title: Ð Ð°Ð·ÑÐ°Ð±Ð¾ÑÐºÐ° Ð¼Ð°ÑÐµÐ¼Ð°ÑÐ¸ÑÐµÑÐºÐ¾Ð¹ Ð¼Ð¾Ð´ÐµÐ»Ð¸ Ð»ÑÐ¼Ð±Ð´Ð°-Ð¼ÐµÑ Ð°Ð½Ð¸Ð·Ð¼Ð° Ð§ÐµÐ±ÑÑÐµÐ²Ð° Ð² ÑÑÐµÑ Ð¼ÐµÑÐ½Ð¾Ð¹ Ð¿Ð¾ÑÑÐ°Ð½Ð¾Ð²ÐºÐµ
title: Ð²ÑÐ¿ÑÑÐºÐ½Ð°Ñ ÐºÐ²Ð°Ð»Ð¸ÑÐ¸ÐºÐ°ÑÐ¸Ð¾Ð½Ð½Ð°Ñ ÑÐ°Ð±Ð¾ÑÐ° Ð±Ð°ÐºÐ°Ð»Ð°Ð²ÑÐ°
titleType: Subtitle
title: Development of a mathematical model of the Chebyshev's Lambda mechanism in a three-dimensional setting
Creators: name: ÐÐ¸ÑÑÐ¾ÑÐ°Ð½Ð¾Ð²Ð°, ÐÐ»Ð¸Ð½Ð°
Publisher: name: Ð¡Ð°Ð½ÐºÑ-ÐÐµÑÐµÑÐ±ÑÑÐ³ÑÐºÐ¸Ð¹ Ð¿Ð¾Ð»Ð¸ÑÐµÑÐ½Ð¸ÑÐµÑÐºÐ¸Ð¹ ÑÐ½Ð¸Ð²ÐµÑÑÐ¸ÑÐµÑ ÐÐµÑÑÐ° ÐÐµÐ»Ð¸ÐºÐ¾Ð³Ð¾
Year: 2020
Subjects: Ð¸Ð½ÑÐµÑÐ²Ð°Ð»ÑÐ½ÑÐ¹ Ð°Ð½Ð°Ð»Ð¸Ð·
Ð»ÑÐ¼Ð±Ð´Ð°-Ð¼ÐµÑ Ð°Ð½Ð¸Ð·Ð¼ Ð§ÐµÐ±ÑÑÐµÐ²Ð°
Ð¼ÐµÑÐ¾Ð´ ÐÑÐ°Ð²ÑÐ¸ÐºÐ°
Ð¿Ð»Ð¾ÑÐ°Ð´Ñ ÑÐ¸Ð³ÑÑÑ
interval analysis
Chebyshev's Lambda mechanism
interval Krawczyk method
area of the shape

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description: This given work is devoted to studying Chebyshev's Lambda mechanism in three-dimensional setting, the application of the obtained results to analyze the causes of excessive friction in the bearing by interval analysis methods. The research set the following goals: 1. Finding the kinematics of Chebyshev's Lambda mechanism links in a three-dimensional setting; 2. Finding the condition for jamming the bearing; 3. Determination of the contact area of increased friction in the bearing. In the course of the work, the necessary mathematical models were developed, as well as a number of algorithms for solving the tasks. First of all, a mathematical model of Chebyshev's lambda mechanism was constructed in a three-dimensional setting and an algorithm was developed that calculates the kinematics of all links of the mechanism. In the second place, the obtained result is formulated as a statement of the problem of intersection of second-order curves with interval parameter uncertainties. Then an algorithm was developed that made it possible to calculate the intersection points of the interval ellipse and circle. In the third stage, an algorithm was developed that calculates the area of the part of the interval ellipse that is not intersected with the interval circle. The dependence of this area on the crank angle is constructed. The developed mathematical model and software code will be used as a tool for design and analysis work shutter mechanism for the protection of optical mirrors in the laser diagnostics of plasmas produced in the FTI im. A. F. Ioffe RAS, for the international project ITER.