How to build a scan of a truncated cone

A reamer is a surface of geometric bodies, deployed on the plane. To build a scan of any surface is necessary to consistently combine all the flat elements with a single plane.

You will need

• Pencil, compass, template, triangle, ruler

Instruction

1. Example. To build a scan of a truncated cone. The lateral surface of a truncated cone has flat elements, because it is a curve surface. To obtain an approximate sweep perform the following construction (figure 1).
2. Fill the cone to the polyhedron. On the horizontal projection of the circumference of the bottom base of the cone , divide the arc 12(1₁2₁), 23(2₁3₁), etc. And the circumference of the upper base divide by arcs 67(6₁7₁), 78(7₁8₁), etc., Connect these arcs by chords. The result is written in the truncated cone a truncated octagonal pyramid. Her face is a trapezoid, with the base – chord 1₁2₁, 6₁7₁, etc., and the other two opposite side – the side edges 1₁6₁, 2₁7₁ etc. These facets of the trapeze and are flat elements that are aligned with the plane of the drawing in the scan.
3. In every face swipe diagonally 1₁7₁, 2₁8₁, etc., divide them into two triangles. Determine the actual size (N. D.) diagonal 17 by way of a right triangle. To do this, check the height of the front projection of a truncated cone h. At right angles to h put the horizontal projection of the diagonal 1₁7₁. Received 1₀7₁ the hypotenuse is equal to the actual value (B. V.) diagonal 17.
4. When building a scanner all dimensions shall be full size. In 1672 faces of the inscribed pyramid all the elements are represented without distortion: the actual value of the rib 16 is equal to its frontal projection 1₂6₂, chord 67 (6₁7₁), 12 (1₁2₁) Proektirovanie in full size on the plane P. The actual value of the diagonal 1₀7₁ found by way of a right triangle.
5. Building sweep. On the vertical straight line (or direct random position) put the cut 1₀6₀=1₂6₂. From the point 6₀ radius 6₁7₁ make a notch, and 1₀ radius 1₀7₁ (present) – the second. The resulting point 7₀ connect direct with 1₀ and 6₀. From the point 1₀ make the notch radius 1₀2₀=1₁2₁, and from the point 7₀ radius 7₀2₀=1₀6₀. Get the point 2₀, connect it to the points 1₀ and 7₀.Built a-line 1₀6₀7₀2₀ is aligned with the plane of the drawing face of the pyramid inscribed in the truncated cone.
6. All the faces of the inscribed pyramid is equal, so using the same dimensions, build all adjacent faces and connect direct point 1₀, 2₀, 3₀, etc. of the Obtained flat figure will scan the lateral surface of the pyramid inscribed in a truncated cone.
7. Connect point 1₀, 2₀, 3₀ etc. the bottom base and the point 6₀, 7₀, 8₀, etc. of the upper base of the truncated cone curved curve line. The resulting figure is a net of a truncated cone.