination of the surface to one reference plane and the inclination of an edge to the other plane. The document outlines a three-step process for solving these problems: 1) Draw front and top views assuming an initial position, 2) Consider surface inclination and redraw views, 3) Consider edge inclination and draw final views. It provides examples of applying this process to rectangles, triangles, and other shapes with given surface and edge inclinations.
B.tech i eg u3 projection of planes, solid and development of surfacesRai University
This document provides information on projections of planes and surfaces in engineering graphics. It begins with definitions of key terms like true shape, apparent shape, and reduced shape as they relate to projections. It then presents examples of how to draw projections of different plane figures in different orientations, such as when the surface is parallel to or inclined to the horizontal or vertical planes. It provides pictorial representations and orthographic projections for various cases including rectangles, pentagons, hexagons, and circles oriented in different ways. The document concludes with example problems demonstrating how to apply the concepts.
The document discusses the process of determining the true shape of a plane figure given its projections. It describes using an auxiliary plane method with the following steps:
1. Draw the given front and top views.
2. Select a line in the views representing true length and draw a plane perpendicular to it.
3. Project one view onto the auxiliary plane.
4. Draw a second plane parallel to the projected view and project the other view onto it.
5. The projected view on the second plane represents the true shape of the object.
The method converts one inclined view to a line view using an auxiliary plane, then projects the other view onto a parallel plane to obtain the true shape.
The document provides information on the projection of plane figures:
1) It explains the basics of plane projection problems, including what is typically given (projections of the plane) and asked for (its position relative to reference planes).
2) Plane figures can have their surface parallel or inclined to the horizontal or vertical planes, and edges parallel or inclined to the other reference plane. The document demonstrates solving problems through 3 steps of initial positioning, surface inclination, and edge inclination.
3) Several example problems are worked through step-by-step to show determining the front, top, and side views of planes in different orientations, such as a pentagon inclined to the horizontal plane and a side to the vertical plane
Here are the steps to solve this problem:
1. Draw the top view of the rhombus with the longer diagonal horizontal at 100 mm.
2. This top view represents the true shape and size of the square in its top view.
3. Since the top view shows the true shape, the surface of the square must be parallel to the VP.
4. Draw the front view of the square below the top view, with the sides parallel to the XY line and of length 100 mm each.
5. The front view will also show the true shape and size of the square since its surface is parallel to the VP.
Therefore, the front view of the square is another square of side 100 mm, drawn
1. The document discusses projections of planes and how to solve problems involving planes inclined to both the horizontal and vertical planes.
2. It provides examples of solving problems step-by-step, beginning with an initial position and then accounting for surface and side inclinations.
3. To determine the true shape of a plane from given projections, the auxiliary plane method is described where a plane perpendicular to the true length is drawn and views are projected onto it.
1. The document discusses the process of determining the projections of plane figures that are positioned in different orientations relative to reference planes.
2. It describes how the inclination of a plane figure's surface relative to the horizontal or vertical plane, as well as the inclination of its edges, are given.
3. The document outlines a three step process to determine the front, top, and side views of an object: 1) assume an initial position, 2) apply surface inclination, 3) apply edge inclination.
1. The document discusses the procedure for solving problems involving projections of planes. It describes the key steps of assuming initial positions, drawing front and top views, and accounting for any surface or edge inclinations.
2. Examples are provided to demonstrate solving problems involving rectangles, triangles, circles, and other shapes in different orientations. The procedure is explained through clear diagrams.
3. Determining the true shape of a plane figure from given projections can be done using an auxiliary plane method, which involves selecting a true length, drawing perpendicular planes, and projecting views to obtain the true shape.
The document provides instructions for drawing orthographic projections of points, lines, and solids. It defines key terms like object, observer, horizontal and vertical planes. Points and lines can be placed in four quadrants defined by the horizontal and vertical planes. Front, top and side views are drawn by placing the views in the same plane for the observer. Examples are given of drawing the projections of a point and various orientations of lines, including determining true lengths and inclinations from the given views. Notations and procedures for determining views, true lengths, and angles are defined.
This document provides information about engineering graphics and orthographic projections. It begins by introducing projections of points, lines, planes and solids. It then discusses coordinates and quadrants. The majority of the document explains how to draw orthographic projections of various geometric elements including points in different quadrants, straight lines in different orientations, planes in different positions, and solids. It provides examples and step-by-step instructions for creating projections of these elements in first, second, third and fourth quadrants. The document concludes by introducing different types of solids and announcing details about an upcoming exam.
1. The document discusses the process of projecting plane figures in 3D space onto 2D planes.
2. It explains that plane figures are defined by their position relative to horizontal and vertical reference planes, through angles of inclination of surfaces and edges.
3. The procedure for solving projection problems is outlined as a 3-step process: 1) assume an initial position and draw front and top views, 2) project the inclined surface, 3) project the inclined edge or side.
1. The document discusses the concept of traces of a line, which are the points where a line or its extension intersect reference planes like the horizontal plane (H.T.) and vertical plane (V.T.).
2. It provides steps to locate the horizontal trace (H.T.) and vertical trace (V.T.) when given the projections of a line.
3. Several example problems are included that demonstrate how to draw the projections of a line and locate its traces, given information about the line's inclination, length, or position relative to the reference planes.
1. The document provides instructions for sectioning solids, developing surfaces of solids, and intersections of solids. It includes definitions of terms like section plane and sectioning.
2. Illustrations show how to determine the true shape of sections and develop the surfaces of remaining parts of solids that have been cut by a section plane.
3. The document contains examples of typical section planes and resulting shapes for various solids like cones, pyramids, and prisms. It also provides practice problems for using these techniques.
Projection of solids - ENGINEERING DRAWING/GRAPHICSAbhishek Kandare
Projection of solids
HIS 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.
1. The document discusses the procedure for projecting plane figures by considering their position and orientation relative to the horizontal and vertical planes.
2. It explains that the position of a plane figure will be defined by specifying the inclination of its surface to one reference plane and the inclination of one of its edges to the other plane.
3. The document provides examples of applying the three step procedure to solve projection problems: 1) assume initial position and draw front and top views, 2) consider surface inclination and redraw views, 3) consider edge inclination and draw final views.
