Modeling an Equation Driven Involute Spur Gear in Solidworks

The method given in this video works when diameter of base circle is bigger than that of the dedendum circle.
When the number of teeth is increased to big enough, the base circle diameter will become smaller than than the diameter of dedendum circle. Then the gear profile will be all involute. One can use similar approach given in this video for such case.
The tutorial file for this video can be downloaded from
drive.google.c...

[@maceatnight]

Wow, wish I had Dr. Cao as my professor. What an excellent demonstration and accompanying material. Thank you for making this accessible to everyone!

[@sitimustaffa2178]

Thank you so much for this great tutorial. I'm really glad to learn the equation driven function for drawing the involute, instead of drawing numerous tangent lines and confusing myself. You've helped me out so much!

[@mattcrossman6518]

Thank you so much for this. Absolutely spectacular. I'm using this to make a clock, and I found that by simply inputting "N" for the number of instances in the circular pattern you can have it auto update. Also, I made the diametral pitch dependent on the pitch diameter via adding another variable. Just a couple things to make changing gear sizes easier.

[@mattamiller]

Can you explain why you made the diametrical pitch dependent on the pitch diameter? What does this solve?

[@mattcrossman6518]

Matthew Miller I'm using SDW 2014, not sure if it will work on older versions. I simply put "N" (without quotes) into the field "Number of Instances" when I did the circular pattern. This way I can make a bunch of different size gears without having to update the number of teeth in the equations AND the circular pattern. As for the pitch diameter, I just made another variable (named pitchdia I think) and changed the value for "P" to an equation based on "pitchdia." This really doesn't solve anything for most practical uses, but when you're making a bunch of different sized gears, it shaves a minute or two off each one.

[@_Waldezas]

I wish, I had lectures like these 10 years ago in university. Great tutorial! Thank You!

[@MrAndydamgaard]

Thank you so much! I am helping a client design a machine utilizing a few existing parts and needed to create gears with a dimetral pitch of 4.62. I couldn't make it work, but with this, it was a breeze!

[@edwinacosta8416]

Thanks Yang, the tutorial is detailed and easy to follow. Save me tons of time!.

[@mohdrizwan7053]

Your video has certainly helped my team design our own gears for a design project. Your video is very clear and concise. Thank you Sir.

[@edwardvivanco1090]

Great tutorial. This video captures the difference between hobbyist level CAD and actual mechanical engineering XD

[@ErosNicolau]

Great tutorial, sir! Just one note: when creating the circular pattern, one might need to be sure to have the "Geometry pattern" checkbox checked in the circular pattern dialog box, otherwise it might not let one propagate the fillet as well

[@PaoloCostaBaldi]

Damn it. I just lost an hour erasing and redoing everything step by step. I was going crazy until I figured it out on my own.... I was going nuts! Now that I'm reading your comment I feel trolled xD BTW great tutorial Yang Cao, but you should have used an equation in the circular pattern, that's pretty obvious. So you don't have to manually adjust it every time. Number of patterns must be equal to "N". Same thing for the fillets, you could have used an equation like "fillet radius equals 0.5*clearance" or sth like that.

[@jtcook63]

You are a gentleman and a scholar. Thank you so much for this comment.

[@andrewhudson6199]

I had an issue with that, but I changed my fillet so that it was included in the sketch, and then set it to an equation.

[@karmdeepsingh6208]

Thank you sir. True legend lol

[@aakashjogalekar2661]

thanks alot for this

[@inventorjosh8049]

This is fantastic! I was able to follow along using OpenSCAD instead of Solidworks because of how detailed your explaination was. It also cleared up a bunch of questions I had regarding gears in general. Thanks for sharing!

[@tugaminhoto4969]

Hello, thanks very much, you saved my life :D Just a suggestion, to automatic define the root fillet, i used 0.8*c, so we got 80% of clearance (a safe value).

[@post2pa]

Hello, I very much enjoyed your presentation and demo, excellent, you kindly explained all the steps and it was relatively easy to follow, much appreciated. Thanks.

