# Brainstorm¶

## Decision on what motors to use¶

To decide what motor I should use, the key parameter is torque. To give a rough estimate, if the robot were to move forward with 1 wheel,

$T = F_f * (D/2)$

Where $$T$$ is the Torque, $$F_f$$ is the friction to overcome, and $$D$$ is the diameter of the wheel.

However, the robot is driven by 3 wheels, of which 2 are active, and 1 is non-active. A rough sketch would be:

And hence, the formula becomes:

$T = F_f * (D/2)/(2cos30^{\circ})$

$$F_f$$ is given by

$F_f = {\mu}_f * F_n$

Whereby $$F_n$$ is the normal force on the surface, i.e. the robot’s weight.

Table of parameters

Name Value
$${\mu}_f$$ 0.05
gravity constant 9.8

To make some assumptions, suppose we take the robot’s weight to be roughly $$5kg$$, and the rolling friction coefficient of wheel threads to ground is $$0.05$$ (check out this article and this article), then each wheel needs to support weight of:

$F_n = 5 * 9.8 N / 3= 16.33N$

And the friction to overcome is hence:

$F_f = 0.05 * 16.33 = 0.8167 N$

Assume we are using our current wheel, which is $$60mm$$ in diameter

$T = 0.8167 * 0.03 / (cos(30^{\circ})) = 0.02829 Nm = 0.2885kgcm$

Formula is abstracted into code here.

However, to overcome the initial friction, the values need to be much higher. According to this project, they mentioned a value of 2-3 times is probably a safe estimate. Hence the final torque per motor would need to be roughly $$0.8655kgcm$$.

Technically, we can use DC motors to drive our robot no problem. However, if we think from the other direction, which is the max spec of the motor we can get and conversely get the wheel diameter, weight etc of the robot, it should also work.

Alternatively, we can play around properties of the robot as a whole:

#### Current specs¶

Name Value
mass 5kg
wheel diameter 6cm
##### What if we used NEMA 17?¶

According to NEMA17 specs, a 40mm length motor is around $$22 Ncm$$ to $$40 Ncm$$, which is around $$2.2kgcm - 4.0kgcm$$. That means we can either:

1. increase the wheel diameter of the robot
2. add more weight to the robot

To determine that, we need to look at how fast we want the robot to travel. Currently, I am looking at a top speed of roughly $$0.5m/s$$ (upper bound), and cotinuous speed of around $$0.3m/s$$.taking into consideration trigonometry, the wheel needs to rotate at

$V_{wheel} = V_{cont.} /cos30^{\circ} = 0.5/cos30^{\circ} = 0.5774 m/s$

After some checking, it seems that I can make the motor run at 1kHz, suppose it runs at full step, this means it can do 5 rotations per second.

speed to rotation conversion:

$V_{wheel} = speed(in RPS) * wheel circumference = 5 * {\pi} * D = 0.942m/s$

This is interesting, as it means that we have designed the robot incorrectly, or underestimated the capabilities of the robot (at laest on paper). This means we can definitely let the robot move faster. Further testing is required to verify the speeds of the platform

Last update: November 23, 2022