This document contains descriptions of 23 problems involving projections of lines and objects. The problems provide information about the positions of various lines and objects in relation to reference planes (ground and vertical planes). For each problem, you are asked to draw the projections, determine lengths, angles, distances, and other values based on the information provided. The goal is to visualize the 3D situations and use principles of projections to solve practical geometric problems.
1. The document provides instructions for solving problems involving projections of plane figures. It describes determining the true shape of a plane figure when its front and top views are given.
2. Key steps include drawing the given views, selecting a true length line, projecting that view onto an auxiliary plane perpendicular to the true length line, and projecting the other view onto a parallel plane to obtain the true shape.
3. Example problems demonstrate applying this procedure to find the true shape from given front and top view projections. Determining the true length line and using auxiliary planes allows converting between projected and true shapes.
introduction of engineering graphics ,projection of points,lines,planes,solids,section of solids,development of surfaces,isometric projection,perspective projection
Projection of straight line engineering drawingAnurag Harsh
The document discusses various concepts related to projections of straight lines including:
- Definitions of straight lines and their projections in different views
- Notations used to describe lengths, angles and positions of straight lines
- Different positions of straight lines relative to reference planes including perpendicular, parallel and inclined lines
- Examples demonstrating how to draw projections of straight lines given data on their positions, lengths and angles
The document contains 12 exercises involving the projections of various geometric shapes and solids including lines, planes, prisms, pyramids, cones and composite solids. Many of the exercises involve determining lengths, angles of inclination, traces, true shapes, developments of cut surfaces, and shortest paths on developments. Projections are drawn to illustrate the orientation and measurements of each geometric object under different cutting plane conditions.
1) The document discusses different types of solids and their classification into two groups - Group A solids have the same shape for the top and base, while Group B solids have the base of some shape and just a point for the top.
2) Instructions are provided on how to solve problems involving solids, with a three step approach of first assuming the solid standing on the relevant plane, then considering its inclination, and finally drawing the final projections.
3) Several example problems are worked through step-by-step to demonstrate how to draw the projections of solids like prisms, pyramids, cylinders and cones in different orientations. Dimensional parameters and terminology used in problems involving solids
1) The document discusses different types of solids and their classification into two groups - Group A solids have the same shape for the top and base, while Group B solids have the base of some shape and just a point for the top.
2) Instructions are provided on how to solve problems involving solids, with a three step approach of first assuming the solid standing on the relevant plane, then considering its inclination, and finally drawing the final projections.
3) Several example problems are worked through step-by-step to demonstrate how to draw the projections of solids like prisms, pyramids, cylinders and cones in different orientations. Dimensional parameters and terminology used in problems involving solids
The document discusses the steps to solve problems involving projections of planes. It begins by outlining what information is typically provided in the problem and what is asked. It then demonstrates the procedure with examples of a rectangle in different orientations. Key steps include: 1) Drawing initial front and top views assuming the surface is parallel to a reference plane, 2) Accounting for any surface inclinations, 3) Accounting for any edge inclinations to draw the final projections. Important assumptions and what view shows the true shape are also discussed. Example problems are worked through to demonstrate applying the procedure and noting differences in constructions.
The document provides instructions for projecting plane figures by:
1. Describing the plane figure and its position relative to the horizontal and vertical planes.
2. Projecting the figure in three steps: initial position, surface inclination, and side/edge inclination.
3. Key assumptions are made for the initial position depending on whether the surface is parallel to the horizontal or vertical plane.
4. Worked examples are provided to demonstrate projecting figures with different combinations of surface and side/edge inclinations.
1. The document discusses projections of planes and how to solve problems involving planes inclined to both the horizontal and vertical planes.
2. It provides examples of solving problems step-by-step, beginning with an initial position and then accounting for surface and side inclinations.
3. To determine the true shape of a plane from given projections, the auxiliary plane method is described where a plane perpendicular to the true length is drawn and views are projected onto it.
1. The document discusses the process of determining the projections of plane figures that are positioned in different orientations relative to reference planes.
2. It describes how the inclination of a plane figure's surface relative to the horizontal or vertical plane, as well as the inclination of its edges, are given.
3. The document outlines a three step process to determine the front, top, and side views of an object: 1) assume an initial position, 2) apply surface inclination, 3) apply edge inclination.
1. The document discusses the procedure for solving problems involving projections of planes. It describes the key steps of assuming initial positions, drawing front and top views, and accounting for any surface or edge inclinations.
2. Examples are provided to demonstrate solving problems involving rectangles, triangles, circles, and other shapes in different orientations. The procedure is explained through clear diagrams.
3. Determining the true shape of a plane figure from given projections can be done using an auxiliary plane method, which involves selecting a true length, drawing perpendicular planes, and projecting views to obtain the true shape.
The document provides instructions for drawing orthographic projections of points, lines, and solids. It defines key terms like object, observer, horizontal and vertical planes. Points and lines can be placed in four quadrants defined by the horizontal and vertical planes. Front, top and side views are drawn by placing the views in the same plane for the observer. Examples are given of drawing the projections of a point and various orientations of lines, including determining true lengths and inclinations from the given views. Notations and procedures for determining views, true lengths, and angles are defined.
This document provides information about engineering graphics and orthographic projections. It begins by introducing projections of points, lines, planes and solids. It then discusses coordinates and quadrants. The majority of the document explains how to draw orthographic projections of various geometric elements including points in different quadrants, straight lines in different orientations, planes in different positions, and solids. It provides examples and step-by-step instructions for creating projections of these elements in first, second, third and fourth quadrants. The document concludes by introducing different types of solids and announcing details about an upcoming exam.
1. The document discusses the process of projecting plane figures in 3D space onto 2D planes.
2. It explains that plane figures are defined by their position relative to horizontal and vertical reference planes, through angles of inclination of surfaces and edges.
3. The procedure for solving projection problems is outlined as a 3-step process: 1) assume an initial position and draw front and top views, 2) project the inclined surface, 3) project the inclined edge or side.
1. The document discusses the concept of traces of a line, which are the points where a line or its extension intersect reference planes like the horizontal plane (H.T.) and vertical plane (V.T.).
