I am reading the book Convex , Polyhedra, 2005, Springer Verlag , written by A. D. Alexandrov. In chapter 10, he introduces the term hinge mechanism consisting of the edges and vertices of a convex polyhedron,( probably is what we call framework). What I do not understand is:
Why hinges and not universal joints ? (hinges allow only planar rotation)
Is it a bad translation or here hinge means something else?
Thanks.
These are two different joint types.
(1) When two planes intersect they make a dihedral angle D between them and and the intersection line is called the hinge when rotation about this hinge line /axis/ joint is possible and it is said to have a single degree of motion freedom: $ 0< D < 2 \pi.$
(2) When a line/rod attached to a steel ball for example at the origin moves all around in two or more planes with no change in the position of center of the ball. We have two degrees of spherical coordinate freedom with $ 0< \theta < 2 \pi $ and $ -\pi < \phi < + \pi. $
These latter movement freedoms exists for a universal (or Hooke's ) joint in an automobile propeller shaft application for example and is kinematically equivalent to a ball joint with two degrees of freedom.