Engineering Drawing

1.Introduction

Drawing is the act or art of creating a picture, diagram, or representation using lines, typically with a pencil, pen, or crayon. Drawing represents objects on a two-dimensional sheet. These objects can be real or imagined by engineers, technicians, or designers.

Drawings are classified into two main types:

1.     Artistic Drawing: Created by artists based on imagination, without strict rules. Different people may interpret these drawings differently.

2.     Engineering Drawing: Created by engineers or technicians following standard rules, providing clear and consistent information about objects. It’s considered a universal graphic language.

For example, an engineering drawing of a rectangle with a circle inside it can clearly show the shape, size, and location of the objects. Complete engineering drawings also include details like material, surface finish, and tolerances.

Importance: Engineering drawings convey information more clearly than written descriptions.

1.1 Types of Engineering Drawing:

1.     Freehand Sketch: Drawn without instruments.

2.     Instrumental Drawing: Drawn using instruments for accuracy.

3.     Computer-Aided Drawing (CAD): Created using software like AutoCAD.

1.2 Drawing Instruments

1.3 Preparation for Drawing

Preparation is a critical step that sets the foundation for a successful drawing:

@ Setting Up the Drawing Board: Secure the drawing paper using clips or tape to ensure it doesn’t move during the drawing process.

@ Cleaning Instruments: Ensure all drawing tools are clean and in good working condition to avoid smudges and inaccuracies.

@ Planning the Layout: Decide on the scale and layout of the drawing. This includes determining the placement of views (e.g., top, front, side) and ensuring there is enough space for dimensions and notes.

1.4 Line Types:

1.5  Size of Drawing Paper

1.6  Scales

In engineering drawing, scales are used to represent objects proportionally on a drawing sheet. Here are the main types:

1. Full-Size Scale (1:1): The drawing size is the same as the actual object.

2. Reducing Scale: The drawing is smaller than the actual object. Examples: 1:2, 1:5, 1:10 (1 unit on the drawing equals 2, 5, or 10 units in real life).

3. Enlarging Scale: The drawing is larger than the actual object. Examples: 2:1, 5:1, 10:1 (2, 5, or 10 units on the drawing equal 1 unit in real life).

These scales help fit large objects onto a sheet or enlarge small details for clarity.

1.7 Dimensioning

Dimensioning is crucial in engineering drawings to convey the exact size, shape, and location of different parts and features. Types of dimensioning line:

1.     Dimension Lines: These lines indicate the size of an object. They are drawn with arrowheads at each end, pointing to the extension lines, and a numerical value in the middle. For example, if you’re drawing a bolt, the dimension line will show its length and diameter.

2.     Extension Lines: These lines extend from the object to the dimension lines, showing the exact points being measured. They start a small distance away from the object to avoid clutter and ensure clarity. For instance, if you’re dimensioning a hole, the extension lines will extend from the edges of the hole to the dimension line.

3.     Leader Lines: These lines point to specific features and provide additional information, such as notes or labels. They are often used for details that cannot be easily dimensioned directly on the drawing. For example, a leader line might point to a surface finish or a specific material requirement.

These elements ensure that the drawing conveys all necessary information for manufacturing or construction accurately, making it possible for engineers and builders to understand and execute the design precisely.

2.Geometrical Construction

2.1 Construction Involving Lines and Angles

Geometric constructions involving lines and angles are fundamental in engineering drawing. These constructions use basic tools like a compass and straightedge to create precise shapes and angles without numerical measurements.

1.     Line Segment Bisector: To bisect a line segment, place the compass at one end of the segment and draw arcs above and below the line. Repeat from the other end, and draw a line through the intersection points of the arcs.

2.     Perpendicular Bisector: Similar to the line segment bisector, but the line drawn through the intersection points will be perpendicular to the original segment.

3.     Angle Bisector: To bisect an angle, draw an arc across both rays of the angle. From the points where the arc intersects the rays, draw two arcs that intersect each other. Draw a line from the vertex of the angle through the intersection of these arcs.

4.     Constructing Parallel Lines: Using a set square or a compass, draw a line parallel to a given line through a specific point.

2.2 Construction of Polygons

Constructing polygons involves creating shapes with a specific number of sides, all of which are equal in length.

1.     Equilateral Triangle: Draw a line segment and use a compass to draw arcs from each endpoint. The intersection of the arcs forms the third vertex.

2.     Square: Draw a line segment, then use a set square to draw perpendicular lines from each endpoint. Measure the same length on these perpendicular lines to form the other vertices.

