What if both wheels were powered by pedalling?

There have been front drive designs, but all variations I've seen are either impractical, structurally inferior, or both. There is no real benefit to having both wheels deliver power, and that would add a gigantic amount of weight and likely be quite problematic. Imagine needing two separate drive trains that involve separate chains, cassettes, derailleurs, etc.., and that al would need to be tuned together somehow? No matter how you designed it,it would add substantial weight to the bike, and no real functional benefit. It might be novel and fun, but just not practical.

While I'm aware of the fact the link-only answers are frowned upon in this community, I'd just leave this here. I'm not too sure, but I guess you might as well be able to buy one if you so wish.

https://twicycle.com/

As anyone can easily conclude, having a driving front wheel on a traditional bicycle would be mechanically more complex than achieving the same result with the rear wheel. The front wheel is primarily used for steering, that is it rotates around a vertical (almost) axle. Relegating the steering to somewhere else (i.e. to the back wheel) is not an option as it makes a very unstable system (riding a bicycle rearwards proves it). The rear wheel is either fixed relative to the cranks, or at least stays in the same plane as the frame.

Side note: children's tree-wheelers and ancient penny-farthings have pedals directly attached to the front wheel and do not suffer from this problem.

So, any design that has a driving front wheel needs extra complexity to overcome this issue: to deliver power from the pedals in the middle of the frame to the wheel. This is doable, but results in more components, more weight, less reliability and less efficiency. If we only want to power one of two wheels, the rear wheel wins.

Now, suppose we want to have a design where both wheels are powered by the rider. It has to be noted that the golden rule of mechanics mandates that no advantage in power will be achieved: the same power generated by the rider will be distributed over two places, instead of only one (plus losses on friction, higher in the case of two drivetrains). If there is any potential benefit in having two-wheeled drive, it has to lie somewhere else, e.g. in increased control over the ride.

Side note: we do not consider additional "pedaling with hands" here. It would theoretically give the rider more power at the cost of less steering control.

Let's consider two categories of bicycles: road (primarily racing) and off-road (primarily MTB but also e.g. fat bikes in snow)

• road bicycles are ridden over pavement of different quality. Both tires touch the road all the time. The traction between tires and the surface is already good enough to transfer all power generated by the rider into forward acceleration of the bicycle. The second drivetrain won't change or improve over that.

• off-road bicycles are ridden over uneven or loose terrain. There are often moments when only one wheel touches the ground, while another one is briefly in the air or has otherwise lost traction. In such conditions, having the remaining wheel as driving does become useful. In conventional designs, rear suspension allows to increase traction of the driving wheel by allowing it to better follow the terrain's profile. Simply speaking, when encountering a bump, the wheel, instead of jumping off and flying into the air, stays closer to the ground and regains traction faster.

It would seem to make sense to have a full-suspended and dual-wheel-driven bicycle to keep both types of benefits off-road.

This is becoming really involved at this point. Modern rear wheel suspension designs are extremely complex and finely tuned, partially because they have to deal with the chain that limits their efficiency (see pedal kickback). Repeating the same thing at the front wheel is possible, I would assume (e.g. with a linkage fork instead of a traditional telescoping one), but again it results in additional weight and complexity.

Who knows, maybe one day such designs will become available to athletes and regular consumers, once (and if) other options to improve bicycle capabilities have been exhausted. In the end, the bicycle design is limited by human abilities: there is no point in making a bike with crazy high traction if no human with enough power to climb it exist.

As long as you can transmit the force you want to the terrain through one wheel, there is no advantage to driving the second one. As a road biker, I have no problem here. I cannot generate enough torque to break the rear wheel free, so it wouldn't help me at all to drive both wheels. The reason off-road drivers want four wheel drive is that one or both rear wheels can lose traction in bad terrain and they want the front wheels to pick up the slack. That may apply to mountain bikes, I can't say. Carrying drive force through a steering joint is complicated. You need to find a reason to justify that complication, not just a wish for symmetry.

Many two wheel drive mountain bikes exist. Here's one article advertising a new one:

There’s been no shortage of attempts to build a workable two wheel drive bicycle over the years, but this latest effort from Double of Japan looks like one of the most compelling yet.

https://www.bikeradar.com/news/this-is-a-two-wheel-drive-bike-done-right-sort-of/

They do offer better traction in some situations but I've never seen one with a limited slip differential between front and rear, which means they need a freewheel for each wheel to avoid stressing the drivetrain (you really don't want one wheel pushing backwards!). The extra weight and drivetrain complexity is always there but the extra traction is only useful very occasionally.

