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David Rehman
David Rehman

Isometric Drawing Exercise !!LINK!!

The picture below shows three views of a figure from the front, right, and top. The entire figure uses a total of seven cubes. Can you construct the figure using the isometric drawing tool? (Be sure to use cubes of the proper color, too.)

Isometric Drawing Exercise

Students learn about one-axis rotations, and specifically how to rotate objects both physically and mentally to understand the concept. They practice drawing one-axis rotations through a group exercise using cube blocks to create shapes and then drawing those shapes from various x-, y- and z-axis ro...

Students learn about two-axis rotations, and specifically how to rotate objects both physically and mentally about two axes. Students practice drawing two-axis rotations through an exercise using simple cube blocks to create shapes, and then drawing on triangle-dot paper the shapes from various x-, ...

(Have the slide presentation up and displayed to the class, starting with slide 3.) Spatial visualization is useful for practicing engineers, has been shown to be a significant predictor of success for students in engineering, and is also a learned skill. That means we can improve our spatial visualization skills by practicing. Today, we are going develop our skills in drawing three-dimensional objects. Spatial visualization skills help you in many subjects and hobbies that require the imagination of three-dimensional shapes, such as geometry, chemistry, physics, athletics (like tennis and gymnastics) and various computer games. Practicing spatial visualization enables you to understand three-dimensional figures and representations more readily and perform better in these subjects and hobbies.

Figure 1. A non-isometrically drawn cube (left) compared to an isometrically drawn cube (right).copyrightCopyright 2015 Jacob Segil, College of Engineering and Applied Science, University of Colorado Boulder

(Direct the class through the following exercise: Have partner #1 close their eyes. Show all partner #2 students the left image in slide 6, which is the same as Figure 2. Inform partner #1 to keep their eyes closed while partner #2 describes the image. Let the object description continue for a couple of minutes. When finished, have partner #1 draw the object as accurately as possible.)

Engineers use computer-aided drafting software programs such as AutoCAD to create blueprints and design plans. Figure 4 (also on slide 5) shows a house that was depicted isometrically using AutoCAD.

Finally, have students turn their towers on their sides so that three cubes are touching the desk/table surface. Now, ask the students to draw the stacked tower at this angle on isometric paper. Expect their drawings to resemble one of the two images on the right side of slide 8 (same as Figure 5-far right; click the mouse/keyboard to reveal it), depending on which way they oriented the object.

At this point, stop and make sure that all students are getting the hang of drawing on isometric triangle-dot paper. If students are struggling, spend more time on the first three steps. If necessary, display the answers for the class and/or demonstrate how to draw each of the three images. Notice how the faces in between the cubes and the backside/bottom of each cube are not drawn directly; we know that those sides are part of the cubes, but the isometric drawing cannot depict all details of a 3-D object.

Question/Answer: Ask students: Why are isometric drawings important to engineers? (Point to make: Isometric drawings represent three-dimensional objects on a two-dimensional surface. By doing this, engineers can depict complicated 3-D objects in a way that is easy to share and describe. Without isometric drawings, engineers would require 3-D models of each idea/concept, which would be costly, cumbersome and inconvenient.)

Worksheet: After completing the classroom instruction on isometric drawing, assign students to complete the Isometric Drawing Worksheet. Observe whether students are able to draw the rotated objects or if they are struggling. Assist them if necessary. Review their answers to gauge their depth of understanding.

This film shows how drawing skills and techniques are applied to enable quick conversations between engineers, architects and others in the design of a building (The Templeman Library, University of Kent).

Any engineering drawing should show everything: a complete understanding of the object should be possible from the drawing. If the isometric drawing can show all details and all dimensions on one drawing, it is ideal. One can pack a great deal of information into an isometric drawing. However, if the object in figure 2 had a hole on the back side, it would not be visible using a single isometric drawing. In order to get a more complete view of the object, an orthographic projection may be used.

Which views should one choose for a multiview drawing? The views that reveal every detail about the object. Three views are not always necessary; we need only as many views as are required to describe the object fully. For example, some objects need only two views, while others need four. The circular object in figure 6 requires only two views.

