Cycloid

[dancedanceyo]

Does anyone know how to make a cycloid in AutoCAD? As in a ramp with theoretically the fastest acceleration, I haven't used AutoCAD much so I will need step-by-step help. I need this to have a template for a ramp I'm planning on making

 

Additional:

height of 1meter and base of .75meter

[JD Mather]

What is the purpose of the ramp design?

Are you a student?

[dancedanceyo]

The purpose is to trace a board of wood with it and cut it out in the shape a ramp. I'm participating in a competition that requires a vehicle only powered by gravity

[bill_borec]

yo,

 

We might be able to help you a little better if you could provide a sketch or a picture or a link to a sketch or picture of what you are trying to design.

 

Is your ramp to be elliptical? spiral curve? simple arc? triangular? Help us help you!

[nestly]

I imagine it to look like a ski jump ramp, but I'm not a physics guy, so I have no idea if a ski jump ramp is a cycloid. Is this different than an ellipse?

Image courtesy of Wiki....

[dancedanceyo]

It seems to look like this:

[rickh]

The change of slope along a cycloid is different from an ellipse. If you got a cycloid and an ellipse to have the same max/min x and y values, those would be the only points that touched both the cycloid and the ellipse. Not sure if that makes sense, but to test you can throw both equations in excel real quick and compare values at certain intervals.

 

As far as plotting a cycloid in acad, I would only guess that your best option is to draw a polyline with a lot of vertices to 'look' like a cycloid. I don't think you can get an exact continuous curve for that function (I could be wrong). I know a lot of the folks here can do the calcs in lisp and make a list to then draw the polyline at those vertices from 0 to 2pi.....but I myself am rather slow at writing routines.

[Organic]

Use the equations for a cycloid on the Wikipedia article you linked to to find the arc length? Then the distance between the arc will simply be the permiter of the circle (using your example). Once you know these two pieces of information it is easy to draw in AutoCad.

 

Draw => Arc => Start, center, length should do it (or similar commands if you use the ribbon)

 

I haven't tried it though.

[rickh]

Here is one option. I made a quick excel chart because I was curious...input the number of vertices for a polyline (the level of accuracy), and input the radius of the cycloid. This will list x,y values for however many iterations of 2PI you want (I stopped the functions at 400 rows, but you can drag them down for more accuracy if needed). It also shows where the first PI and 2PI occur, so you know where one cycloid cycle is.

 

After inputting those two values, just copy the three columns in green to notepad. this will give x,y values. Highlight one of the tabs that notepad created, press CTRL+C to copy the 'tab', then press CTRL+H, and then in the find box press CTRL+V, and leave the replace box blank...pick 'replace all'. Lastly, press CTRL+A to select all, then CTRL+C to copy. In Autocad, start the PLINE command, then press CTRL+V to paste the vertices in. Watch it work.

 

It sounds like a lot of work as I look back at this post, but it is very simple. You could also use the SPLINE command if you want. I'm just not good enough with lisp to make a pline from a list....maybe one day. Additionally, in the excel chart, there is an ellipse being calculated at the same time. You can follow the same steps to draw an ellipse...though you don't need to....I mainly wanted to compare the slopes. I forced the ellipse to stop at 2PI for obvious reasons.

 

Oh, and this will always be created starting at 0,0 by the way.

 

cycloid-vs-ellipse.xls

Edited March 17, 2012 by rickh

[rickh]

Dink87522,

 

I think an arc is always circular. The cycloid will produce more of a parabolic-ish shape. The closest would be an ellipse, but the defining equations are different so they must create different curves.

[rickh]

Additional:

height of 1meter and base of .75meter

 

Looking further into the function of a cycloid, and your conditions to meet, I don't think that a cycloid can meet these restrictions...might you need a trochoid instead?

Attached is the same calc file, but modified for the trochoid, which can also produce the cycloid. You can search trochoid on wiki to see the easy explanation...as far as what exact radii to use, well it's your competition. Start calculating some tangential acceleration I suppose using radii values that create a ramp with these parameters.

good luck...

 

sorry to all for the post...post...post....

trochoid-vs-ellipse.xls

[JD Mather]

The purpose is to trace a board of wood with it and cut it out in the shape a ramp. I'm participating in a competition that requires a vehicle only powered by gravity

 

If you are a student you can download Autodesk Inventor Professional for free from http://www.autodesk.com/edcommunity and Inventor will create the ramp for you based on any motion law you want.

 

[SLW210]

Looking further into the function of a cycloid, and your conditions to meet, I don't think that a cycloid can meet these restrictions...might you need a trochoid instead?

Attached is the same calc file, but modified for the trochoid, which can also produce the cycloid. You can search trochoid on wiki to see the easy explanation...as far as what exact radii to use, well it's your competition. Start calculating some tangential acceleration I suppose using radii values that create a ramp with these parameters.

good luck...

 

sorry to all for the post...post...post....

[ATTACH]33692[/ATTACH]

 

A trochoid is a cycloid. TROCHOID

[rickh]

A trochoid is a cycloid. TROCHOID

 

Acutally, a cycloid is a trochoid; in which the radius to the tracing point is the same as the radius to the edge of the wheel of revolution (b=a in the link you provided). A trochoid is not necessarily a cycloid, but a cycloid is definitely a trochoid.