3.     Regular Pentagon: Use a protractor to measure and mark angles of 72° from a central point, then connect these points to form the pentagon.

4.     Hexagon: Draw a circle and use the compass to step off six equal arcs along the circumference. Connect these points to form the hexagon.

2.3 Construction Using Circular Arcs and Tangents

Circular arcs and tangents are essential for creating smooth curves and transitions in engineering drawings.

1.     Constructing Tangents: To draw a tangent from a point outside a circle, draw a line from the point to the circle’s center. Bisect this line and draw a circle with the midpoint as the center and the radius equal to half the line segment. The points where this circle intersects the original circle are the points of tangency.

2.     Drawing Arcs: Use a compass to draw arcs with specific radii. For compound curves, draw multiple arcs with different radii that are tangent to each other.

2.4 Construction of Conic Sections

Conic sections include ellipses, parabolas, and hyperbolas, which are formed by the intersection of a plane with a cone.

1.     Ellipse: Use the string method, where two pins are placed at the foci of the ellipse, and a string is looped around them. Keeping the string taut, trace the ellipse with a pencil.

2.     Parabola: Use the focus-directrix method, where a point (focus) and a line (directrix) are given. Draw perpendicular lines from the directrix and use the distance from the focus to determine points on the parabola.

3.     Hyperbola: Similar to the ellipse, but with two foci and a different set of geometric properties.

2.5 Construction of Standard Curves

Standard curves are used in various engineering applications to represent data or design elements.

1.     S-Curves: Used in project management to represent cumulative progress over time. The curve starts slowly, accelerates in the middle, and slows down towards the end.

2.     Calibration Curves: Used in scientific experiments to determine the concentration of unknown samples by comparing them to a set of standard samples.

3.     Bezier Curves: Used in computer graphics and CAD software to create smooth, scalable curves defined by control points.

3.DESCRIPTIVE GEOMETRY

3.1 Meaning of Projection

Projection is a fundamental concept in descriptive geometry, used to represent three-dimensional objects on two-dimensional surfaces. This is essential for technical drawing, engineering, and architecture. There are two main types of projection:

1.     Orthographic Projection: This involves projecting points from the object perpendicular to the projection plane. It includes views like front, top, and side.

2.      Perspective Projection: This involves projecting points from the object to a single point (the eye or camera), creating a more realistic view but with distortion.

3.2 Planes of Projection

Planes of projection are the reference planes used to create different views of an object. Let’s consider a cube as an example:

JHorizontal Plane (HP): Imagine placing the cube on a table. The table represents the HP. The top view of the cube is projected onto this plane.

JVertical Plane (VP): Imagine standing the cube against a wall. The wall represents the VP. The front view of the cube is projected onto this plane.

JProfile Plane (PP): Imagine a plane perpendicular to both the table and the wall. The side view of the cube is projected onto this plane.

3.3  Dihedral Angles or Quadrants

Dihedral angles are the angles formed between two intersecting planes. In descriptive geometry, the space around an object is divided into four quadrants by the intersection of the HP and VP:

First Quadrant: Above the HP and in front of the VP. This is the most commonly used quadrant in technical drawing.

Second Quadrant: Above the HP and behind the VP.

Third Quadrant: Below the HP and behind the VP.

Fourth Quadrant: Below the HP and in front of the VP.

3.4 Projection of a Point

To project a point, you need to determine its position relative to the projection planes. For example, consider a point (P) located 5 units above the HP and 3 units in front of the VP:

Horizontal Projection: Drop a perpendicular from (P) to the HP. The point where it intersects the HP is the horizontal projection.

Vertical Projection: Drop a perpendicular from (P) to the VP. The point where it intersects the VP is the vertical projection.

3.5 Projection of Straight Lines

Projecting straight lines involves projecting the endpoints of the line onto the projection planes and connecting these projections:

True Length: The actual length of the line in space. For example, a line segment (AB) with endpoints (A (2, 3, 5)) and (B (5, 7, 9)) has a true length calculated using the distance formula.

Apparent Length: The length of the line as seen in the projection. For instance, the top view of (AB) might show a shorter length due to the angle of projection.

3.6 Projection of Planes

Projecting planes involves projecting the edges of the plane onto the projection planes. This helps in understanding the true shape and size of the plane:

Edge View: When the plane is seen edge-on, it appears as a line. For example, a rectangular plane parallel to the VP will appear as a line in the top view.

