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6. In the linkage below, the angular velocity of link 2 is 100 rad/s CCW. The linkage dimensions are given. When 02 is 90°, find 03, w3, and the velocity magnitude of point C on link 3 by using analytical method. A*A= 1.75 in A*B= 2.5 in AC = 5 in 02 3 B Y 03 02 3 B X ケフ 2. 2.

6. In the linkage below, the angular velocity of link 2 is 100 rad/s CCW. The linkage dimensions are given. When 02 is 90°, find 03, w3, and the velocity magnitude of point C on link 3 by using analytical method. A*A= 1.75 in A*B= 2.5 in AC = 5 in 02 3 B Y 03 02 3 B X ケフ 2. 2.

Elements Of Electromagnetics
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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### Problem Description In the linkage below, the angular velocity of link 2 is 100 rad/s counter-clockwise (CCW). The linkage dimensions are given. When \(\theta_2\) is 90°, find \(\theta_3\), \(\omega_3\), and the velocity magnitude of point C on link 3 by using the analytical method. ### Linkage Dimensions - \(A^*A = 1.75\) in - \(A^*B = 2.5\) in - \(AC = 5\) in ### Diagrams Explanation The diagrams illustrate a mechanical linkage system. Here's a detailed explanation: 1. **Top Diagram**: - Shows a schematic of the linkage system. - Point \(A\) is the pivot for link 2, which is rotating counter-clockwise. - Link 2 makes an angle \(\theta_2\) with the horizontal axis. - Link 3 connects to link 2 and ends at point C. - The goal is to find the parameters when \(\theta_2 = 90^\circ\). 2. **Bottom Diagram**: - Illustrates a more detailed linkage arrangement. - \(\theta_3\) is the angle link 3 makes with the horizontal axis. - \(r_1\), \(r_2\), and \(r_3\) are vectors showing the dimensions and orientations of the links. - The diagram includes axes \(X\) and \(Y\) to indicate directions. - Link 4 is connected between point B and C. The task includes using these diagrams to calculate \(\theta_3\), the angular velocity of link 3 (\(\omega_3\)), and the velocity magnitude of point C using analytical methods.
Transcribed Image Text:### Problem Description In the linkage below, the angular velocity of link 2 is 100 rad/s counter-clockwise (CCW). The linkage dimensions are given. When \(\theta_2\) is 90°, find \(\theta_3\), \(\omega_3\), and the velocity magnitude of point C on link 3 by using the analytical method. ### Linkage Dimensions - \(A^*A = 1.75\) in - \(A^*B = 2.5\) in - \(AC = 5\) in ### Diagrams Explanation The diagrams illustrate a mechanical linkage system. Here's a detailed explanation: 1. **Top Diagram**: - Shows a schematic of the linkage system. - Point \(A\) is the pivot for link 2, which is rotating counter-clockwise. - Link 2 makes an angle \(\theta_2\) with the horizontal axis. - Link 3 connects to link 2 and ends at point C. - The goal is to find the parameters when \(\theta_2 = 90^\circ\). 2. **Bottom Diagram**: - Illustrates a more detailed linkage arrangement. - \(\theta_3\) is the angle link 3 makes with the horizontal axis. - \(r_1\), \(r_2\), and \(r_3\) are vectors showing the dimensions and orientations of the links. - The diagram includes axes \(X\) and \(Y\) to indicate directions. - Link 4 is connected between point B and C. The task includes using these diagrams to calculate \(\theta_3\), the angular velocity of link 3 (\(\omega_3\)), and the velocity magnitude of point C using analytical methods.
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