Calculate Arm from Torque and Force vectors?

[chipmeisterc]

Hi all,

If Torque = Arm cross Force
Is it possible to calculate the arm from the torque and the force?

I have tried to solve this using cross product of torque and force to give me the arm direction. Then normalizing the result and multiplying by torque magnitude / force magnitude. However I am guessing this is wrong as it doesn't take into account only the component of the force vector that is generating a torque. I am also wondering if this is even possible or if there are many solutions?

I essentially have a resulting force and torque and would like to work backwards from this to find the point at which the force was applied.

Any help much appreciated!

 

[A.T.]

I essentially have a resulting force and torque and would like to work backwards from this to find the point at which the force was applied.

There is an infinite number of points at which a given force will produce the same given torque.

 

[chipmeisterc]

Which lie along the force direction vector ( transmissibility? )

 

[chipmeisterc]

Will the following give me a valid possible position even if the force isn't perpendicular to the arm? -
Normalize( Torque cross Arm ) * ( Torque.Magnitude / Force.Magnitude )

If so, I do know roughly what plane the force should occur on so I am wondering if I can find my force position using the above then slide from that position using the force direction (transmissibility) until it hits my plane and that is where the force probably occurred?