Spatial motion model of Yo-Yo Mechanism

Theoretical mechanics


Yudintsev V. V.

Samara National Research University named after Academician S.P. Korolev, 34, Moskovskoye shosse, Samara, 443086, Russia



The article considers the spatial motion of the Yo-Yo mechanism. When employing the Yo-Yo mechanism for an angular velocity damping of an object performing complex spacio movement, the effect of this movement on the operation of this mechanism should be accounted for. As an option of Yo-Yo mechanism implementation, which assumes an object’s complex spatio movement, the author considers implementation of a mechanism as a part of autonomous docking module meant for capturing space debris’ objects. After the docking module separation from the space tow and its docking with a space debris object, it is possible to use the Yo-Yo mechanism for an object’s longitudinal angular velocity damping.

To analyze the spatial motion effect fn the object, on which the Yo-Yo mechanism is installed, on the movement of mechanism’s elements (wire ropes with loads) a mathematical model of the spatio motion was developed. Besides the angular motion of an object the model supposes the location of the plane of the wire ropes reel-out at a distance of an object’s center of masses, as well as the possibility of asynchronous movement of the mechanism’s wire ropes. To form the equations of motion, the Lagrange formalism was used. Equations were set down for each phase of the Yo-Yo mechanism motion.

The performance of the mathematical model is demonstrated by several numerical examples of the of the angular velocity damping of the debris’ object of a prolate and oblate type in terms of the ratio between the principal moments’ of inertia values. It is shown that the determining factor affecting the motion of the wire ropes of the mechanism is the transverse angular velocity of the object. The initial transverse angular velocity of the carrier leads to the exit of the Yo-Yo mechanism wires’ from the plane of the wire ropes reel-out, which can lead to disruption of its operation. The Yo-Yo mechanism can be used as part of an autonomous docking module to decrease the space debris objects’ angular velocity, such as spent orbital stages of carrier rockets with a longitudinal moment of inertia less than transverse moments of inertia.


angular velocity, stabilization, tether system, Yo-Yo mechanism, spatial motion, space debris


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