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Mathcad Community Challenge March 2022 - Planetary Gear Calculator

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Let’s face it, planetary gears are cool. They are used in all kinds of mechanisms, including transmissions, motors, and turbines. Your challenge, should you choose to accept it, is to use Mathcad to build a worksheet that calculates the gear ratios and output speeds of a planetary gear under different configurations.

The math behind the gear ratios is straightforward. But users should be able to select:

  • The sun or planet carrier as the input;
  • The planet carrier or ring as the output; and,
  • The ring, sun, or planet carrier as the stationary component.

How can the user select the desired component? How can you add intelligence to the worksheet to prevent an incorrect combination of input, output, and stationary?

What inputs do you want for your calculator? You will have to make some choices. Your choices could include:

  • Number of planets
  • Number of teeth
  • Component diameters
  • Module / pitch

Tools that you might consider include Combo boxes, programs, and functions involving strings.

Here are some technical references to get you started:

KHK Gears


How Stuff Works

Once again, this is a great project for students to work on in teams. Make the worksheet as simple or as complicated as you want. Others can build on your work, and you can build on others. Let’s see what the community can create! Good luck!


Find the Mathcad Community Challenge Guidelines here!


Okay, let's get cracking.


I've included a solution, but I'm not entirely happy with the document structure or the elegance of the solution.  Especially the configuration structure I'm not really fond of.


If a better way of working is found, I'm very interested to learn about it.



Bert Beirinckx

Wow, Bert, you put a lot of thought into this. I'm going to take some time digesting this but you clearly put a lot of thought into this. Thanks!


Community, what do you think about Bert's solution? Kudos  to him for being the first. Does anyone think they can build on this?


bump as a reminder that March is ending pretty soon.

As an Engineer, I am required to wait until the last moment of the deadline to make my submission 😉


Here you go.

Unfortunately I am working in Mathcad Prime 7, the company hasn't upgraded to the latest version yet.  May I ask to also provide a PDF?


Kind regards,



Correction - found a mistake in sign of one of the terms. Edited the sheet. See newly attached file

Gosh, maybe I should make an earlier deadline...!


But nice-looking work.


Solutions so far have covered the topic excellently, so thought I would expand.

Drawing of optimum configuration of Sun, Planetary, and Ring gears.

Have yet to draw the other planetary gears but time is running out.




Know its late.

To position gears P2 and P3 in the system need to track the epicycloid and center of P2/P3 rolling around the sun gear.


No problem. 😛


With that, thank you to everyone who participated and shared knowledge.


Dave will look through these all in detail and we'll have a follow up a little later this April. Cheers!

Edit: Orrrr very early May.

Sorry for the delay on the blog write-up and getting it published, but here it is:


@terryhendicott @adhariya @BertBeirinckx  are all featured with your solutions. A lot of great techniques to learn from y'all!

And you have all received your badges for participating. Thank you so much!

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Last update:
‎Mar 01, 2022 02:04 PM
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