Another method to implement continuously variable behavior is what locomotives and many garden tractors use - instead of connecting the engine to the wheels, they connect it to a generator (for the locomotive) or a hydraulic pump. The output of the generator is connected to electric motors to drive the #train, or the hydraulic pump to a hydraulic motor to drive the tractor.

This is durable and simple... but it's hideously inefficient, there's lots of loss at every stage.

Power-split transmissions combine this approach with planetary gearing, to provide both a mechanical path for engine power, and an electric/hydraulic (depending on the transmission) path.

So, I'm going to link to this video by Sturmey-Archer, which details their 3-speed bicycle hub gear: https://www.youtube.com/watch?v=K3QJTTcDXJo

I'll summarize that by saying, basically, a planetary gear gives you multiple ratios by holding one part still, moving a second part, and taking the output from a third part.

What if, instead of holding one part still, you varied its speed, though?

If you do that, something interesting happens: the ratio of input to output speed changes.

If you've got Flash on your device, I'd highly recommend looking at E. A. Hart's simulation of the Toyota Prius's power-split transmission: http://eahart.com/prius/psd/

So, note that the engine (the planet carrier) always has a mechanical path to the wheels (the ring gear). But, MG1 can vary its speed to adjust the ratio between the engine to the wheels.

Of course, for it to vary its speed, MG1 has to apply reaction torque somehow - this usually means that it works as a generator, increasing load on the engine. Ignoring the battery's needs, the excess power is sent over an electrical path to MG2, so (minus losses) all power eventually makes it to the wheels.

If the engine RPM needs to be lowered, it can work as a motor, and get power from MG2 instead.

This also works hydraulically as well, as demonstrated by the Fendt Vario transmission used in tractors: https://www.youtube.com/watch?v=-iDGe-31kgg

There are two main downsides compared to a serial powertrain - the maximum engine speed at very low vehicle speed may be limited and minimum engine speed at very high vehicle speed may be limited, and you have to place the engine such that it can be connected to the wheels.

Now, all of the examples I've given have been #cars and #tractors using engines (Honda's also used the concept in a couple #motorcycles and #ATVs)... but there's nothing that says that a power split transmission has to have an *engine* driving it.

So, an efficient, lightweight #bicycle CVT is something that's been seen as a holy grail for many years. Human power is uniquely hard here, because humans output very high torque, very intermittently.

VDP true CVTs are wholly unsuited for #bicycles - they require very high clamping force to handle very high torque... but that means incredibly high power losses. There have been experiments with variable diameter chain sprockets, but those aren't truly continuously variable, and have plenty of their own problems.

NuVinci has a commercial hub design using a planetary ball setup and a pressure-sensitive drive fluid: https://www.youtube.com/watch?v=4n15N6yS2dE

However, efficiency is still quite terrible at ~84%.

Note that most bicycle transmissions are in the mid to high 90s% efficiency, so that's simply not acceptable.

The serial approach has also been tried, with the Mando Footloose: https://www.youtube.com/watch?v=w00a2eHwk-w

Problem with that is, any kind of generator that can handle a human rider's torque would be colossally heavy... and this one can't handle it. And, it's still inefficient.

But, what about power-splits? Not all of the torque has to go through the electrical path, there, after all...