If the screw object is a child of the bone as shown, then use the bone’s rotation to reorient it to the angle you want and animate the bone’s rotation using the Normal option, most likely rotating on the bone’s Y axis. The screw as a child will follow the bone’s animation.
Parenting to a bone: Select child object, select parent bone, Ctrl+P, choose “Bone.” The object will then require no weight painting for that bone.
Just press Play to see it working. The you can stop it and rotate the bone about its X or Z axes and press play again then you can watch it for hours :spin: