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%.
@dogbot The C-HR Hybrid actually is a power-split transmission (the same one as the current-generation Prius), although I have heard that Toyota programmed the C-HR to rev a bit higher for more responsiveness. (I've not driven a C-HR Hybrid, though - we only get a non-hybrid with a VDP CVT in the US.)
I actually own a Gen 4 Prius, and find that while it's changing RPM a lot, it'll often rev quite low if it doesn't need much power from the engine.
@bhtooefr ah, makes sense. The car was generally very good. With a really good automatic, it would have been brilliant. It only seemed to do 20 mph on the batteries before the engine kicked in and then it was super high revving. I guess I'm used to autos changing a bit more seamlessly.
@dogbot Interesting that they went to a lot of engine right away - after warmup, I can (very slowly) get my Prius all the way up to 40 or so without ever using the engine. (In practice driving on 35 MPH speed limit roads, I'll probably get the engine up to what sounds like about 2500-3000 RPM during moderate acceleration, then lift off and the engine shuts off.)
@bhtooefr I did experiment with driving it very carefully to see if I could get more out of the battery but it seemed to be set that way. Even so, it only used a fraction of amount of fuel I would expect a non hybrid to use to do the distance I used it for. Certainly peaked my interest and I'll be keeping an eye on them in future. Looker, too...
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...
In practice, any power-split bicycle transmission, especially nowadays, will be an #ebike transmission... but I don't believe any are in production.
There's a paper out there where researchers at National Taiwan University and University of Michigan studied possible configurations of a power-split ebike: https://huei.engin.umich.edu/wp-content/uploads/sites/186/2015/02/DSCC_2014_Li.pdf
And, there's a British company, NexxtDrive, working on power-split ebike transmissions, but they're only looking to license AFAIK: http://www.nexxtdrive.com/
(As an aside, having looked at NexxtDrive's patents, they seem to have decided to deal with the excessive torque problem by simply using a freewheel that prevents the input from outrunning the output - it means that the lowest gear that the hub can handle is direct drive, but you can always use the sprocket ratios to get what you need out of it.)
Now if someone would just make such a hub design that I can retrofit to, say, my #recumbent trike (which currently has a Sturmey-Archer 8-speed)...
@bhtooefr have to say, I've never driven a CVT I liked. I had a Toyota C-HR Hybrid a few weeks back and it was great except for the transmission. Just always too highly revved. Never quite in the right gear when in motion.