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LoesungA10ab_2001

# LoesungA10ab_2001 - Universitt Duisburg a Institut fr...

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Universit¨ at Duisburg Institut f¨ur Mechatronik und Systemdynamik Prof. Dr.-Ing. habil. M. Hiller Computergest¨utzte Kinematik und Dynamik von Mechanismen WS 2001/02 osung A10 Seite 1 Musterl¨ osung Aufgabe 10 Gegeben: Gelenkwinkel θ 1 , θ 2 , θ 3 Geschwindigkeiten ˙ θ 1 , ˙ θ 2 , ˙ θ 3 α 1 , 2 = 90 a) Gesucht : 1 T 4 , 1 r 1 , 4 (Position) Schreibweise: ( x, y, z ) vor Drehung ( x 0 , y 0 , z 0 ) nach Drehung Drehachse: z-Achse Transformationsmatrix und Ortsvektor: Koerper1 : 1 0 T 2 = h 1 0 e 2 x , 1 0 e 2 y , 1 0 e 2 z i = 1 0 0 0 0 - 1 0 1 0 1 0 r 1 , 2 = 0 - c 1 , 2 s 1 , 2 Koerper2 : 2 0 T 3 = 1 0 0 0 1 0 0 0 1 2 0 r 2 , 3 = d 2 , 3 0 0 Koerper3 : 2 0 T 3 = 1 0 0 0 0 - 1 0 1 0 3 0 r 3 , 4 = d 3 , 4 0 - s 3 , 4 Relativbewegung: (Drehgelenke immer um z-Achse) i T i 0 ( θ 1 ) = cos θ i - sin θ i 0 sin θ i cos θ i 0 0 0 1 , i 0 r i,i 0 = 0 0 0 , i = 1 , 2 , 3 Absolutbewegung 1 T 2 0 = 1 T 1 0 1 0 T 2 2 T 2 0 = cos θ 1 cos θ 2 - cos θ 1 sin θ 2 sin θ 1 sin θ 1 cos θ 2 - sin θ 1 sin θ 2 - cos θ 1 sin θ 2 cos θ 2 0 1 T 3 0 = 1 T 2 0 2 0 T

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LoesungA10ab_2001 - Universitt Duisburg a Institut fr...

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