True Shape: When the plane is parallel to the projection plane, its true shape is visible. For instance, a rectangular plane parallel to the HP will show its true shape in the top view

4.Application of Descriptive Geometry

Descriptive geometry is a branch of geometry that allows the representation of three-dimensional objects in two dimensions. It is essential in fields like engineering, architecture, and design for solving spatial problems and visualizing complex structures.

4.1 Lines and Perpendicular Lines

In descriptive geometry, lines are fundamental elements. Understanding their properties and relationships is crucial:

Perpendicular Lines: Two lines are perpendicular if they intersect at a right angle (90°). This is often used in constructing orthogonal projections and ensuring structural integrity in designs.

Oblique Line: An oblique line is neither parallel nor perpendicular to a given plane. It intersects the plane at an angle other than 90°. Understanding oblique lines is essential for visualizing and solving problems involving inclined surfaces.

4.2 Point View

The point view of a line is the view where the line appears as a point. This occurs when the line is viewed along its length. It is useful for determining the true length of the line and its orientation in space.

4.3 Shortest Distance

The shortest distance between two geometric entities (points, lines, planes) is a critical concept in descriptive geometry:

Between a Point and a Line: The shortest distance is the perpendicular distance from the point to the line.

Between Skew Lines: Skew lines are non-parallel, non-intersecting lines. The shortest distance between them is the length of the perpendicular segment connecting them.

4.4 Edge View of an Oblique Plane

The edge view of an oblique plane is the view where the plane appears as a line. This is achieved by projecting the plane onto a plane perpendicular to its normal. It helps in understanding the plane’s orientation and true shape.

4.5 True Shape of an Oblique Plane

The true shape of an oblique plane is obtained by projecting it onto a plane parallel to it. This view reveals the actual dimensions and shape of the plane, which is crucial for accurate design and analysis.

4.6 True Angle Between Two Intersecting Lines

The true angle between two intersecting lines is the angle measured in a plane perpendicular to the lines’ intersection. This is important for understanding the spatial relationship between the lines.

4.7 Intersection Between a Line and a Plane

The intersection between a line and a plane is a point where the line penetrates the plane. This concept is used to determine where structural elements intersect and how they fit together.

4.8 True Angle Between a Line and a Plane

The true angle between a line and a plane is the angle between the line and its projection onto the plane. This helps in understanding how inclined a line is relative to a plane.

4.9 True Angle Between Two Planes

The true angle between two planes is the dihedral angle formed by the planes. It is measured by projecting the planes onto a common line of intersection. This is essential for visualizing and constructing complex surfaces.

4.10 Shortest Distance Between Skew Lines

The shortest distance between skew lines is found by constructing a perpendicular segment connecting the lines. This distance is crucial for ensuring proper clearance and avoiding collisions in designs.

4.11 True Angle Between Skew Lines

The true angle between skew lines is the angle between their projections onto a plane perpendicular to the shortest distance segment. This angle helps in understanding the spatial relationship between the lines.

5.Multiview Drawings

Multiview drawings are essential in technical fields like engineering and architecture. They provide a comprehensive way to represent three-dimensional objects on two-dimensional planes, allowing for precise communication of an object’s dimensions and shape.

5.1 Classification of Projections

Projections are classified based on how the views are generated:

Orthographic Projection: This involves projecting views perpendicular to the projection plane. It includes front, top, and side views.

Axonometric Projection: This includes isometric, dimetric, and trimetric projections, where the object is rotated along one or more of its axes relative to the plane of projection.

Oblique Projection: The object is projected with one face parallel to the projection plane, and the other faces are projected at an angle.

5.2 Systems of Orthographic Projection

Orthographic projection systems are used to create multiview drawings:

First-Angle Projection: Commonly used in Europe and Asia. The object is placed in the first quadrant, and views are projected onto planes that are behind and below the object.

Third-Angle Projection: Commonly used in the United States and Canada. The object is placed in the third quadrant, and views are projected onto planes that are in front of and above the object.

5.3 Comparison Between First Angle and Third Angle Projections

JFirst Angle Projection: The right view is placed on the left side of the front view, and the top view is placed below the front view.

JThird Angle Projection: The right view is placed on the right side of the front view, and the top view is placed above the front view.

5.4 Types of Views

Multiview drawings typically include several types of views:

Principal Views: Front, top, and right-side views.

Auxiliary Views: Used to show features that are not parallel to the principal planes.

Section Views: Used to show internal features by cutting through the object.

Detail Views: Enlarged views of small or complex features.

