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- เผยแพร่เมื่อ 8 ก.พ. 2025
- 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...
Wow, wish I had Dr. Cao as my professor. What an excellent demonstration and accompanying material. Thank you for making this accessible to everyone!
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!
I wish, I had lectures like these 10 years ago in university. Great tutorial! Thank You!
Great tutorial. This video captures the difference between hobbyist level CAD and actual mechanical engineering XD
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.
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.
Can you explain why you made the diametrical pitch dependent on the pitch diameter? What does this solve?
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.
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
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.
You are a gentleman and a scholar. Thank you so much for this comment.
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.
Thank you sir. True legend lol
thanks alot for this
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!
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!
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.
Thanks Yang, the tutorial is detailed and easy to follow. Save me tons of time!.
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).
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.
Thanks for putting together this video, really appreciate it. Comprehensive and easy to understand.
Well, that's about as good a demo as can be done. Nice job, sir. And thanks for a solid technique.
This is an amazing tutorial, thank you very much for taking the time to make it and sharing it with the world!
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
Circular pattern when linked revert back to same value any idea
Why pattern 20 when he got 18 teeth? it happened to me when i designed my gear (different characteristics)
I really love it, job well done!!! You have won a new subscriber :)
Very good work. I have now a complete parametric gear !
Thank you very much !
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.
Thank you so much!! I needed to crank up a bit but it was totally worth it!
Im so happy I can make gears now!!!!
This is best video about gears in SW! Pro. Thank you!
It basically saved my life thanks sir
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).
+Jeff Biss
Have you, by any chance, figured out yet why it fails at 39 teeth? I'm experiencing the same problem.
+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.
+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.
Nice info,thanks for sharing it with us, well done :)
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?
That is just a value for "t" I randomly selected after a few trial.
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)
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.
Thank you for the post! Helped me immensely!
Unreal tutorial! Thank you so much!
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
finally sb who knows his shit. though those long ass equations in the notepad could be given in desription to copy
Excellent video
Thank you my Teacher
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! =)
This was an excellent lesson. I managed to create this in AutoCAD INVENTOR. If anyone needs the Equation Formula for INVENTOR, I've listed them below. INVENTOR is very particular about the syntax and unit parameters:
BaseCircleDiameter / 2 ul * ( cos(1 rad * t) + t * sin(1 rad * t) )
BaseCircleDiameter / 2 ul * ( sin(1 rad * t) - t * cos(1 rad * t) )
BaseCircleDiameter / 2 ul * ( cos(1 rad * -t -2 * BaseCircleDiameter / 1 in * 3.14159265359/180) - t * sin(1 rad * -t-2 * BaseCircleDiameter / 1 in * 3.14159265359/180) )
BaseCircleDiameter / 2 ul * ( sin(1 rad * -t -2 * BaseCirceDiameter/ 1 in * 3.14159265359/180) + t * cos(1 rad * -t-2 * BaseCirceDiameter/ 1 in * 3.14159265359/180) )
tmin = 0.00001
tmax = 0.68
Thank you so much for this sir !! this is Absolutely well done and very helpfull !!
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.
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.
THANKS a bunch from australia :)
Very helpful video. Thank you very much!
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)"?
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
Thanks a lot Mr. Yang Cao.
This method looks pretty strong
Awesome tutorial. Thanks!
Great video sir!
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.
Good to know. Thanks for the information.
For number inside of the circular pattern could you not just call the variable "number or teeth"?
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
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?
Would it be possible to mirror the second involute istead of using another parametric curve?
Thank you so much sir!! I m really greatful!!
Do you have similar explaination for Internal Spur Gear Modeling?
Fantastic tutorial
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
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.
this is the best. It helps. Thanks
any odds you could make the drive public?
Thank you soooo much.....it was very helpful....😃
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.
Hi there, on your notepad, the alpha equation is different than shown on the PDF. It is wrong?
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
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
Great Work Many thanks
Do you have vedio on helical gear tooth cut ..like you showed on spur gear
Thank you so much man
nice explanation.. so easy to understand.. I wanna try this..... wanna download the file... please approve my request...
great tutorial! learned a lot from this video. Thank you! :D
why t2 is 0.68?
where does the 0.68 come from in the involute curve parametric equation
Very good! Two question. The parametric part remains blue is it still undefined then?
Excellent video
why the tooth Involute curve created by equation is not defined? it color is blue.
Thanks
Can I add the module in the equations instead of updating manually??
And add also the relation between module and number of teeth and the pitch??
