Since your are weightless in space, your arm has no weight, right? Does this mean that bending it in space requires no energy? Why or why not?
The short answer is yes, bending your arm in the weightlessness of space still requires energy. You are correct that bending your arm does not require us to overcome the weight of your arm, but we do have to overcome its inertia. Inertia refers to the sluggishness that massive objects have (even in the weightlessness of outer space) given how much matter they have.
A bit of explanation to clarify things: we could just as well ask does it take any energy to push a 100,000 lbs. asteroid a distance of five feet while in the weightlessness of space?
I'm sure you'd agree that the asteroid doesn't weigh anything at all in outer space. But that doesn't mean you can just float up and thump it with your finger and expect it to take off at near light-speed. You still have to push on it (and expend energy in doing so) to overcome its inertia.
The simple summary of all of this is that when we try to move objects in outer space, we don't have to fight against any gravitational weight, but we still have to overcome the basic sluggishness that massive objects have (i.e. inertia).
Movement of your body parts (hands, legs eyelids, etc.) occurs due to the contraction of muscle fibers. This process requires energy (from cleavage of ATP molecule to form ADP). This is the only way an astronaut can move his arm.
Transforming the internal energy (chemical) into mechanical energy requires the expenditure of ATP. So, the answer is yes.
But, you can make it smaller, I guess.
- An astronaut in a spaseship (air around):
Body joints and adjacent body tissues still have non-zero friction.
So do clothes.
Air has some viscosity.
Every body part has some inertia. You need to accelerate it and then decelerate it near the new position. Muscles are especially bad at deceleration - they use more or less the same energy as in acceleration ("static muscle work"). (A well-designed electric machine would get back a great deal of energy used for the acceleration when decelerate.)
Muscles themselves work in pairs at every joint. When one contracts, the other elongates and the one that elongates consumes some energy from the other that contracts (see "muscle tonus").
- An astronaut in a spacesuit: all of the above + compressing or decompressing the air when moving the joints.
One can imagine a (very simplified) spacesuit as an inflated baloon that has its own form. Every movement of the astronaut changes the form and the baloon reacts rather forcefuly against these changes.