The acceleration of the robot directly affects the torque required. If you want to have a heavy robot accelerate fast, you will need a very powerful motor, whereas a small robot accelerating slowly will need very little power. Many factors affect the acceleration of a robot including the selected motors, overall efficiency and external factors (wind and friction).
In a worst case scenario, your robot will need to accelerate up an incline. The maximum torque your robot will require is calculated based on this acceleration and uses the following equation:
T = (a + g*sinβ) * mR/n
∑Fx = ma = f – mgsinβ (balance the forces in the x-direction)
Therefore f = ma+mgsinβ = m(a+sinβ)
∑T = f * R
Substitute the f from the force balance into the torque balance. Divide by the number of drive wheels to get the torque needed per wheel:
∑T = (a + gsinβ) mR /n
Where:
f = force of friction acting on one wheel
m/n = weight of the robot propelled by each drive wheel
a = total acceleration of the robot
R = radius of the wheel
β = incline angle
So how is it then that large objects are hard to move and accelerate? The most important factor when trying to move an object from rest is the static friction. Once static friction has been overcome, the value is "lowered" to that of kinetic friction. If friction were to be removed entirely, it does not require a lot of force to move a large object. Low friction surfaces include ice, oil and air tables.
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