# How to design a coaxial 1:2 gear without reversing direction?

I am trying to design a gear that has a 1:2 speed ratio (input:output). This design is very limited in space and for simplicity and space savings requires the input and output shafts to be coaxial.

This leads me to think of using a planetary gearset, but in order to achieve a 1:2 gear ratio, we must use a fixed planet carrier gear, which reverses the direction of the output, which is not desired. Using a fixed ring or sun is not possible when targeting a 1:2 ratio because the ring and sun would have to be the same size. Am I missing something, or is there no simple way to make a 1:2 gear ratio with coaxial shafts, or do I require a reverse gear attached to the output of a planetary gear with fixed planet carrier?

• If the space is so limited, just use a motor with double the speed... – Solar Mike Apr 18 '19 at 6:01
• This design does not use a motor but uses existing mechanical motion for the input drive. I have shaft that is turning and not driven by a motor, and want it to drive another coaxial shaft at 2x the speed, in the same direction. – Alex Rosenberry Apr 18 '19 at 14:12
• Can you stand a ratio of 25:49? 20-tooth and 28 tooth gears should be findable, and a pair of 20:28 stages could be arranged with a coaxial output. – TimWescott Apr 19 '19 at 0:37

An "orbitless" drive can achieve this in a similar envelope as a planetary:

Orbitless demo

"Nutating" gears can also provide similar results.

A fixed planet carrier planetary will have opposing rotation between the sun and ring, if there is an odd number of planets in line between the sun and ring (most typical planetary applications). If you have an even number of planets on each leg of the carrier and the carrier is fixed, your ring and sun will rotate in the same direction. Crude diagram below.

Your sun gear will need to have half as many teeth as your ring gear to achieve your 2:1 ratio, that means the planets will need to combine to have half as many teeth as the sun (eg 20 tooth planets, 80 tooth sun, 160 tooth ring). At a minimum you should have 9 teeth on a gear, meaning your smallest possible ring gear would have a 0.6" pitch diameter with 120 diametral pitch (very fine) teeth. In my experience the minimum number of teeth you should have is 24 (regardless of pitch) to avoid undercutting. This would make your smallest ring gear 192 tooth, making your pitch diameter 1.6".

• If you use the link button you can add proper working hyperlinks. Alternatively use [text to be displayed](http://example.com/page/). You have managed to format the link as program code. – Transistor Feb 12 '20 at 21:22
• Thanks, still a noob at the internet. – jko Feb 12 '20 at 21:43
• You might as well learn. I think the Internet is going to be big! There's a help button on the editor toolbar which explains the markdown syntax rather well. – Transistor Feb 12 '20 at 21:45

EDIT: I misread the original post and suggested a solution that provides 1:2 gearing in one direction only. In other words, a gearing system that works in forward but freewheels in reverse. Reading the question over, this is not what the OP requested.

I would recommend splitting your two requirements out into separate subassemblies:

1. A 1:2 speed ratio, easily achievable as you suggested via planetary gears
2. One-way driving, which you can use a ratcheting mechanism for.

For ratcheting assemblies, I'd suggest something that looks like DT Swiss's "Star drive" mechanism for bicycle freehub assemblies. See image 4 here; the entire assembly contains just one spring and a set of identical toothed discs to obtain reliable one-way drive. A mechanism like this one can be designed in-line with your shafts, has a low part count, and is proven to work well with outer diameters of about 25 mm (and my guess is that it could go a lot smaller).

Late to the party... a simpler alternate solution to planetary gearsets is available for coaxial input/output if you don't care about symmetry around the drive shaft. it's used in some tower clocks.

The solution is to choose tooth counts that yield the same sum between two sets of pinions and wheels (which will have equivalent radius sums) across 3 axles (input/transfer/output).

The fastest way to find valid sets is to choose your (R)atio (expresed as large over small), and your minimum (P)inion sizes and plug them into the following to get the matching (W)heel sizes

• $$W1 = ceil( sqrt( R * P1 * P2 ) + abs( P1 - P2 ) / 2 )$$
• $$W2 = ceil( sqrt( R * P1 * P2 ) - abs( P1 - P2 ) / 2 )$$
• If $$(R * P1 * P2 = W1 * W2)$$ the set is valid, if not you can increase either P1 or P2 and retest

The smallest pinion will mesh with largest wheel at the same axle distance as their alternates

It's even simpler if the ratio is a perfect square, just take the square root of said ratio and multiply by your pinion size of choice to get the wheel size (makes a matching set)

for the OP question, a wheel of 16 teeth on the input shaft, meshing with a pinion of 8 teeth on a transfer shaft, that also includes a wheel of 12 teeth, meshed with a pinion of 12 teeth on the output shaft gives the desired result of 1:2 speed increase (and is reversible for torque increase)

The radius from the input/output axles is usually smaller than an equivalent simple planetary gearset for the same tooth modulus and minimum pinion sizes, and handles the 1:2 ratio in the same direction that simple planetary gearsets cannot. The downside as mentioned is that it's not symmetric, so the torque load will be uneven on the axles (which may not matter, and can be designed around)