Physics of the trikke tricycle I love my trikke, but I still do not understand what propels it forwards.
It is very clear that the energy comes from my legs and not from my arms (I only have to touch the handle bar ever so lightly), but I do not see how my shifting weight from side to side can result in a forward pointing force.
How is the side to side movement converted into a forward moving force?
(And just to be clear: My trikke is not electric).
 A: First off, you might as well ask, what makes any vehicle go forward? When you're riding a bike, you're just pushing pedals up and down, so how does that end up making the bike go forward? When you're driving a car, how does the engine make the car go forward? After all, the pistons in the engine just oscillate back and forth.
The answer in all cases is that the forward force ultimately comes from friction with the ground. If a bike, trikke, or car were on perfectly frictionless ice, they all wouldn't be able to go forward. Of course, this doesn't mean that the ground itself is suppling the energy. For bikes or cars, you (or the engine) supply the energy, but the friction force is necessary to convert it into useful forward motion; without friction, the energy just makes the wheels spin in place. 
Now specifically, the trikke works just like ice skates and rollerskates work. In the first half of a step on the trikke, you let your body fall down a bit, slightly forward and to the left. If you were on a frictionless surface, this would make your upper body move forward and your lower body move backward, generating no net motion. But because there is friction with the ground, your entire body and the trikke are overall accelerated forward and to the left. In the second half of the step, you move your body back up; that's the part that requires energy input from the legs. Then this is repeated in a step where you fall down forward and to the right, giving a net forward motion. 
A: The front wheel provides a friction force perpendicular to the direction it is pointing. Since the wheel turns the trikke one way, the reactive force of the road on the wheel pushes the other way. Since this is perpendicular to the wheel, there is a component of forward force on the bike (or backwards as the case may be). 
As with swinging on a swing, your body (or the part of the brain responsible for controlling it) works out what to do. Not so easy to bring that knowledge to the level of conscious thought. You have to lean in to the turn of the trikke or you would fall off (like riding a bicycle). 
You turn the handlebar with your arms, but the force is transmitted through the frame of the trikke. Your legs supply the energy through shifting your weight.
A: See the technical studies at http://www.lastufka.net/trikke/. The main physical principle is angular torque via angular momentum transfer from the body to the Trikke. The generation of motion is very much like cross country skiing according to skiers. Both legs and arms can contribute to the angular momentum transfer. The motion is more like a washing machine agitator - side-to-side motion cannot physically contribute as all forces perpendicular to the wheels get canceled by friction and only those parallel (via torque) produce motion. "Leaning" (technically cambering the front wheel via the steering column) helps the rider generate torque, but is not necessary.
