How Do You Calculate Angular Speed and Acceleration for a Rotating Robot Arm?

[umarfarooq]

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

 

[umarfarooq]

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

 

[piercas]

I would first like to commend you on your detailed and thorough attempt at solving this problem. Your equations and calculations seem to be correct, and your final answer for the angular acceleration of link AB appears to be consistent with the given information.

However, as a scientist, I would also suggest that you double-check your calculations and equations to ensure that they are accurate and that you have accounted for all relevant factors. Additionally, it may be helpful to provide more context or information about the problem, such as the dimensions or other specifications of the robot's arm, to provide a more complete and accurate solution. Overall, your approach and solution seem to be on the right track, but as with any scientific problem, it is important to thoroughly check and verify all calculations and assumptions to ensure accuracy.