5.5 Procedure for Making a Multiview Drawing

Select the Views: Choose the views that best describe the object.

Draw the Front View: Start with the front view, which is the most descriptive.

Project the Other Views: Use projection lines to create the top and side views.

Add Dimensions: Include all necessary dimensions to fully describe the object.

Check for Accuracy: Ensure all views are aligned and accurately represent the object.

5.6 Precedence of Lines

In multiview drawings, certain lines take precedence over others:

Visible Lines: Represent the edges of the object that are visible in the view.

Hidden Lines: Represent edges that are not visible in the view.

Center Lines: Represent the axes of symmetry or paths of motion.

Dimension Lines: Indicate the size and location of features.

6.Sectional Views

Sectional views are used in technical drawings to reveal the interior features of an object that are not visible from the outside. By cutting through the object and removing a portion, sectional views provide a clearer understanding of complex internal structures.

6.1 Full Sectional View

A full sectional view is created by cutting through the entire object along a single plane. This type of view is useful for showing the complete internal structure of the object. For example, a full section of a cylindrical object would show the internal features along the entire length of the cylinder.

6.2  Half Sectional View

A half sectional view involves cutting through only half of the object. This is typically used for symmetrical objects, where one half shows the internal features and the other half shows the external features. This type of view is particularly useful for objects like gears or bearings.

6.3 Offset Sectional View

An offset sectional view is used when the internal features are not aligned along a single plane. The cutting plane is “offset” or bent to pass through these features. This allows for a more comprehensive view of the internal components without having to create multiple sectional views.

6.4 Hatching Lines

Hatching lines, or section lines, are used to indicate the areas of the object that have been cut through. These lines are typically drawn at a 45-degree angle and spaced evenly. Different materials can be represented by varying the pattern and spacing of the hatching lines.

6.5  Exceptional Rules of Sectional Views

There are several rules and conventions to follow when creating sectional views:

1. Do not section thin parts: Thin parts like washers or gaskets are not sectioned as they would appear as solid lines.

2. Do not section standard parts: Standard parts like bolts, nuts, and screws are not sectioned to avoid cluttering the drawing.

3. Aligned sections: Features that are not aligned with the cutting plane can be rotated into the plane for clarity.

7.Auxiliary Views

Auxiliary views are used in technical drawings to show the true size and shape of inclined or oblique surfaces that cannot be accurately represented in the principal views (front, top, and side). These views are essential for providing a complete understanding of complex geometries.

7.1  Procedure for Drawing an Auxiliary View

Creating an auxiliary view involves several steps:

1.     Identify the Inclined Surface: Determine which surface of the object needs to be shown in true size and shape.

2.     Draw the Principal Views: Start with the orthographic views (front, top, and side) of the object.

3.     Project Perpendicular Lines: From the inclined surface, draw projection lines perpendicular to the surface.

4.     Establish a Reference Line: Draw a reference line (fold line) parallel to the inclined surface.

5.     Transfer Measurements: Measure distances from the principal views and transfer them to the auxiliary view along the projection lines.

6.     Complete the Auxiliary View: Connect the transferred points to form the true shape of the inclined surface.

7.2 Unilateral and Bilateral Auxiliary Views

Unilateral Auxiliary Views: These views are projected on one side of the reference line. They are used when the inclined surface is only on one side of the object.

Bilateral Auxiliary Views: These views are projected on both sides of the reference line. They are used when the inclined surface extends across the entire object.

7.3 Projection of Curved Surfaces on an Inclined Surface

Projecting curved surfaces onto an inclined plane involves:

Identify Key Points: Select key points along the curved surface.

Project Points: Draw projection lines from these points perpendicular to the inclined plane.

Transfer Points: Transfer the distances from the principal views to the auxiliary view.

Connect Points: Connect the transferred points to form the true shape of the curved surface on the inclined plane.

8.Development of Surfaces

The development of surfaces involves unfolding or unrolling a three-dimensional object into a two-dimensional plane. This process is crucial in manufacturing, sheet metal work, and various engineering applications where flat patterns are cut and then formed into complex shapes.

8.1 Classification of Solids

Solids can be classified based on their geometric properties:

Polyhedral: Solids with flat polygonal faces, such as cubes and pyramids.

Curved Solids: Solids with curved surfaces, such as cylinders, cones, and spheres.

8.2 Axis of the Solid, Right Solid, and Oblique Solid

Axis of the Solid: The straight line around which the solid is symmetrically arranged.

