# TECHNICAL GRAPHICS COMMUNICATION 4TH EDITION PDF

TECHNICAL GRAPHICS COMMUNICATIONS, FOURTH EDITION. Published by PDF format for viewing and printing hard copies. These problems include. TECHNICAL GRAPHICS COMMUNICATION FOURTH EDITION by Gary R. Bertoline. Postado por Green Mechanic. No comments: Post a Comment. Technical Graphics Communication 4th Ed - Gary R. Bertoline (Free Download PDF). In its fourth edition, Technical Graphics Communication.

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In its fourth edition, Technical Graphics Communication has become a standard in the field of engineering and technical graphics. This text presents both. Editorial Reviews. About the Author. Gary Bertoline is the Associate Vice President for Technical Graphics Communication 4th Edition, Kindle Edition. by Gary. Technical Graphics Communication -> Gary Robert Bertoline Pdf In its fourth edition, Technical Graphics Communication has become a.

Mark the diagonals at two-thirds the distance from the center of the circle to the corner of the square. Sketch the circle by creating eight short arcs, each between two adjacent marks on the perimeter. Start at any mark and sketch an arc to the next mark on either side of the first one, whichever is most comfort-able for you. Rotate the paper and sketch the next arc from the last mark you touched to the next mark on the perimeter. Repeat this step until all eight arc segments have been sketched.

For smoother sketches, rotate the paper in the opposite direction from the one you used to draw the arc. Overdraw the arcs with a thick, black, more contin-uous line to complete the sketched circle. For small circles, use a square A or multiple center lines B C to guide the construction process. For large circles, use a scrap of paper with the radius marked on it as a guide D.

A proportion is the ratio between any two dimensions of an object. These proportions are represented in the sketch by a series of preliminary lines, which are drawn light and fast, and which may or may not represent the locations of the final lines in the sketch. Their purpose is to form a backbone, a structure inside which the final linework can be drawn.

Construction lines are very light, thin lines used to roughly lay out some of the details of sketches or drawings. Do not try to draw the construction lines to exact lengths since lengths are marked later, either by intersecting lines or short tick marks.

Construction lines have two primary features: For example, the construction lines become the paths for the final straight lines. Points marked by the inter-sections of construction lines guide the drawing of circles. Usually, both of these features are used in creating sketches. Since all the dimensions of a sketch are estimated, groups of construction lines forming boxes and other shapes are an important tool for preserving the shape and proportion of the object and its features as the sketch is developed.

Grid paper can be used as a guide in creating construc-tion lines but should not be thought of as a substitute, since the grid does not directly represent the proportions of the object, and there are many more grid lines than there are features on the object. The goal is to draw con-struction lines on top of the grid to reveal the form of the object.

With experience, you may be able to make do with fewer construction lines, but while you are learning how to create properly proportioned sketches, you should use more, rather than fewer, construction lines to guide you.

Each feature has a proportion that can be represented by a series of construction lines. The following steps describe how to proportion a drawing by breaking it down into its component features. Creating a Proportioned Sketch Step 1.

Gage the proportion of the overall size of the object. For the first sketch, use two over-all dimensions of the object: Lightly sketch a box that represents the ratio of these two dimen-sions Figure 2. This box is called a bounding box because it represents the outer dimensional limits of the feature being drawn.

If the object is rectangular in shape, the final linework will follow the perimeter of the bounding box. Inside the first bounding box, draw other boxes to represent the larger features of the object, and within those boxes draw still others to represent the smaller features of the object. Often, a construction line can be used for more than one box. The final boxes each show the proportions of one feature of the object. Continue to draw bounding boxes until the smallest features of the object have been represented.

As you gain experience, you may find that some of these smaller fea-tures need not be boxed; instead, their final lines can be sketched directly. When all of the features of the object have been boxed, begin sketching the final linework, which is done significantly darker than the construction lines. If there is not enough contrast between the construction lines and the final linework, then the con-struction lines become a distraction.

Make the final lines darker, or the construction lines lighter, or both; however, do not erase your construction lines. One of the most difficult sketching techniques to learn is making a sketch look well proportioned. For example, Figure 2. Proportioning skills will improve with practice.

A good rule of thumb is, if the drawing does not look or feel right, it probably is not. In the poorly proportioned monitor in Figure 2.

We live in a three-dimensional 3-D world, and representing that world for artistic or technical purposes is largely done on two-dimensional 2-D media.

Although a sheet of paper is technically three-dimensional, the thickness of the paper the third dimension is useless to us. It should be noted that the computer screen is a form of two-dimensional medium, and images projected on it are governed by the same limita-tions as projections on paper.

Modern techniques, such as holograms, stereograms, and virtual reality devices, are attempts to communicate three-dimensional ideas as three-dimensional forms. However, drawings are still the primary tool used for representing 3-D objects. Most projection methods were developed to address the problem of trying to represent 3-D images on 2-D media Figure 2. Projection theory and methods have taken hundreds of years to evolve, and engineering and technical graphics is heavily dependent on projection theory.

The poorly proportioned monitor looks too wide. Various projection techniques have evolved to solve this problem. Sketching Objects Step 1. Collect magazine photographs or clippings that show 2-D images or patterns. These can range from pic-tures of faces, to company logos, to fronts of buildings, etc. Lay tracing paper over an image and tape the paper down. Lightly sketch an overall bounding box of the object. Look at the image contained in the bounding box.

