Descriptive Geometry/Rotating a plane

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Finding a shape, like a triangle for instance, in true length consists of first treating the triangle like lines, and then finding it in edge view.

  1. Create a line intersecting two edges of the shape parallel to the folding plane.
  2. Create a new folding plane perpendicular to the line created will give the point view and the triangle in edge view
  3. Rotation can now be used to find this triangle in true shape by projecting back into top view.
  4. Rotate the line in the third view by using an arbitrary axis (either lying on the line or off the line).
  5. Rotate the line so that it is parallel to the previous folding line.
  6. Project this rotated line back to top view so the triangle in true shape is revealed

Example 01: Determine the true shape of the quadrilateral plane by using rotation

  • Draw a horizontal line parallel to the folding line in front view, transfer it to top view, and this line will be in true length
  • Create a folding line perpendicular to the horizontal line to get the quadrilateral in edge view
  • Now, rotate the edge view of the quadrilateral parallel to the folding line
  • In top view, draw construction lines through each points parallel to the folding line
  • Transfer the points back to the previous view. Where each construction line intersects with thee construction line though each point is the location of the new points.
  • Connect all the points and you will have the plane in true shape

http://commons.wikimedia.org/wiki/File:Example_Problem_01.pdf

Example 02: Determine the true shape of the quadrilateral plane by rotating about an axis outside the plane

  • Draw a horizontal line parallel to the folding line in front view, transfer it to top view, and this line will be in true length
  • Create a folding line perpendicular to the horizontal line to get the quadrilateral in edge view
  • To rotate the the edge view of the quadrilateral parallel to the folding line, draw a construction line perpendicular to the rotation Axis to the edge view
  • Use it to rotate the points parallel to the folding line
  • In top view, draw construction lines through each points parallel to the folding line
  • Transfer the rotated edge view back. Where each construction line intersects with the construction line through each point is the location of the new points.
  • Connect all the points and you will have the plane in true shape

http://commons.wikimedia.org/wiki/File:Example_Problem_02.pdf

Practice Problems:

Problem 1:

Question: An archer fires an arrow at a rectangular piece of plywood, creating a punctured hole through the plywood's center. Represent the hole the arrow makes in true shape if the radius of the hole is .5". Use methods of revolution to solve this problem.


Problem 2: A planet orbits around a sun in the image seen. If the radius of its orbit is 10,000 miles (roughly 1 inches scaled) determine the shape of its orbit in top view. Use methods of revolution to solve this problem

Problem 3: Find the dihedral angle between the two planes through the method of revolution