Full Version: Cycloid curve

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Maybe add curves for more teeth, out of phase...

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Well, may have been mistaken. I'm not sure if it is a curtate cycloid. Have to think about it some more tomorrow.
It gets confusing.
Still need to get an envelope for many points around the radius of a roller, most of which are out of phase.

There is a Rhino curtate violin program...

- Brian

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Hey Brian,
This is the path I got, and it does seem a little off. The orange curve is from your script. The cutup arcs are the path that should be a through point curve snaped to the mids to create the cycloid.

I havnt ran through the entire process yet to figure out the size of the rollers and how it relates to the spacing and the overall size yet. I have to run some things through first.

Talk later.

Attachments:
cycloid_curve_path.zip

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Seems number 17 gives the construction by Points ! ;)
M3 = perpendicular at the M Point
MT = Tangentcy to at the M Point
Cd= C'M

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My conclusions, right or wrong: Motion is relative to the linear gear at the "pitch line."

The roller pinion is NOT rolling along on the outer radius.
It is rolling along at the "pitch line" (?), formed by the point of contact of the rollers with the teeth. (?)
X axis Velocity is determined by the speed of rotation at this radius.

So this point on the roller determines the a radius, and traces out a full radius of a cycloid.
So the radius at the innermost point of the roller would trace out a slightly curtate cycloid.
The radius at the outermost point of the roller would trace out a slightly prolate cycloid
Other points on the perimeter of the roller cylinder would plot slightly curtate or prolate cycloids, out of phase a bit.
The whole envelope determines the tooth profile at the top.

The very outer radius of the roller pinion is just support material. It actually would trace a prolate cycloid.

It is confusing.

- Brian

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Utilizing the proper a_Radius at the pitch line, the diameter of one of the (ten or so) rollers determines
the b_radius for the slightly curtate curve traced by the innermost point of one of the rollers,
as well as the b_radius for the slightly prolate curve traced by the outermost point of the one of the rollers.

Modifying the script to compute these two points as a pair, for each t_radian distance, and
then creating a diameter circle there, will create an envelope.
Maybe make the circles planar surfaces.
There will be t * 2 * PI * number of circles, but MoI should handle this easily.
Then boolean add the circles to create the envelope, (?)
And boolean deduct the envelope from a rectangular rail, to form the upper portion of (some of) the teeth. (?)

? - Brian

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Maybe you could help me create the teeth for a specific pin size and count? This is the part I'm at now.

So I made a great rack, but how to equate the a and b values with how many pins in the roller of a specific size?

I could have those values dictate the amount of pins, but how to create the teeth in the rack per the pin count of my choice? I guess thats just an offsetting value of a single tooth made?

[EDIT] You were posting while I was typing:

You've gone beyond what I can speak to about it.... Any examples you give would help alot......

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I don't know if this will help, Burr.
Here's a cycloid curve that I generated in a CAD/CAM application that I use - perhaps you could scale it to your required size?


Martin.

Attachments:
CycloidSample.3dm

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Hi Burr

I'm not an engineer.
Looking at the NEXEN pdf, http://www.nexengroup.com/nxn/files/literatures/364_21262.pdf,
The RPS20 Pinion, as an example, has 10 rollers, a pitch circle diameter of 63.7 mm, and travels 200 mm per rev.
(PI * 63.7 = 200.1194520336698292900703835149mm)
I did not see the diameter of one roller, but this could be measured off of the side view.
Also need the radius, from the center of the Pinion, to the center of a roller. Will this come out to be the same as the pitch circle diameter/2?
These two values should enable the creation of a script to create an envelope, for the teeth of the rack.

Rack of 1000mm has 50 teeth. Rack tooth pitch, Peak to peak distance of the teeth, is 20.

CAD drawings, RPS20: http://www.nexengroup.com/nxn/products/details/id/966660
Also has several rack CAD drawings.

 


"---Maybe you could help me create the teeth for a specific pin size and count?---" I will try to help.

First create the pinion cross section with all of the relevant radii.
I think that the pinion determines what the rack teeth will look like.

Here is another script version, CycloidInterp, with Interpcurve and 200 pts per cycle, which makes a "more accurate" cycloid
See post 18 for updated script.

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Open RPS20 pinion DXF in MoI, measure distances.

Roller diameter is 10 mm
Shaft radius is 25 mm diameter. (not needed)
Radius from center of shaft to center of roller is 30 mm.
Pitch Circle radius is 63.7/2 = 31.85. This is not quite the same as 30 mm.

So now the Curtate and Prolate radii can be calculated.
Will try for a new script for envelope later

Got to go to work now. Will look again tonight.

- Brian

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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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