 # MiniSumo and Torque

In this section we are considering Torque with regard to drive selection and ability to push. Torque is a measure of force applied to produce a rotational motion and is derived by multiplying the magnitude of the force by it's distance from the pivot point, we'll use the standard units on Newton Metres (Nm). If we consider a lever pivoted at one end and apply a forces to it we can see that 2N at 1m gives the same result as 1N at 2m. In this case we have 2 Nm acting in equal and opposite directions, the lever will be stationary.

Torque (T) = Force (F) x Distance (d) measured in Nm

Look at the wheel radius as a lever, we can calculate the force pushing us along the dohyo resulting from motor torque or the torque resulting from the 'bot being pushed on the dohyo. There are limits that we might consider such as maximum and stall motor torque, or the point at which friction is over come and the wheels start to slip.

 Force (F) = Torque (T) / Wheel Radius (r) or Torque (T) = Force (F) x Wheel Radius (r) We've considered friction before in relation to how much push we could resist. If we don't want to stall our motors then we need to use this to calculate the minimum torque rating of our drive.
RN = m.g
F = μRN
T = Fr    or    μRNr

If we consider a 500g minisumo with 40mm wheels and rubber tyres we have μ = 0.9, RN = 4.9N & r = 0.02m

T = 0.9 x 4.9N x 0.02m = 0.0882 Nm    or    88.2 Nmm

If our 'bot is against a fixed object and the torque from our drive is below 88.2Nmm then we'll stall the motor. It should be noted that motors draw much higher current when stalled compared to free running, this would have to be factored into your drive circuits. However with more torque from our drive when we hit an fixed object the wheels will over come friction and start to spin/slide. When we improve the "stiction" of our wheels then we need to reconsider the torque of our drive.

## Evaluating Drives for Torque

Presented with a Hitec HS-311 servo, modified for continuous rotation, with moulded wheels and rubber band tyres we can make an assessment of it's suitability. From the data sheet we can find it produces 3.0 kg.cm torque, that is 294.3 Nmm. With the moulded wheel radius, 33.5mm, the force imparted at the dohyo is 8.78 N which is much higher than the maximum 4.9N reaction force to the 'bots mass. This servo is more than able to drive our minisumo forward, as two servos are more likely the drive force is doubled. Rubber tyres have a μ value around 0.9 but this could be increased dramatically before the servo would stall.

Looking for a low cost motor/gear box you might commonly find 3.6 kg.cm or 20 oz.in. While the first gives more torque than the HS-311 servo the latter, which equates to 1.962 kg.cm or 141.2 Nmm. With a similar wheel size we could reach just 4.21N at the dohyo, below the stall torque when considered individually.