# Angular Speed/Acceleration

1. May 22, 2007

### umarfarooq

1. The problem statement, all variables and given/known data

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

2. Relevant 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

3. 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
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

2. May 22, 2007

### umarfarooq

this is the diagram theta 1 is between OA and theta 2 between AB. OA = 0.8m and OB 0.6m

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