Mentally identify as many features on the object as you can. The features may be small and self-contained or a collection of several smaller features. Refine the drawing by sketching a series of pro-gressively smaller bounding boxes. Start with the larger features and work downward. If desired, you can then darken some of the lines rep-resenting the image, to highlight the most important lines of a feature. What are the most important lines of a feature?

Experiment with different lines to see which are more critical than others in representing the form of the image. Buy a roll of tracing paper from your local blueprint or art supply store. These four types of projection can be placed in two major categories: The other three types of projection, grouped as pictorial sketches, present the object in a single, pictorial view, with all three dimensions repre-sented.

There are always trade-offs when using any type of projection; some are more realistic, some are easier to draw, and some are easier to interpret by nontechnical people.

Axonometric projection is a parallel projection tech-nique used to create a pictorial drawing of an object by rotating the object on an axis relative to a projection, or pic-ture plane. In multiview, axonometric, and oblique projec-tion, the observer is theoretically infinitely far away from the projection plane.

In addition, for multiviews and axono-metric projections the lines of sight are perpendicular to the plane of projection; therefore, both are considered orthographic projections. The differences between multi-view drawing and an axonometric drawing are that, in a multiview, only two dimensions of an object are visible on each view and more than one view is required to define the object, whereas in an axonometric drawing, the object is rotated about an axis to display all three dimensions, and only one view is required.

Axonometric drawings are classified by the angles between the lines comprising the axonometric axes. The axonometric axes are axes that meet to form the corner of the object that is nearest to the observer. When all three angles are unequal, the drawing is clas-sified as a trimetric projection. When two of the three angles are equal, the drawing is classified as a dimetric projection. When all three angles are equal, the drawing is classified as an isometric equal measure projection.

Mechanically drawn pictorials can often be as hard to draw as multiviews. Various 2-D CAD-based tools have eased the process of creating pictorials. Probably the easiest way of creating such views is to use a 3-D CAD package to create a model.

This model can easily represent pictorial views and can also generate views for a multiview drawing. Another way of classifying projections relates to whether they use parallel projection or perspective projection. This type of projection is the basis of most engineering and technical graphics. Perspective projection distorts the object so that it more closely matches how you perceive it visually. Since it is much easier to lay out a sketch in parallel than in perspective projection, you will probably find yourself doing a majority of your sketching using parallel projection, even though it is less realistic.

Only when the object spans a large distance—such as a house or bridge—will it be useful to represent the distortion your eyes perceive as the object recedes from view. Although there are a number of ways of orienting an object to represent all three dimensions, isometric pictorials have a standard orientation that makes them particularly easy to sketch. Start by looking at the two-point perspective in Figure 2.

Then, instead of having the width and depth construction lines converge on vanishing points, have them project parallel to each other at a degree angle above the baseline Figure 2. The sketches shown in B, C, and D are called pictorial because they represent the object as a 3-D form. The multiview sketch uses multiple flat views of the 3-D object to accurately represent its form on 2-D paper.

Begin the sketch by extending the isometric axes shown in Step 1, Figure 2. Sketch a horizontal construc-tion line through the bottom of the vertical line. Sketch a line from the base of the vertical line to the right, at an approximate angle of 30 degrees above the horizontal construction line. Sketch a line from the base of the vertical line to the left, at an approximate angle of 30 degrees above the horizontal construction line.

The corner of the axis is labeled point 1; the end of the width line is labeled point 2; the end of the depth line is labeled point 4; and the top of the height line is labeled point 3. The lengths of these lines are not important, since they will be treated as con-struction lines, but they should be more than long enough to rep-resent the overall dimensions of the object.

Estimate the overall width, height, and depth of the object using the estimating tech-niques described earlier in this chapter. Use these dimensions to sketch a block that would completely enclose the object. Blocking in the object Step 3. Sketch in the front face of the object by sketching a line parallel to and equal in length to the width dimension, passing the new line through point 3.

Sketch a line parallel to and equal in length to the vertical line 1—3 , through points 5—2. The front face of the object is complete. From point 3, block in the top face of the object by sketching a line parallel to and equal in length to line 1—4.

This line is labeled 3—6. Sketch a line parallel to and equal in length to line 3—5, from point 6. This line is labeled 6—7. Sketch a line from point 5 to point 7. This line should be par-allel to and equal in length to line 3—6. Block in the right side face by sketching a line from point 6 to point 4, which is par-allel to line 1—3. The bounding box of the object, sketched as construction lines, is now finished. The box serves the same purpose as the one drawn in Figure 2.

Many CAD systems will automatically produce an isometric view of a 3-D model when the viewing angle is specified. Some CAD systems have predefined views, such as isometric, which are automatically created after selection. Making an Isometric Sketch Make an isometric sketch of the object shown in Figure 2. Sketching the isometric axis Step 1. Isometric sketches begin with defining an isometric axis, which is made of three lines, one vertical and two drawn at 30 degrees from the horizontal.

These three lines of the isometric axis represent the three primary dimensions of the object: Although they are sketched at an angle of only 60 degrees to each other, they represent mutually perpendicular lines in 3-D space. Begin by estimating the dimensions to cut out the upper front corner of the block, and mark these points as shown in Step 4. Sketch the height along the front face by creating a line parallel to line 1—2; label it 8—9.

