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An involute gear can also be a flower



It turns out that there is a lovely application in the Application Center that goes into detail about the geometry of involute gears  (gears that can rotate without sliding contact friction), here. In particular, it deals correctly with undercut required for gears with relatively few teeth. I had reason to play around with this recently and ended up with this spring-themed visualization.

At this link you will find a workbook that includes this application as one worksheet and another worksheet that goes through the perspective transformations to end up with the image above: spring-gears.maple
spring workbook involute application-center gear flower

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