Epitrochoid

Roulette

To construct the figure:
1) Start with point A and a segment a.
2) Divide a in N equal parts, say N=5 (tool: Divide in N parts - while pressing F5 key)
3) Set points B, C, so that AB=(3a)/5, AC=(4a)/5 (tool: Parallel-Equal or Ctrl+Alt+Q)
4) Draw with center A, circle b(through B), circle c(through C).
5) Set a point D on the contour of c (point-tool while pressing shift-key, next to c).
6) Create a new motor object.
7) Create moving-point E, starting at D (right-click on the motor, select "Moving", then
using this tool, select 1st: D, 2nd: the motor itself).
8) Press the motor button once to move E to some distance from D, so that you can distinguish
the two points. Then press again the motor-button to stop the move.
9) Set a point F, so tha EF is parallel-equal to a/5 (Parallel-equal tool Ctrl+Alt+Q).
10) Create moving (rotating) point G, starting at F and rotating about E (right-click on the motor, select "Moving", then using this tool, click 1st: F, 2nd: the motor).
11) Press the motor button once to move G a little further from F (initially they are identical).
Then press again to stop the movement.
12) Draw circle e, with center E, passing through G.

13) Set some points on the contour of e (Divide in N parts-tool, pressing F3 click at G).
14) Join E to these points to give the impression of wheel's spikes.
15) Attach a pen to G.
16) Press the motor-button to start the movement.
17) Press the F2 key while the system moves. The pen traces the epicycloid g.

Notice that the turning wheel e has 1/3 of the radius of the fixed circle b, therefore the name _3to1
of the document. You can analogously produce epicycloids _NtoM ( M <N) for otherwise arbitrary
integers. You can even create epicycloids with arbitrary ratio R/r , R being the fixed-circle-radius
and r the moving-circle-radius.

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