title: Ð§Ð¸ÑÐ»ÐµÐ½Ð½Ð¾Ðµ Ð¼Ð¾Ð´ÐµÐ»Ð¸ÑÐ¾Ð²Ð°Ð½Ð¸Ðµ Ð½ÐµÐ»Ð¸Ð½ÐµÐ¹Ð½ÑÑ ÑÐ¾ÑÐ¼ ÐºÐ¾Ð»ÐµÐ±Ð°Ð½Ð¸Ð¹ ÑÑÐµÑ Ð·Ð²ÐµÐ½Ð½Ð¾Ð³Ð¾ Ð¼Ð°Ð½Ð¸Ð¿ÑÐ»ÑÑÐ¾ÑÐ°
title: Numerical simulation of nonlinear oscillation modes of a three-link manipulator
Creators: name: Ð¡Ð¼Ð¸ÑÐ½Ð¾Ð², ÐÐ»ÐµÐºÑÐµÐ¹
name: ÐÑÐ»Ð¾Ð², Ð¡ÐµÑÐ°ÑÐ¸Ð¼
name: Ð¡Ð¼Ð¾Ð»ÑÐ½Ð¸ÐºÐ¾Ð², ÐÐ¾ÑÐ¸Ñ
name: "Ð¡Ð¸ÑÑÐµÐ¼Ð½ÑÐ¹ Ð°Ð½Ð°Ð»Ð¸Ð· Ð² Ð¿ÑÐ¾ÐµÐºÑÐ¸ÑÐ¾Ð²Ð°Ð½Ð¸Ð¸ Ð¸ ÑÐ¿ÑÐ°Ð²Ð»ÐµÐ½Ð¸Ð¸", Ð¼ÐµÐ¶Ð´ÑÐ½Ð°ÑÐ¾Ð´Ð½Ð°Ñ Ð½Ð°ÑÑÐ½Ð¾-Ð¿ÑÐ°ÐºÑÐ¸ÑÐµÑÐºÐ°Ñ ÐºÐ¾Ð½ÑÐµÑÐµÐ½ÑÐ¸Ñ (26; 2022; Ð¡Ð°Ð½ÐºÑ-ÐÐµÑÐµÑÐ±ÑÑÐ³)
Publisher: name: ÐÐÐÐÐ¢ÐÐ¥-ÐÐ ÐÐ¡Ð¡
Year: 2023
Subjects: Ð Ð¾Ð±Ð¾ÑÑ Ð¿ÑÐ¾Ð¼ÑÑÐ»ÐµÐ½Ð½ÑÐµ
ÑÐ³Ð»Ñ Ð¾ÑÐºÐ»Ð¾Ð½ÐµÐ½Ð¸Ñ Ð·Ð²ÐµÐ½ÑÐµÐ² Ð¾Ñ Ð²ÐµÑÑÐ¸ÐºÐ°Ð»Ð¸
ÑÐ³Ð»Ñ Ð¿Ð¾Ð²Ð¾ÑÐ¾ÑÐ° Ð² ÑÐ°ÑÐ½Ð¸ÑÐ°Ñ
Ð½ÐµÐ»Ð¸Ð½ÐµÐ¹Ð½Ð°Ñ ÑÐ¾ÑÐ¼Ð° ÐºÐ¾Ð»ÐµÐ±Ð°Ð½Ð¸Ð¹
ÑÐ°ÑÑÐ¾ÑÐ° Ð¸ Ð¿ÐµÑÐ¸Ð¾Ð´ Ð½ÐµÐ»Ð¸Ð½ÐµÐ¹Ð½ÑÑ ÐºÐ¾Ð»ÐµÐ±Ð°Ð½Ð¸Ð¹
deviation angles of links from the vertical
angles of rotation in joints
nonlinear oscillation mode
frequency and period of nonlinear oscillations

description: Ð ÑÐ°Ð±Ð¾ÑÐµ ÑÐ°ÑÑÐ¼Ð°ÑÑÐ¸Ð²Ð°ÑÑÑÑ Ð²Ð¾Ð¿ÑÐ¾ÑÑ Ð¾ Ð¿Ð¾ÑÑÑÐ¾ÐµÐ½Ð¸Ð¸ Ð½ÐµÐ»Ð¸Ð½ÐµÐ¹Ð½ÑÑ ÑÐ¾ÑÐ¼ ÐºÐ¾Ð»ÐµÐ±Ð°Ð½Ð¸Ð¹ ÑÑÐµÑÐ·Ð²ÐµÐ½Ð½Ð¾Ð³Ð¾ Ð¼Ð°Ð½Ð¸Ð¿ÑÐ»ÑÑÐ¾ÑÐ°, ÑÐ°Ð±Ð¾ÑÐ°ÑÑÐµÐ³Ð¾ Ð² Ð¿Ð¾Ð»Ðµ ÑÐ¸Ð»Ñ ÑÑÐ¶ÐµÑÑÐ¸ Ð¸ Ð¾Ð±Ð»Ð°Ð´Ð°ÑÑÐµÐ³Ð¾ Ð¸Ð´ÐµÐ½ÑÐ¸ÑÐ½ÑÐ¼Ð¸ Ð¿Ð°ÑÐ°Ð¼ÐµÑÑÐ°Ð¼Ð¸ Ð½ÐµÐ²ÐµÑÐ¾Ð¼ÑÑ Ð·Ð²ÐµÐ½ÑÐµÐ² Ð¸ ÐºÐ¾Ð½ÑÐµÐ²ÑÑ Ð³ÑÑÐ·Ð¾Ð², Ñ Ð¸ÑÐ¿Ð¾Ð»ÑÐ·Ð¾Ð²Ð°Ð½Ð¸ÐµÐ¼ ÑÐ¸ÑÐ»ÐµÐ½Ð½ÑÑ Ð¿ÑÐ¾ÑÐµÐ´ÑÑ. ÐÑÐ¸Ð²Ð¾Ð´Ð¸ÑÑÑ Ð½ÐµÐ»Ð¸Ð½ÐµÐ¹Ð½Ð°Ñ Ð¼Ð°ÑÐµÐ¼Ð°ÑÐ¸ÑÐµÑÐºÐ°Ñ Ð¼Ð¾Ð´ÐµÐ»Ñ ÐºÐ¾Ð»ÐµÐ±Ð°Ð½Ð¸Ð¹ ÑÐ¸ÑÑÐµÐ¼Ñ, Ð¸ Ð² ÑÐµÐ·ÑÐ»ÑÑÐ°ÑÐµ ÐµÐµ Ð¾Ð±ÑÑÐµÑÐ° Ð¿ÑÐ¸ Ð¿Ð¾Ð¼Ð¾ÑÐ¸ ÑÐ¸ÑÐ»ÐµÐ½Ð½Ð¾Ð³Ð¾ Ð¸Ð½ÑÐµÐ³ÑÐ¸ÑÐ¾Ð²Ð°Ð½Ð¸Ñ Ð¾Ð¿ÑÐµÐ´ÐµÐ»ÑÑÑÑÑ Ð½Ð°ÑÐ°Ð»ÑÐ½ÑÐµ ÑÑÐ»Ð¾Ð²Ð¸Ñ Ð´Ð²Ð¸Ð¶ÐµÐ½Ð¸Ñ, Ð¿ÑÐ¸Ð²Ð¾Ð´ÑÑÐ¸Ðµ Ðº Ð¾Ð´Ð½Ð¾ÑÐ°ÑÑÐ¾ÑÐ½ÑÐ¼ ÐºÐ¾Ð»ÐµÐ±Ð°Ð½Ð¸ÑÐ¼ Ð¿Ð¾ Ð¿ÐµÑÐ²Ð¾Ð¹, Ð²ÑÐ¾ÑÐ¾Ð¹ Ð¸Ð»Ð¸ ÑÑÐµÑÑÐµÐ¹ Ð½ÐµÐ»Ð¸Ð½ÐµÐ¹Ð½Ð¾Ð¹ ÑÐ¾ÑÐ¼Ðµ. ÐÐ±ÑÑÐ¶Ð´Ð°ÑÑÑÑ Ð¾ÑÐ½Ð¾Ð²Ð½ÑÐµ ÐºÐ°ÑÐµÑÑÐ²ÐµÐ½Ð½ÑÐµ Ð¾ÑÐ¾Ð±ÐµÐ½Ð½Ð¾ÑÑÐ¸ Ð¸ ÐºÐ¾Ð»Ð¸ÑÐµÑÑÐ²ÐµÐ½Ð½ÑÐµ ÑÐ°ÑÐ°ÐºÑÐµÑÐ¸ÑÑÐ¸ÐºÐ¸ Ð²ÑÐµÑ ÑÑÐµÑ Ð½ÐµÐ»Ð¸Ð½ÐµÐ¹Ð½ÑÑ ÑÐ¾ÑÐ¼ ÐºÐ¾Ð»ÐµÐ±Ð°Ð½Ð¸Ð¹. ÐÑÐ¾Ð¼Ðµ ÑÐ¾Ð³Ð¾, ÑÑÑÐ¾ÑÑÑÑ Ð³ÑÐ°ÑÐ¸ÑÐµÑÐºÐ¸Ðµ Ð·Ð°Ð²Ð¸ÑÐ¸Ð¼Ð¾ÑÑÐ¸, ÐºÐ¾ÑÐ¾ÑÑÐµ Ð¸Ð»Ð»ÑÑÑÑÐ¸ÑÑÑÑ Ð¸Ð·Ð¼ÐµÐ½ÐµÐ½Ð¸Ðµ Ð²ÑÐµÑ ÐºÐ»ÑÑÐµÐ²ÑÑ Ð²ÐµÐ»Ð¸ÑÐ¸Ð½ Ð½Ð° Ð¿ÐµÑÐ¸Ð¾Ð´Ðµ Ð½ÐµÐ»Ð¸Ð½ÐµÐ¹Ð½ÑÑ ÐºÐ¾Ð»ÐµÐ±Ð°Ð½Ð¸Ð¹ Ð´Ð»Ñ ÐºÐ°Ð¶Ð´Ð¾Ð¹ Ð¸Ð· Ð½ÐµÐ»Ð¸Ð½ÐµÐ¹Ð½ÑÑ ÑÐ¾ÑÐ¼. ÐÐ¾Ð»ÑÑÐµÐ½Ð½ÑÐµ ÑÐµÐ·ÑÐ»ÑÑÐ°ÑÑ Ð¿ÑÐµÐ´ÑÑÐ°Ð²Ð»ÑÑÑ Ð¸Ð½ÑÐµÑÐµÑ Ð´Ð»Ñ Ð°Ð½Ð°Ð»Ð¸ÑÐ¸ÑÐµÑÐºÐ¾Ð¹ Ð¼ÐµÑÐ°Ð½Ð¸ÐºÐ¸ Ð¸ ÑÐµÐ¾ÑÐ¸Ð¸ Ð½ÐµÐ»Ð¸Ð½ÐµÐ¹Ð½ÑÑ ÐºÐ¾Ð»ÐµÐ±Ð°Ð½Ð¸Ð¹, Ð° ÑÐ°ÐºÐ¶Ðµ Ð¾Ð½Ð¸ Ð¼Ð¾Ð³ÑÑ Ð¾ÐºÐ°Ð·Ð°ÑÑÑÑ Ð¿Ð¾Ð»ÐµÐ·Ð½ÑÐ¼Ð¸ Ð¸ Ð¿ÑÐ¸ ÑÐµÑÐµÐ½Ð¸Ð¸ ÐºÐ¾Ð½ÐºÑÐµÑÐ½ÑÑ Ð¿ÑÐ¸ÐºÐ»Ð°Ð´Ð½ÑÑ Ð·Ð°Ð´Ð°Ñ Ð² Ð¾Ð±Ð»Ð°ÑÑÐ¸ ÑÐ¾Ð±Ð¾ÑÐ¾ÑÐµÑÐ½Ð¸ÐºÐ¸ Ð¸ Ð±Ð¸Ð¾Ð¼ÐµÑÐ°Ð½Ð¸ÐºÐ¸.
description: The paper deals with the construction of nonlinear oscillation modes of a three-link manipulator operating in the gravity field and having identical parameters of weightless links and end loads, using numerical procedures. A nonlinear mathematical model of system oscillations is presented, and as a result of its calculation using numerical integration, the initial conditions of motion are determined leading to single-frequency oscillations on the first, second or third nonlinear mode. The main qualitative features and quantitative characteristics of all three nonlinear oscillation modes are discussed. In addition, graphical dependencies are constructed that illustrate the change in all key quantities in the period of nonlinear oscillations for each of the nonlinear modes. The results obtained are of interest for analytical mechanics and the theory of nonlinear oscillations, and they can also be useful in solving specific applied problems in the field of robotics and biomechanics.