Sketch degree lines from points 8 and 9 and label these lines 9—10 and 8— Now sketch a line from point 10 to point Sketch vertical lines from points 10 and 11 and label the new lines 10—12 and 11— Sketch a line from point 12 to point 13 to complete the front cutout of the block. With a simple sketch, you can often lay out all of your con-struction lines before having to darken in your final linework. CHAPTER 2 Sketching and Text 35 With more complicated sketches, the sheer number of con-struction lines can often cause confusion as to which line belongs to which feature.

The confusion can be worse in an isometric sketch, where the lines represent three dimensions rather than two. Therefore, after the marks are made for the last two features in Step 5, you can begin darkening in some of the lines representing the final form.

Estimate the distances to create the angled surface of the block, and mark these points, as shown in Step 5. From the marked point on line 11—13, sketch a degree line to the rear of the block on line 4—6. Label this new line 14— From the marked point on line 12—13, sketch a degree line to the rear of the block on line 6—7.

Label this new line 16— Sketch a line from point 14 to point 16 and from point 15 to point 17 to complete the sketching of the angled surface. Lines 14—16 and 15—17 are referred to as nonisometric lines because they are not parallel to the isometric axis.

Estimate the distances for the notch taken out of the front of the block, and mark these points, as shown in Step 5. Draw vertical lines from the marked points on line 1—2 and line 8—9. Label these lines 18—19 and 20—21, as shown in Step 6. Sketch degree lines from points 19, 20, and 21 to the estimated depth of the notch. Along the top surface of the notch, connect the endpoints of the degree lines, and label this new line 22— The degree line extending back from point 20 is stopped when it intersects line 18—19, as shown in Step 6.

To complete the back portion of the notch, drop a vertical line from point 22, as shown in Step 6. Stop this new line at the intersection point of line 19— The rough isometric sketch of the block is complete.

Note that we have not mentioned hidden features represent-ing details behind the visible surfaces. The drawing convention for isometric sketches calls for disregarding hidden features unless they are absolutely necessary to describe the object. Darken all visible lines to complete the isometric sketch. Since the construction lines are drawn light, there is no need to lighten them in the completed sketch.

The basic procedures are to determine the desired view, create the isometric axes, box in the object using the overall length, width, and depth dimensions from the three-view drawing Figure 2. Step by Step: Determine the desired view of the object, then sketch the isometric axes. Construct the front isometric plane using the W and H dimensions. Construct the top isometric plane using the W and D dimensions. Construct the right side isometric plane using the D and H dimensions. Determine dimensions X and Y from the front view and transfer them to the front face of the isomet-ric drawing.

Project distance X along an isometric line parallel to the W line. Project distance Y along an iso-metric line parallel to the H line. Point Z will be located where the projectors for X and Y intersect.

Sketch lines from point Z to the upper corners of the front face. Project point Z to the back plane of the box on an isometric line parallel and equal in length to the D line. Sketch lines to the upper corner of the back plane to complete the isometric sketch of the object. Notice that the degree angles do not measure 45 degrees in the isometric view. This is an example of why no angular measures are taken from a multiview to con-struct an isometric sketch.

In an isometric drawing, the object is viewed at an angle, which makes circles appear as ellipses. When sketching an isomet-ric ellipse, it is very important to place the major and minor axes in the proper positions.

Remember Figure 2. The following are the key features of the isometric ellipse on each plane: The orientation of the ellipse is set according to the face on which the circle lies.

The correct orientation is shown in A , and examples of incorrect orientations are shown in B. The center of the box and the midpoints of the sides are found, and arcs are then drawn to create the ellipse. Sketching an Isometric Cylinder Figure 2. Sketch the isometric axis. To sketch the bounding box for the cylinder, begin on one degree axis line and sketch an isometric square with sides equal to the diame-ter of the cylinder. This square will become the end of the cylinder.

Next, mark the length of the cylinder on the other degree axis line, and sketch the profile and top rectan-gles of the bounding box. For the profile rectangle, the length represents the length of the cylinder, and the height represents the diameter of the cylinder.

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For the top rectan-gle, again the length represents the length of the cylinder, but the width represents the diameter of the cylinder. Note that only three long edges of the bounding box are drawn the hidden one is not , and only two lines for the back end Sketching an Isometric Ellipse Figure 2.

Notice that the steps are almost identical to those for sketching a circle as explained earlier in this chapter. The difference is in the orientation and proportion of the primary axes. This isometric ellipse will be drawn on the front plane. Begin by sketching an isometric square whose sides are equal to the diameter of the circle.

Add construction lines across the diagonals of the square. The long diagonal is the major axis, and the short diagonal is the minor axis of the ellipse. The two diago-nals intersect at the center of the square, which is also the center of the isometric ellipse. Sketch construction lines from the midpoints of the sides of the square through the center point.

These lines represent the center lines for the isometric ellipse. The mid-points of the sides of the isometric square will be tangent points for the ellipse and are labeled points A, B, C, and D. Sketch short, elliptical arcs between points B and C and points D and A.

Finish the sketch by drawing the elliptical arcs between points C and D and points A and B, completing the ellipse. Isometric grid paper is made of vertical and degree grid lines, as shown in Figure 2.

There are two primary advantages to using isometric grid paper. First, there is the advantage obtained by using any kind of grid paper. This can be especially useful when transferring the dimensions of a fea-ture from one end of the object to the other.

Unlike square grid paper, each intersection on an isometric grid has three lines passing through it, one for each of the primary axis lines. This can create some confusion when counting out grid blocks for proportions. Just remember which axis line you are using and count every intersection as a grid block. The second advantage of the isometric grid is the assistance it provides in drawing along the primary axis lines.