2. It provides steps to locate the horizontal trace (H.T.) and vertical trace (V.T.) when given the projections of a line.
3. Several example problems are included that demonstrate how to draw the projections of a line and locate its traces, given information about the line's inclination, length, or position relative to the reference planes.
1. The document provides instructions for sectioning solids, developing surfaces of solids, and intersections of solids. It includes definitions of terms like section plane and sectioning.
2. Illustrations show how to determine the true shape of sections and develop the surfaces of remaining parts of solids that have been cut by a section plane.
3. The document contains examples of typical section planes and resulting shapes for various solids like cones, pyramids, and prisms. It also provides practice problems for using these techniques.
Projection of solids - ENGINEERING DRAWING/GRAPHICSAbhishek Kandare
Projection of solids
HIS 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.
1. The document discusses the procedure for projecting plane figures by considering their position and orientation relative to the horizontal and vertical planes.
2. It explains that the position of a plane figure will be defined by specifying the inclination of its surface to one reference plane and the inclination of one of its edges to the other plane.
3. The document provides examples of applying the three step procedure to solve projection problems: 1) assume initial position and draw front and top views, 2) consider surface inclination and redraw views, 3) consider edge inclination and draw final views.
This document contains descriptions of 23 problems involving projections of lines and objects. The problems provide information about the positions of various lines and objects in relation to reference planes (ground and vertical planes). For each problem, you are asked to draw the projections, determine lengths, angles, distances, and other values based on the information provided. The goal is to visualize the 3D situations and use principles of projections to solve practical geometric problems.
1. The document provides instructions for solving problems involving projections of plane figures. It describes determining the true shape of a plane figure when its front and top views are given.
2. Key steps include drawing the given views, selecting a true length line, projecting that view onto an auxiliary plane perpendicular to the true length line, and projecting the other view onto a parallel plane to obtain the true shape.
3. Example problems demonstrate applying this procedure to find the true shape from given front and top view projections. Determining the true length line and using auxiliary planes allows converting between projected and true shapes.
introduction of engineering graphics ,projection of points,lines,planes,solids,section of solids,development of surfaces,isometric projection,perspective projection
Projection of straight line engineering drawingAnurag Harsh
The document discusses various concepts related to projections of straight lines including:
- Definitions of straight lines and their projections in different views
- Notations used to describe lengths, angles and positions of straight lines
- Different positions of straight lines relative to reference planes including perpendicular, parallel and inclined lines
- Examples demonstrating how to draw projections of straight lines given data on their positions, lengths and angles
The document contains 12 exercises involving the projections of various geometric shapes and solids including lines, planes, prisms, pyramids, cones and composite solids. Many of the exercises involve determining lengths, angles of inclination, traces, true shapes, developments of cut surfaces, and shortest paths on developments. Projections are drawn to illustrate the orientation and measurements of each geometric object under different cutting plane conditions.
1) The document discusses different types of solids and their classification into two groups - Group A solids have the same shape for the top and base, while Group B solids have the base of some shape and just a point for the top.
2) Instructions are provided on how to solve problems involving solids, with a three step approach of first assuming the solid standing on the relevant plane, then considering its inclination, and finally drawing the final projections.
3) Several example problems are worked through step-by-step to demonstrate how to draw the projections of solids like prisms, pyramids, cylinders and cones in different orientations. Dimensional parameters and terminology used in problems involving solids
1) The document discusses different types of solids and their classification into two groups - Group A solids have the same shape for the top and base, while Group B solids have the base of some shape and just a point for the top.
2) Instructions are provided on how to solve problems involving solids, with a three step approach of first assuming the solid standing on the relevant plane, then considering its inclination, and finally drawing the final projections.
3) Several example problems are worked through step-by-step to demonstrate how to draw the projections of solids like prisms, pyramids, cylinders and cones in different orientations. Dimensional parameters and terminology used in problems involving solids
The document discusses the steps to solve problems involving projections of planes. It begins by outlining what information is typically provided in the problem and what is asked. It then demonstrates the procedure with examples of a rectangle in different orientations. Key steps include: 1) Drawing initial front and top views assuming the surface is parallel to a reference plane, 2) Accounting for any surface inclinations, 3) Accounting for any edge inclinations to draw the final projections. Important assumptions and what view shows the true shape are also discussed. Example problems are worked through to demonstrate applying the procedure and noting differences in constructions.
The document provides instructions for projecting plane figures by:
1. Describing the plane figure and its position relative to the horizontal and vertical planes.
2. Projecting the figure in three steps: initial position, surface inclination, and side/edge inclination.
3. Key assumptions are made for the initial position depending on whether the surface is parallel to the horizontal or vertical plane.
4. Worked examples are provided to demonstrate projecting figures with different combinations of surface and side/edge inclinations.
The document provides instructions for projecting plane figures by:
1. Describing the plane figure and its position relative to the horizontal and vertical planes.
2. Projecting the figure in three steps: initial position, surface inclination, and side/edge inclination.
3. Key assumptions are made for the initial position based on whether the surface is parallel to the horizontal or vertical plane.
4. Worked examples are provided to demonstrate projecting figures with different combinations of surface and side/edge inclinations.
- The document discusses drawing projections of solids. It provides steps to solve problems involving drawing projections of solids that are inclined or freely suspended.
- It explains that three views are typically needed to represent a 3D solid on a 2D surface: a front view, top view, and side view. It outlines a three step process for drawing projections of inclined solids: 1) assume the solid is standing on the plane it is inclined to, 2) draw projections in that position, 3) draw projections considering the remaining inclinations.
- It provides examples of applying these steps to problems involving solids like prisms, pyramids, cylinders and cones in different orientations. Guidelines are given for determining which
The document discusses the procedure for drawing projections of plane figures that are inclined to the horizontal and vertical planes. It provides examples of drawing projections for various objects including rectangles, triangles, circles, hexagons and pentagons in different orientations. The procedure involves three steps - drawing the initial projections assuming the plane is parallel to a reference plane, then drawing the second projections after inclining the surface, and finally the third projections after inclining an edge or side. Hints and solutions are provided for sample problems applying this three-step process.