Right Solid: A solid whose axis is perpendicular to its base, like a right cylinder or right cone.

Oblique Solid: A solid whose axis is not perpendicular to its base, resulting in a slanted appearance.

8.3  Frustum of Solid and Truncated Solids

Frustum of a Solid: The portion of a solid that remains after cutting it with a plane parallel to its base. For example, a frustum of a cone is created by slicing off the top part.

Truncated Solids: Solids that are cut by a plane that is not parallel to the base, resulting in a slanted cut.

8.4 Projection of Right Solids

The projection of right solids involves representing the solid on a plane using orthographic projection. This helps in visualizing the true shape and size of the solid’s faces.

8.5 Projection of Oblique Solids

Projecting oblique solids can be more complex due to their slanted nature. The projection must account for the angles and dimensions accurately to represent the true shape.

8.6  Projections of a Sphere

A sphere is projected as a circle in any orthographic view. However, the true shape and size of sections through the sphere can be represented using auxiliary views.

8.7 Projection of Points on the Surfaces of the Solids

Projecting points on the surfaces of solids involves determining their exact location on the developed surface. This is essential for accurate pattern making and fabrication.

8.8 Development of Right Solids

The development of right solids involves unfolding the surfaces into a flat plane. For example, the development of a cylinder results in a rectangle (the side) and two circles (the bases).

8.9 Development of Frustums of Right Solids

Developing frustums of right solids involves creating a pattern that includes the truncated top and the base, along with the slanted sides.

8.10 Development of Truncated Right Solids

The development of truncated right solids requires careful measurement of the slanted cut to ensure the pattern accurately represents the solid’s shape.

8.11 Development of Oblique Solids

Developing oblique solids is more complex due to their slanted nature. The pattern must account for the angles and dimensions to ensure an accurate representation.

8.12 Development of a Sphere

The development of a sphere is typically done using gores or segments, which are pie-shaped pieces that can be assembled to form the sphere.

9.Intersection of Solids

The intersection of solids involves determining the common volume or surface where two or more solids meet. This is crucial in engineering and design for understanding how different components fit together and interact.

9.1  Classification of Intersection Curves

Intersection curves can be classified based on the types of solids involved:

Linear Intersections: Where the intersection forms straight lines.

Curved Intersections: Where the intersection forms curved lines, such as ellipses or parabolas.

9.2 Nature of Intersection Curves

The nature of intersection curves depends on the geometry of the intersecting solids:

Simple Intersections: Involve basic shapes like cylinders and prisms.

Complex Intersections: Involve more intricate shapes like cones and spheres.

9.3 Intersection of Cylinder and Cylinder

When two cylinders intersect, the intersection curve is typically an ellipse. This can be visualized by projecting the cylinders onto a plane and finding the points of intersection.

9.4 Intersection of Prism and Prism

The intersection of two prisms results in a polygonal line. This is determined by projecting the edges of one prism onto the faces of the other and connecting the points of intersection.

9.5 Intersection of Cylinder and Prism

The intersection of a cylinder and a prism involves projecting the circular base of the cylinder onto the faces of the prism. The resulting intersection curve can be a combination of straight and curved lines.

9.6 Intersection of Cone and Cylinder

The intersection of a cone and a cylinder typically results in a conic section, such as an ellipse or a hyperbola. This is determined by projecting the cone’s surface onto the cylinder.

9.7 Intersection of Pyramid and Prism

The intersection of a pyramid and a prism involves projecting the edges of the pyramid onto the faces of the prism. The resulting intersection curve is a series of straight lines connecting the points of intersection

9.8 Intersection of Cone and Prism

The intersection of a cone and a prism results in a combination of straight and curved lines. This is determined by projecting the cone’s surface onto the faces of the prism.

9.9 Intersection of Pyramid and Cylinder

The intersection of a pyramid and a cylinder involves projecting the edges of the pyramid onto the curved surface of the cylinder. The resulting intersection curve can be complex, involving both straight and curved lines.

9.10 Intersection of Inclined Cylinders

When two inclined cylinders intersect, the intersection curve is typically more complex and can involve multiple conic sections. This requires careful projection and measurement to determine accurately.

9.11 Intersection of Solids with their Axes Offset

When solids with offset axes intersect, the intersection curve is more complex due to the misalignment. This requires advanced projection techniques to accurately determine the points of intersection.

9.12 Effect of Intersection on Any Object

The intersection of solids affects the overall geometry and structural integrity of the object. Understanding these intersections is crucial for ensuring proper fit and function in assemblies.