Dynamics_Part65

# Dynamics_Part65 - j Combining with the equation for v 3...

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Inspection of the figure above shows that r 1 /A = R i , r 2 /A = 2 R i , r 3 /A = 3 R i Combining these equations yields v 1 = 5 4 R j , v 2 = 2 ω S R j , v 3 = 3 R j where we assume the spider rotates clockwise. Now, by developing equations for v 2 relative to Point 1 and v 3 relative to Point 2, we can solve for the angular velocities ω B and ω S . That is, we know that v 2 = v 1 + ω B × r B/ 1 Assuming gear B rotates clockwise, then ω B = ω B k . The displacement vector is r B/ 1 = R i . Using the value computed for v 1 above, we find v 2 = 5 4 R j + ( ω B k ) × ( R i ) = w ω B 5 4 + W R j Also, we have v 3 = v 2 + ω B × r 3 /B = w ω B 5 4 W R j + ( ω B k ) × ( R i ) = w 2 ω B 5 4 W R
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Unformatted text preview: j Combining with the equation for v 3 developed above, we have 3 Ω R = w 2 ω B − 5 4 Ω W R = ⇒ 3 Ω = 2 ω B − 5 4 Ω Solving for ω B , there follows ω B = 17 8 Ω (b) Using the two equations developed for v 2 in Part (a), 2 ω S R = w ω B − 5 4 Ω W R = ⇒ 2 ω S = ω B − 5 4 Ω We found in Part (a) that ω B = 17 8 Ω . Substituting into the equation above and solving for ω S yields ω S = 7 16 Ω...
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