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Since, motion of the ball on the beam depends on the beam angle alpha, shouldn't this system have a single degree of freedom?

  • $\begingroup$ No, the ball can still move independently. $\endgroup$
    – joojaa
    Dec 25, 2017 at 20:29
  • $\begingroup$ Could you be more specific? As far as I know, the acceleration acting on ball due to gravity only depends on beam angle alpha, which finally affects ball's motion. $\endgroup$
    – Swati
    Dec 26, 2017 at 7:07
  • $\begingroup$ Does not matter thats not at all what degrees of freedom are about. If its free to move its a degree of freedom, period. What forces cause it to move has no bearing on the problem. And no its not just gravity that causes it to move. Assuming there is something that stops the ball to jump out of contact, and we assume itbdoes not alide then: The fourbar has one freedom and the ball a second. So the system has 2 degrees of freedom. However in reality the sustem has 7 degrees of feedom the way its depicted. $\endgroup$
    – joojaa
    Dec 26, 2017 at 7:12
  • $\begingroup$ Got that it is not attached to the beam and it can move on its own by rolling, but that motion is not independent of beam's motion, I mean rolling of ball is only excited by movement of beam (neglecting friction). $\endgroup$
    – Swati
    Dec 26, 2017 at 7:22
  • $\begingroup$ Does not matter its not constrained to the beam. Degrees of freedom only talks about direct constraints not indirect dynamic effects $\endgroup$
    – joojaa
    Dec 26, 2017 at 7:30

1 Answer 1


Try to think of degrees of freedom as objects that can move independently of each other. They may be coupled like in your system such as alpha and theta so you can describe one of them with the other... however the ball is not. I would suggest "the art of modeling in science and engineering with mathematica" https://www.amazon.com/Modeling-Science-Engineering-Mathematica-Second/dp/1584884606

If you'd like a good read.


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