Although estimating a vertical line is not difficult, estimating a degree line and keeping it consistent throughout the sketch is more challenging. Remember that the only dimensions that can be transferred directly to an isometric sketch are the three primary dimensions.

These dimensions will follow the lines of the grid paper. When blocking in an isometric sketch, lay out the dimensions on construction lines that run parallel to the grid lines. Angled surfaces are created using construction lines that are nonisometric; that is, they do not run paral-lel to any of the grid lines and are drawn indirectly by con-necting points marked on isometric construction lines.

Sketching Semi-Ellipses Figure 2. This isometric ellipse will be drawn on the profile plane. Begin by sketching an isometric square whose sides are equal to the diameter of the arc. Add construc-tion lines across the diagonals of the square.

The two diagonals intersect at the center of the square, which is also the center of the isometric ellipse. Sketch construc-tion lines from the midpoints of the sides of the square through the center point. The midpoints of the sides of the isometric square will be tangent points for the ellipse and are labeled points A, B, and C.

The long diagonal is the major axis, and the short diagonal is the minor axis. Sketch short, elliptical arcs between points B and C and points B and A, which creates the elliptical arc on the near side of the object.

The back part of the semi-ellipse can be sketched by con-structing degree parallel lines that are equal in length to the depth of the part, from points A, B, and C. Finish by darkening the final lines and lightening the construction lines. Some examples are given in Figure 2. Sketch objects with a variety of features. Some should require sketching isometric ellipses, while others should have angled surfaces that require nonisometric lines. Foreword This is a set of lecture notes on cryptography compiled for 6.

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Sketching a Circle or Arc The following steps demonstrate how to sketch a circle or arc. Refer to Figure 2. Orient the paper in a comfortable position and relax your grip on the pencil. Lightly mark the corners of a square with sides equal in length to the diameter of the circle or arc to be sketched.

Lightly sketch the square, using short strokes to create the straight lines. Mark the midpoints of the four sides of the square. This gives you four marks on the perimeter of the circle. Sketch diagonals across the corners of the square. Where the diagonals cross is the center of the circle.

Mark the diagonals at two-thirds the distance from the center of the circle to the corner of the square. Sketch the circle by creating eight short arcs, each between two adjacent marks on the perimeter. Start at any mark and sketch an arc to the next mark on either side of the first one, whichever is most comfortable for you.

Rotate the paper and sketch the next arc from the last mark you touched to the next mark on the perimeter. Repeat this step until all eight arc segments have been sketched. For smoother sketches, rotate the paper in the opposite direction from the one you used to draw the arc.

Overdraw the arcs with a thick, black, more continuous line to complete the sketched circle. For small circles, use a square A or multiple center lines B C to guide the construction process. For large circles, use a scrap of paper with the radius marked on it as a guide D. A proportion is the ratio between any two dimensions of an object. These proportions are represented in the sketch by a series of preliminary lines, which are drawn light and fast, and which may or may not represent the locations of the final lines in the sketch.

Their purpose is to form a backbone, a structure inside which the final linework can be drawn. Construction lines are very light, thin lines used to roughly lay out some of the details of sketches or drawings. Do not try to draw the construction lines to exact lengths since lengths are marked later, either by intersecting lines or short tick marks. Construction lines have two primary features: For example, the construction lines become the paths for the final straight lines.

Points marked by the intersections of construction lines guide the drawing of circles. Usually, both of these features are used in creating sketches. Since all the dimensions of a sketch are estimated, groups of construction lines forming boxes and other shapes are an important tool for preserving the shape and proportion of the object and its features as the sketch is developed.

Grid paper can be used as a guide in creating construction lines but should not be thought of as a substitute, since the grid does not directly represent the proportions of the object, and there are many more grid lines than there are features on the object.

The goal is to draw construction lines on top of the grid to reveal the form of the object. With experience, you may be able to make do with fewer construction lines, but while you are learning how to create properly proportioned sketches, you should use more, rather than fewer, construction lines to guide you.

Each feature has a proportion that can be represented by a series of construction lines. The following steps describe how to proportion a drawing by breaking it down into its component features. If the object is rectangular in shape, the final linework will follow the perimeter of the bounding box.

Inside the first bounding box, draw other boxes to represent the larger features of the object, and within those boxes draw still others to represent the smaller features of the object. Often, a construction line can be used for more than one box. The final boxes each show the proportions of one feature of the object. Continue to draw bounding boxes until the smallest features of the object have been represented.

As you gain experience, you may find that some of these smaller features need not be boxed; instead, their final lines can be sketched directly. When all of the features of the object have been boxed, begin sketching the final linework, which is done significantly darker than the construction lines. Gage the proportion of the overall size of the object. For the first sketch, use two overall dimensions of the object: Lightly sketch a box that represents the ratio of these two dimensions Figure 2.

This box is called a bounding Height Step 4 Figure 2. Introduction to Graphics Communications for Engineers Experiment with different lines to see which are more critical than others in representing the form of the image. Buy a roll of tracing paper from your local blueprint or art supply store. Well Proportioned Poorly Proportioned Figure 2.

The poorly proportioned monitor looks too wide. If there is not enough contrast between the construction lines and the final linework, then the construction lines become a distraction.

