Triple gear

prusaprinters

<p><a href="http://www.youtube.com/watch?v=I9IBQVHFeQs">Video</a>.</p><p>In this unusual mechanism three gears mesh together in pairs, and yet they can turn!</p><p>If you take three ordinary gears and put them together so that each gear meshes with the other two, then none of the gears can turn because neighbouring gears must turn in opposite directions. Triple gear avoids this problem by having the three "gears" arranged like linked rings - the gears then rotate along skew axes, and the opposite direction rule no longer applies (although see also Oskar van Deventer's <a href="http://shpws.me/lrqz">Magic Gears</a> for another possible solution).</p><p>This is joint work with Saul Schleimer. We were inspired by another of Oskar's designs, his <a href="http://shpws.me/lmqP">Knotted Gear</a>, which consists of two linked rings that gear with each other, and of course we wondered if it would be possible to do three linked rings!</p><p><a href="http://arxiv.org/abs/1304.6859">Paper</a> describing the mathematics behind the Triple gear, and how we designed it.</p><p><a href="https://www.printables.com/model/167515-triple-gear-solid">Triple gear (solid)</a> is a non-hollow version, which should make it easier to produce on a home printer.</p><p><a href="https://www.printables.com/model/167511-baseplate-for-triple-gear">Baseplate</a> and <a href="https://www.printables.com/model/167510-axle-for-triple-gear">axle</a> for Triple gear are designed to work with this, and give a way to drive the gears using a motor. For axles without the baseplate or motor fitting, see <a href="https://www.printables.com/model/167514-15cm-axle-for-triple-gear">15cm axle for Triple gear</a> and <a href="https://www.printables.com/model/167513-30cm-axle-for-triple-gear">30cm axle for Triple gear</a>.</p><p>Triple gear is also available at <a href="http://shpws.me/mQ6F">Shapeways</a>.</p><p>Things that could be improved upon:</p><ul><li>Make the motion smoother</li><li>Less wiggle room for the gears - at the moment they can move quite far out of the 3-fold symmetric position</li><li>Can the gears be made to rotate at different speeds?</li></ul><p>Category: Math Art</p>