1. The document describes various solids and their dimensional parameters including rectangular prisms, triangular prisms, square pyramids, cylinders, and cones. It discusses their faces, edges, and other geometric features.
2. Methods for solving problems involving solids are presented. Problems can be solved in three steps: 1) assume the solid is standing on the plane it is inclined to, 2) draw projections considering the solid's inclination, and 3) draw final projections considering any remaining inclinations.
3. Several example problems are shown applying this three-step method to solids inclined to horizontal and vertical planes in different positions like standing, resting, or freely suspended. This includes determining front, top/
1. The document discusses the process of projecting plane figures in 3D space onto 2D planes.
2. It explains that plane figures are defined by their position relative to horizontal and vertical reference planes, through angles of inclination of surfaces and edges.
3. The procedure for solving projection problems is outlined as a 3-step process: 1) assume an initial position and draw front and top views, 2) project the inclined surface, 3) project the inclined edge or side.
The document discusses different types of solids and their projections. It classifies solids into two groups - Group A solids have the same shape for the top and base, including cylinders and prisms. Group B solids have the base of some shape and a point for the top, including cones and pyramids. It provides steps for drawing projections of solids in different positions and orientations, including problems showing projections of specific solids like pyramids, cylinders, and cones in various configurations.
The document discusses different types of solids and their projections. It is divided into two major sections.
Section one classifies solids into two groups - Group A solids have the same shape for the top and base, such as prisms and cylinders. Group B solids have the base of one shape and a point top called the apex, such as pyramids and cones. It then provides examples and diagrams of different solids.
Section two provides steps for solving problems involving solids. It explains how to assume the solid is standing on a plane based on its orientation, and how to draw front and top views. It also categorizes example problems and provides solutions for problems involving solids like py
1. The document discusses different types of solids and their classification into two groups based on the shape of their top and base.
2. It provides instructions on how to solve problems involving solids by assuming their position and orientation, and drawing their front, top, and side views in three steps.
3. Examples of problems involving solids like cubes, pyramids, cylinders, and cones in different orientations are presented along with their step-by-step solutions.
1. The document discusses different types of solids and their classification into two groups: Group A solids have the same shape for the top and base, while Group B solids have the base of some shape and just a point for the top.
2. It provides details on the dimensional parameters of solids like cylinders, cones, prisms and pyramids. It also describes how to solve problems involving solids in three steps: assuming the solid standing on a reference plane, drawing the front and top views, and considering any remaining inclinations.
3. An example problem is given involving drawing the projections of a freely suspended pentagonal pyramid with conditions specified.
1. The document discusses different types of solids and their classification into two groups based on the shape of their top and base.
2. It provides instructions on how to solve problems involving solids through a three step process of assuming the solid in different positions and drawing their front and top views.
3. Examples of problems involving solids like cubes, pyramids, cylinders and cones in different orientations are presented along with their step-by-step solutions.
1. The document discusses different types of solids and their classification into two groups: Group A includes solids with bases of the same shape as the top like cylinders and prisms, while Group B includes solids with the top being a single point called the apex, like cones and pyramids.
2. It provides details on the dimensional parameters of different solids like their faces, edges, bases, etc. It also discusses different positions of solids relative to planes like standing, resting, or lying.
3. Steps to solve problems involving solids inclined to horizontal and vertical planes are outlined. The document contains examples of problems involving solids like cylinders, cones, cubes, and tetrahed
This document contains information about various 3D shapes or solids. It divides solids into two groups: Group A includes cylinders and prisms which have bases and tops of the same shape, while Group B includes cones and pyramids which have a pointed top. The document provides details on the dimensional parameters, projections and solving problems related to different solids. It also discusses positions of the center of gravity for freely suspended solids.
A plane is a two dimensional object having length and breadth only. Its thickness is always neglected. Various shapes of plane figures are considered such as square, rectangle, circle, pentagon, hexagon, etc.
There are two types of planes
Perpendicular planes which have their surface perpendicular to any one of the reference planes and parallel or inclined to the other reference plane.
2. Oblique planes which have their surface inclined to both the reference planes.
The document discusses the process of projecting plane figures in three steps:
1. Draw front and top views assuming an initial position with the surface parallel to either the HP or VP.
2. Project the views again after considering the surface inclination.
3. Draw final projections accounting for any edge inclinations.
It provides examples of applying this process to different shapes including rectangles, triangles, circles, and hexagons in various orientations. Guidance is given on making assumptions in the initial position and sequentially projecting views while considering the given surface and edge inclinations.
Similar to Ist Year Engineering Graphics E D For B E Students (1) (1) (17)
Ist Year Engineering Graphics E D For B E Students (1) (1)
1.
