- #1
umarfarooq
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Homework Statement
The link OA of a robots arm is rotating clockwise with a constant angular speed of 0.8 rad/s. At the same time the link AB is also rotating clockwise so that the end B moves down the vertical dashed line. Determine the angular speed and the acceleration of the link AB when θ1 = 30 degrees. θ2 = 60 degrees
Homework Equations
cp = crossproduct
Va = Omega(oa)R(oa)
Vb = Va + (Omegaa/b)cp(Ra/b)
Ab = Aa + ALPHAa/b cp R(b/a) - ((Omegaa/b)^2)* Ra/b
The Attempt at a Solution
Va = Omega xRoa = 0.8x0.8 = 0.64m/s
Vb = Va + (Omegaa/b)cp(Ra/b), Va = 0.64i, Vb = -Vbj, Ra/b = (0.6cos30i -0.6sin30j), Omegaa/b = Omegaa/bk
Equate i's to get Omegaa/b = 2.13rad/s
Equate j's to get Vb = 1.109m/s down
For Aa, it is in the i direction only so Aa = (Omega(oa)^2)R(oa) = (0.8x0.8)x0.8 = 0.512 rad/s^2
so Ab = Aa + ALPHAa/b cp R(b/a) - ((Omegaa/b)^2)* Ra/b
equate i's
0 = 0/512 - ALPHAa/b x 0.6sin30 - (2.13^2)x 0.6cos 30
ALPHAa/b = 6.15 rad/s^2
equate j's
i get Ab = 4.56 rad/s^2 down
Could anyone verify my calculations. i would be very greatful please see the attachment for the diagram
