LoesungA8_2001 - Gerhard-Mercator-Universitt Duisburg...

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Unformatted text preview: Gerhard-Mercator-Universitt Duisburg Fachgebiet Mechatronik Prof. Dr.-Ing. habil. M. Hiller Computergest¨utzte Kinematik und Dynamik von Mechanismen WS 2001/02 L¨ osung A8 Seite 1 Musterl¨ osung Aufgabe 8 Gegeben: • Orientierung eines K¨ orpers durch 3 Euler-Winkel Ψ = 45 ◦ , Θ = 90 ◦ , Φ = 45 ◦ • Winkelgeschwindigkeit im K¨ orperfesten Koordinatensystem 3 ω = £ 2 4 1 / T rad s a) Gesucht: Winkelgeschwindigkeit ω im Inertialsystem Transformationsmatrix aus Euler-Winkeln (Skript 4.54): T 3 =   cos Ψ cos Φ- sin Ψ cos Θ sin Φ- cos Ψ sin Φ- sin Ψ cos Θ cos Φ sin Ψ sin Θ sin Ψ cos Φ + cos Ψ cos Θ sin Φ- sin Ψ sin Φ + cos Ψ cos Θ cos Φ- cos Ψ sin Θ sin Θ sin Φ sin Θ cos Φ cos Θ   einsetzen: T 3 = 1 2   1- 1 √ 2 1- 1- √ 2 √ 2 √ 2   Winkelgeschwindigkeit: ω = T 3 3 ω = 1 2   1- 1 √ 2 1- 1- √ 2 √ 2 √ 2     2 4 1   rad s =   - 1 + √ 2 2- 1- √ 2 2 3 √ 2    rad s b) Gesucht: zeitliche ¨ Anderung ˙ Ψ , ˙ Θ und ˙ Φ der Euler-Winkel 1) Kinematische Euler-Gleichungen im K¨...
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This note was uploaded on 03/15/2012 for the course MAVT KIN07 taught by Professor Hiller during the Spring '01 term at Swiss Federal Institute of Technology Zurich.

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LoesungA8_2001 - Gerhard-Mercator-Universitt Duisburg...

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