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mingyichen95

Harmonic Drive Gearbox

Updated: Oct 23, 2023

I think this is a quite obscure mechanism that toppled my gearbox hierarchy.


Traditionally gearboxes are made of spur gears going from stage to stage:







Then there are weirder ones like a planetary gearbox (this one is in an automatic transmission for your car):










There is a similar goal to the two examples presented so far: gear reduction

gear reduction in a more simple model is using a smaller gear at the input shaft to drive a larger gear at the output shaft (here A is input and B is output):







The result, is that B will spin at a slower angular velocity than A. Note that the linear velocity at the gear to gear contact is the same. So what's the gain or usefulness? At the center of B, if we have a shaft, it will result in a higher torque capability than the original input through the center of A. Note capability- if A has a motor shaft attached, and B has no load through a center shaft connected to it, the motor at A will spin with no load, drawing minimal current, and generating minimal heat. This will be the same for a car engine if B is carrying no resisting load: the engine will expend less gas. The mechanism would, however, help the engine or motor push or spin something it would otherwise not be able to if it was not connected to this simple gearbox. Of course we can compound the gear ratios to get an even higher reduction. This can be seen in the first example where an 8-teeth driver drives a 24-teeth grey gear. This same gear is connected to another 8-teeth driver and drives a 32-teeth gear. The achieved gear reduction is 12:1. An even more compact design can be shown in the second example of planetary gear boxes, a center shaft drives the middle sun gear in green, and the revolving gears on the side (planet gears in blue) are connected to a plate in red. The planet gear rotate about the sun gear with the help of the casing grooves or ring gear. That plate in red has a solid connection to a sun gear on the other side also in red. This sun gear drives the planet gears for the next stage. We can stack stages to get big gear reductions in a relatively small volume. The input shaft can also be in line with the output shaft. The reduction for each stage is the ratio of (sun gear teeth)/(sun gear teeth+ring gear teeth). Note this is for the case when the ring gear is the stationary element. In an automatic transmission, the members held stationary can vary from gear shifts.


Now enter harmonic drive gearboxes, also called strain wave gearing (It's bizzare):





Oh boi (with the i). I will try my best to describe this. At the center is an egg shaped hub. This is solid metal. It is surrounded by ball bearings. There is a flexspline in red hugging the ball bearings. The input shaft is connected to the solid egg hub. when you spin the egg, this expands a certain portion of the flexspline and contracts another portion. On the outside, there is a circular spline in blue that is rigid. The flex spline will mesh with the circular spline and push the circular spline a little bit every revolution. The circular spline is attached to an output shaft in line with the input shaft. The result is a typical single-stage gear reduction in the neighborhood of 100:1! Of course, there are drawbacks. It's expensive due to the complexity of the flexible flexspline. The torque carrying capability can be worse than a typical planetary gearbox. There is a bottom gear ratio limit of around 1:60, making it less flexible than other solutions. As a result of the high gear ratio, the input needs to be 2000-6000 rpm.




I'm coming across a lot of other interesting mechanisms that I overlooked in my years alive, so stay tuned

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