Can a hinge joint technically allow rotatory motion?
It is about the movement of the bone along its major axis of movement. A hinge joint moves like a lever while a pivot joint involves rotation side to side like an axle.
It helps if you look at a example of a bone that has both types of joints. The radial head is part of both a pivot and hinge joint, with the ulna it rotates allowing the hand to pronate and is a pivot joint, while with the humerus it is a hinge allowing the arm to swing through an arc.
Keep in mind these are biological terms and not strict engineering descriptions, biology is more interested in how tissues move relative to each other. Biological terms are not interchangeable with geometry and engineering, nor are they designed to be perfectly rigorous, they are descriptive in nature. In biology rotation is a term reserved for more wheel and axle type motion where a bone is revolving around its own axis.


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