Jim, I'm not familiar with robots, but in a placing of a stab I can only think of 3 axis; pitch, roll and yaw

any rotation of the stab can be defined by these 3 axes. The "elevation" or height and the forward position of the stab is not determined by "new" axes but rather a system of coordinates in the basic 3 axis reference environment (X,Y,Z)

One can always evoke the axis of symmetry, but the stab has it's own axis (or axes) of symmetry regardless of it's position in space.
The alining of the two (stab & fuse) requires rotation(s) about the 3 axes (X,Y,Z) plus some linear movement (up-down; back-forward) which is determined by coordinates in the basic 3 axes (X,Y,Z) environment...

Cheers,
Vasek