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Recall
for any two points, R and S, in the same rigid link the relative
acceleration equation is:
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aR
= aS + α
x rSR -
ω2 rSR
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Strategy: Apply the relative acceleration equation
for each link, moving from the upper arm, to the lower arm, and finally to
the disk. Recall aA = 0
and α1 = 0.
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For
the upper arm aB = aA + α1
x AB i -
ω12 AB i
= ˗ 52 (˗ 0.45 i) = 11.25 i m/sec2
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For
the lower arm aC = aB + α2
x (˗ BC) j ˗ ω22 (˗ BC) j
aC =
11.25 i ˗ 2k x (-0.675) j ˗
32 (˗ 0.675) j =
9.9 i + 6.075 j m/sec2
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For
the disk aP
= aC + α3
x r i
˗ ω32 r i = 9.9 i + 6.075 j - k x 0.1 i ˗ (˗ 5)2
0.1 i
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aP =
9.9 i + 6.075 j - 0.1 j ˗ 2.5 i = 7.4
i +
5.975 j m/sec2 (result)
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Now
the acceleration of P relative to B is aP ˗
aB =
2.025 i
-
2.75 j ˗ (- 2.25
j )
aP/B =
7.4 i +
5.975 j ˗ (11.25 i ) = ˗
3.85 i
+ 5.975 j m/sec2 (result)
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Click
here for another example.
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