Make the final lines darker, or the construction lines lighter, or both; however, do not erase your construction lines. One of the most difficult sketching techniques to learn is making a sketch look well proportioned. For example, Figure 2. Proportioning skills will improve with practice. A good rule of thumb is, if the drawing does not look or feel right, it probably is not. In the poorly proportioned monitor in Figure 2. We live in a three-dimensional 3-D world, and representing that world for artistic or technical purposes is largely done on two-dimensional 2-D media.

Although a sheet of paper is technically three-dimensional, the thickness of the paper the third dimension is useless to us.

It should be noted that the computer screen is a form of two-dimensional medium, and images projected on it are governed by the same limitations as projections on paper. Modern techniques, such as holograms, stereograms, and virtual reality devices, are attempts to communicate three-dimensional ideas as threedimensional forms. However, drawings are still the primary tool used for representing 3-D objects.

Most projection methods were developed to address the problem of trying to represent 3-D images on 2-D media Figure 2. Projection theory and methods have taken hundreds of years to evolve, and engineering and technical graphics is heavily dependent on projection theory. Sketching Objects Step 1. Collect magazine photographs or clippings that show 2-D images or patterns.

These can range from pictures of faces, to company logos, to fronts of buildings, etc. Lay tracing paper over an image and tape the paper down. Lightly sketch an overall bounding box of the object. Look at the image contained in the bounding box. Mentally identify as many features on the object as you can. The features may be small and self-contained or a collection of several smaller features.

Refine the drawing by sketching a series of progressively smaller bounding boxes. Start with the larger features and work downward. If desired, you can then darken some of the lines representing the image, to highlight the most important lines of a feature.

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What are the most important lines of a feature? Various projection techniques have evolved to solve this problem. The sketches shown in B, C, and D are called pictorial because they represent the object as a 3-D form. The multiview sketch uses multiple flat views of the 3-D object to accurately represent its form on 2-D paper. The most common types of projection used in sketching are multiview, isometric one type of axonometric , oblique, and perspective, as shown in Figure 2.

These four types of projection can be placed in two major categories: The other three types of projection, grouped as pictorial sketches, present the object in a single, pictorial view, with all three dimensions represented. There are always trade-offs when using any type of projection; some are more realistic, some are easier to draw, and some are easier to interpret by nontechnical people.

Axonometric projection is a parallel projection technique used to create a pictorial drawing of an object by rotating the object on an axis relative to a projection, or picture plane.

In multiview, axonometric, and oblique projection, the observer is theoretically infinitely far away from the projection plane. In addition, for multiviews and axonometric projections the lines of sight are perpendicular to the plane of projection; therefore, both are considered orthographic projections. The differences between multiview drawing and an axonometric drawing are that, in a multiview, only two dimensions of an object are visible on each view and more than one view is required to define the object, whereas in an axonometric drawing, the object is rotated about an axis to display all three dimensions, and only one view is required.

Axonometric drawings are classified by the angles between the lines comprising the axonometric axes. The axonometric axes are axes that meet to form the corner of the object that is nearest to the observer. When all three angles are unequal, the drawing is classified as a trimetric projection.

When two of the three angles are equal, the drawing is classified as a dimetric projection. When all three angles are equal, the drawing is classified as an isometric equal measure projection.

Mechanically drawn pictorials can often be as hard to draw as multiviews. Various 2-D CAD-based tools have eased the process of creating pictorials. Probably the easiest way of creating such views is to use a 3-D CAD package to create a model. This model can easily represent pictorial views and can also generate views for a multiview drawing.

Another way of classifying projections relates to whether they use parallel projection or perspective projection. This type of projection is the basis of most engineering and technical graphics.

Perspective projection distorts the object so that it more closely matches how you perceive it visually. Since it is much easier to lay out a sketch in parallel than in perspective projection, you will probably find yourself doing a majority of your sketching using parallel projection, even though it is less realistic.

Only when the object spans a large distance—such as a house or bridge—will it be useful to represent the distortion your eyes perceive as the object recedes from view.

Although there are a number of ways of orienting an object to represent all three dimensions, isometric pictorials have a standard orientation that makes them particularly easy to sketch.

Start by looking at the two-point perspective in Figure 2. Then, instead of having the width and depth construction lines converge on vanishing points, have them project parallel to each other at a degree angle above the baseline Figure 2. Begin the sketch by extending the isometric axes shown in Step 1, Figure 2. Sketch a horizontal construction line through the bottom of the vertical line.

Sketch a line from the base of the vertical line to the right, at an approximate angle of 30 degrees above the horizontal construction line. Sketch a line from the base of the vertical line to the left, at an approximate angle of 30 degrees above the horizontal construction line. The corner of the axis is labeled point 1; the end of the width line is labeled point 2; the end of the depth line is labeled point 4; and the top of the height line is labeled point 3.

The lengths of these lines are not important, since they will be treated as construction lines, but they should be more than long enough to represent the overall dimensions of the object. Estimate the overall width, height, and depth of the object using the estimating techniques described earlier in this chapter. Use these dimensions to sketch a block that would completely enclose the object. Blocking in the object Many CAD systems will automatically produce an isometric view of a 3-D model when the viewing angle is specified.

Some CAD systems have predefined views, such as isometric, which are automatically created after selection. Making an Isometric Sketch Make an isometric sketch of the object shown in Figure 2.

Sketching the isometric axis Step 1. Isometric sketches begin with defining an isometric axis, which is made of three lines, one vertical and two drawn at 30 degrees from the horizontal.