[@moondmullins]

Thanks for putting together this video, really appreciate it. Comprehensive and easy to understand.

[@MunchFaceBro]

Super helpful video. Some advice would be set the number of instances of your circular pattern to "n" and the fillet to a fraction of "c" (for example he used R.10 with a .125 clearance, so you could set your fillet to 4/5*"c") to ensure it will never be larger.

[@jaekib]

Well, that's about as good a demo as can be done. Nice job, sir. And thanks for a solid technique.

[@VinceTibo]

This is an amazing tutorial, thank you very much for taking the time to make it and sharing it with the world!

[@pianoquatrevingtquinze9220]

Very good work. I have now a complete parametric gear ! Thank you very much !

[@iggypeters5564]

Thank you so much!! I needed to crank up a bit but it was totally worth it!

[@iggypeters5564]

Im so happy I can make gears now!!!!

[@marcap599]

Thank you for sharing! Note: to write equation you may need to write with " " the variables. Improvements: - Number of tooth can be linked to the circular pattern instances - Fillet radius can be setted as Diameral Pitch / 10, this prevent manual adjust - Alpha calculation is not required, simply link the line to the intersection with Diametral pitch, than simpler equation as 360/4/N. - Not necessary to write two equation, can be used one than mirror it

[@ramkrishnan2844]

Circular pattern when linked revert back to same value any idea

[@Θυραςεικοσιτρια]

Why pattern 20 when he got 18 teeth? it happened to me when i designed my gear (different characteristics)

[@welcomethanks5192]

屏幕录像专家。。。记得当时看黑客视频就是用这个软件。 现在在油管上看到了，满满的回忆啊

[@magicofengineering6508]

It basically saved my life thanks sir

[@Pompiduskus]

This is best video about gears in SW! Pro. Thank you!

[@ClayClaim]

I really love it, job well done!!! You have won a new subscriber :)

[@lephtovermeet]

I just wanna thank you for this, this is an incredibly helpful tutorial and your other videos are very helpful as well. You're a fantastic professor. I wish SolidWorks had a gearing tool though. Also, it would be helpful if you could speak up a little bit in your videos.

[@RixtronixLAB]

Nice info,thanks for sharing it with us, well done :)

[@sledder43]

Unreal tutorial! Thank you so much!

[@TheZarolis]

finally sb who knows his shit. though those long ass equations in the notepad could be given in desription to copy

[@cooley1971]

Thank you for the post! Helped me immensely!

[@James-rf5tn]

THANKS a bunch from australia :)

[@maherrehaif1986]

Excellent video Thank you my Teacher

[@kaioid]

Thank you so much for this sir !! this is Absolutely well done and very helpfull !!

[@richardcavanagh]

Very helpful video. Thank you very much!

[@shanilperera]

Thanks a lot Mr. Yang Cao.

[@chadwassink7846]

Excellent video - very helpful. One question though. At 9:45 you enter 0.68 into the T2 field. What does this value represent, and how is it derived?

[@YangCaoUBC]

That is just a value for "t" I randomly selected after a few trial.

[@project-moe]

he chose 0.68 so he can put bounds on the curve of that first involute line, otherwise it would keep plotting for all infinite points of t (reference for anyone else wondering)

[@domkelly1972]

this determines the length of the curve from the start . it is the end point of the curve. it just needs to be long enough to go past the outer edge of the gear body so you can trim it later. type 2.00 in that field and you will see what happens.

[@stevenfan2465]

Awesome tutorial. Thanks!

[@rcdieselrc]

In SW 2013 if you double click the pattern and edit the dimension in the view window, you can enter the global variable there. This also works for helix.

[@juandavidlasantagarcia9571]

Fantastic tutorial

[@Dan-qp1el]

Great video sir!

[@hishambaharin7652]

Awesome tutorial! I think you can also drive the fillet and circular pattern using equations. That would make it a little more time saving. Thanks again for this tutorial! =)

[@jeffbisscrx]

Dr. Cao, thanks for posting this! Now to find out why Solidworks fails at 39 teeth (when the dedendum circle diameter is greater than the base circle diameter).

