51 Replies Latest reply on May 18, 2018 6:18 PM by Marcos Rodríguez

# Involute Curve by mathmitical forumula

We've got the need to develop an involute curve using real math. We have found functions to define the curve now we just need to know how to use them to develop the gear tooth in SolidWorks. Anyone have a way to do this?

Thank you
Mac Baker

President
Richmond SWUG
• ###### Involute Curve by mathmitical forumula
Hello Mac-

Look in the Help File, Insert Curve.

Use an Excel spreadsheet to calculate the x, and y points. Then in SolidWorks Insert a Curve based upon the generated data points.

Also, do a Google search on the Add-In software for SolidWorks called GearTrax, an application to generate Gears and Tooth Profiles.
• ###### Involute Curve by mathmitical forumula
Create sketch points in a model based on the equations you described. Connect those points using a fit spline. Or, consider Gear Trax http://www.camnetics.com/GearTrax.htm

• ###### Involute Curve by mathmitical forumula
An SW spline does not have the same mathematical DOF's as an involute. If you "connect the dots", there will be some error.

I have made gear tooth profiles using the "unwrapping" method to set up defining points. The involute follows the path of the end of a string being unwrapped from the base diameter (base diameter <> pitch diameter but can be found w/ combination of pitch diameter and pressure angle).

I have a gear model at http://www.esoxrepublic.com/models/ A bit cumbersome, but it worked for its purpose. It uses the unwrap method. Also, the profile is mirrored so the curvature of the resulting spline at the root is not thrown off by spline end conditions.
• ###### Involute Curve by mathmitical forumula
Error would decrease with the number of points supplied to the fit-spline. As far as quantitatively how many points you would need to get an acceptable error level - I don't know. Any idea Roland?? With the end condition... you could supply involute points past the tip of the tooth and include those in the fit spline. Then you could cut off the spline at the tip of the tooth and that would negate the end condition there... Alot of work. Thats why I mentioned Gear Trax. I'll check out your gear that you did using your method. Curious...
• ###### Re: Involute Curve by mathmitical forumula

there seems to be several files in this folder. which one do you mean?

• ###### Involute Curve by mathmitical forumula
Here's a macro I wrote that automates the process somewhat. Hope it helps. The more points you use, the more accurate the curve.
• ###### Involute Curve by mathmitical forumula
That's the most and best help I've ever recieved. Thanks to everyone!!!
Have a great weekend. I'll put my engineer on it and we'll send a thankyou after we get the part up and working.

Cheers!!
Mac
• ###### Involute Curve by mathmitical forumula
Has anyone been able to create an involute curve in SolidWorks using the new Equation Driven Curve feature? Involute curves can be created in Pro-E using the Variable Section Sweep (VSS) with trajpar ("trajectory parameter").

When does SolidWorks plan to offer a equivalent of Pro-E's Variable Section Sweep function? This is one area of surface creation I have not yet seen matched by SolidWorks. The VSS is also good for sweeping a draft angle along a split line. In SolidWorks, this requires multiple guide curves for the sweep function.

I have a model of a spur gear in Pro-E that serves as a start part for creating new gears. The involute curve is equation driven (VSS w/ trajpar), and so far I have not been able to recreate this gear in SW.

Regards,

Chris Thompson
• ###### Involute Curve by mathmitical forumula
Involute Curve Equation

x = A(cosT + TsinT)
y = A(sinT - TcosT)

SolidWorks equation driven curve did not this kind of formula, I guess?
Unlike IDEAS or Pro/E
• ###### Involute Curve by mathmitical forumula
Lin and all,

What about an equation that approximates this one? A ploynomial expression that approaches this?

http://www.me.ynu.ac.jp/labora...aekawa/involuteEWC.pdf
• ###### Involute Curve by mathmitical forumula

Peter Yodis wrote:

Lin and all,

What about an equation that approximates this one? A ploynomial expression that approaches this?

http://www.me.ynu.ac.jp/labora...aekawa/involuteEWC.pdf

I read through this PDF but still can not figure out how to do it in SolidWorks.
• ###### Involute Curve by mathmitical forumula
Sorry Lin... Looks like SolidWorks new curve from equation will not work with parametric equations. Ashame. It seems very handicapped. Maybe its been done on purpose to keep it from encroaching on some add-ins turf - like GearTrax. Or maybe we need to keep paying subscription money to get the eventual working version in 2011 or 2012. New features seem to be teasers of what could be possible if we just kept paying our subscription money. They string us along...
• ###### Involute Curve by mathmitical forumula
Here's an example file showing how to create a true involute curve in the X-Y plane using the equation driven curve.

