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Looking for help with this formula

  1. Aug 19, 2008 #1
    The torque equation of joint in 2 link manipulator is given by:
    T= J (dω /dt)+J˚ (dω2/dt)+Cω2 ω +Dω22 +T
    i couldn't find how to write 2 as super script an subscript online any way what i don't know is what C&D stand for in here .can u pls help me?
  2. jcsd
  3. Aug 20, 2008 #2


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    Welcome to PF!

    Hi mitra1343! Welcome to PF! :smile:
    To write 2, either:

    i] hit the X2 tag above the reply box, or

    ii] type [noparse]2[/noparse] :smile:

    Sorry … what's ω2 ω? and ω22? and why is T on both sides?

    Can you type it out again, and tell us the context also? :smile:
  4. Aug 20, 2008 #3


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    If you can point us to where the equation comes from that would be a big help. My guess off the top of my head is that C and D are length dimensions.
  5. Aug 20, 2008 #4
    hi how are u and thanks so much for ur reply
    the formula is about a 2 link planar manipulator .assume that joint l is directly driven by a dc servomotor.(because i don't know how to write power and subscript in messages the formula looks strange that is those numbers in there )any way the formula is T= J (dω /dt)+J˚ (dω2/dt)+Cω2 ω +Dω22 +Tg
    Where J is the combined moment of inertia of motor and manipulator
    J˚ Is the coupling inertia between the 2 joints Cω2 ω is caused by coriolis force; Dω 2 2 is contributed by the centripetal force due to the velocity in the other joint; and Tg is the toeque due to gravity.
    but i can't underestand what C and D stand for will u pls help me ?the formula is from the book robotics for engineers by yoram koren thanks so much again
  6. Aug 21, 2008 #5


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    Hi mitra1343! :smile:
    (you need to "close" every sub or sup with a [/sub] or [/sup] :wink:)

    (or just use the X2 or X2 tags just above the Reply box)

    I'm still not entirely getting this formula …

    do you mean T= J(dω/dt) + J˚(dω2/dt) + Cω2ω + Dω22 +Tg ?

    From the PF Library:

    Coriolis force is minus mass times twice the cross-product of angular momentum, and the velocity of the object:

    [tex]-2m\,\mathbf{\omega} \times \mathbf{v}[/tex]

    Centrifugal force depends on position rather than velocity:
    [tex]m\,\mathbf{\omega} \times (\mathbf{\omega} \times \mathbf{r})\,=\,m\,\mathbf{\omega} \times \mathbf{v}[/tex].
  7. Aug 21, 2008 #6
    thank u very much ,yes i meant the same formula u have written ,what exactly D stands for , i'm just an interested beginner with little background of physics thanks again for ur kind reply
  8. Aug 22, 2008 #7


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    I would have to see the equiation in the reference. I am only taking guesses.
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