[@tobyteddy222]

+Jeff Biss Have you, by any chance, figured out yet why it fails at 39 teeth? I'm experiencing the same problem.

[@jeffbisscrx]

+tobyteddy222, nope, I have not figured out why. I have contacted my reseller and they said that they are looking into it, I sent them my part file. I think that it has something to do with base circle being a smaller diameter than the dedendum circle. If you look at the results of 39 teeth, you'll see that the tooth base produces "notches" with the involutes. Trimming the dedendum circle and each involute turns one of the involutes red and the "The sketch has not been undated..." message is displayed. I will post any resolution when I get it.

[@jeffbisscrx]

+tobyteddy222, I still haven't received a reason why this fails but have developed a work around: 1. Open an new sketch on the same plane as that which holds the equation driven involutes. 2. Select the involutes and the base (dedendum) circle. 3. Click Convert Entities. Those features are now copied onto the new sketch with no equation driven relations between them. They can now be trimmed as required so that you can use the new sketch to Extrude Cut the disc. After you extrude cut, simply create a Circular Pattern using that Cut-Extrude feature and you're done! You can now create spur gears of any number of teeth up to 105. There is a problem with this method because 360/(4*N)-alpha equals zero when N = 105.3916. So, gears with 106 and more teeth will fail.

[@achmadrizal34]

this is the best. It helps. Thanks

[@kasigarilavanya986]

Thank you soooo much.....it was very helpful....😃

[@pietrotabachidangelofurtad9232]

Would it be possible to mirror the second involute istead of using another parametric curve?

[@DK-xl2qq]

Equation Driven Curve: "D2@Sketch2" - Circle Name from which is shape created "D2@Sketch2"*.5*(cos(t)+t*sin(t)) "D2@Sketch2"*.5*(sin(t)-t*cos(t)) Mirrored Curve: "D2@Sketch2"*.5*(cos(-t-2*"D4@Sketch2"*pi/180)-t*sin(-t-2*"D4@Sketch2"*pi/180)) "D2@Sketch2"*.5*(sin(-t-2*"D4@Sketch2"*pi/180)+t*cos(-t-2*"D4@Sketch2"*pi/180)) Remember you need to be in Sketch2 to make it work.

[@mohammedsharabas86]

Excellent video

[@Apocobat]

any odds you could make the drive public?

[@Jptoutant]

This method looks pretty strong

[@shadyengineer1988]

Thanks a lot for this awesome tutorial. Till now, it is the best one with scientific basis. The voice is clear, the accent is very good, and referring to lecture is very nice. Can you please tell me why the "base circle diameter=Pitch circle diameter*cos(Phi)"?

[@watchingdemon3942]

khkgears.net/new/images/basic_gear_terminology_and_calculation/Fig.-2.6-Working-Gear-Nomenclature.jpg This is the link to a picture, on which you'll see that it's a simple right-angled triangle

[@sjh7132]

Thanks for the demo. I noticed on SW14, that for the circular pattern, I was able to set the number of instances to be the global variable N so it auto updates. Also the fillet radius can be set to "c" / 3 or 4 or whatever.

[@YangCaoUBC]

Good to know. Thanks for the information.

[@sugavaneshwarang2570]

Thank you so much man

[@ahmedalhashemi4161]

Great job sir!

[@pollux7961]

great tutorial! learned a lot from this video. Thank you! :D

[@ThePolymath1]

great job displaying the exact equations necessary to produce a gear that can be changed with only a couple variables. Could you produce a video teaching us how to build equation driven helical bevel / miter gears?

[@bpetnoi1472]

For number inside of the circular pattern could you not just call the variable "number or teeth"?

[@parthnanadikar2815]

Thank you so much sir!! I m really greatful!! Do you have similar explaination for Internal Spur Gear Modeling?

[@savvashadjixenophontos8362]

thanks for the tutorial, very good! Can you give me a solution for a number of teeths >420 and metric module 4?