It certainly is not very practical at all, and I'm not saying this is an acceptable workaround. More of an interesting challenge to see if it's possible.
• ###### Re: Involute Curve by mathmitical forumula

I tried opening your model and this is what I see:

I would appreciate if you would explain how I can learn from this to " create a true involute curve in the X-Y plane using the equation driven curve"?

• ###### Involute Curve by mathmitical forumula
Mac,

Spread sheet for calculating involute spline points.

Janusz
• ###### Re: Involute Curve by mathmitical forumula

I just can't see any macro here. Is it because it has been removed or I don't see it?

• ###### Re: Involute Curve by mathmitical forumula

It is sad to see that this question had been asked back in 2008 and yet there is no clear answer to it.

One might needs to make a fully parametric mechanical design including different involute gears in SW, and unfortunately it seems to be impossible at the moment. at least I haven't been able to do that. What I have done so far:

1. tried using "equation deriver curvatures" option with the equation x=r_b*(sin(t)-t*cos(t)) and r_b*(cos(t)+t*sin(t)). apparently I am making some mistake while importing the list of equations and variables from an external file and for that reason it does not work.

2. I tried recording the steps in a macro. but as far as I have understood the visual basic script takes the equations as strings. so one needs to go through a lot of hassle to edit those string to match with value of the base circle diameter.

I put the equations, the visual basic macro and model itself here for others. maybe it can help you, or even you are able to resolve the issue!

P.S. apparently SW forum has removed the option to attach files!!! please find the files here

P.S.1. No Seriously SW team, everybody is going forward and you are going back?! even the open source CAD software FreeCAD now has the option of fully parametric equation curves!

• ###### Re: Involute Curve by mathmitical forumula

This is for a helix but you can create global variables and use them in the equation driven curve

• ###### Re: Involute Curve by mathmitical forumula

what version of Solidwork Are you using? these feature has been removed in 2017 as far as I know.

• ###### Re: Involute Curve by mathmitical forumula

Yes Im on 2015, I wonder why they did that?  How can they even do that as models will break?

Looking at the help file it says you can use a dimension

Have you got an old file to open and see what happens in 2017?

• ###### Re: Involute Curve by mathmitical forumula

thanks for the immediate reply. Meanwhile I tried it again in a new file and it did work!!! as I have explained in other commects I import the list of variables from an external file and the ones imported can't be used!!! but when I define new variables manually they can be used. It is now very confusing because other people have also reported that this feature has been removed!

• ###### Re: Involute Curve by mathmitical forumula

happy you got it going

• ###### Re: Involute Curve by mathmitical forumula

HI Rob,

If 3d curve has a parameter, SW 2017 reports error. Links between parameters of 3D curve and global variables in SW 2017 are not working. May be some trick is required, but I can't figure out how to deal with it....

I don't have old samples to test.

• ###### Re: Involute Curve by mathmitical forumula

The attached is based on:

That should get you enough information to get started.  Though in 2014 SW the attached model doesn't work for all cases. It's been a while since I looked at it, but I think it had to do with the base and root circles.  The attached gear doesn't work if they switch places.

However, if you are doing this for a production part, you may look into an aftermarket add-on.

• ###### Re: Involute Curve by mathmitical forumula

I'm apparently making some mistakes while importing the list of equations and variable so I when I use those variables in the equations it does not work!

• ###### Re: Involute Curve by mathmitical forumula

Yeah, I looked at it again and you are right it isn't very stable.  Like I said I haven't looked at it in a while.  I sunk some time into it and had some work come up and I never nailed it down to be as robust as I wanted.  But, with the video and the example part you should be able to create the gear you need.  It is disappointing that SW doesn't come with true gears in the Toolbox.  If you need to do this regularly, there are plug-ins that you may want to look into.

