I have this almost epitrochoid. I need to create the rotor with one more lobe, so it’s 3:4. I know it’s necessary to rotate the blue circle D6 inside the black circle D8 Enveloped.3dm (113.3 KB) with the violet epitrochoid to create the stator.
But how can I do it?

How about you construct a line between the centers of D8 and D6, then use the D8 center to rotate D6 and the purple with the desired angle taking this constructed line as reference.

Thank you. But I can notice I didn’t draw cycloids. It’s just curved, it didn’t roll. I have no reference. I think it’s a small 3 teeth gear rotating inside a 4 teeth gear. I don’t know the angles.

Divide each circle into segments in inverse proportion to their diameters. I’ve chosen 32 divisions for the large circle and 32 x 6 /8 = 24 for the smaller, but smaller segments might be needed to get sufficient accuracy

Sub-select (ctrl-shift-click) the rotor and copy it to the new layer

Repeat steps 5 through 7 until you have processed one quarter of the large circle segments, then select the copied outlines and polar array them around the large circle centre with No. of Items set to 4 to fill the remaining quadrants (i.e. take advantage of the symmetry to complete the outlines more quickly)

At intervals around the outlines place points on the outermost curve. I extended the radial lines and placed points where they intersected the outermost outline

Thank you very, very, much for your efforts. I messed the point in “Set Current” and “Copy objects” so I tried copy and paste. The rotor seems to reach 90º but it didn’t work out. What I’m missing? I don’t find a way to finish this. I tried to make 360º but it didn’t work out either.

The job of constructing curves like this is tedious. Grasshopper can reduce the tedium - and allow you to experiment with more sample points. Out of interest I created the following grasshopper script for your curve (in Rhino 6 I’m afraid):