[@kosztaz87]

Well this is way above my level, probably I will just guess the dimensions of my gears.

[@kd4science717]

thank you so much sir!!!!!!

[@masoudborhani9216]

thanks mr cao...

[@jaimemendez1913]

Dr Yang, really helpful video. Question from my side (couple of years after your video and the majority of the responses) But, can you please describe / explain why are you using "t2=0.68" which such value? I've reviewed your material, and I don't see, yet, the correlation Could you please help me to understand? Thanks

[@MunchFaceBro]

I played with it. I could be totally wrong but I think t2=.68 just guarantees the involute curve will extend past the addendum circle diameter. Like if you made both t2s=.75, the gear would still be exactly the same.

[@marcali1551]

Great Work Many thanks Do you have vedio on helical gear tooth cut ..like you showed on spur gear

[@dar73760]

I find my solution thank you:)

[@loganikapi4399]

Great video! Helped me a lot. Just one comment. When you named your global variables, you called "P" Diametral pitch but I think that should be the pitch diameter (in) and you called "dp" pitch diameter when that should be diametral pitch(teeth/in). The values are correct though. Thank you so much for your help.

[@rotako100]

Very good! Two question. The parametric part remains blue is it still undefined then?

[@mechtechstation]

thankyou so much

[@DestructorEFX]

Hi there, on your notepad, the alpha equation is different than shown on the PDF. It is wrong?

[@cephalopogg]

If you're referring to the *180/pi, this is the conversion from radians to degrees. This is here because the equation calls for radians, (notice "phi rad"), however our pressure angle is in degrees

[@inhosung2807]

I really appreciate your effort. I am just beginner of solidworks and followed your lecture and got it. As you mentioned I encountered the base circle diameter is smaller than dedendum circle diameter. Do you have other lecture for this or should I draw from the beginning? Please let me have your tip for this. Thanks in advance

[@WadeLeanidas]

GREAT VID

[@CarlosColucci]

why does this don't work when I go to more teeth? it collapses in 42 teeth. the dedendum circle becomes bigger than the base circle and it doesn't work. it is a great tutorial but I've been struggling with this all day long...

[@seimela]

thats bad

[@holycrapitsjake_]

it probably has to do with the pressure angle you're working with. remember that if we want to constrain the dedendum and base circles, we can express their relationship as: (pitch diam) - 2(dedendum) < (base diam) with pitch diameter equal to (module)*(num of teeth), or (num teeth)/(diametral pitch) and base diameter equal to (pitch diameter)*cos(pressure angle), just like the textbooks give us. you can solve for your max number of teeth by moving all other variables to the opposite side, but you should see that the num of teeth at 20 degrees pressure angle is mathematically limited to like 41 or something.

[@valeriarocca8148]

Hello Mr. Cao. I am trying to create my initial equations just like you do on the video. However, I am not able to do so. After I enter the Global Variable name I press enter and continue to the Value/Equation area. Once there, I enter the value I want and press enter, but it does not accept the value. I cannot continue beyond that point. Hope you can make a suggestion to my problem. Thank you in advance.

[@subaiyalfarrukh3042]

Hello Sir, can you please make a video on internal spur gear involute shape as well? I am struggling to design it. It will be very helpful for me in my research field

[@RdelaCourt1]

Thanks for uploading this, it really helped me understand the process a lot more. I have made my version of your model, are there any conditions that need to be modified to account for a much larger spur gear? I am trying to model the angle but my value comes back as a negative value and cannot define the angle. Diametral Pitch = 0.3333 No of teeth = 110 Pressure angle = 20° Addendum Diameter = 336mm Pitch Diameter = 330mm Base Circle = 322mm Dedendum Diameter = 322.8mm My tan and beta angle values in the involute curve come back with a value of -0.3° Has anyone used this to create a relatively large spur gear?

[@gtti89]

Hi and thanks for sharing this great tutorial! It has been very helpful. Can I ask, is this gear design based on a "zero backlash" basis? And if so, how would you recommend building in backlash? Is there way to do it using global variables such as modifying the pitch circle diameter or module etc? Many thanks again!

