Looking for help with this formula

[mitra1343]

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?

 

[tiny-tim]

Welcome to PF!

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?

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

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

ii] type [noparse]²[/noparse]

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?

 

[FredGarvin]

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.

 

[mitra1343]

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˚ (dω_{2/dt)+Cω2 ω +Dω2^{2 +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}}

 

[tiny-tim]

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 …
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

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

(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 +T_g ?

From the PF https://www.physicsforums.com/library.php?do=view_item&itemid=86":

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

$$-2m\,\mathbf{\omega} \times \mathbf{v}$$

Centrifugal force depends on position rather than velocity:
$$m\,\mathbf{\omega} \times (\mathbf{\omega} \times \mathbf{r})\,=\,m\,\mathbf{\omega} \times \mathbf{v}$$.

 

[mitra1343]

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

(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 +T_g ?

From the PF https://www.physicsforums.com/library.php?do=view_item&itemid=86":

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

$$-2m\,\mathbf{\omega} \times \mathbf{v}$$

Centrifugal force depends on position rather than velocity:
$$m\,\mathbf{\omega} \times (\mathbf{\omega} \times \mathbf{r})\,=\,m\,\mathbf{\omega} \times \mathbf{v}$$.

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

 

[FredGarvin]

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