How to calculate the Torque required for Direct drive BLDC (Gimbal) Motors


Please help in in calculating the torque requirement for Gimbal Motors which are kept in two orientations

Please find the attached image for the detailed problem description.

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There is a simple suggestion for measuring torque in Stepper Motor Basics but I don't know if it would be useful for your situation. It may give you some ideas.

If your motors need to start and stop then the rotary inertia of the load will also need to be taken into account.

If the rotating loads are balanced and if you have good quality low-friction bearings it is likely that very little torque will be required to overcome friction and most of the effort will be needed to deal with rotary inertia when starting and stopping. Gentle acceleration will help.


Torque needed in case 1 is zero, theoretically, and in reality you need enough to overcome bearing friction.

Torque needed in case 2 could be anything, as the torque there depends on how far the centre of mass is from the axis, and the mass itself. Torque = mgr, where m = mass, g = 9.8, r = off-axis distance, all in SI units (always work in SI units for mechanics problems, saves making stupid mistakes, much easier).

However if you want the load to accelerate at more than a low rate you'll need torque to overcome inertia too.

For rotation inertia is called "moment of inertia" or "MoI", and depends on the mass and geometry. Torque needed = MoI * angular acceleration.

MoI is measured in kg.m^2, angular acceleration in radians/s^2

The unit of torque is Nm (newton-metres). It is not N/m, but you often see that mistake made particularly in datasheets from motor manufacturers.

Equivalently you can measure torque in J/rad (joules per radian). Same thing expressed in terms of energy.