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)