Calculation of Counterbalance Mass

[bsheikho]

Hi,

I've been grappling with a calculation that appears to give me a good result, however my gut feeling says other wise. Could someone please check the layout and possibly confirm my final answer. Attached is the layout of the system.

The system: -There is a long arm, d1+d2 is one link. then end of d2 to m2 is the second link.
-m2 is constrained in all directions except vertical up/down movement. (by putting the mass on a linear shaft with linear bearings)
The goal is to calculate m2, everything else is given, and Theta is a variable.

my final answer i reach to is: m2= (m1)*(d1/d2)*(1/2)

The point is that it seems that the mass of object two is independent of the angle. and can be fixed, however I have a feeling that tells me that its not that simple.

I can also upload how I got the final answer, but I'd prefer to see how others would tackle the situation.

Any help is appreciated.
Many Thanks!.

 

[mfb]

I agree with your answer.
The mechanics require both instances of $\theta$ to be the same, increasing the angle lowers m2 by $2d_2 \cos(\theta) d\theta$ and raises m1 by $d_1 \cos(\theta) d\theta$. That leads to balance with the condition you posted.

 

[bsheikho]

I agree with your answer.
The mechanics require both instances of $\theta$ to be the same, increasing the angle lowers m2 by $2d_2 \cos(\theta) d\theta$ and raises m1 by $d_1 \cos(\theta) d\theta$. That leads to balance with the condition you posted.

Excellent! Thank you.