The other problem chain driven ones have is limited steering range (see the one in the article above). That's not a problem on FWD speedbikes where the steering range is limited by the fairing (often to +/- 5 degrees or so), but for technical mountain biking it's a huge issue. I commonly steer +/- 90 degrees in technical sections, and even on normal trail climbs half that. But getting a +/-45 degree swing out of a universal or CV joint is hard to impossible.

There are also flexible cable drives. Those trade more steering movement for more losses and generally shorter service life (ie, the only one I tried broke, luckily not when I was riding it). With a flexible shaft some wind-up is actually useful, as it gives a bounce in the drive to help you over large bumps. But it's disconcerting when riding and overall burns effort from the rider to counter the wind-up all the time while helping occasionally.

A rigid shaft drive could in theory have a rotating linkage with 180 degrees of steering freedom, but would be quite complex to build. It would also need a telescoping section if there was front suspension, and likely significant gearing to reduce the shaft size (and the torque on the sliding section as well as on the steering).

However, would there be any potential benefits if, somehow, both wheels were connected to the crankset so that the input power could be shared between the wheels?

There would be some benefits but more drawbacks.

For example, currently on bikes rear tire is the one to wear fastest. This suggests a tire replacement schedule where the new tire is installed to the front and the old front tire is installed to the rear, as otherwise the front tire would die of old age and cause a life-threatening accident due to its sudden failure. Both-wheel drive would not necessitate this tire replacement schedule, but most bicyclists do not see observing the correct tire replacement schedule a problem.

However, the drawbacks outweigh benefits. As the front tire is the one that is steered, it would require some special power transmission mechanism. The automotive solution (CV joints) does not work given the form factor of a bike. I suspect the only reasonable power transmission is electric, i.e. put a motor in the front wheel hub. Then you would need a generator in the rear wheel hub. Those would unnecessarily increase bicycle weight and work at such poor efficiency that the energy loss would be huge, far greater than the energy loss in chain drive.

Some electric bikes actually have a hub motor in the front. Those are not favored over mid-drive motors because hub motors have poor torque at high speeds (the marketers may quote quite high torque figures but those are at standstill) and weigh a lot because reduction gearing is not easy in the front hub unlike it is in mid-drive motors. Furthermore, the limited torque in front hub motors does not go through the drivetrain, thus meaning you lack the inherent advantage of the dynamic speed/torque range given by the bicycle derailleur gear system. Also a front hub motor requires a torque sensor on the bottom bracket so it anyway requires a non-standard bottom bracket. Mid-drives make the bottom bracket the only non-standard component. One advantage of front hub motors is that they even out the wear between front and rear tires, but this advantage does not outweigh the disadvantages of front hub motors.

Bicycles have an uneven weight distribution so on flat terrain 67% of the weight is on the rear wheel and 33% is on the front wheel. Thus both-wheel drive would give only 50% more traction and not 100% more traction. Not only that but bicycles don't require much traction except when going up a steep hill, and if the hill is steep, nearly 100% of the weight is on the rear wheel anyway with the front wheel practically unloaded. This front-wheel-unloaded phenomenon also shows why front hub motors in electric bikes are a bad idea: if you climb a steep hill sitting, and if your height is long, the front wheel being unloaded causes the front drive motor to be dangerous if it has enough torque to actually propel the bicycle up that hill. The front wheel will slip, causing you to fall!

That would effectively give you an all-wheel-drive bicycle with torque force halved on each of them. While both wheels have road contact, you do not loose anything except for the extra parts' weight. But the problem is bicycles don't have a differential device. Meaning your wheels will likely get different torque and angular speed, meaning you will waste muscle power on struggling with tyre resistance, plus leading to uneven tyre wearing out, making the effect even more noticeable. Also mind different path radii on stiff turns - all these require differential, and all automobile have one, especially AWD, 4x4 and heavy trucks.

Looks like the strong point of the dual wheel drive motorcycle is very high climbing angle, as high as 60 degrees. Hence dual drive mountain bike should have a good potential for a very steep climbing. Ok you can also pull a bear with this bike but unlikely to happen very often.

But I think human cannot sustain the necessary power for more than few seconds. Only some purpose-built trail full of very steep sections few meters long would maybe justify such a bicycle.