Full Version: Cycloid curve

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The DXF seems to be a little imprecise.?
aRadius = 31.85
b radius = 30.0

Okay, plot the curtate center of the roller with CurtateInterp script, and sweep with a 10mm diameter line.
Comes out pretty close.
The tooth profile and the swept surface look pretty good at the backlash meeting point.

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Here is the resulting curve for the teeth, in Red color.
Lopped off the top and did a fillet.

I think that does it, within some level of precision. :-)

- Brian

Edit: There is probably some formula for the curve, derived from "instantaneous velocity centers," or something.
There must be some formula for calculating the pitch circle diameter. (?)

There is a paper that did something like that for epi and hypocycloidal speed reducers

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Thanks Brian for all the time to help out with that!

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The CycloidInterp script works well for modeling the Revoloop. (German patent was applied for.)

http://forum.alibre.com/viewtopic.php?f=10&t=17773&p=110124#p110124

This would make a 3D print, or even a CNC router project.
It may be more of a novelty than a practical gear(?)

- Brian

Image Attachments:
RedProlateCycloid_BlueOffset02.png 

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Hi,

is is right that there are different cycloid scripts uploaded here ?
I could not find ou the difference between them.

Here my question regarding epicycloids :
- How can I build several epicycloids nested within each other
like the 2 shown in the attachment ?



 

Image Attachments:
Epicycolid.png 

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Hi Tom,

re:
> - How can I build several epicycloids nested within each other
> like the 2 shown in the attachment ?

After you've created one, try using Construct > Offset on it to build a new nested one.

- Michael

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Offset is the first which came in my mind - but it does not work.
I tried trimming the Epicyloid curve in segments but nothing either.
Thats why i posted the question here.

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Hi Tom,

I used Hypotrochoid script to emulate your inner curve, with a:b ration of 5:1, a = 10, b = 2, c = 4.5 seems to be a close match.

Per Michael's suggestion, I tried offset for a larger curve, with 4 of 5 lobes working well.
I manipulated one lobe with trims and joins and circular array, and join, to match your drawing...
May try again after work.

- Brian

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Hi Tom, can you please post the .3dm model file with the epicycloid curve in it that won't offset?

- Michael

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Post deleted.
Thanks to Michael and Tom for lesson on unchecking Trim in Offset command in following messages.

Bothsides checkbox is also interesting.

- Brian

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Hi Michael,

It is possible to offset, but after that,
I have to trim and blend, etc.

I am going through many variations and itrations, so it would
be a time saver to generate the desired curve with one click.

I tried the script fatlines but it causes a crah when working with an Epicyloid.

Image Attachments:
FILE.jpg 

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Thank you Brian, Ill have a look !

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Hi Tom, if you could please post the .3dm file with the curve in it, instead of only screenshots it could make it easier to give suggestions.

From what I tell from your latest screenshot there, it looks like you should just uncheck the "Trim" option in Offset so that it will generate the full curve for you instead of trying to cut out pieces at self intersections.

- Michael

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- Fatlines with very thiny values (0.1, or 0.05) by Max Smirnov http://moi3d.com/forum/index.php?webtag=MOI&msg=7594.31
- Kill original lines
- increase size
- Trim All

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Hi Michael,

Sorry, I had upload but forgot to take a second look.

Anyway you gave me the key - I were not aware about the trim function in the offset
command so I am happy to have learnt about another function former unknown to me.

Back to MOI which fits like a bespoke glove for my work as an artist and designer
who wants to visualize inmediately what he has in mind without being distracted by a myriad
of buttons and commands ! I am really happy that I discovered your little gem a while ago.

Attachments:
FILE.3dm

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No problem Tom, I'm glad that offset will work for you!

@Pilou - re: FatLines - FatLines uses curve booleans which is not really expecting to work with self intersecting curves like in this case.

- Michael

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Here is an update to the _CycloidInterp script, renamed to _CycloidTrochoid.

This script plots a Trochoid or Cycloid on the x axis.
A common Trochoid has the bRadius equal to the aRadius, and is a Cycloid.
Interpcurve factory is used, to avoid cusp rounding.
Rewritten by Brian McMillin, September 2018.
A Brachistochrone is an inverted Cycloid.
A Gerstner wave is a trochoidal wave.
If b>a, the trochoid is a prolate cycloid.
If b<a, the trochoid is a curtate cycloid.

Note the different behavior of the display of the ignore checkbox,between MoI3 and MoI4.
For MoI4, the three lines of text are centered with the checkbox.
For MoI3, the first line of text is horizontal to the checkbox, with the other three lines below. (A preferred look???)

Can the (vertical?) centering be changed in the MoI4 display of the .htm file?

- Brian

Script updated 9/25/2018, with Michaels input, if the 3 people who downloaded it want the update.

Edit, Only one cycle is plotted, due to cusp problem with 2+ cycles.

Attachments:
_CycloidTrochoid.zip

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Hi Brian, re: checkbox positioning, it is possible to change that one checkbox's position by putting this in the head section of your _CycloidTrochoid.htm file:

		<style>
			#ignore_bRadius {
				align-items:flex-start;
			}

			#ignore_bRadius .checkbutton_box {
				margin-top:0.2em;
			}
		</style>

- Michael

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Thank you Michael

That works.
Unfortunately, the values of aRadius and bRadius are now set to zero, in MoI4, but are ok in MoI3 :-)
?

- Brian

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Hi Brian,

re:
> Unfortunately, the values of aRadius and bRadius are now set to zero, in MoI4, but are ok in MoI3 :-)

That's a bug in v4 with handling whitespace characters in the default value. If you remove the line break for the default="" attributes that should avoid the bug right now.

So where you currently have:

			<tr>
				<td>aRadius</td>
				<td><input id="aRadius" class="numericinput" default="10
				" style="persist:true;"></td>
			</tr>

Remove the line break like so:

			<tr>
				<td>aRadius</td>
				<td><input id="aRadius" class="numericinput" default="10" style="persist:true;"></td>
			</tr>

I'll fix it up for the next v4 beta, thank you for reporting it.

- Michael

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