• ###### Re: Involute Curve by mathmitical forumula

During the last couple of hours I have been trying to implement a parametric gear. Well, it is disappointing to say that it seems impossible at this moment. there are two bugs in within the SW which cause issues:

1. apparently when you calculate something inside the curvature it gives some values which are slightly different than the one calculated in the equations/variables table. Having some background in Programing, I think the issue happens due to the memory limitations of different variable types. for example they are using double float for variables but when the variables goes through different paths they end up differently although the equations are analytically the same. The solution for SW team would be to add a symbolic solver to their kernel instead of the fully numerical one.

2. the second issue is that when you define a "equation driven curve" you can still move it around!!! and when you want to connect other sketches to the curve they move it around even change it!. it seams the SW kernel does not calculate the curve in real time. it just calculate once and then you can do what ever you want. and if you use the anchor to fix it then the SW will not be able to update it!.

I will spend a little bit more to see if i can resolve the issue. if not then I will move to FreeCAD.

• ###### Re: Involute Curve by mathmitical forumula

Regarding 1., I do not have your programming background, but what you are describing makes sense.  I have seen some odd behavior and what you are describing could be the cause.

Regarding 2., I completely agree that this behavior is unacceptable.

Both of these issues fall under the ONE and TWO thread about bug fixes and stability and I believe that Dassault is taking these bugs and crashes seriously (there were something like 37 crash fixes in SP3).  If you look at SOLIDWORKS World 2017 Top Ten in full swing...  you will see that for the users, bug fixes is #1 on the list.

So, please create a service request and when the SPR gets posted, post it here so that people can see it and vote on it.

In the meantime, you are correct, you may have to use another application or an add-in to accomplish your goal.

• ###### Re: Involute Curve by mathmitical forumula

Thanks for the reply. Since my last post here, I a have found another bug.  Unfortunately when you make a curve based on some parameters, the curve does not update when you change the reference parameters. you have to go to the curve definition make a fake edit and then update and then remove the fake edit to get it updated!!!

• ###### Re: Involute Curve by mathmitical forumula

Sounds like typical SolidWorks behavior....

Have a look at Dennis Dohogne's gear.

• ###### Re: Involute Curve by mathmitical forumula

I made this "Robust  Involute Spur Gear Generator - Better 02.SLDPRT"

See attachment

It has in it an equation driven parametric “equation driven curve” for generating an involute tooth form.

As well as incorporating some "IF" "THEN" branches to make it a more "Robust" template.

I use conditional statements in it to check whether a condition is true or not and suppress/unsuppress features.

For modeling a TRUE Involute Spur Gear in Solidworks

This template is built with some "IF" "THEN" statements

So it is a bit more Robust than my previous postings

This is with the Gullet of the first tooth cut on the "Y" axis

Note: this template is set for the User input of the following:

"Diametrical Pitch" ,  "Number of Teeth"  & "Pressure Angle"

AS GLOBAL VARIABLES

"DiametralPitch"=

“NumTeeth"=

“PressureAngle"=

It could use some improvement to somehow shorten the rebuild time

• ###### Re: Involute Curve by mathmitical forumula

Thanks Robert Conklin,

I'll definitely have a look at it.

• ###### Re: Involute Curve by mathmitical forumula

It seems great! and actually the only stable solution I have seen so far. I was wondering if you could be so kind to:

1. make it metric. I know you US guys are used to inch, but believe me rest of the word don't
2. for my work I need to drive the gears given the maximum outside diameter OD_r, whole depth h and pressure angle phi. what I do
• I calculate Module from Whole depth. in metric m=h/2.157
• then I calculate the number of teeth: N=int (OD_r/m-2)
• then I calculate the final outside diameter OD_f=m(N+2)
• Pitch Diameter PD=OD_f-2*a
• Base diameter BD=PDcos(phi)

...

• ###### Re: Involute Curve by mathmitical forumula

I do not know what your constraints are, but really you should base things on the Pitch diameter rather than the outside diameter.

Matt has a good point about Excel.  Do you have Excel installed on your computer?

• ###### Re: Involute Curve by mathmitical forumula

well, usually that's the case. but in my project I need to start from those 3 parameters I did mention.

and yes, not having Excel installed was the problem. I will install it.

