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Ways to make an epicycloid curve?
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* November 01, 2015, 02:35:25 PM
Hi, I'm trying to design something and I need to make an epicycloid curved line. I'm using TC 18 Pro and I don't see a way to do this. Is there a way to make a curved line with an equation? Or some kind of addon that I can download to do this?

Thanks,
-Kyle

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* November 01, 2015, 02:56:09 PM
#1
I didn't actually know what one was, had to check internet for it, looking at this page - https://en.wikipedia.org/wiki/Epicycloid I just wondered if there any particular one you are interested in (if any).

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* November 01, 2015, 07:38:05 PM
#2
One way (see attached screenshot)...

Place a Point object (red) (white cross) on the generating circle (pale yellow), Group the two, and set the Center of Extents of the Group at the center of the circle. Place the generating circle tangent to the base circle (blue). Radial-copy the Group about the center of the base circle, setting "Angle" equal to 360/"Sets" and "Rot" equal to "Angle" x [(Base circle dia/generating circle dia) + 1]. Draw one Spline by Fit Points (green) through the Point objects that define one loop of the curve, then Radial-copy it about the center of the base circle to generate the complete epicycloid. (It might be necessary to add some extra points manually, to define where the curve touches the base circle. Small red circles are these extra points.)

Note: Don't use a Star for the Point object. Since ths shape is not symmetrical about the X axis, its location is somewhat ambiguous.

Henry H
« Last Edit: November 02, 2015, 02:39:18 PM by Henry Hubich »

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* November 02, 2015, 06:29:30 AM
#3
Thanks Henry,

That's exactly what I needed. Thank you so much.

To get the curve to touch the base circle you have to figure out how many cusps (points where it touches the base circle) you want to have. Then (base circle radius/cusps) will give you the radius of the generating circle.

Base circle = 10 radius
Cusps = 4
Generating Circle = 2.5 radius

This way the points will land on the base circle exactly.

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* November 02, 2015, 08:45:01 AM
#4
I just wanted to add the way to make a hypocycloidal curve as well. This is the same type of curve, but on the inside of the circle. Everything is the same as making the epicycloid curve except for the Rotation equation. Here is what it should be.

"Rotation" equal to 360 - ["Angle" x (Base circle dia/generating circle dia)]

Sorry if my equation isn't very pretty, but it gets the job done.


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