These three lines of the isometric axis represent the three primary dimensions of the object: Although they are sketched at an angle of only 60 degrees to each other, they represent mutually perpendicular lines in 3-D space. Sketch in the front face of the object by sketching a line parallel to and equal in length to the width dimension, passing the new line through point 3. Sketch a line parallel to and equal in length to the vertical line 1—3 , through points 5—2. The front face of the object is complete.

From point 3, block in the top face of the object by sketching a line parallel to and equal in length to line 1—4.

This line is labeled 3—6. Sketch a line parallel to and equal in length to line 3—5, from point 6. This line is labeled 6—7. Sketch a line from point 5 to point 7. This line should be parallel to and equal in length to line 3—6. Block in the right side face by sketching a line from point 6 to point 4, which is parallel to line 1—3. The bounding box of the object, sketched as construction lines, is now finished.

The box serves the same purpose as the one drawn in Figure 2. Begin by estimating the dimensions to cut out the upper front corner of the block, and mark these points as shown in Step 4. Sketch the height along the front face by creating a line parallel to line 1—2; label it 8—9. Sketch degree lines from points 8 and 9 and label these lines 9—10 and 8— Now sketch a line from point 10 to point Sketch vertical lines from points 10 and 11 and label the new lines 10—12 and 11— Sketch a line from point 12 to point 13 to complete the front cutout of the block.

With a simple sketch, you can often lay out all of your construction lines before having to darken in your final linework. CHAPTER 2 Sketching and Text With more complicated sketches, the sheer number of construction lines can often cause confusion as to which line belongs to which feature.

The confusion can be worse in an isometric sketch, where the lines represent three dimensions rather than two. Therefore, after the marks are made for the last two features in Step 5, you can begin darkening in some of the lines representing the final form.

Estimate the distances to create the angled surface of the block, and mark these points, as shown in Step 5. From the marked point on line 11—13, sketch a degree line to the rear of the block on line 4—6.

## Technical Graphics Communication

Label this new line 14— From the marked point on line 12—13, sketch a 30degree line to the rear of the block on line 6—7. Label this new line 16— Sketch a line from point 14 to point 16 and from point 15 to point 17 to complete the sketching of the angled surface.

Lines 14—16 and 15—17 are referred to as nonisometric lines because they are not parallel to the isometric axis. Estimate the distances for the notch taken out of the front of the block, and mark these points, as shown in Step 5. Draw vertical lines from the marked points on line 1—2 and line 8—9. Label these lines 18—19 and 20—21, as shown in Step 6. Sketch degree lines from points 19, 20, and 21 to the estimated depth of the notch.

Along the top surface of the notch, connect the endpoints of the degree lines, and label this new line 22— The degree line extending back from point 20 is stopped when it intersects line 18—19, as shown in Step 6. To complete the back portion of the notch, drop a vertical line from point 22, as shown in Step 6.

Stop this new line at the intersection point of line 19— The rough isometric sketch of the block is complete. Note that we have not mentioned hidden features representing details behind the visible surfaces. The drawing convention for isometric sketches calls for disregarding hidden features unless they are absolutely necessary to describe the object.

Darken all visible lines to complete the isometric sketch. Since the construction lines are drawn light, there is no need to lighten them in the completed sketch. The basic procedures are to determine the desired view, create the isometric axes, box in the object using the overall length, width, and depth dimensions from the three-view drawing Figure 2.

Determine the desired view of the object, then sketch the isometric axes. Construct the front isometric plane using the W and H dimensions. Construct the top isometric plane using the W and D dimensions. Construct the right side isometric plane using the D and H dimensions. Determine dimensions X and Y from the front view and transfer them to the front face of the isometric drawing. Project distance X along an isometric line parallel to the W line. Project distance Y along an isometric line parallel to the H line.

Point Z will be located where the projectors for X and Y intersect. Sketch lines from point Z to the upper corners of the front face. Project point Z to the back plane of the box on an isometric line parallel and equal in length to the D line. Sketch lines to the upper corner of the back plane to complete the isometric sketch of the object. Notice that the degree angles do not measure 45 degrees in the isometric view. This is an example of why no angular measures are taken from a multiview to construct an isometric sketch.

In an isometric drawing, the object is viewed at an angle, which makes circles appear as ellipses. When sketching an isometric ellipse, it is very important to place the major and minor axes in the proper positions. Remember Figure 2. The following are the key features of the isometric ellipse on each plane: The orientation of the ellipse is set according to the face on which the circle lies. The correct orientation is shown in A , and examples of incorrect orientations are shown in B.

The center of the box and the midpoints of the sides are found, and arcs are then drawn to create the ellipse. Sketching an Isometric Ellipse Figure 2. Notice that the steps are almost identical to those for sketching a circle as explained earlier in this chapter.

The difference is in the orientation and proportion of the primary axes. This isometric ellipse will be drawn on the front plane.

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Begin by sketching an isometric square whose sides are equal to the diameter of the circle. Add construction lines across the diagonals of the square. The long diagonal is the major axis, and the short diagonal is the minor axis of the ellipse. The two diagonals intersect at the center of the square, which is also the center of the isometric ellipse.

Sketch construction lines from the midpoints of the sides of the square through the center point.

## Technical Graphics Communications

These lines represent the center lines for the isometric ellipse. The midpoints of the sides of the isometric square will be tangent points for the ellipse and are labeled points A, B, C, and D. Sketch short, elliptical arcs between points B and C and points D and A. Finish the sketch by drawing the elliptical arcs between points C and D and points A and B, completing the ellipse.

