Plane motion

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