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4.22 Transformations

A 3D CAD package uses the default Cartesian coordinate system to store information about the model. One way it may be stored is as a matrix (rows and columns of numbers) representing the vertices of the object. Once the object is defined, the software uses mathematical methods to transform the matrix (and the object) in various ways. There are two basic kinds of transformations: those that transform the model itself (called geometric transformations) and those that merely change the view of the model (called viewing transformations).

Geometric Transformations

The model stored in the computer is changed using three basic transformations (or changes): moving (sometimes called translation), rotating, and scaling. When you select a CAD command that uses one of these transformations, the CAD data stored in your model are converted mathematically to produce the result. Commands such as Move (or Translate), Rotate, and Scale transform the object on the coordinate system and change the coordinates stored in the 3D model database.

Figure 4.78 shows a part after translation. The model was moved over 2 units in the X-direction and 3 units in the Y-direction. The corner of the object is no longer located at the origin of the coordinate system.

4.78

4.78 Translation. This model has been moved 2 units in the X-direction and 3 units in the Y-direction.

Figure 4.79 illustrates the effect of rotation. The rotated object is situated at a different location in the coordinate system. Figure 4.80 shows the effect of scaling. The scaled object is larger dimensionally than the previous object.

4.79

4.79 Rotation. This model has been rotated in the X-Y plane.

4.80

4.80 Scaling. This model has been scaled to 1.5 times its previous size.

Viewing Transformations

A viewing transformation does not change the coordinate system or the location of the model on the coordinate system; it simply changes your view of the model. The model’s vertices are stored in the computer at the same coordinate locations no matter the direction from which the model is viewed on the monitor (Figure 4.81).

4.81

4.81 Changing the View. Note that the location of the model relative to the coordinate axes does not change in any of the different views. Changing the view does not transform the model itself.

Although the model’s coordinates do not change when the view does, the software does mathematically transform the model database to produce the new appearance of the model on the screen. This viewing transformation is stored as a separate part of the model file (or a separate file) and does not affect the coordinates of the stored model. Viewing transformations change the view on the screen but do not change the model relative to the coordinate system.

Common viewing transformations are illustrated in Figure 4.82. Panning moves the location of the view on the screen. If the monitor were a hole through which you were viewing a piece of paper, panning would be analogous to sliding the piece of paper to expose a different portion of it through the hole. Zooming enlarges or reduces the view of the objects and operates similar to a telephoto lens on a camera. A view rotation is actually a change of viewpoint; the object appears to be rotated, but it is your point of view that is changing. The object itself remains in the same location on the coordinate system.

4.82 4.82 4.82 4.82

4.82 Common View Transformations. Panning moved the view of the objects in (a) to expose a different portion of the part in (b). In (c), the view is enlarged to show more detail. In (d), the view is rotated to a different line of sight. In each case, the viewing transformation applies to all the objects in the view and does not affect the location of the objects on the coordinate system. (Notice that the position relative to the coordinate system icon does not change.)

Viewing controls transform only the viewing transformation file, changing just your view. Commands to scale the object on the coordinate system transform the object’s coordinates in the database.

Examine the six models and their coordinates in Figure 4.83. Which are views that look different because of changes in viewing controls? Which look different because the objects were rotated, moved, or scaled on the coordinate system?

4.83

4.83 Geometric or Viewing Transformation? Three of these models are the same, but the viewing location, zoom, or rotation has changed. Three have been transformed to different locations on the coordinate system.

You will use the basic geometric shapes and concepts outlined in this chapter to build CAD models and create accurate freehand sketches. The ability to visualize geometric entities on the Cartesian coordinate system will help you manipulate the coordinate system when modeling in CAD.

Ribs in SolidWorks are built-in features. To create a rib, you simply draw a line and specify a width, and SolidWorks creates the rib and ends it at the first surface it encounters. To create the center rib, Albini sketched a line on the plane at the top of the bosses and specified a width (ribs on a plastic part are usually two thirds of the thickness of the walls). The rib was formed down to the top surface of the holder lid. For the ribs around the bosses, Albini did as Obi Wan Kenobi might have advised: “Use the symmetry, Luke.” He sketched the lines for ribs radially from the center points of the bosses (see Figure 4.88). To create the ribs, Albini created four of them on one boss, then mirrored them once to complete the set for one boss, then mirrored all the ribs from one boss to the other boss. Once all the ribs were formed, he cut the tops off the ribs and bosses to achieve the shape shown in Figure 4.89.

4.88

4.88 Bosses and Ribs. Sketched circles were extruded to form the bosses on the top of the magnet chamber. The dotted lines shown here on the top of the chamber pass through the center point of the bosses and were used to locate the center rib and radial ribs.

4.89

4.89 This view of the magnet carrier shows the symmetry of the ribs and the shape that resulted from “slicing off” the top of the bosses after the ribs were formed. (Images courtesy of Marty Albini. This case study is provided as a courtesy by the owner of the intellectual property rights, Park City Entertainment. All rights reserved.)

The result was a stiffer rib and a shape that could not be achieved with a single rib operation. To complete the part, circles were drawn concentric to the bosses and extruded to form holes that go through the part (see Figure 4.90). Draft was added to the ribs and walls to make the part release from the mold easily. Fillets were added to round all the edges, reducing stresses and eliminating hot spots in the mold. Then, the part was mirrored to create the other half. The center rib and tab for attaching the cable were added and more edges filleted. Draft was added to the inside of the holder, and the part was complete.

4.90

4.90 Circles concentric with the bosses were extruded to form the holes before the part was mirrored and remaining features added to finish the magnet carrier.

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