## Transcribed Text

4. The main section of robot arm - section AB - rotates in a vertical plane about a
horizontal axis at A. This section has a length I and is at an angle 0 with a
horizontal datum line through point A.
The second section of the arm - section BC - rotates in the same vertical plane
about a horizontal axis at B. This section has a length b and is at an angle with a
horizontal datum line through point B.
The main section AB rotates about point A with an angular speed WAB. The second
section BC rotates about point B with an angular speed WBC. You will manage the
direction of motion by setting the sign for the magnitude of the angular speeds: a
(+) sign for counterclockwise (CCW), a (-) sign for clockwise (CW).
Use unit vector (ijk) notation to find the following. Give your answers in
algebraic form (i.e., I for length of AB, WAB for angular speed of AB, etc). You will
plug in numbers at the end.
a) Find the radius vector to B from A. Also give the angular velocity vector for
AB. Give your answer in terms of I, 0, and WAB. (8 pts)
b) Find the vector for the velocity of point B. For full credit complete the
vector cross product term. (7 pts)
c) Find the radius vector to C from B. Also give the angular velocity vector for
BC. Give your answer in terms of b, 0, and WBC. (8 pts)
d) Find the vector for the velocity of point C. For full credit complete the
vector cross product term. (7 pts)
Now, we'll put in numbers. For the following values
Values: 0 = 35°
$ = 20°
I
= 1 meter b=0.3 m
WAB = 0.05 rad/sec CCW
Wac=0.02 rad/sec ( CCW
e) Find the magnitude of the velocity of point B.
Find the velocity of point B (vector).
Find the velocity of point C (vector).
(10 pts)

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