In a gimbal or hinge compensator the hinge pin(s)are positioned in the middle of the flexible elemet. Unit rotates around the pin. If you model the flexible element with length and you check the element connection point movements you will see 2 or 3 dimensional movement in x, y and z directions. Those point movements are relatively small but they are there.

I have not found any mistake in CAESAR II hinge or gimbal calculations if modelled correctly and system is used for metal compensators only.