Help wanted for scripting an "epicycloid" for sketcher

[manuelkrause]

Hi people,
can someone point me to the ways how to create a scripted sketch for an epicyloid?
The result should be either point based or even better usable for later FC part design. Spline?
I've currently hand-made the first steps, by constrained geometry, but they're getting slower over each new constraint.

EDIT: on my slow CPU ~3min. at a next angular constraint.

Many thanks in advance!
BR,
Manuel

[hjh]

Added a little bit to the requirements.

The question seems to be how to create your own 2d-shape object type given by equations (indicated red below in the screen shot)

https://en.wikipedia.org/wiki/Epicycloid

Epicycloid_Wikipedia_Screenshot_2019-01-05.png (83.8 KiB) Viewed 1991 times

The red curve is given by the formula.

epicycloid_formula_wp.png (5.45 KiB) Viewed 1987 times

--HJH

[manuelkrause]

Added a little bit to the requirements.

The question seems to be how to create your own 2d-shape object type given by equations (indicated red below in the screen shot)

https://en.wikipedia.org/wiki/Epicycloid

Epicycloid_Wikipedia_Screenshot_2019-01-05.png

--HJH

Many thanks,
but my main question is, how to guide it (the Epicyloid formula) into a python usable formula, to gather coordinates for points etc. I've read the wikipedia etc.

Manuel

[manuelkrause]

Added a little bit to the requirements.

The question seems to be how to create your own 2d-shape object type given by equations (indicated red below in the screen shot)

https://en.wikipedia.org/wiki/Epicycloid

Epicycloid_Wikipedia_Screenshot_2019-01-05.png

The red curve is given by the formula.
epicycloid_formula_wp.png

--HJH

Don't understand me wrong. I just want to get the curves into usable sketch points.

[hjh]

It seems that the issue is to follow the Octahedron example

https://www.freecadweb.org/wiki/Scripted_objects

and create a class Epicycloid.
What makes it more complex is that the new shape is given by a formula and not by discrete points.
Maybe there is an example in the documentation somewhere how to describe an object shape with a formula, not discrete points.
BTW could you please indicate how you produced what is seen on your screen shot?

--HJH

[saso]

There are some macros
https://www.freecadweb.org/wiki/Macro_Draw_2D_Function
https://www.freecadweb.org/wiki/Macro_D ... D_Function
https://www.freecadweb.org/wiki/Macro_3 ... tric_Curve

[manuelkrause]

It seems that the issue is to follow the Octahedron example

https://www.freecadweb.org/wiki/Scripted_objects

and create a class Epicycloid.
What makes it more complex is that the new shape is given by a formula and not by discrete points.
Maybe there is an example in the documentation somewhere how to describe an object shape with a formula, not discrete points.
BTW could you please indicate how you produced what is seen on your screen shot?

--HJH

Do you understand a little German? Doesn't matter if not. Main actual math of it I re-derived from wikipedia. The base data info was from http://rx7ch.com/files/wankelmotor_matura_arbeit.pdf (german). Page 16 and following.
For the work for the screenshot I stupidly made all the geometric settings in the sketch. One degree on main circle, two degrees on rolling circle, including some distance always rotated with the rolling circle, leading to the needed resulting curve point.

BR,
Manuel

[manuelkrause]

There are some macros
https://www.freecadweb.org/wiki/Macro_Draw_2D_Function
https://www.freecadweb.org/wiki/Macro_D ... D_Function
https://www.freecadweb.org/wiki/Macro_3 ... tric_Curve

Thank you very much for this collection !
I need to have a closer look at them during next days.

Best regards,
Manuel

[JoshM]

Oh--that's cool. I tried it out and this should get you going. I tried it with R = 3, 5, and 15, and from wiki link, it looks correct.

Epicycloid_Macro.png (144.11 KiB) Viewed 1909 times

Epicycloid_Macro2.png (165.17 KiB) Viewed 1905 times

Epicycloid_Macro3.png (167.67 KiB) Viewed 1905 times

Code: Select all

import FreeCAD
from FreeCAD import Gui
from FreeCAD import Base
from FreeCAD import Vector
import Part
import math
import Sketcher
import os
import Draft

R = 3.0		# Big Radius
r = 1.0		# Little Radius
k = R/r		# Altenate form constant
K = (k + 1)

Num_Theta_Points = 1000
Theta_Step = ((2* math.pi / Num_Theta_Points))

Epicycloid_Points = []	
for t in range(0, (Num_Theta_Points - 1), 1): 
	Theta = (t * Theta_Step)
	
	x = (r * K * math.cos(Theta)) - (r *  math.cos(K * Theta))
	y = (r * K * math.sin(Theta)) - (r *  math.sin(K * Theta))
	epicycloid_point = Base.Vector(x, y, 0.0)
	Epicycloid_Points.append(epicycloid_point)
	
Draft.makeBSpline(Epicycloid_Points)

I placed this in the XY plane, but you should be able to manipulate to your own needs from here I suspect. You can convert to a Sketch in DraftWB, but I don't think that will help you much--this has 3003 degrees of freedom in the Sketcher;)

I looked a bit further, and this isn't correct yet for fractional k values.

Cheers,
Josh

[DjangoFreeCAD]

Here is a Script which draw the Epicycloid in the Sketch

Create a new document and sketch and then launch the macro

You will see how the drawing is made by the movement of a line and a circle

FreeCAD2 Macro.jpg (32.48 KiB) Viewed 1859 times

FreeCAD Macro.jpg (52.15 KiB) Viewed 1859 times

FreeCAD3 Macro.jpg (45.56 KiB) Viewed 1859 times