2. FV-3 T V-3 FV-1 T V-1 FV-2 T V-2 SURFACE PARALLEL TO HP PICTORIAL PRESENTATION SURFACE INCLINED TO HP PICTORIAL PRESENTATION ONE SMALL SIDE INCLINED TO VP PICTORIAL PRESENTATION ORTHOGRAPHIC TV-True Shape FV- Line // to xy ORTHOGRAPHIC FV- Inclined to XY TV- Reduced Shape ORTHOGRAPHIC FV- Apparent Shape TV-Previous Shape HP a 1 b 1 c 1 d 1 VP VP a’ d’ c’ b’ VP a’ d’ c’ b’ For Fv For Tv For F.V. For T.V. For T.V. For F.V. HP a b c d a 1 ’ d 1 ’ c 1 ’ b 1 ’ HP a 1 b 1 c 1 d 1 CASE OF A RECTANGLE – OBSERVE AND NOTE ALL STEPS. A B C
3. PROCEDURE OF SOLVING THE PROBLEM: IN THREE STEPS EACH PROBLEM CAN BE SOLVED : ( As Shown In Previous Illustration ) STEP 1. Assume suitable conditions & draw Fv & Tv of initial position. STEP 2. Now consider surface inclination & draw 2 nd Fv & Tv. STEP 3. After this,consider side/edge inclination and draw 3 rd ( final) Fv & Tv. ASSUMPTIONS FOR INITIAL POSITION: (Initial Position means assuming surface // to HP or VP) 1.If in problem surface is inclined to HP – assume it // HP Or If surface is inclined to VP – assume it // to VP 2. Now if surface is assumed // to HP- It’s TV will show True Shape. And If surface is assumed // to VP – It’s FV will show True Shape. 3. Hence begin with drawing TV or FV as True Shape. 4. While drawing this True Shape – keep one side/edge ( which is making inclination) perpendicular to xy line ( similar to pair no. on previous page illustration ). APPLY SAME STEPS TO SOLVE NEXT ELEVEN PROBLEMS A B Now Complete STEP 2. By making surface inclined to the resp plane & project it’s other view. (Ref. 2 nd pair on previous page illustration ) C Now Complete STEP 3. By making side inclined to the resp plane & project it’s other view. (Ref. 3 nd pair on previous page illustration )
4. X Y a b c d a’ b’ c’ d’ a 1 b 1 c 1 d 1 a 1 b 1 c 1 d 1 a’ b’ d’ c’ c’ 1 d’ 1 b’ 1 a’ 1 45 0 30 0 Surface // to Hp Surface inclined to Hp Side Inclined to Vp Problem 1: Rectangle 30mm and 50mm sides is resting on HP on one small side which is 30 0 inclined to VP,while the surface of the plane makes 45 0 inclination with HP. Draw it’s projections. Read problem and answer following questions 1. Surface inclined to which plane? ------- HP 2. Assumption for initial position? ------// to HP 3. So which view will show True shape? --- TV 4. Which side will be vertical? ---One small side. Hence begin with TV, draw rectangle below X-Y drawing one small side vertical.
5. c 1 X Y 30 0 45 0 a’ 1 b’ 1 c’ 1 a c a’ a b 1 b’ b a 1 b c a’ 1 b’ 1 c’ 1 c’ Hence begin with FV, draw triangle above X-Y keeping longest side vertical . Surface // to Vp Surface inclined to Vp side inclined to Hp Problem 2: A 30 0 – 60 0 set square of longest side 100 mm long, is in VP and 30 0 inclined to HP while it’s surface is 45 0 inclined to VP.Draw it’s projections ( Surface & Side inclinations directly given ) Read problem and answer following questions 1 .Surface inclined to which plane? ------- VP 2. Assumption for initial position? ------// to VP 3. So which view will show True shape? --- FV 4. Which side will be vertical? ------longest side.
6. c c 1 X Y 45 0 a’ 1 b’ 1 c’ 1 a c a’ a b 1 b’ b a 1 b a’ 1 b’ 1 c’ 1 c’ 35 10 Problem 3: A 30 0 – 60 0 set square of longest side 100 mm long is in VP and it’s surface 45 0 inclined to VP. One end of longest side is 10 mm and other end is 35 mm above HP. Draw it’s projections (Surface inclination directly given. Side inclination indirectly given) Read problem and answer following questions 1 .Surface inclined to which plane? ------- VP 2. Assumption for initial position? ------// to VP 3. So which view will show True shape? --- FV 4. Which side will be vertical? ------longest side. Hence begin with FV, draw triangle above X-Y keeping longest side vertical . First TWO steps are similar to previous problem. Note the manner in which side inclination is given. End A 35 mm above Hp & End B is 10 mm above Hp. So redraw 2 nd Fv as final Fv placing these ends as said.
7. Read problem and answer following questions 1. Surface inclined to which plane? ------- HP 2. Assumption for initial position? ------ // to HP 3. So which view will show True shape? --- TV 4. Which side will be vertical? -------- any side. Hence begin with TV,draw pentagon below X-Y line, taking one side vertical . Problem 4: A regular pentagon of 30 mm sides is resting on HP on one of it’s sides with it’s surface 45 0 inclined to HP. Draw it’s projections when the side in HP makes 30 0 angle with VP a’ b’ d’ b 1 d c 1 a c’e’ b c d 1 b’ 1 a 1 e’ 1 c’ 1 d’ 1 a 1 b 1 c 1 d 1 d’ a’ b’ c’e’ e 1 e 1 a’ 1 X Y 45 0 30 0 e SURFACE AND SIDE INCLINATIONS ARE DIRECTLY GIVEN.
8. Problem 5: A regular pentagon of 30 mm sides is resting on HP on one of it’s sides while it’s opposite vertex (corner) is 30 mm above HP. Draw projections when side in HP is 30 0 inclined to VP. Read problem and answer following questions 1. Surface inclined to which plane? ------- HP 2. Assumption for initial position? ------ // to HP 3. So which view will show True shape? --- TV 4. Which side will be vertical? -------- any side. Hence begin with TV,draw pentagon below X-Y line, taking one side vertical . X Y a’ b’ d’ c’e’ SURFACE INCLINATION INDIRECTLY GIVEN SIDE INCLINATION DIRECTLY GIVEN: b’ d’ a’ c’e’ a 1 b 1 c 1 d 1 e 1 b 1 c 1 d 1 a 1 e 1 b’ 1 e’ 1 c’ 1 d’ 1 a’ 1 30 a b c d e 30 0 ONLY CHANGE is the manner in which surface inclination is described: One side on Hp & it’s opposite corner 30 mm above Hp. Hence redraw 1 st Fv as a 2 nd Fv making above arrangement. Keep a’b’ on xy & d’ 30 mm above xy.
