# Calculate Arm from Torque and Force vectors?

• chipmeisterc
In summary, the conversation discusses the possibility of calculating the arm from the given torque and force. One approach is to use the cross product of torque and force to determine the direction of the arm, but this method may not take into account the component of the force vector that generates torque. It is also mentioned that there may be an infinite number of points where the given force can produce the same torque, along the force direction vector. The individual also suggests using the formula Normalize( Torque cross Arm ) * ( Torque.Magnitude / Force.Magnitude ) to find a valid possible position, even if the force is not perpendicular to the arm. They also mention finding the force position by sliding from the calculated position until it hits the desired plane.

#### 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!

chipmeisterc said:
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.

Which lie along the force direction vector ( transmissibility? )

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?

## What is the formula for calculating arm from torque and force vectors?

The formula for calculating arm is: arm = torque / force. This means that the arm is equal to the torque divided by the force vector.

## How do I determine the direction of the arm vector?

The direction of the arm vector is determined by the direction of the force vector. If the force vector is pointing in the positive x-direction, then the arm vector will also be in the positive x-direction.

## What is the unit of measurement for arm?

The unit of measurement for arm is typically meters (m). This is because torque is typically measured in Newton-meters (Nm) and force is measured in Newtons (N), so the resulting arm value will be in meters.

## Can arm be negative?

Yes, arm can be negative. This occurs when the direction of the force vector is opposite to the direction of the torque vector. In this case, the arm will have a negative value, indicating that the force is creating a clockwise rotation instead of a counterclockwise rotation.

## What is the significance of calculating arm from torque and force vectors?

Calculating arm from torque and force vectors is important in understanding the mechanics of rotational motion. It allows us to determine the amount of force needed to create a certain amount of torque, and vice versa. This is useful in many engineering and scientific applications, such as designing machines and analyzing the movement of objects.