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 occured?

 

[PJC01]

I would first like to clarify that the term "arm" in this context refers to the distance between the point of application of the force and the axis of rotation. In order to calculate the arm from torque and force vectors, we need to use the formula Torque = Force x Arm, where the arm is perpendicular to both the force and the torque vectors.

To calculate the arm, we need to first determine the direction of the arm vector. This can be done by taking the cross product of the torque and force vectors, as mentioned in the original post. However, it is important to note that the resulting vector will only give us the direction of the arm, not its magnitude.

To find the magnitude of the arm, we need to consider the components of the force vector that are perpendicular to the arm. This can be done by taking the dot product of the force vector with the normalized arm vector. The resulting value will give us the magnitude of the arm.

It is important to note that there may be multiple solutions for the arm, as the direction of the arm can vary depending on the orientation of the force and torque vectors. Therefore, it is important to carefully consider the direction and magnitude of the arm when using this formula.

In conclusion, it is possible to calculate the arm from torque and force vectors using the formula Torque = Force x Arm. However, it is important to consider the direction and magnitude of the arm carefully in order to find the correct solution. I hope this helps and please let me know if you need any further clarification.