9. 45 0 30 0 a’ b’ 1 c’ 1 d’ a’ b’ d’ c’ a c b d a 1 b 1 c 1 d 1 b’ c’ a’ 1 d’ 1 d 1 b 1 c 1 a 1 X Y 30 0 b’ 1 c’ 1 c 1 a’ 1 d’ 1 d 1 b 1 c 1 a 1 TL Problem 6: A rhombus of diagonals 40 mm and 70 mm long respectively has one end of it’s longer diagonal in HP while that diagonal is 35 0 inclined to HP. If the top-view of the same diagonal makes 40 0 inclination with VP, draw it’s projections. Problem 7: A rhombus of diagonals 40 mm and 70 mm long respectively having one end of it’s longer diagonal in HP while that diagonal is 35 0 inclined to HP and makes 40 0 inclination with VP. Draw it’s projections. Read problem and answer following questions 1. Surface inclined to which plane? ------- HP 2. Assumption for initial position? ------ // to HP 3. So which view will show True shape? --- TV 4. Which diagonal horizontal? ---------- Longer Hence begin with TV,draw rhombus below X-Y line, taking longer diagonal // to X-Y c 2 45 0 a’ d’ a’ b’ d’ c’ a c b d a 1 b 1 d 1 b’ c’ X Y The difference in these two problems is in step 3 only. In problem no.6 inclination of Tv of that diagonal is given,It could be drawn directly as shown in 3 rd step. While in no.7 angle of diagonal itself I.e. it’s TL, is given. Hence here angle of TL is taken,locus of c 1 Is drawn and then LTV I.e. a1 c1 is marked and final TV was completed.Study illustration carefully. Note the difference in construction of 3 rd step in both solutions.
10. T L 45 0 30 0 30 0 Problem 8 : A circle of 50 mm diameter is resting on Hp on end A of it’s diameter AC which is 30 0 inclined to Hp while it’s Tv is 45 0 inclined to Vp.Draw it’s projections. Problem 9 : A circle of 50 mm diameter is resting on Hp on end A of it’s diameter AC which is 30 0 inclined to Hp while it makes 45 0 inclined to Vp. Draw it’s projections. Read problem and answer following questions 1. Surface inclined to which plane? ------- HP 2. Assumption for initial position? ------ // to HP 3. So which view will show True shape? --- TV 4. Which diameter horizontal? ---------- AC Hence begin with TV,draw rhombus below X-Y line, taking longer diagonal // to X-Y a d c b a’ b’ d’ c’ X Y a’ b’ d’ c’ a 1 b 1 d 1 c 1 a 1 b 1 d 1 c 1 a’ 1 b’ 1 c’ 1 d’ 1 a 1 b 1 d 1 c 1 a d c b a’ b’ d’ c’ a’ b’ d’ c’ a 1 b 1 d 1 c 1 a’ 1 b’ 1 c’ 1 d’ 1 The difference in these two problems is in step 3 only. In problem no.8 inclination of Tv of that AC is given,It could be drawn directly as shown in 3 rd step. While in no.9 angle of AC itself i.e. it’s TL, is given. Hence here angle of TL is taken,locus of c 1 Is drawn and then LTV I.e. a 1 c 1 is marked and final TV was completed.Study illustration carefully. Note the difference in construction of 3 rd step in both solutions.
11. Problem 10: End A of diameter AB of a circle is in HP A nd end B is in VP.Diameter AB, 50 mm long is 30 0 & 60 0 inclined to HP & VP respectively. Draw projections of circle. TL X Y 30 0 60 0 Read problem and answer following questions 1. Surface inclined to which plane? ------- HP 2. Assumption for initial position? ------ // to HP 3. So which view will show True shape? --- TV 4. Which diameter horizontal? ---------- AB Hence begin with TV,draw CIRCLE below X-Y line, taking DIA. AB // to X-Y The problem is similar to previous problem of circle – no.9. But in the 3 rd step there is one more change. Like 9 th problem True Length inclination of dia.AB is definitely expected but if you carefully note - the the SUM of it’s inclinations with HP & VP is 90 0 . Means Line AB lies in a Profile Plane. Hence it’s both Tv & Fv must arrive on one single projector . So do the construction accordingly AND note the case carefully .. SOLVE SEPARATELY ON DRAWING SHEET GIVING NAMES TO VARIOUS POINTS AS USUAL, AS THE CASE IS IMPORTANT
12. X Y Problem 11: A hexagonal lamina has its one side in HP and Its apposite parallel side is 25mm above Hp and In Vp. Draw it’s projections. Take side of hexagon 30 mm long. Read problem and answer following questions 1. Surface inclined to which plane? ------- HP 2. Assumption for initial position? ------ // to HP 3. So which view will show True shape? --- TV 4. Which diameter horizontal? ---------- AC Hence begin with TV,draw rhombus below X-Y line, taking longer diagonal // to X-Y As 3 rd step redraw 2 nd Tv keeping side DE on xy line. Because it is in VP as said in problem. a b c d e f ONLY CHANGE is the manner in which surface inclination is described: One side on Hp & it’s opposite side 25 mm above Hp. Hence redraw 1 st Fv as a 2 nd Fv making above arrangement. Keep a’b’ on xy & d’e’ 25 mm above xy. 25 f’ e’ d’ c’ b’ a’ f’ e’ d’ c’ b’ a’ a 1 b 1 c 1 d 1 e 1 f 1 c 1 ’ b’ 1 a’ 1 f’ 1 d’ 1 e’ 1 f 1 a 1 c 1 b 1 d 1 e 1
13. A B C H H/3 G X Y a’ b’ c’ g’ b a,g c b a,g c 45 0 a’ 1 c’ 1 b’ 1 g’ 1 FREELY SUSPENDED CASES . Problem 12: An isosceles triangle of 40 mm long base side, 60 mm long altitude Is freely suspended from one corner of Base side.It’s plane is 45 0 inclined to Vp. Draw it’s projections. 1.In this case the plane of the figure always remains perpendicular to Hp . 2.It may remain parallel or inclined to Vp. 3.Hence TV in this case will be always a LINE view. 4.Assuming surface // to Vp, draw true shape in suspended position as FV. (Here keep line joining point of contact & centroid of fig. vertical ) 5.Always begin with FV as a True Shape but in a suspended position. AS shown in 1 st FV. IMPORTANT POINTS Similarly solve next problem of Semi-circle First draw a given triangle With given dimensions, Locate it’s centroid position And join it with point of suspension.
