Sheet Metal Technology by David Gingery

Sheet Metal Technology by David Gingery

Author:David Gingery [Gingery, David]
Language: eng
Format: azw3
Publisher: David J. Gingery Publishing, LLC
Published: 2016-01-20T16:00:00+00:00


You have seen that a cylinder may look like a square or rectangle in a side plan view and a cone may look like a triangle. Yet another geometric shape that looks like a triangle in a side plan view is a pyramid. And a top plan view of a pyramid looks like a square with lines drawn from corner to corner as in figure 16. The routine for the solution of this pattern problem is called “Triangulation” because we use a right triangle to solve the true length of some of the lines. The solution of the pyramid pattern is similar to that of the cone in some respects, but Triangulation is significantly different than radial line development in its many applications.

The triangulation routine is based upon the law of right triangles. A right triangle is one with an angle of 90 degrees between two legs. If you draw two right triangles each with base and perpendicular leg of the same length the hypotenuse of both triangles will be the same length. And so we use what can be termed a “solution triangle” to solve the unknown lengths seen in the plan views. It is a very simple process that will enable you to develop patterns for seemingly complex figures with great ease.

As in other routines, we begin by drawing a full size top and side plan view. Again the perspective view gives you a clear concept of what the figure is to be, but it is not useful in the solutions process.

The corners in the top plan view are marked A, B, C, and D. Since you are viewing the figure as though looking straight down at the peak, point C, you are seeing the true dimensions of each of the four base sides and so they do not have to be solved. But the vertical lines are not true because you are viewing them at an angle.

Point X represents the center of the base which is directly below point C and so it is not visible. But if a vertical line were drawn from point X to point C it would represent the vertical leg of a right triangle. The true length of the vertical leg can’t be found in the top plan view. But the true length of the base of the triangle is found between A and X, B and X, D and X and E and X. Although point X is not visible in the top plan view, the true length of the base is clearly seen between each corner and point C since point C is directly above X.

Notice that the side plan view presents the two base corners designated A and B as though the upper figure were rotated 90 degrees to give a direct side view. Again we see the base dimension in its true length between A and B. But the diagonal lines between A and C and B and C are not true length because they are seen at an angle.



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