aerial robotics lecture 1b_1 basic mechanics

7/25/2019 Aerial Robotics Lecture 1B_1 Basic Mechanics

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Lecture 1B.1

Basic Mechanics

This module is going to explore how quad rotors work. We’ll look at the basic

mechanics and draw some conclusions about how to design quad rotors.

The lectures will cover the following topics:

Basic mechanics

Control

esign considerations

!gilit"

Component selection

#ffects of si$e

%et&s start with the basic mechanics.

! quad rotor has four rotors that support the vehicle&s weight. #ach rotor spins and

generates the thrust:

'f "ou plot the thrust( or the thrust force( against the )*+s of the motors or their

angular velocit"( "ou&ll find that the relationship is approximatel" quadratic. #ver"

time a rotor spins( there&s also a drag that the rotor has to overcome. That drag

moment is also quadratic:



'n the case of a quad rotor( ever" rotor has to support roughl" one fourth of the weight

in equilibrium. ,o( b" looking at the thrust forces vs. rpm curve( "ou can determine

the speed that&ll be required to produce one fourth the weight. This gives "ou the

operating speed( -.



f course( that operating speed produces a drag moment( and ever" rotor has to

overcome the drag moment. /ou have to select the si$e of the motor( so that the" can

produce the torque needed to overcome this drag moment.

,o when the robot is hovering( the rotor speeds( i( compensate for the weight( mg.

0sing the weight "ou can determine the basic operating speed for ever" rotor. !ndthat in turn tells "ou what torque "ou need to appl" at ever" motor:

The equations are fairl" simple if "ou assume that "ou know the constant of

proportionalit" between the force and the square of the )*+( k 1( and the constant of

proportionalit" between the drag moment and the square of the )*+( k +.

1i 2 k 1i3

+i 2 k +i3

The resultant force can be calculated quite easil". 't&s the sum of the four thrusts and

the gravit" force.

1 2 14 5 13 5 16 5 17 8 mg



!lso( if "ou know where the centre of mass is( "ou can quickl" calculate moments

about the centre of mass. Then the total moment is obtained b" calculating the

moments due to the forces exerted b" the rotors and the reactions due to the rotors

spinning in counter8clockwise or clockwise directions 9these reactions are moments(

and add to the net moment.

'f the distance from the centre of mass to the motor is r i( and the reaction due to the

motor is +i( the resultant moment is given b":

+ 2 r 414 5 r 313 5 r 616 5 r 717 5 +4 5 +3 5 +6 5 +7

'n equilibrium( the resultant force is obviousl" $ero( and the resulting moment is also

$ero.

But what happens when the resultant forces and moments are non8$ero; 'n this case("ou’ll get a net acceleration.

To keep things simple let&s first consider an acceleration in the vertical direction.

!s we have seen( when ever" motor thrust is the same( and their sum equals the

weight of the quadrotor( the vehicle will hover. 'f "ou increase the motor speeds( but

keep all 7 equal( then the robot accelerates upwards. 'f "ou decrease the motor speeds(

keeping them all equal( obviousl" the robot will accelerate down.

The combination of motor thrusts and the weight determines which wa" the robot

accelerates.

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aerial robotics lecture 1b_1 basic mechanics

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