14. X Y e’ c’ d’ b’ a’ p’ g’ b c a p,g d e b c a p,g d e Problem 13 : A semicircle of 100 mm diameter is suspended from a point on its straight edge 30 mm from the midpoint of that edge so that the surface makes an angle of 45 0 with VP. Draw its projections. 0.414R G A P 20 mm CG First draw a given semicircle With given diameter, Locate it’s centroid position And join it with point of suspension . 1.In this case the plane of the figure always remains perpendicular to Hp . 2.It may remain parallel or inclined to Vp. 3.Hence TV in this case will be always a LINE view. 4.Assuming surface // to Vp, draw true shape in suspended position as FV. (Here keep line joining point of contact & centroid of fig. vertical ) 5.Always begin with FV as a True Shape but in a suspended position. AS shown in 1 st FV. IMPORTANT POINTS
15. SOLIDS To understand and remember various solids in this subject properly, those are classified & arranged in to two major groups. Group A Solids having top and base of same shape Cylinder Prisms Triangular Square Pentagonal Hexagonal Cube Triangular Square Pentagonal Hexagonal Cone Tetrahedron Pyramids ( A solid having six square faces) ( A solid having Four triangular faces) Group B Solids having base of some shape and just a point as a top, called apex .
16. SOLIDS Dimensional parameters of different solids. Top Rectangular Face Longer Edge Base Edge of Base Corner of base Corner of base Triangular Face Slant Edge Base Apex Square Prism Square Pyramid Cylinder Cone Edge of Base Base Apex Base Generators Imaginary lines generating curved surface of cylinder & cone. Sections of solids( top & base not parallel) Frustum of cone & pyramids. ( top & base parallel to each other)
17. X Y STANDING ON H.P On it’s base. RESTING ON H.P On one point of base circle. LYING ON H.P On one generator. (Axis perpendicular to Hp And // to Vp.) (Axis inclined to Hp And // to Vp) (Axis inclined to Hp And // to Vp) While observing Fv, x-y line represents Horizontal Plane. (Hp) Axis perpendicular to Vp And // to Hp Axis inclined to Vp And // to Hp Axis inclined to Vp And // to Hp X Y F.V. F.V. F.V. T.V. T.V. T.V. While observing Tv, x-y line represents Vertical Plane. (Vp) STANDING ON V.P On it’s base. RESTING ON V.P On one point of base circle. LYING ON V.P On one generator.
18. STEPS TO SOLVE PROBLEMS IN SOLIDS Problem is solved in three steps: STEP 1: ASSUME SOLID STANDING ON THE PLANE WITH WHICH IT IS MAKING INCLINATION. ( IF IT IS INCLINED TO HP, ASSUME IT STANDING ON HP) ( IF IT IS INCLINED TO VP, ASSUME IT STANDING ON VP) IF STANDING ON HP - IT’S TV WILL BE TRUE SHAPE OF IT’S BASE OR TOP: IF STANDING ON VP - IT’S FV WILL BE TRUE SHAPE OF IT’S BASE OR TOP. BEGIN WITH THIS VIEW: IT’S OTHER VIEW WILL BE A RECTANGLE ( IF SOLID IS CYLINDER OR ONE OF THE PRISMS) : IT’S OTHER VIEW WILL BE A TRIANGLE ( IF SOLID IS CONE OR ONE OF THE PYRAMIDS): DRAW FV & TV OF THAT SOLID IN STANDING POSITION: STEP 2 : CONSIDERING SOLID’S INCLINATION ( AXIS POSITION ) DRAW IT’S FV & TV. STEP 3 : IN LAST STEP, CONSIDERING REMAINING INCLINATION, DRAW IT’S FINAL FV & TV. AXIS VERTICAL AXIS INCLINED HP AXIS INCLINED VP AXIS VERTICAL AXIS INCLINED HP AXIS INCLINED VP AXIS INCLINED VP AXIS INCLINED HP AXIS INCLINED VP AXIS INCLINED HP GENERAL PATTERN ( THREE STEPS ) OF SOLUTION: GROUP B SOLID. CONE GROUP A SOLID. CYLINDER GROUP B SOLID. CONE GROUP A SOLID. CYLINDER Three steps If solid is inclined to Hp Three steps If solid is inclined to Hp Three steps If solid is inclined to Vp Study Next Twelve Problems and Practice them separately !! Three steps If solid is inclined to Vp AXIS TO VP er AXIS TO VP er
19. PROBLEM NO.1, 2, 3, 4 GENERAL CASES OF SOLIDS INCLINED TO HP & VP PROBLEM NO. 5 & 6 CASES OF CUBE & TETRAHEDRON PROBLEM NO. 7 CASE OF FREELY SUSPENDED SOLID WITH SIDE VIEW. PROBLEM NO. 8 CASE OF CUBE ( WITH SIDE VIEW) PROBLEM NO. 9 CASE OF TRUE LENGTH INCLINATION WITH HP & VP. PROBLEM NO. 10 & 11 CASES OF COMPOSITE SOLIDS. (AUXILIARY PLANE) PROBLEM NO. 12 CASE OF A FRUSTUM (AUXILIARY PLANE) CATEGORIES OF ILLUSTRATED PROBLEMS!
20. X Y a b c d o o’ d’ c’ b’ a’ o 1 d 1 b 1 c 1 a 1 a’ 1 d’ 1 c’ 1 b’ 1 o’ 1 (APEX NEARER TO V.P) . (APEX AWAY FROM V.P.) o’ d’ c’ b’ a’ o 1 d 1 b 1 c 1 a 1 o 1 d 1 b 1 c 1 a 1 Problem 1. A square pyramid, 40 mm base sides and axis 60 mm long, has a triangular face on the ground and the vertical plane containing the axis makes an angle of 45 0 with the VP. Draw its projections. Take apex nearer to VP Solution Steps : Triangular face on Hp , means it is lying on Hp: 1.Assume it standing on Hp. 2.It’s Tv will show True Shape of base( square) 3.Draw square of 40mm sides with one side vertical Tv & taking 50 mm axis project Fv. ( a triangle) 4.Name all points as shown in illustration. 5.Draw 2 nd Fv in lying position I.e.o’c’d’ face on xy. And project it’s Tv. 6.Make visible lines dark and hidden dotted, as per the procedure. 7.Then construct remaining inclination with Vp ( Vp containing axis ic the center line of 2 nd Tv.Make it 45 0 to xy as shown take apex near to xy, as it is nearer to Vp) & project final Fv. For dark and dotted lines 1.Draw proper outline of new view DARK. 2. Decide direction of an observer. 3. Select nearest point to observer and draw all lines starting from it-dark. 4. Select farthest point to observer and draw all lines (remaining)from it- dotted.