Sketching an Isometric Cylinder Figure 2. Sketch the isometric axis. To sketch the bounding box for the cylinder, begin on one degree axis line and sketch an isometric square with sides equal to the diameter of the cylinder.

This square will become the end of the cylinder. Next, mark the length of the cylinder on the other degree axis line, and sketch the profile and top rectangles of the bounding box. For the profile rectangle, the length represents the length of the cylinder, and the height represents the diameter of the cylinder.

For the top rectangle, again the length represents the length of the cylinder, but the width represents the diameter of the cylinder. Where the center lines intersect with the top and front sides of the isometric square, mark points A and B. Sketch construction lines from points A and B to the back end of the bounding box and mark points C and D. Sketch an arc between points C and D. On the isometric square, locate the two points where the long diagonal intersects with the ellipse.

From those two points, sketch two degree lines to the back of the bounding box. These degree lines are tangent to the ellipse on the front of the cylinder. Then, sketch short elliptical arcs from points C and D to the tangent lines, as shown in the figure. The cylinder should now be visible in the bounding box.

Darken all visible lines to complete the cylinder. Note that the major axis of the ellipse is perpendicular to the axis running through the center of the cylinder, and the minor axis is coincident to it. Sketching Semi-Ellipses Figure 2. This isometric ellipse will be drawn on the profile plane. Begin by sketching an isometric square whose sides are equal to the diameter of the arc. The midpoints of the sides of the isometric square will be tangent points for the ellipse and are labeled points A, B, and C.

The long diagonal is the major axis, and the short diagonal is the minor axis. Sketch short, elliptical arcs between points B and C and points B and A, which creates the elliptical arc on the near side of the object. The back part of the semi-ellipse can be sketched by constructing degree parallel lines that are equal in length to the depth of the part, from points A, B, and C.

Finish by darkening the final lines and lightening the construction lines. Isometric grid paper is made of vertical and 30degree grid lines, as shown in Figure 2.

There are two primary advantages to using isometric grid paper. First, there is the advantage obtained by using any kind of grid paper. This can be especially useful when transferring the dimensions of a feature from one end of the object to the other. Unlike square grid paper, each intersection on an isometric grid has three lines passing through it, one for each of the primary axis lines. This can create some confusion when counting out grid blocks for proportions. Just remember which axis line you are using and count every intersection as a grid block.

The second advantage of the isometric grid is the assistance it provides in drawing along the primary axis lines. Although estimating a vertical line is not difficult, estimating a degree line and keeping it consistent throughout the sketch is more challenging.

Remember that the only dimensions that can be transferred directly to an isometric sketch are the three primary dimensions. These dimensions will follow the lines of the grid paper. When blocking in an isometric sketch, lay out the dimensions on construction lines that run parallel to the grid lines. Angled surfaces are created using construction lines that are nonisometric; that is, they do not run parallel to any of the grid lines and are drawn indirectly by connecting points marked on isometric construction lines.

Some examples are given in Figure 2. Sketch objects with a variety of features. Some should require sketching isometric ellipses, while others should have angled surfaces that require nonisometric lines.

Start with simpler forms that only contain isometric lines and work toward more complex forms. Another approach is simply to leave out some of the details. You can capture the essence of the form by representing just its primary features. This is a common approach in creating ideation sketches. The cost and availability of isometric grid paper can be a discouraging factor in using it to create lots of sketches.

You can minimize the expense by using roll tracing paper over a sheet of grid paper. The two sheets can be held together with low-tack tape or put in a clipboard. With practice, you will find that grid paper is not needed and you can create sketches on the tracing paper alone. A multiview drawing is a collection of flat 2-D drawings that work together to give you an accurate representation of the overall object. With a pictorial drawing, all three dimensions of the object are represented in a single view.

The disadvantage of this approach is that not all the features in all three dimensions can be shown with optimal clarity. In a multiview projection, however, each view concentrates on only two dimensions of the object, so particular features can be shown with a minimum of distortion Figure 2. Enough views are generated to capture all the important features of the object. Given their advantages, why are multiview drawings not always used?

For one thing, there are the multiple views, rather than a single view, to be drawn. These views must be coordinated with one another to represent the object properly.

You have to carefully visualize the views as you sketch them, and so does the person viewing them. Without training and experience, you might find it hard to Stapler Screwdriver Figure 2. This method of viewing an object results in a single view, with only two of the three dimensions represented. Therefore, it takes multiple views to show all three dimensions. Poor Orientation No! Poor Orientation B Figure 2. Objects should be positioned in their natural orientation A ; for this car, that position is on its wheels.

The choice between multiviews and pictorials is often one of exact representation of features versus ease of sketching and viewing. Orienting and Selecting the Front View When creating a multiview drawing of a design, the selection and orientation of the front view is an important first step. The front view is chosen as the most descriptive of the object; for example, what would normally be thought of as the side of the car is chosen as the front view because it is the most descriptive Figure 2.

In addition, the object must be properly oriented in the view. The orientation of the object is based on its function. For example, for an automobile, the normal or operating position is on its wheels, rather than on its roof or bumpers Figure 2. Choosing the Views for a Multiview Drawing Another way to understand the views of an object is to pick it up and turn it around. This may be hard to imagine with something like a car, but many of the objects you will be sketching are considerably smaller and can be held in the hand.

