How does hinge joint work?

Hi,

I'm making snake game but the movement is not grid based. I wanted the movement to be smooth based on a speed factor and the rotation will be in a circular movement based on an angular rotation speed. I know about the algorithm used in the classical snake game, but somehow I've got a hard time implementing it to my case.

I've also tried using HingeJoint, but it didn't work as I expected because of, well, physics. But it is pretty close to what I have in mind actually. So I think I need to roll up my own hinge joint. My question is, can anybody here tell me the theory behind hinge joint?

Thanks in advance.