To prepare a drawing, one can use manual drafting instruments (figure 12) or computer-aided drafting or design, or CAD. The basic drawing standards and conventions are the same regardless of what design tool you use to make the drawings. In learning drafting, we will approach it from the perspective of manual drafting. If the drawing is made without either instruments or CAD, it is called a freehand sketch.

This cross-sectional view (section A-A, figure 17), one that is orthogonal to the viewing direction, shows the relationships of lengths and diameters better. These drawings are easier to make than isometric drawings. Seasoned engineers can interpret orthogonal drawings without needing an isometric drawing, but this takes a bit of practice.

The diagonal lines on the section drawing are used to indicate the area that has been theoretically cut. These lines are called section lining or cross-hatching. The lines are thin and are usually drawn at a 45-degree angle to the major outline of the object. The spacing between lines should be uniform.

A second, rarer, use of cross-hatching is to indicate the material of the object. One form of cross-hatching may be used for cast iron, another for bronze, and so forth. More usually, the type of material is indicated elsewhere on the drawing, making the use of different types of cross-hatching unnecessary.

Usually hidden (dotted) lines are not used on the cross-section unless they are needed for dimensioning purposes. Also, some hidden lines on the non-sectioned part of the drawings are not needed (figure 12) since they become redundant information and may clutter the drawing.

This drawing is symmetric about the horizontal centerline. Centerlines (chain-dotted) are used for symmetric objects, and also for the center of circles and holes. We can dimension directly to the centerline, as in figure 31. In some cases this method can be clearer than just dimensioning between surfaces.

Isometric Drawing Exercise To complete the Isometric Drawing Exercise, return to the Sketching and Freehand Drawing Fundamentals page, open up the Isometric Drawing Exercise page and print a copy of the exercise. Your task will be to draw nine isometric objects freehand, using the box method as demonstrated in this presentation.

Here are some limbering up exercises wot get you started. To keep your pencil sharper longer, and for more even lines widths, try turning your pencil slowly while completing the lines in the exercises below.

Now that you are warmed up, we will take the straight and curved lines from the sketching exercise and use them to form letters. The entire alphabet can be formed from the straight and curved lines you have practiced.

Look at the lettering below. If your printing is similar, and is easily readable, you can skip this exercise and go on to oblique sketching. If not, do some practicing. Some of the work ahead (and tests) require good lettering.

In this more difficult exercise, you are to make oblique sketches of the objects shown. The third problem is drawn in isometric. You are to sketch it in oblique. Convert problem four from orthographic to an oblique sketch.

In sketching isometric circles and arcs, there are three positions in which they are normally sketched, depending upon the surface where the circular feature is located. Those surfaces, or picture planes are:

Of all the methods of making drawings, orthographic projection is the most commonly used by draftsperson. Although the other methods serve their purposes, they cannot always show the parts of an object as well as orthographic representation.

Orthographic projection is a system of projecting from view to view to graphically describe the object. As a way of reviewing, study the views of the small garage in this drawing. Notice the location and relationship of each view to the other views.

An exercise apparatus that is mountable to a substrate, having a channel, a belt, and at least one buckle. The buckle has a bottom portion that is adapted to fit within the channel such that the buckle can move along the channel and resist moving in either perpendicular direction. The buckle has a top portion that includes an opening for attaching exercise equipment and at least one cam. The cam is selectively engaged with the belt such that when the cam is disengaged, the buckle can be moved along the belt and when engaged, the buckle resists movement with respect to the belt.

2. The mountable exercise apparatus of claim 1 wherein the channel includes a rail portion and the bottom portion of the at least one buckle has a foot which is sized to fit within the rail portion such that the at least one buckle is movable along the channel and resists moving in either perpendicular direction thereto.

7. The mountable exercise apparatus of claim 1 wherein the bottom portion of the at least one buckle further comprises two or more wheels operably mounted thereto, each of the two or more wheels are sized to fit within the channel such that the at least one buckle is movable along the channel and resists moving in either perpendicular direction thereto. 041b061a72


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