Imagine picking up the object shown in Figure 2. A different principal view of the object is produced for every 90 degrees of rotation. Rotate it back to where you started and then rotate it so you are looking at its right side. There are an infinite number of intermediate views of the object between the points of rotation at which you stopped; for right now, however, consider only those views that are rotated 90 degrees from each other.

These are considered regular or principal views, and each represents two primary dimensions of the object. If you continue rotating the object in degree increments, you will see as many as six regular views Figure 2. A multiview drawing should have the minimum number of views necessary to describe an object completely. Normally, three views are all that are needed; however, the three views chosen must be the most descriptive ones.

The object is viewed from six mutually perpendicular viewpoints. The six views are called front, top, bottom, rear, right side, and left side. The most descriptive views are those that reveal the most information about the design, with the fewest features hidden from view. Of the six orthographic views, which are the most descriptive? Although all the views given reveal much about the size and shape of the object, some are more descriptive than others. The choice of views is determined as follows: Identify the most descriptive or important features of the object.

Determine the views that best represent those features. Introduction to Graphics Communications for Engineers After deciding on the most descriptive features of the part, choose the views that show these features. Part of this selection will involve determining which views do the best job of neither obscuring nor hiding other features. For example, the object in Figure 2. There are only two views that show the hole and rounded top: Although both views show these features equally well, the front view is chosen over the rear view because it does not hide the slot cut in the base.

The L-shaped profile is shown equally well in both the right and left side views, and they have an equal number of hidden features. Although either view can be used, convention favors choosing the right side view.

The slot in the base is shown in both the top and bottom views. However, the top view has fewer hidden lines, so it is preferred over the bottom view for the sketch.

For this object then, the preferred views are the front, top, and right side views. Look at them carefully and identify their important features. Orient each object so that the most important features are seen. Make this view the front view. Before rotating them, try to imagine what the top and right side views will look like. Now rotate them and see if that is how they look. Do all of the important features show up in these three views?

If not, what other front view can you select that would result in seeing all of the important features in the three views? Next, look at some larger items you cannot pick up. For each object, move around it and look at it from different viewpoints.

Try to imagine picking it up and rotating it. Is there any difference in how the object looks if you pick it up and rotate it rather than walk around it?

Hidden lines have been omitted for clarity. Sketched Alphabet of Lines Standard engineering drawing practice requires the use of standard linetypes, which are called the alphabet of lines. The sizes show the recommended line thicknesses.

The technique includes line conventions, proportioning, and methods for creating circles, arcs, and ellipses. A knowledge of the proper and effective technique will assist the beginner in creating legible multiview sketches. In engineering and technical drawing, it is important that hidden features be represented so that the reader of the drawing can clearly understand the object.

Many conventions related to hidden lines have been established over the years. These conventions are as follows: Visible line 2. When this happens, the conventional practice called the precedence of lines dictates the linetype to draw when two or more lines in a view overlap Figure 2. For example, in Figure 2. The precedence of lines requires that the visible lines be drawn and the hidden lines not be shown in the top view. Notice that whenever a hidden or visible line has precedence over a center line, the center line is still drawn in the view by leaving a space and then extending it beyond the edge Figure 2.

Construction line Figure 2. For example, a visible line has precedence over all other types of lines, and a hidden line and a cutting plane line have precedence over a center line. Whenever we are representing a hole, cylinder, or cone on a technical drawing, the conventional practice is to draw center lines, which are used to 1 locate the centers of circles and arcs; 2 represent the axes of cylinders, cones, and other curved surfaces; and 3 represent lines of symmetry.

In the top view, horizontal and vertical center lines are drawn to locate the center of the circle. In the front view, a very thin center line. For very long cylinders, the center line is drawn as a series of long and short segments.

Notice that center lines are used in both the circular and horizontal views of a hole. When adding center lines to the circular view of a very small hole, a solid center line may be used rather than a dashed line, as shown in part C. Part D shows how center lines are used to locate the centers of holes around a bolt circle.

Part E shows how center lines, along with phantom lines, are used to show a path of motion. However, multiview sketches rarely have more than three views. Multiview sketches are important in that they provide more accurate geometric information than a pictorial sketch, without requiring the time that a formal multiview drawing would take.

If dimensions are provided, they are usually only for a particular feature s and are often only approximations, since these sketches are used early in the design process before final specifications have been made. As is the goal with all sketches, multiview sketches should be done quickly and clearly. Straightedges, such as triangles and T-squares, should be avoided since they will only slow you down and will compel you toward a level of finish that is inappropriate in sketches.

In addition, you should draw only as many views as are necessary to show the features accurately. An initial analysis of the features should tell you if one, two, or three views are needed to clearly show the elements of interest. Though not truly a multiview, it is still meant to represent only two dimensions of the object, which is the basic concept of multiview drawings.Other approaches are to guide the tendencies of the designer.

John Heskett, a 20th-century British writer on design claimed, "Design, stripped to its essence, can be defined as the human nature to shape and make our environment in ways without precedent in nature, to serve our needs and give meaning to our lives.

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However, when you want the guidance of existing lines on the paper, it is most useful to have the lines running along both dimensions, forming a grid. Start on. Some popular approaches include: Sociotechnical system design, a philosophy and tools for participative designing of work arrangements and supporting processes — for organizational purpose, quality, safety, economics and customer requirements in core work processes, the quality of peoples experience at work and the needs of society KISS principle , Keep it Simple Stupid , which strives to eliminate unnecessary complications.

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