Do you remember as little, but fearless Buratino defeated terrible Karabasa-Barabas? The villain was hooked by the long beard for a knot when ran for the wooden little man around a tree. A trajectory which was described by the director of puppet theater – an evolvent of a circle or development of a circle. On an evolvent teeths at cogwheels and gears are processed. Therefore to be able to build such curve each engineer has to.
It is required to you
- Sheet of paper, pencil, compasses, ruler, curve, square
Instruction
1. Arrange the sheet of paper so that its long party lay along a table edge. Mentally divide it across and verticals into 4 parts. Approximately in the middle of the top right part put the end O. Tsirkul draw a circle, the set radius, with the center in a point of the Lake.
2. In the top part of a circle, somewhere at the level of 12 hours, put the end and designate by its figure 12. In a point 12, put compasses which distance between legs, is equal to radius R circles. Make notch compasses on a circle. On the right designate a notch 2, and at the left - 10. In the same way make notches of points 2 and 10. A notch down from a point 2 – a point 4, and down from a point 10 – a point 8. From a point 4, similarly constructed notch, is a point 6.
3. Connect points the 12 and 6 straight line. Also construct on it by means of the square the perpendicular passing through a point of the Lake. At the left designate a point of intersection of a circle and a perpendicular by figure 9, and on the right – figure 3.
4. Above mark the notch on a circle made compasses of a point 3 with figure 1, and below – 5. And the notches made of a point 9 – figures 11 and 7.
5. A piece connect each numbered point to the center of a circle. As a result the circle broken as the dial for about 12 hours of equal sectors will turn out.
6. From a point 12 construct a tangent to a circle to the left, i.e. the line perpendicular to radius. Similarly carry out tangents through all other points.
7. Calculate circle length on a formula: L=2πR, where π ≈ 3.14. And also find 1/12 part from circle length: L ₒ=L/12.
8. From a point 12 on a tangent postpone a piece equal 11•L ₒ and put B12 end.
9. From a point 11 on a tangent postpone a piece 10 long • L ₒ. Put B11 end.
10. From a point 10 – a piece 9•L ₒ. Put B10 end. And so on. A point at number 1 and a point of B1 coincide.
11. A curve connect points of B1, B2, … B12. The received curve is also a circle evolvent.