Creating a cycloid

[CanisLupus]

Does anyone have a method for drawing a cycloid in VCarve Pro? I need to create the red line shown in the image below.



FYI, from its Wikipedia entry, "... a cycloid is the curve traced by a point on a circle as it rolls along a straight line without slipping."

Thanks!
Scott

[CarveOne]

I was able to save it as a .png file format using screen capture and an old version of Gimp. The resolution is not very high, though with some better expertise it might get better.

CarveOne

[jimandi5000]

Does anyone have a method for drawing a cycloid in VCarve Pro? I need to create the red line shown in the image below.



FYI, from its Wikipedia entry, "... a cycloid is the curve traced by a point on a circle as it rolls along a straight line without slipping."

Thanks!
Scott

What is the diameter of the circle?

[adze_cnc]

You could use an online cycloid to DXF creator such as this one from the University of Waterloo: https://cs.uwaterloo.ca/~smann/C5/

See also: http://www.cgl.uwaterloo.ca/smann/ccycloid/

[4DThinker]

Not hard to to figure out. The height is the diameter of the circle, and the width of each bump is the circumference of the circle. Each bump is half of an ellipse. All the needed tools are in VCarve/Aspire. Once you have one bump drawn use the linear array tool to make a row of them as long as you need.

[TReischl]

Not hard to to figure out. The height is the diameter of the circle, and the width of each bump is the circumference of the circle. Each bump is half of an ellipse. All the needed tools are in VCarve/Aspire. Once you have one bump drawn use the linear array tool to make a row of them as long as you need.

Umm, sorry, no. A cycloid is not an ellipse. An ellipse is a conic section.

A cycloid is not a conic section.

It is not possible to fit an ellipse to a cycloidal curve. They are very different things that look similar.

Here is an example of trying to fit a true ellipse to a cycloid:

[JimmyD]

Haven't tried this, just thinking out loud.

What if you use the equation below and generate the x,y points in excel and then import those points into aspire using that routine from Paul (can't think of his last name or the routine at the moment).

Cycloid, the curve generated by a point on the circumference of a circle that rolls along a straight line. If r is the radius of the circle and θ (theta) is the angular displacement of the circle, then the polar equations of the curve are x = r(θ - sin θ) and y = r(1 - cos θ).

[adze_cnc]

I still think my suggestion is best. Using the equation presented and wiritng a gadget in LUA is also possible but I suspect beyond the capabilities of the original poster (sorry about presuming, CanisLupus).

[mtylerfl]

It’s so simple to do without any equations.

Just draw a circle, use the Measure Tool to find the circumference, use that figure to draw a line that length, center-align the circle and line with the circle base on the line, then use the Arc Drawing tool to snap to the line ends and centered circle top. Done!

(I guess I can make a couple minute video, if anyone got lost there!)

[TReischl]

Ummm, a no on that one two Michael, sorry.

If that were the case then all that curve would be is a portion of a circle.

JimmyD above is correct, it is a curve defined by a formula (the one he showed).

The real question IMHO is if the OP needs a true cycloid or just something close. If all he needs is close then tracing a curve thru the gif file posted earlier would work just fine.

It seems to me that I watched a video a few months ago about cycloids and there was something about them being constant acceleration or something like that. Would have to go dig that up. The guy had models that showed some really neat stuff about marbles rolling down unequal tracks arriving at the end at the same time. Could be wrong about that. . . . but I do know that cycloidal curves are used in gear reducers.

[TReischl]

I still think my suggestion is best. Using the equation presented and wiritng a gadget in LUA is also possible but I suspect beyond the capabilities of the original poster (sorry about presuming, CanisLupus).

+1 on that Stephen.

[mtylerfl]

Ummm, a no on that one two Michael, sorry...

Well, It’s good I’m not on the team that calculates the trajectory for Mars landings and such. I might miss!

[4DThinker]

OK, as a cycloid segment is not elliptical, then plotting points as you rotate a circle section along a line the same length as the circumference will likely be the simplest way. All you need is 1/2 of one bump, then mirror it, then join to get one bump you can then copy as many times as you want. Connect the plotted points with segments of a polyline, then smooth each Node.

4D

[CanisLupus]

I still think my suggestion is best. Using the equation presented and wiritng a gadget in LUA is also possible but I suspect beyond the capabilities of the original poster (sorry about presuming, CanisLupus).

No need to apologize. I went the Excel route to generate a list of X, Y values and used that to create the geometry in CAD. It works but I've been trying to do more in VCarve, less in CAD as an attempt to learn more about VCarve's capabilities. Writing a gadget using LUA is possible but I'm asking to avoid writing functionality that's already in VCarve.

A gadget might be the best solution since I could programmatically weed out nodes that are too close together and result in short line segments.

Thanks!
Scott

[CanisLupus]

...
It seems to me that I watched a video a few months ago about cycloids and there was something about them being constant acceleration or something like that. Would have to go dig that up. The guy had models that showed some really neat stuff about marbles rolling down unequal tracks arriving at the end at the same time.
...

They are fascinating and worth digging into if you find physics and nerdy stuff interesting.

The model you mentioned is a common demonstration. I watched a video with billiard balls and another one with a large model (maybe 20 feet long) that used bowling balls. The key takeaway, no matter where on the cycloid the marble is placed, it will arrive at the bottom of the cycloid at the same time as a marble placed in a different location, even at the very top or near the bottom.

Check out Brachistochrone curve, Tautochrone curve, isochronous curve, and pendulum motion.

And here are two videos:

(Adam Savage and Vsauce)