Accurate Cycloid

Bill_Carson · January 3, 2018, 3:17pm

Has anyone got one in Rhino format ? or know how to generate the curve within Rhino.

tom.norris23 · January 3, 2018, 4:04pm

Im not sure if this is what you want, and it is only an appox as it steps but:

Bill_Carson · January 3, 2018, 5:05pm

Thanks Tom and Richard, I don’t have grasshopper so wasn’t able to test yours. Richard I was thinking yours would be pretty spot on but as you commented it is coincidental. When I scaled and added numbers to it, the error is significant. I was very surprised as my friend supplied a mathematical cycloid (red curve) that had me scratching my head. The purple curve is mine generated by interpolation of points and corresponds quite well though curvature analysis shows it has some kinks where it transitions to vertical. Richard your curve is smoother, but flawed. If nothing else, Thank You both for confirming my own work, which I doubted.

tom.norris23 · January 3, 2018, 5:11pm

Bill do you have the rhinoWIP, should have GH inside it?

I have baked the GH model but if you scale it then the accuracy will be lost?

Cycloid.3dm (18.3 KB)

Bill_Carson · January 3, 2018, 5:30pm

Thanks Tom, just checked the numbers direct from your 3DM, and scaled, it has error too, but could be attributed partly as faceting. Again it helped to confirm my approach and numbers. The gap should always be the circumference of the circle that sets the height, as a fast rule. Generating accurate cycloids is a lot harder than it looks. Fortunatley once you have it, it should just scale within Rhino for each diameter, I shall see.

Again many thanks to you both for responding.

tom.norris23 · January 3, 2018, 5:31pm

Cycloid2.3dm (35.7 KB)

Was just in the process uploading one at the scale you are using

Helvetosaur · January 3, 2018, 5:37pm

Just curious why you didn’t use an Interpolate Curve component instead of a polyline? --Mitch

tom.norris23 · January 3, 2018, 5:38pm

No good reason, I just though it might distort the curvature more than facating

Bill_Carson · January 3, 2018, 5:46pm

Can confirm that interpolated curve is more accurate and scales accurately within Rhino. This had been bugging me for a couple of days.

Bill_Carson · January 3, 2018, 10:31pm

Thanks Richard, my friends curve was an SVG file which didn’t translate properly. We have since confirmed a correct mathematical curve against my point generated curve and they are an exact match, removing my doubts about how I generted my own cycloid curve.

For the record, the mathematical curve had 630 points, the Rhino interpolated curve 15.