21. Problem 2: A cone 40 mm diameter and 50 mm axis is resting on one generator on Hp which makes 30 0 inclination with Vp Draw it’s projections. h a b c d e g f X Y a’ b’ d’ e’ c’ g’ f’ h’ o’ o 1 o 1 o 1 30 Solution Steps: Resting on Hp on one generator, means lying on Hp: 1.Assume it standing on Hp. 2.It’s Tv will show True Shape of base( circle ) 3.Draw 40mm dia. Circle as Tv & taking 50 mm axis project Fv. ( a triangle) 4.Name all points as shown in illustration. 5.Draw 2 nd Fv in lying position I.e.o’e’ on xy. And project it’s Tv below xy. 6.Make visible lines dark and hidden dotted, as per the procedure. 7.Then construct remaining inclination with Vp ( generator o 1 e 1 30 0 to xy as shown) & project final Fv. a’ h’b’ e’ c’g’ d’f’ o’ a 1 h 1 g 1 f 1 e 1 d 1 c 1 b 1 a 1 c 1 b 1 d 1 e 1 f 1 g 1 h 1 a’ 1 b’ 1 c’ 1 d’ 1 e’ 1 f’ 1 g’ 1 h’ 1 For dark and dotted lines 1.Draw proper outline of new vie DARK. 2. Decide direction of an observer. 3. Select nearest point to observer and draw all lines starting from it-dark. 4. Select farthest point to observer and draw all lines (remaining) from it- dotted.
22. X Y a b d c 1 2 4 3 45 0 35 0 Problem 3: A cylinder 40 mm diameter and 50 mm axis is resting on one point of a base circle on Vp while it’s axis makes 45 0 with Vp and Fv of the axis 35 0 with Hp. Draw projections.. Solution Steps: Resting on Vp on one point of base, means inclined to Vp: 1.Assume it standing on Vp 2.It’s Fv will show True Shape of base & top( circle ) 3.Draw 40mm dia. Circle as Fv & taking 50 mm axis project Tv. ( a Rectangle) 4.Name all points as shown in illustration. 5.Draw 2 nd Tv making axis 45 0 to xy And project it’s Fv above xy. 6.Make visible lines dark and hidden dotted, as per the procedure. 7.Then construct remaining inclination with Hp ( Fv of axis I.e. center line of view to xy as shown) & project final Tv. a b d c 1 2 4 3 a’ b’ c’ d’ 1’ 2’ 3’ 4’ 4’ 3’ 2’ 1’ d’ c’ b’ a’ 4’ 3’ 2’ 1’ d’ c’ b’ a’ a 1 b 1 c 1 d 1 1 2 3 4
23. b b 1 X Y a d c o d’ c’ b’ a’ o’ c 1 a 1 d 1 o 1 o’ 1 a’ 1 b’ 1 c’ 1 d’ 1 d’ c’ b’ a’ o’ c 1 b 1 a 1 d 1 o 1 Problem 4: A square pyramid 30 mm base side and 50 mm long axis is resting on it’s apex on Hp, such that it’s one slant edge is vertical and a triangular face through it is perpendicular to Vp. Draw it’s projections. Solution Steps : 1.Assume it standing on Hp but as said on apex.( inverted ). 2.It’s Tv will show True Shape of base( square) 3.Draw a corner case square of 30 mm sides as Tv(as shown) Showing all slant edges dotted, as those will not be visible from top. 4.taking 50 mm axis project Fv. ( a triangle) 5.Name all points as shown in illustration. 6.Draw 2 nd Fv keeping o’a’ slant edge vertical & project it’s Tv 7.Make visible lines dark and hidden dotted, as per the procedure. 8.Then redrew 2 nd Tv as final Tv keeping a 1 o 1 d 1 triangular face perpendicular to Vp I.e.xy. Then as usual project final Fv.
24. X Y 1’ p’ p’ Problem 5: A cube of 50 mm long edges is so placed on Hp on one corner that a body diagonal is parallel to Hp and perpendicular to Vp Draw it’s projections. b c d a a’ d’ c’ b’ a’ d’ c’ b’ a 1 b 1 d 1 c 1 a 1 b 1 d 1 c 1 a’ 1 d’ 1 c’ 1 d’ 1 Solution Steps: 1.Assuming standing on Hp, begin with Tv,a square with all sides equally inclined to xy.Project Fv and name all points of FV & TV. 2.Draw a body-diagonal joining c’ with 3’( This can become // to xy) 3.From 1’ drop a perpendicular on this and name it p’ 4.Draw 2 nd Fv in which 1’-p’ line is vertical means c’-3’ diagonal must be horizontal. .Now as usual project Tv.. 6.In final Tv draw same diagonal is perpendicular to Vp as said in problem. Then as usual project final FV. 1’ 3’ 1’ 3’
25. Y X T L 90 0 c’ 1 Problem 6: A tetrahedron of 50 mm long edges is resting on one edge on Hp while one triangular face containing this edge is vertical and 45 0 inclined to Vp. Draw projections. a o b c b’ a’ c’ o’ a’ a 1 c 1 o 1 b 1 a 1 o 1 b 1 45 0 c 1 b’ c’ o’ a’ 1 o’ 1 b’ 1 IMPORTANT: Tetrahedron is a special type of triangular pyramid in which base sides & slant edges are equal in length. Solid of four faces. Like cube it is also described by One dimension only.. Axis length generally not given. Solution Steps As it is resting assume it standing on Hp. Begin with Tv , an equilateral triangle as side case as shown: First project base points of Fv on xy, name those & axis line. From a’ with TL of edge, 50 mm, cut on axis line & mark o’ (as axis is not known, o’ is finalized by slant edge length) Then complete Fv. In 2 nd Fv make face o’b’c’ vertical as said in problem. And like all previous problems solve completely.
26. CG CG FREELY SUSPENDED SOLIDS: Positions of CG, on axis, from base, for different solids are shown below. H H/2 H/4 GROUP A SOLIDS ( Cylinder & Prisms) GROUP B SOLIDS ( Cone & Pyramids)