# Torque calculation for a shaft end effector

I would like to calculate the max torque and the rpm to select the right motor. the application does not require a very fast rotation speed (rpm) however it should be accurately controlled. I understand that the torque $$T = L*m*g$$, also it is $$T = I*{\alpha}$$ and if not mistaken the inertia in this case $$I = 1/2 *MR^2$$ but what would be the right way to implement these equations in this case, as the axis of rotation is about the shaft itself.

• I believe that the torque required will depend on how quickly you want to accelerate the payload to its final speed and how much friction the motor will need to overcome. Feb 6 '20 at 23:39

I will try share some light in this matter.

Your understanding of the torque is only valid when the distance vector is not parallel with the axis of rotation (in your case is parallel). In your case that L is not the distance that you should consider for your problem, only the inertia generated by the added mass/payload.

Is the center of mass of the payload (7kg) aligned with the rotation axis of the shaft ? If not, then you should consider the parallel axis theorem to add the corresponding inertia. You can get these inertia parameters from a CAD software or by approximating the shape of your part with a basic shape like a cylinder or cube.

To consider the torque needed to move it also consider what is the position that it is mounted, like horizontal, vertical or other angle. Then, you can add the torque needed from the gravity payload.

You should also consider the reduction added by the gearbox which increase/decrease the torque in the shaft and decrease/increase the velocity depending on the configuration you have. The motor inertia in the shaft should be multiplied by the gearbox ratio ^2 .

Later you can consider acceleration and deceleration needed for your application.

• the payload is aligned with the axis of the shaft. The shape can be adjusted to be a normal cylinder. it's normally mounted horizontally with an angle downward of 45°. the gear ratio is 2 (increase). Based on those details, what would be the formulas to get the inertia, torque and angular acceleration ? Dec 29 '19 at 8:49