# Full Version: Cycloid curve

From: BurrMan [#1]
2 Sep 2013
To: ALL

Hello Michael,
I wanted to design a roller pinion and got stuck. I think I need a cycloid curve and was wondering if there was a way to get this in MoI.

Basically a roller pinion looks like this:

I want to draw this in MoI, which would need curves like this:

I got stuck on an arc, and figured out it wasnt the curve I need. I did a 3 point arc like this:

Here's a file attached too. Eventually, the blue circles would be included. I just start with a quad seperated circle for simplicity.

So I think I figured I needed a cycloid curve and have found some math that derives this. Is there a way with one of the MoI tools for me to draw out this path?

Maybe Bemfarmer's next parametric script? :o

Thanks.

Attachments:
roller_pinion.zip

Image Attachments:
cycloid curve.jpg  roller pinion.jpg  roller pinion_curve.jpg

From: bemfarmer [#2]
2 Sep 2013
To: ALL

Hi Burr

I'm sure something can be done, fairly easily.
I studied epicycloids, etc. two to three year ago.
I recollect that there is a similar drive with a patent, I think it had epi or hypo track. (?)

First step is to review the math, etc

Already did a Moi epicycloid script a couple years ago. It is on the forum.

Typing this is acting weird tonight.
- Brian

The drive can be used on CNC I think, very fast?

From: Michael Gibson [#3]
2 Sep 2013
To: ALL

Hi Burr, I guess probably the easiest approach is to use whatever programming language you're most comfortable with to do the math formulas you need and to emit a series of x,y,z points to a text file. Then you can use the ImportPointFile plug-in (http://kyticka.webzdarma.cz/3d/moi/#ImportPointFile) to read in those points as a curve, either as the control points of the curve or as points to interpolate through.

There is not any already set up method in MoI to make those particular kinds of curves.

- Michael

From: BurrMan [#4]
2 Sep 2013
To: ALL

Thanks Michael....

From: BurrMan [#5]
2 Sep 2013
To: ALL

Hi Bem,
Yeah, I was looking at your epi and Hypo cycloid scripts, to see if I could derive anything.. Not there yet.

There's a drive on a flowjet cnc that is the patent I think your refering to.... ( I think the image I grabbed as a ref is from the flowjet setup) Thats these guy's:

http://www.nexengroup.com/

From: bemfarmer [#6]
2 Sep 2013
To: ALL

Found a 1906 patent :-)

The epi and hypo scripts do not form this shape, I guess.

Still doing research...

-Brian

From: bemfarmer [#7]
3 Sep 2013
To: ALL

The curve(s) formed by the rollers are called "curtate cycloids" (Another backward paper calls them Prolate. )
There are equations here: http://mathworld.wolfram.com/CurtateCycloid.html

They are used on violins and archtop guitars, so a script might have some utility:-)

http://liutaiomottola.com/formulae/curtate.htm

A modified sine wave script would be ?easy?
Maybe the curve could be booleaned to make the gear "rack," or a portion of it anyway?

- Brian

From: BurrMan [#8]
3 Sep 2013
To: ALL

Hey Bem,
So I got results by follwing a guy that graphed out the points I needed. Oddly enough it reminded me of a barrel on a wave:

I think I'll go get in the ocean tomorrow!

"""""""""Maybe the curve could be booleaned to make the gear "rack," or a portion of it anyway?""""""""""

Yes, these curves will be used to cut the radius' at the topmost portion of the rack teeth. The base point of the rack is a simple arc, but for the top part to be "tight", the teeth need to have the radius to allow the rollers "contact" in more than one place at a time. no backlash. It makes for constant contact on more than one roller.

""""""""curtate cycloids""""""

Thanks. The terms help me find the info I need :)

Anyway, I got what I need, so dont pull out any hair, but I thought of you because this falls right inline with all your other parametric scripts.

Image Attachments:
barrel.jpg

From: bemfarmer [#9]
3 Sep 2013
To: ALL

Here is a quick script patterned on the sinewave script.
Have to get some actual radius estimates.
There are two radii for each roller. The two curves cross over.
Need to form an "envelope" ?

- Brian

Attachments:
Cycloid.7z

From: bemfarmer [#10]
3 Sep 2013
To: ALL

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

From: bemfarmer [#11]
3 Sep 2013
To: ALL

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

From: BurrMan [#12]
3 Sep 2013
To: ALL

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

From: Frenchy Pilou (PILOU) [#13]
3 Sep 2013
To: ALL

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

From: bemfarmer [#14]
3 Sep 2013
To: ALL

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

From: bemfarmer [#15]
3 Sep 2013
To: ALL

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

From: BurrMan [#16]
3 Sep 2013
To: ALL

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......

From: blowlamp [#17]
3 Sep 2013
To: ALL

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

From: bemfarmer [#18]
3 Sep 2013
To: ALL

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.

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

Attachments:
CycloidInterp.7z

From: bemfarmer [#19]
3 Sep 2013
To: ALL

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

From: bemfarmer [#20]
3 Sep 2013
To: ALL

The DXF seems to be a little imprecise.?

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 sweept surface look pretty good at the backlash meeting point.