Transformation Constraints--World Space Only?

Hello. I am having a problem setting up Transformation constraints. In World Space the parts move as they should, but when I set the constraint to local space, the parts do not move at all. What am I doing wrong?

Local space has to do with bones; bone works in its own local space. Everything else use Global. Are you using bones?

I tried adding bones to my model, but still the bones will not move when set to local space.