# Force-torque sensor reading when a robot is stationary

Let's say I have a robot arm with a force-torque sensor on the wrist, between the final motor and the gripper. If the arm and wrist are stationary, then what would the reading on the sensor be?

I know this might sound like a silly question, but I don't understand which of the following would be true:

• The reading would be g (gravity), since the only force acting on the sensor is gravity.
• The reading would be g + w, where w is the weight of the gripper, because both gravity and the gripper's weight are acting on the sensor.
• The reading would be 0, because whilst g + w are acting down on the sensor, since the arm is stationary, there must be an equal an opposite upward force applied by the robot, which exactly cancels out the downwards force.

Which of these is correct? And consequently, why are the other two not correct?

Thanks!

The answer is $$\vec{G}$$! and also any $$\vec{\tau}$$ torque caused by it, if the axis connecting the geometrical center of the sensor (assuming it measures torques relative to its geometrical center) to the centre of gravity of the gripper.
$$\vec{G} = m * \vec{g}$$
where $$m$$ is the mass of the gripper, $$g$$ is the gravitational ACCELERATION, not force and G is the gravitational pull (force) on the gripper.