# Build Epitrochoid

Hi all,

I’m trying to build an epitrochoid. I’m rotating the small circle with the point 1.5 degrees around the big circle. After that how many degrees I must rotate the de small circle around it axle to and then from the epitrochoid?

Any help is welcome.

Ludwig

Epitrochoid.3dm (33.4 KB)

Hi Ludwig,

If the small circle has to move a distance around the circumference of the big circle and if is not to slip, then it must rotate so that its circumference travels the same distance. The circumferences of the circles are in the same proportion as their radii, in this case 3 to 1. So for a movement of 1.5 degrees around the large circle, the small circle must rotate 4.5 degrees.

Regards
Jeremy

Edit:

Hello - is the goal to build one of these or to know the answer to the question of how amny degrees? It is much easier, it seems to me to work out how to calculate some sample points from the formluas for these shapes, than to construct - but maybe that is what you need to do…?

At any rate, for the heck of it, here’s a python that may help -
Epitrochoid.py (2.4 KB)

To use the Python script use `RunPythonScript`, or a macro:

`_-RunPythonScript "Full path to py file inside double-quotes"`

The requested point radius is the distance of the point from the minor circle center.

-Pascal

1 Like

Thank you very much Jeremy.

Hi Pascal, Python is not my thing my I think I should try. Thank you.

Hi, @luizdecastro1981 If you want you can play with this too
Epitrochoid-.gh (11.2 KB)

1 Like

Hi vickthor. It’s the Heaven on earth. I must try it. Thank you very much.

Jeremy,

I tried.I divided the small circle into equal parts of 1,5 degrees. Many parts! It will be complicated to turn the small circles. May I know how exactly is your method?

Thanks,

LuizEpitrochoid 2.3dm (126.1 KB)

Jeremy,

I tried.I divided the small circle into equal parts of 1,5 degrees. Many parts! It will be complicated to turn the small circles. May I know how exactly is your method?

Thanks,

Luiz
Epitrochoid 2.3dm (126.1 KB)

If the angular division of the big circle is 1.5 degrees the the angular division of the small one should be 4.5 degrees. But you don’t need to plot so many points. I did it with an angle of 4 degrees on the large circle and 12 degrees on the small one.

Once divided, here’s what I did:

Group the small circle, its dividing lines and its point.
If a line a is aligned with line b, then move the small circle, from c, to d. You may need to zoom in and you will need to use osnaps to the end of each line.
Rotate the small circle, with the rotation centre at d and entering an angle of 16 degrees (i.e. the sum of the division angles 4 and 12), so as to align line e with line f.
Place a new point at the position of the grouped point, again using osnaps (to the point).
Repeat until you have all points then use Curve through points (_CurveThruPt) to draw the epitrochoid through them.
Epitrochoid3.3dm (85.6 KB)

Regards
Jeremy