• ###### Re: Involute Curve by mathmitical forumula

Understood about having to use the OD.  The main thing is that you understand how all the parameters relate to one another and can get where you want to go from your starting point.  You might have to modify the amount of addendum and dedendum in my Design Table spreadsheet, but you should have no problem with that.

• ###### Re: Involute Curve by mathmitical forumula

In my case, I have a rather complicated mechanism, with lots of other parts related to each other in a complex network which I can't even draw. I want to have the gears parametrically designed so every time I change one thing, everything gets adapted automatically. consider a planetary gear for instance...

• ###### Re: Involute Curve by mathmitical forumula

I will look at that -- Making it Metric

• ###### Re: Involute Curve by mathmitical forumula

I just did it myself. Considering that I can't attach any files here (**) I will put some pictures:

1. first you need to change the documents unit
2. then you go to equation editor, select the "Automatic solve order" option on the bottom. add the parameters I need, and then generate your main parameters based on them:

** seriously guys, how do you do that? I don't even have the option for attaching here!!!

• ###### Re: Involute Curve by mathmitical forumula

Then look for this in the lower right corner:

I don't know why this isn't just on the standard reply screen.

• ###### Re: Involute Curve by mathmitical forumula

Heer you may find the metric version in the attchemnt

P.S. SW why attaching should be so difficult? seriously why?!

• ###### Re: Involute Curve by mathmitical forumula

Maybe you could be so kind to make a YouTube tutorial explaining what you have done here? I need to make other types of gears as well and I could use your knowledge.

• ###### Re: Involute Curve by mathmitical forumula

Here is a nice accurate involute profile parametric gear file.  It is metric and it is only for straight spur gears.  Just go to the design table and enter the parameters in the green cells.  The choice for stub or standard is a drop-down selection.

SWX2016 introduced the ability to make a line segment and an arc segment equal in length.  This made doing the geometric definition of the involute easy.

Enjoy!!

• ###### Re: Involute Curve by mathmitical forumula

Dennis Dohogne

Thanks!  We were revisiting this in our office.  I'll share this with the group.

• ###### Re: Involute Curve by mathmitical forumula

Sorry for the dumb question, but how can I open the design table?! I go to edit>Design Table, Edit Table but nothing opens!

• ###### Re: Involute Curve by mathmitical forumula

The file is in SWX2016, but you must already be on 2016 or 2017 or you would not be able to open it at all.

I just double checked and was able to get there without any problems.  For what it is worth, I prefer to choose "Edit Table in New Window".

• ###### Re: Involute Curve by mathmitical forumula

You have to have Microsoft Excel to view the design table.  If you have Excel, sometimes the window gets generated "behind" SolidWorks (remember, you are using Beta software).  If that's the case, go to the task bar and look for the excel window.

• ###### Re: Involute Curve by mathmitical forumula

OK that is the problem. this is my design computer and I hadn't installed office here yet.

• ###### Re: Involute Curve by mathmitical forumula

I evolved this parametric gear file over many years because I did not like what I found elsewhere.  Most of the "others" were not true involute curves.  Robert's is and is achieved with an equation.  Mine is also a true involute curve, but it is defined by sketch geometry instead of the involute function in SWX.  This just demonstrates multiple ways to solve a problem in SWX.  My gear file also has a drop-down for choosing Standard or Stub teeth since my needs warranted that.  I am now also looking into profile shifting, but I'm not there yet.

I like using the Design Table to manage the math relating the parameters together and others have told me they also like how easy it is to just enter the values in the green cells and generate the gear.  Note:  The Configuration Name and Description are set to use the defining parameters by using Excel text functions, i.e., if you change the teeth from 16 to 17 or the module or the pressure angle or the tooth type it will be automatically reflected in the Config Name and Description.

For development I use the general gear file I posted.  When I am done with getting the gears that I want then I take the gear file and do a Save As to its proper name for the project and then go into the Design Table and delete all the configurations that are no longer needed.  I'll also change the configuration name and description to be the proper ones for the particular project.  This typically leaves me with a Design Table having only one configuration, but that is perfectly fine with me and with SWX.

• ###### Re: Involute Curve by mathmitical forumula

Despite of it's designed for a sweep cut, it also creates the involute section in a 2D Sketch first.

You'll have to delete the 3D sketch, or leave it.

Enjoy it!