[@garramiro]

Great tutorial, but wouldn't be easier to make the second involute curve as a symmetry from the first one (via the constrution line)?

[@David_Martinez_USA]

According with the TXT this Equation is wrong in my SolidWorks: sqr(dp^2-db^)/db*180/pi -phi The correct Equation is gonna be this one: = sqr ( "dp" ^ 2 - "db" ^ 2 ) / "db" * 180 / pi - "phi"

[@MrApocalypticMessiah]

same here. thanks.

[@raisaratri3752]

No it would be = sqr ( “dp” ^ 2 - “dp” ^ 2 ) / “dp” * 180 / pi - “phr”

[@audrylou290]

Very usefull material. Thanks a lot. When you say "a" need to hear "b" as well. Don't you have a tutorial for internal involute gear too? Hot to direct involute curve toward center now?

[@tanujsiddharth9445]

while draw the equation driven curve, how did you come up with t = 0.68

[@harmonytan6746]

See Chad Wassink's comment below: Yang Cao replied "That is just a value for "t" I randomly selected after a few trial. "

[@kize32]

@@harmonytan6746 Lmao. I was just wondering about that

[@235diga6]

very Nice thanks

[@Bob-jy4ju]

where does the 0.68 come from in the involute curve parametric equation

[@sanmao6920]

Hi Dr Yang Cao, Thanks for the video! it help a lot, but I noticed the link for the tutorial file isn't working any more, I wonder where I can download it again, it's very good information.

[@alializadeh8195]

Thanx

[@joserafaelfarfanfernandez899]

THANK U !!

[@RehuelGalzote]

Can u make the same tutorial for Bevel Gears? Thanks.

[@deepikajonnalagadda3752]

How do you create a curve with profile shift?

[@SMHARIRAMM]

Hello Sir, Kindly provide me access to the drive file... Thank You !

[@andy.billups]

Great video. Used this information to make a template using a design table for not only spur but helical gears as well. The only thing I am unsure of is what determines what the clearance, or fillet radius, is. Does anyone have any knowledge of this?

[@joseluisMartin]

Very nice tutorial Mr Cao, I have a question, do you know, how to design a rack and pinion (obviously I learned how to do a pinion), but I cannot to draw a rack to matching pinion with, I will be very happy, If you could do that. Thank you very much.

[@krishna3305]

Thankyou

[@gabrielbadea1289]

Great!!

[@ilasa1]

Have you tried to build a non circular gear with involute teeth? Something like gearify but with involute teeth. Would be great!

[@rupeshkulkarni7073]

Can we have access to the tutorial you used as base.

[@pushpendratanwar7987]

How to make tooth chamfer in a gear?

[@wanghou6219]

why the tooth Involute curve created by equation is not defined? it color is blue.

[@BaconCookiesBrah]

One mistake that I noticed is during the circular patterning of the filet and extruded cut. The number of instances should be set to the global variable "N" rather than the number 20 which is shown.

[@YangCaoUBC]

The old version of SolidWorks does not allow to do that.

[@aniketmandhare226]

I am using solid works 2016, and when I set the number of instances to global variable N it simply substitutes the current value

[@vivoamazingmoments6513]

Thanks Can I add the module in the equations instead of updating manually??

[@vivoamazingmoments6513]

And add also the relation between module and number of teeth and the pitch??

[@rocking1sum]

Can you please provide the document

[@MotorsportsX]

to clarify.. when you input your equation curve, the genereated curve goes from left to right...0 degrees, to the right, with the given equation... my line goes up... from 0 degrees, vertical...I have No idea why its doing this. I even went back and did it with all your numbers..

[@Jao123456100]

I made the same mistake. You probably wrote the Y(t) equation wrong. My error was putting a plus instead of a minus lol

[@inconnu3871]

How can i do in other to copy the function in Notepad and paste it in solidworks?

[@vinaypatil4298]

I am unable to add new global variables, only one is being entered ... what to do ?

[@MegaBas1c]

That's cool