How to draw Hypocyloid curve?

[Anonymous]

Hi everyone!

Do you know how to draw Hypocyloid curve in sketches?

This is Hypocyloid function: 
x=(R+r)cost-rcos((r+R)t/r)

y=(R+r)sint-rsin((r+R)t/r)

with

R is radius of basic circle

r is radius of circle, the circle turn around basic circle

t is an angle

When I draw the Hypocyloid in Excel, it's OK

This is hypocyloid I draw on Excel from the function above

When I draw it on Inventor, I use to Equation Curve to draw, but it happen mistake:

This is the mistake:

I don't understand why it happen the mistake.

How to fix the mistake?

How to draw the Hypocyloid curve?

Hope everyone help me. Thank you!

[swalton]

Have you tried limiting the equation to a single lobe of the curve?  That may allow you to avoid the section that is causing Inventor difficulty.

If you can get a single lobe working, you can use a sketch or feature pattern to finish out the rest of the curve.

[I_Forge_KC]

The degree of curvature in the "valleys" is too high for Inventor's internal math engine to handle. It's an unfortunate limitation.

As @swalton suggested, try finding the minimum period and then performing an array (or, have multiple EDCs).

[JDMather]

Turn on your sound....

[Cris-Ideas]

Hi,

Limit equation to half of the lobe.

Build one lobe and than pattern it around axis proper number of times.

please also visit this thread equation curve how to constrain for additional information about constraining equation curves tat you will find useful for this case.

You are probably trying to build cycloid that intersects and that's why inventor is not  able to do equation.

Do you have proper conditions for R2/R1 ratio in place?

I attach sample of my cycloids.

Cris.

[Anonymous]

I have done your way. But the curvature isn't exactly. This is a picture of the curve:

The trajectory created in dynamic simulation enviroment is exactly, but when the trajectory export to sketch is not exactly.

I think the curvature is created from 600 points, then it is  connected each other by Spline so it have not exactly.

Look at it's seems right,  but when I zoom out in one coner:

I don't know if I think so right?

I wan't to draw Cycloid gear. Follow theory, Cycloid gear is gear with profin of top gear has Epicycloid form and profin of bottom gear has hypocycloid form.

Follow theory, the curve porfile above's not exactly.

[Anonymous]

Thank you for reply me, but I'm using Inventor version 2016, I can't open attached file - Can you convert attached file to version 2016 or lower version? Thank you so much!

[Cris-Ideas]

No I can not but I will make video and upload so you can follow.

Is it possible for you to install trial of 2017?

Give me your input data for this gear.

Cris.

[Cris-Ideas]

try that I think this may be an older one.

Cris.

[WHolzwarth]

I too think, that there's a precision error in this type of equation curve. There's no smooth transition at the top or bottom of the curves, that is a point with sudden change by theory.

Additionally I tried several parameter changes for Inventor's equation curve, but a once existing curves refuses to update after changes.

Nice animation is linked below. Curves can be changed by mouse for parameters R, r, a:

https://www.geogebra.org/m/tays8KSV

[TheCADWhisperer]

---

@Anonymous wrote:

I think the curvature is created from 600 points, then it is  connected each other by Spline so it have not exactly.

Look at it's seems right,  but when I zoom out in one coner:

I don't know if I think so right?.

---

What is the tolerance in your manufacturing process?

Can you 1. Increase the number of points and 2. Only do one loop so that that the spline does not curve into the next loop at that inflection point and then Circular Pattern the rest of the loops?

[Cris-Ideas]

I have made many of those using precise equation and equation curve.

If parameters are selected so there is no self intersection of hypocycloid I had curve created around whole circle.

As long as equations produce continuous and  not self intersecting curve inventor should draw it without any problem.

If R1=R2*(i+1) where i is whole number there will be no intersections.

In all other cases hypocycloid will be self intersecting. And to get this modelled some special techniques must be used.

Cris.

[Cris-Ideas · Accepted solution]

Here is how you can create curve and solid according to your data.

First video is about the curve it self, please skip to the second video when I start to struggle with creating solid

Second video is how to create solid out of it. It is not as straight forward as you may think.

You can also download this file in AI 2017.

If someone will recreate it in older version please also upload her.

Cris.

[Anonymous]

Finally, I can do it follow solution of Cris-Ideas.

Thank you everybody for your helps!

[Anonymous]

to The CADWhisperer ... 

Can you make a video of your method in your Youtube channel. I downloaded your zip file. But mine is also 2016 version. I am unable to get the joints classified correctly. I have attached a screenshot of it. I am a newbie. So Kindly excuse this basic question. Thanks

[JDMather]

I do not see a Rolling Cylinder on Cylinder Joint in your image.

Attach your assembly here.

[Anonymous]

Sir,

     I have attached the assembly.

[JDMather]

I don't own a rar extractor - I have only Windows OS for zipping and unzipping files on my clean Inventor machine.

[Anonymous]

Sir,

   I will be most obliged if you can make a video showing the full process (Rolling Cylinder on Cylinder part included).