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Richard Kline writes:

Non circular gears are strange. When the topic of square gear trains appears in casual conversation, people tend to think a joke is being made, that it is ‘impossible’ to make a square gear that actually meshes properly. After being drawn into a vicious debate with a co-worker about the existence and plausibility of such gears, I realized I had no choice but to resort to an actual demonstration to sway his view. In the not-too distant past this would have been a virtual impossibility, at the very least I would have had to spend an indeterminate amount of time hunched over a scroll saw, trying to cut splintery wooden gear prototypes by hand. Fortunately, this is the pushbutton world of 2009, a Google search turns up dozens of laser/waterjet cutting services and MakerBots are squeezing out ABS plastic Darth Vader helmets in every good nerd’s house this Christmas. And thus, a project was born…

Gears Squared

Gareth Branwyn

Gareth Branwyn is a freelancer writer and the former Editorial Director of Maker Media. He is the author or editor of a dozen books on technology, DIY, and geek culture, including the first book about the web (Mosaic Quick Tour) and the Absolute Beginner’s Guide to Building Robots. He is currently working on a best-of collection of his writing, called Borg Like Me.



  1. Nick says:

    It looks like one of them is square and the other is slightly indented in the sides, is that the case? Two different shapes?

  2. Johno says:

    If one of those gears is driven at a constant speed, the other one will accelerate and decelerate during each quarter revolution. It’s an excellent project though and I’m sure you had a lot of fun designing it.

    1. Kieran says:

      They both turn at a constant speed

      1. johnrdupree says:

        Since the effective diameter of the gears change, the effective gear ratio also changes.
        The effective diameter is the distance from the center of the gear to the teeth that are engaged with the other gear. At some points during their rotation, the drive gear will have a large effective diameter and the driven gear will have a small one. This will happen when the corner of the drive gear is engaged with the flat of the driven gear. When the flat of the drive gear is engaged with the corner of the driven gear, the situation is reversed. Since the effective gear ratio changes during the revolution, their speed relative to each other must also change. If the drive gear runs at a constant speed, the speed of the driven gear will oscillate between the min and max effective ratios.
        They may turn at the same RPM, but they will not both be doing it at a constant speed.

  3. Anonymous says:

    Awful choice of music in the video clip. Sounds like a bad 80s training video.

  4. K Booher says:

    Read “507 Mechanical Movements”. This has been around for a very long time.

  5. Carl says:

    Nice job. I like your way of demonstrating the motion.

    I made some square gears (and spiral gears, and others) a while back from some 1/2″ aluminum:


  6. Bill in Denver says:

    Would make a great belt buckle!

  7. Bob says:

    Well done. There is a book called the “Mechanical Device Sourcebook” written by Nicholas Chronis that has a section discussing non-circular gears such as are shown here. In fact, they show a tie-tac made using a set. About 20 years ago, I did some research and tracked down who made them. Turns out it was a retired ME professor living in Arizona. He had quite a line of similar tie-tacs, with elliptical, triangular, square, an logarithmic gear sets. I think such jewelry would do well on e-bay today as a business for someone interested and capable of reproducing them. Also, larger sized gear sets, perhaps used in combination (a pair of square, common axle with pair of elliptical, common axle, pair of triangular, etc.) could be used to illustrate teamwork in one of those motivational type displays you see in airline magazines in the business section.

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