Modeling the Kinematics and Dynamics of Universal Joint
( Pp. 48-54)

The universal joint or Hooke joint, or U-joint is the main unit of the cardan transmission, which consists of two joints connected by an intermediate shaft. Cardan gears are widely used in various industries when creating machines with power transfer from the output shaft of the gearbox to the crank shaft in the absence of their coaxiality. A sufficiently large number of works are devoted to the study of the kinematics of the universal joint, and there are no works on its dynamics. Such a description became possible due to the use of matrix and quaternion formalism in describing the movement of the universal joint. In this paper, a complete description of the kinematics of the universal joint in its working cycle in terms of analogues of angular velocities is obtained and, on this basis, the dynamics of the joint is studied, taking into account its inertial characteristics. It is shown that taking into account the inertial characteristics of the U-joint cross can lead to a significant increase in the magnitude of the torque, the effectiveness on the spikes, in contact with the fork of the driven shaft.

Mityushov E.A., Misyura N.E., Lamotkin A.E., Raskatov E.Y., (2022), MODELING THE KINEMATICS AND DYNAMICS OF UNIVERSAL JOINT. Computational Nanotechnology, 4 => 48-54.

Amaresh Goud E., Hussain P. Study analysis of universal joint with the replacement of different material // Journal of Engineering Sciences. 2019. Vol. 10. Issue 12. Pp. 1037-1047.
Cardanus H. De subtilitate rerum. Norimberga: Johannes Petreius, 1550.
Datey S.N., Khamankar S.D., Kuttarmare H.C. Finite element analysis of universal joint // Journal of Mechanical and Civil Engineering. 2014. Vol. 11. Issue 3. Pp. 64-69.
Hooke R. A description of helioscopes, and some other instruments. London: John Martyn, 1676.
LeCain N. Tutorial of Hertzian contact stress analysis. URL: https://wp.optics.arizona.edu/optomech/wp-content/uploads/sites/53/2016/10/Tutorial LeCainNicholas.pdf (data of accesses: 29.11.2022).
Mityushov E.A., Misyura N.E. A quaternionic description of kinematics and dynamics universal joint // J. Phys.: Conf. Ser. 2021. Vol. 1901. Pp. 012-121.
Petrescu F., Petrescu R. The structure, geometry, and kinematics of a universal joint // Independent Journal of Management Production. 2019. Vol. 10. Issue 8. Pp. 1713-1724.
Poncelet J.V. Trait de m canique appliqu e aux machines. Part 1. Li ge: Librairie scientifique et industrielle, 1845.
Vesali F., Rezvani M.A., Kashfi M. Dynamics of universal joints, its failures, and some propositions for practically improving its performance and life expectancy // Journal of Mechanical Science and Technology. 2012. Vol. 26. Pp. 2439-2449.
Willis R. Principles of Mechanisms. London: John W. Parker, 1841.
Yadav K., Jain H. Modeling and finite element analysis of universal joint // Advancement in Mechanical Engineering and Technology. 2021 Vol. 4. Issue 1. Pp. 1-4.
Eresko S.P. Comparative analysis of designs of cardan joints of unequal angular velocities. Bulletin of RSSAU. 2015. Vol. 16. No. 3. Pp. 720-728. (In Rus.)
Zhilin P.A. Vectors and second-rank tensors in three-dimensional space. St. Petersburg: Nestor Publ., 2014.
Kravchenko V.I. et al. New materials and technologies used in the production of cardan transmissions. Bulletin of the Belarussian-Russian University. 2006. No. 4 (13). Pp. 91-99. (In Rus.)
Mityushov E.A., Misyura N.E. Quaternion models in kinematics and dynamics of spherical motion of elements of complex technical systems. Progressive Technologies and Systems of Engineering. 2020. No. 4 (71). Pp. 27-34. (In Rus.)

universal joint, Hooke joint, U-joint, cardan transmission, quaternions, dynamics.