IC19.2 SteamShovel

# IC19.2 SteamShovel - If the velocity of point C of the...

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If the velocity of point C of the excavator is v C = 4 i (m/s) and is constant, what are ϖ AB , α AB , BC , α BC ? Problem Type: Find: Given: v c = 4, a c =0 AB , α AB , BC , α BC Rigid Body Kinematics Same basic strategy – write out expressions relating the kinematics for the different points on the linkages A B AB AB A B B r r a a / 2 / 2 2 2 2 2 × + - = α B C BC BC B C B C r r a a / 2 / 2 2 2 2 2 × + - = (1) (3) ) ˆ 9 . 3 ˆ 0 . 3 ( ˆ ) ˆ 9 . 3 ˆ 0 . 3 ( 2 j i k j i a AB AB B + × + + - = ) ˆ 5 . 0 ˆ 3 . 2 ( ˆ ) ˆ 5 . 0 ˆ 3 . 2 ( 2 j i k j i a a BC BC B C - × + - - = j j i i a AB AB AB AB B ˆ 0 . 3 ˆ 9 . 3 ˆ 9 . 3 ˆ 0 . 3 2 2 + - - - = j j i i j j i i BC BC BC BC AB AB AB AB ˆ 3 . 2 ˆ 5 . 0 ˆ 5 . 0 ˆ 3 . 2 ˆ 0 . 3 ˆ 9 . 3 ˆ 9 . 3 ˆ 0 . 3 0 2 2 2 2 + + + - + - - - = j j i i a BC BC BC BC B ˆ 3 . 2 ˆ 5 . 0 ˆ 5 . 0 ˆ 3 . 2 0 2 2 + + + - = BC BC AB AB 5 . 0 3 . 2 9 . 3 0 . 3 0 2 2 + - - - = BC BC AB AB 3 . 2 5 . 0 0 . 3 9 . 3 0 2 2 + + + - = Do A and B Now B and C (4) (2) Sub in a B from (2) into (4) Break into components x y What are your unknowns? BC BC AB AB , , , Need two more equations (5) (6)

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A B AB B r v / 2 2 2 × + = ϖ B C CB B C r v v / 2 2 2 2 × + = ) ˆ 9 . 3 ˆ 0 . 3 ( ˆ j i k v AB B + × + = j i j i i CB CB AB AB ˆ 3 . 2 ˆ 5 . 0 ˆ 0 . 3 ˆ 9 . 3 ˆ 4 + + + - = j i v AB AB B ˆ 0 . 3 ˆ 9 . 3 + - = ) ˆ 5 . 0 ˆ 3 . 2 ( ˆ j i k v v CB B C - × + = CB AB 5 . 0 9 . 3 4 + - = CB AB 3 . 2 0 . 3 0 + = CB AB ) 0 . 3 / 3 . 2 ( - = CB CB 5 . 0 ) 0 . 3 / 3 . 2 ( 9 . 3 4 + - - = s rad BC / 146 . 1 = s rad AB / 8787 . 0 - = BC AB α 5 . 0 9 . 3 338 . 5 + - = BC AB 3 . 2 ) 146 . 1 ( 5 . 0 0 . 3 ) 8787 . 0 ( 9 . 3 0 2 2 + + + - - = BC AB 5 . 0 ) 146 . 1 ( 3 . 2 9 . 3 ) 8787 . 0 ( 0 . 3 0 2 2 + - - - - = BC AB 3 . 2 0 . 3 354 . 2 + = We need more equations – let’s go to the velocity equation(s).
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IC19.2 SteamShovel - If the velocity of point C of the...

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