All language subtitles for 01_basic-mechanics.en

[MUSIC]

In this module we're gonna
explore how a quad rotor work.

We're gonna look at
the basic mechanics and

draw some conclusions about
how to design quad rotors.

So we'll first start discussing the basic
mechanics underlying a quad rotor.

We'll discuss some very,
very simple approaches to control.

We'll outline some basic
design considerations.

Talk a little bit about
maneuverability and agility, and

think about the components we might
want to select to build a quad rotor.

And in the end we finally want
to explore the effects of size.

So what does it mean to create a bigger
quad rotor, and how does that impact

performance and, conversely, how do things
scale down and you decrease the size?

Let's start with the basic mechanics.

As we discussed before,

a quad rotor has four rotors that
support the vehicle's weight.

So each rotor spins and
generates the thrust.

If you plot the thrust,
or the thrust force,

against the RPMs of the motor or
the angular velocity.

You'll find that this relationship
is approximately quadratic.

Every time a rotor spins, there's also
a drag that the rotor has to overcome.

And that drag moment is also quadratic.

So if you think about a quad rotor,

every rotor has to support roughly one
fourth of the weight in equilibrium.

Which means by looking at
the thrust forces of rpm curve,

you can determine speed that'll be
required to produce one fourth the weight.

So that gives you omega
zero the operating speed.

But of course, that operating
speed produces a drag moment and

every rotor has to
overcome the drag moment.

And that's where motors come in,
you have to size the motor, so

that they can produce the torque
to overcome this drag moment.

So when the robot is hovering, the rotor
speeds compensate for the weight.

Using the weight you can determine
the basic operating speed for every rotor.

And that in turn tells you what torque
you need to apply at every motor.

The equations are fairly simple,
if you assume that you know

the constant of proportionality between
the force and the square of the RPM.

And the constant of proportionality
between the drag moment and

the square of the RPM.

You can calculate the resultant
force quite easily.

It's the sum of the four thrusts and
the gravity force.

And if you know where
the center of mass is,

you can quickly calculate moments
about the center of mass.

And of course the total moment
is obtained by calculating

the moments due to the forces exerted
by the rotors and the reactions

due to the rotors spinning in
counterclockwise or clockwise directions.

Those reactions are moments,
and they add to the net moment

In equilibrium,
the resultant force is obviously zero.

And the result in moment is also zero.

But what happens when these resultant
forces in moments are non-zero?

Well you get acceleration.

To keep things simple let's
first look at the acceleration

in the vertical direction.

So in the vertical direction, again,

every motor thrust is the same, and
they'll add up to support the weight.

But if you increase the motor speeds,
then the robot accelerates up.

If you decrease the motor speeds,
obviously the robot will accelerate down.

So a combination of motor thrusts and

the weight determines which
way the robot accelerates.