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Calculation of Counterbalance Mass

  1. Apr 28, 2015 #1

    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!.

    Attached Files:

    • cB.PDF
      File size:
      39.2 KB
    Last edited: Apr 28, 2015
  2. jcsd
  3. Apr 28, 2015 #2


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    Staff: Mentor

    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.
  4. Apr 28, 2015 #3
    Excellent! Thank you.
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