If Four-Wheel Drive makes cars more surefooted in snow and mud, then it seems logical to assume that two-wheel drive might do the same for a motorcycle. But how could you possibly get power to the front wheel of a motorcycle?

One answer is hydraulics. You can see how the hydraulic approach works in the following video:

The drive train on this motorcycle starts with an 8 HP engine. The engine turns a hydraulic pump to create pressurized hydraulic oil (see How Hydraulic Machines Work for details). Hydraulic lines send the pressurized hydraulic oil to hydraulic motors mounted at the hubs of both wheels. There is also a small tank to hold extra hydraulic fluid – it is visible above the pump at the :40 second in the video.

As a bonus, it is easy to run a hydraulic motorcycle in reverse as shown around :55.

Major manufacturers have also experimented with this approach. For example, Yamaha produced a 2-wheel drive motorcycle using a hydraulically driven front wheel:

A Yamaha 2×2 Hybrid Vehicle using Hydraulic Drive

See also:

Christini all-wheel-drive motorcycles

If you could somehow add a pressurized hydraulic accumulator to the first motorcycle, you would be heading toward a hybrid vehicle. See this article for details on the approach:

Invention – The INGOCAR gets 130 MPG hydraulically