Calculating the Velocity of Pin P in a Rod A-Rod B System

[MarkL]

From B&J Chap 15

Rods A and B are attached to a wall and point to the right.
A collar with pin P moves freely on Rod A.
Rod A is positioned horizontally.
Rod B is 500mm below Rod A and angled 30 degrees up with the wall.
Pin P is attached to a slot in Rod B. Pin P moves freely in the slot.
Determine the velocity of the pin if the angular velocity of:

Rod A is 8 rad/sec clockwise
Rod B is 3 rad/sec clockwise

Answer : 2.4 m/s, 73.9 degrees down and right

I calculated the relative velocity of the pin for each rod separately.
I get the right direction but the wrong magnitude. Go figure.
I have no problem when the pin moves freely on only one rod.
What is the trick when the pin is free to move on both rods.

Thank you

Mark

 

[twits]

Can you give me a picture for illustration ?

 

[DaveC426913]

Howzziss?..

 

[MarkL]

A Rod A P
]o---------------
| /
| /
| /
500mm /
| / Rod B
| /
| /
B /
]o/

Rod A is a circular rod with a circular cylindrical collar that slides left and right along the rod.
Rod B is more or less flat with a slot cut along the length near the end.
The collar has a pin that fits in this slot. This "connects" the rods.
But the collar/pin combo slide freely along both rods.
As the rods swing, the collar, with P, has a velocity and direction.

Some help?

length of Rod A: 0.5*Tan30 = 0.289 m
length of Rod B: 0.5/Cos30 = 0.577 m

v_ap = (8 r/s)*(0.289 m) = 2.31 m/s -- down
v_bp = (3 r/s)*(0.577 m) = 1.73 m/s -- down and 30 degrees right

v_p relative to B(along slot) due to A = 2.31*cos30 = 2 m/s dwn/lft 30deg
v_p relative to A(along A) due to B = 1.731*cos30 = 1.5 m/s to the right

right direction, wrong magnitude!

 

[MarkL]

My picture didn't work. sorry.

Dave's picture is correct except b crosses a.

Thanks Dave