This is a Kintronic Labs LV16-20, 16 uHy/20 Ampere variable coil.  They are most commonly used in an AM directional phasor system.  This particular coil developed a problem where the contact rotor disk froze to the shaft it rides on.  The repair involves removing the disk and shaft.

Before starting any parts removal, it is important to keep the three fiberglass bars in place around the coil.  Otherwise, it could complicate reassembly by a factor of five.  I use #12 solid wire to hold those three bars in place.  In this case, the #12 wire insulation is green so it can be easily seen in the photo.