This paper discusses the equivalence condition of the input and output rotation of a passive rotational joint and provides a general method to compute the output rotation angle. In a Stewart-Gough platform, the fixed base platform is usually connected to the moveable manipulator platform by six identical kinematic chains consisting of rotational joints and linear actuators. When using lead screws for the linear actuators, possible passive rotations of the rotational joints can be harmful because they may lead to additional length variations of the linear actuators or cause extra stresses if the rotations are obstructed. This paper provides a for computing these passive rotations by using vector comparison and demonstrates its application on the examples of a universal joint, a Rzeppa joint, and a Tracta joint.