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?
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...
thats bad
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.
How do you create a curve with profile shift?
Hi, how to use auto double quote with equation?
How can i do in other to copy the function in Notepad and paste it in solidworks?
Hello Sir, Kindly provide me access to the drive file... Thank You !
Great job sir!
Hi Dr Yang Cao, i did succesfully created a pinion with N= 36 Teeth , Moudle= 1.25, with P=0.8 . However when creating the Gear of N=108 Teeth (3:1) ratio, i had a problem with beta angle as it turn to be negative and this cannot be accepted in solidworks , so resulted in a different involute profile for the gear ?. How to solve this problem? and what angle beta should be used for the gear. i would really appreciate your help.
Cheers
Can we have access to the tutorial you used as base.
thnk u for the video, my problem is with m=2.5 angle pressure 20 ans nbr of teeth 45 the base diametre is higher than the dedundum cercle diameter how can i solve this please
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?
Great tutorial, but wouldn't be easier to make the second involute curve as a symmetry from the first one (via the constrution line)?
thanks for the tutorial, very good! Can you give me a solution for a number of teeths >420 and metric module 4?
How to make tooth chamfer in a gear?
Well this is way above my level, probably I will just guess the dimensions of my gears.
i have a problem in equation driven curve . .
it says wrong equation i just copy paste it?
X(t) = "D2@Sketch2"*0.5*(cos(t)+t*sin(t))
Y(t) = "D2@Sketch2"*0.5*(sin(t)-t*cos(t))
+John Medina If youre still having this problem, all you have to do is copy and paste the formula into the x_t and y_t boxes, and you'll notice that the formula turn red in colour which signifies that it has an error. For some reason solidworks doesnt like having things copy and pasted. After this, just click the 'explicit' check box, and then click the 'parametric' checkbox again. It somehow makes solidworks forget that it was copy and pasted and the formula will turn black and it should work. If that doesnt fix your problem, you may need to change D2@Sketch2 to D2@Sketch3 if youve accidentally done it on a new sketch. That worked for me
+Sam Isaac I think if the formula turns red you have a problem with the formula. My issue was having multiple sketches/dimensions not lining up with equations, such as - Equation for Xt in the 2nd involute"D2@sketch2"*0.5*(cos(-t-2*"D4@Sketch2"*pi/180)-t*sin(-t-2*"D4@Sketch2"*pi/180)). Problem I found was that I had D4@Sketch2 on a separate sketch! D1@Sketch3!To maintain consistency/efficiency I kept the formula and changed the sketch to match.
+John Medina i am facing the same issue . .no mater what i type in it says invalid
nice thanks
Could be you have a different language version in SW? I.e. in
german "Sketch" is called "Skizze", therefore straight copy/paste
wouldn't work for involute equations.
We can't see your equation for alpha in the equations manager.
Is there some reason why can't you just mirror the first involute curve across your centerline instead of modeling a separate equation driven curve?
What should I do, when it is saying
Unable to create instance for the pattern. Try again by decreasing the number of instance or the distance between instances
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.
good morning, i have a problem. when i put the value of the number of teeth equal to a high number, like in my case 94, it creates between two teeth a strange thing, how can i do to remove it?
thaks for your attention
Can you please provide the document
I am unable to change gear teeth to 14 or 62. PLease help me out. . .
thanks mr cao...
It is possible to share the pdf document? I have sent you a request.
How can I incorporate profile shift as well?
There seems to be a limit to the number of teeth you can have given a specific a and d because eventually the base circle, which is Dp * cos(phi) becomes larger than the d circle. Is this a real property of these gears, or a side effect of the way we drew it?
Yes. I mentioned the issue in the description of the video. It is possible for the base circle diameter to be "smaller" than the dedendum circle diameter. Gear profile will be all involute. No more straight line between the base and dedendum circle. I haven't been able to figure out a general method to accommodate both cases.
Yang Cao
Ah sorry, I should have noticed that in the description.
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.
The old version of SolidWorks does not allow to do that.
I am using solid works 2016, and when I set the number of instances to global variable N it simply substitutes the current value
I followed your instructions.. just putting in my own numbers for the variables at the beginning... and my first equation curve is completely wrong. im not sure why. sw 2016
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..
I made the same mistake. You probably wrote the Y(t) equation wrong. My error was putting a plus instead of a minus lol
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!
how can you control face width in your method? does face width affect other parameters in gear design?
Base on this model how can be made an matching inner spur gear ?.