# A spherical simulator motion study

## Machine-building Engineering and Machine Science

### Аuthors

Mudrov A. P.*, Faizov M. R.**

Kazan National Research Technical University named after A.N. Tupolev, 10, Karl Marks str., Kazan, 420111, Russia

*e-mail: Mudrov.alex@yandex.ru
**e-mail: faizovmarat92@gmail.com

### Abstract

The article presents a spherical mechanism allowing perform spatial movements along a sphere. A 3D model of the mechanism was developed with the SolidWorks software. The model allows synthesize and examine the mechanism structure. Computing of the angular displacement, speed and acceleration of the connecting rod from the center point of the link and the slide of the mechanism itself was performed. The center point calculation was performed with account for the small and large thickness of the mechanism links Calculations were made for all angles between the links, which were employed for calculation of the spherical mechanism with two degrees of freedom. Based of the obtained mathematical model, computing of the moment of inertia from a given crank motion was performed. The motion parameters along the coordinate axes were determined, which would allow application of the direction cosines formulas. Additional angles calculation used when creating a mathematical model for the moment of inertia were obtained from the spatial sphere around the mechanism. The instant rotation moment of the mechanism was obtained. Using to the obtained data, a certain movement of the mechanism and the time interval of its movement were set, which are reflected by the obtained plots. These plots were obtained for comparing the two methods. The obtained plots reflect the movement of the connecting rod itself, and the slide mechanism. In addition, using Maple, the computation of motion with the moment of inertia of the mechanism itself, with a specified various masses, but with certain geometrical parameters of the mechanism links, was verified.

### Keywords:

crank-slider mechanism, moment of inertia

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