The trajectories construction of the universal joint movement in the configuration space in $\mathbb{R}^3$

In this paper, the study of the movement of the universal joint using the quaternion formalism was carried out, the law of movement of the cross of the universal joint was established with a known law of rotation of the drive shaft. A method of visual interpretation of the law of motion of the crosspiece is proposed, using the mapping of unit quaternions into a three-dimensional ball with radius 2$\pi$.