Lecture Outline Lecture Outline DC motors

inefficiencies, operating voltage and current, stall voltage and current and torque

current and work of a motor

Gearing gear ratios gearing up and down combining gears

Pulse width modulation Servo motors

Definition of Actuator Definition of Actuator

An actuator is the actual mechanism that enables the effector to execute an action.

E.g, electric motors, hydraulic or pneumatic cylinders, pumps…

Actuators and effectors are not the same thing.

Incorrectly thought of the same; “whatever makes the robot act”

DC Motors DC Motors

The most common actuator in mobile robotics is the direct current (DC) motor

Advantages: simple, cheap, various sizes and packages.

DC motors convert electrical into mechanical energy

How?

How DC Motors Work How DC Motors Work

DC motors consist of permanent magnets with loops of wire inside

When current is applied, the wire loops generate a magnetic field, which reacts against the outside field of the static magnets

The interaction of the fields produces the movement of the shaft/armature

=> Electromagnetic energy becomes motion

Motor Inefficiency Motor Inefficiency

As any physical system, DC motors are not perfectly efficient.

The energy is not converted perfectly. Some is wasted as heat generated by friction of mechanical parts.

Inefficiencies are minimized in well-designed (more expensive) motors, and their efficiency can be high.

How high?

Level of Efficiency Level of Efficiency Good DC motors can be made to be

efficient in the 90th percentile. Cheap DC motors can be as low as

50%. Other types of effectors, such as

miniature electrostatic motors, may have much lower efficiencies still.

Operating Voltage Operating Voltage A motor requires a power source

within its operating voltage, i.e., the recommended voltage range for best efficiency of the motor.

Lower voltages will (usually) turn the motor, but will provide less power.

Higher voltages are more tricky; they increase power output at the expense of the operating life of the motor ( the

more you rev your car engine, the sooner it will die)

Current and Work Current and Work When constant voltage is applied, a

DC motor draws current in the amount proportional to the work it is doing.

E.g., if a robot is pushing against a wall, it is drawing more current (and draining more of its batteries) than when it is moving freely in open space.

The reason is the resistance to the motor motion introduced by the wall.

Stall Current Stall Current

If the resistance is very high (i.e., the wall won't move no matter how hard the robot pushes against it), the motor draws a maximum amount of power, and stalls.

The stall current of the motor is the most current it can draw at its specified voltage.

Torque at the Motor Shaft Torque at the Motor Shaft

Within a motor's operating current range, the more current is used, the more torque or rotational force is produced at the shaft.

The strengths of the magnetic field generated in the wire loops is directly proportional to the applied current and thus the produced torque at the shaft.

Stall Torque Stall Torque

Besides stall current, a motor also has its stall torque.

Stall torque is the amount of rotational force produced when the motor is stalled at its operating voltage.

Power of a Motor Power of a Motor The amount of power a motor

generates is the product of the shaft's rotational velocity and its torque.

If there is no load on the shaft, i.e., the motor is spinning freely, then the rotational velocity is the highest

but the torque is 0, since nothing is being driven by the motor.

The output power, then, is also 0.

Free Spinning and Stalling Free Spinning and Stalling

In contrast, when the motor is stalled, it is producing maximum torque, but the rotational velocity is 0, so the output power is 0 again.

Between free spinning and stalling, the motor does useful work, and the produced power has a characteristic parabolic relationship

A motor produces the most power in the middle of its performance range.

Speed and Torque Speed and Torque Most DC motors have unloaded

speeds in the range of 3,000 to 9,000 RPM (revolutions per minute), or 50 to 150 RPS (revolutions per second).

This puts DC motors in the high-speed but low-torque category (compared to some other actuators).

How often do you need to drive something very light that rotates very fast (besides a fan)?

Motors and Robots Motors and Robots DC motors are best at high speed

and low torque. In contrast, robots need to pull loads

(i.e., move their bodies and manipulators, all of which have significant mass), thus requiring more torque and less speed.

As a result, the performance of a DC motor typically needs to be adjusted.

How?

Gearing Gearing

Gears are used to alter the output torque of a motor.

The force generated at the edge of a gear is equal to the ratio the torque and the radius of the gear (T = F r), in the line tangential to its circumference.

This is the underlying law behind gearing mechanisms.

Gear Radii and Force/Torque Gear Radii and Force/Torque

By combining gears with different radii, we can manipulate the amount of force/torque the mechanism generates.

The relationship between the radii and the resulting torque is well defined

The torque generated at the output gear is proportional to the torque on the input gear and the ratio of the two gear's radii.

Example of Gearing Example of Gearing

Suppose Gear1 with radius r1 turns with torque t1, generating a force of t1/r1 perpendicular to its circumference.

If we mesh it with Gear2, with r2, which generates t2/r2, then t1/r1 = t2/r2

To get the torque generated by Gear2, we get: t2 = t1 r2/r1

If r2 > r1, we get a bigger number, if r1 > r2, we get a smaller number.

Gearing Law for Torque Gearing Law for Torque

If the output gear is larger than the input gear, the torque increases.

If the output gear is smaller than the input gear, the torque decreases.

=> Gearing up increases torque => Gearing down decreases torque

The Effect on Speed The Effect on Speed

When gears are combined, there is also an effect on the output speed.

To measure speed we are interested in the circumference of the gear, C= 2 pi r.

If the circumference of Gear1 is twice that of Gear2, then Gear2 must turn twice for each full rotation of Gear1.

=> Gear2 must turn twice as fast to keep up with Gear1.

Gearing Law for Speed Gearing Law for Speed

If the output gear is larger than the input gear, the speed decreases.

If the output gear is smaller than the input gear, the speed increases.

=> Gearing up decreases speed => Gearing down increases speed

Exchanging Speed for Torque Exchanging Speed for Torque

When a small gear drives a large one, torque is increased and speed is decreased. Analogously, when a large gear drives a small one, torque is decreased and speed is increased.

Gears are used in DC motors (which are fast and have low torque) to trade off extra speed for additional torque.

How?

Gear Teeth Gear TeethThe speed/torque tradeoff is achieved

through the numbers of gear teeth Gear teeth must mesh well. Any looseness produces backlash,

the ability for a mechanism to move back & forth within the teeth, without turning the whole gear.

Reducing backlash requires tight meshing between the gear teeth, which, in turn, increases friction.

Gear Reduction Example Gear Reduction Example

To achieve “three-to-one” gear reduction (3:1), we combine a small gear on the input with one that has 3 times as many teeth on the output

E.g., a small gear can have 8 teeth, and the large one 24 teeth

=> We have slowed down the large gear by 3 and have tripled its torque.

Gears in Series Gears in Series Gears can be organized in series, in

order to multiply their effect. Gears in series can save space Multiplying gear reduction is the

underlying mechanism that makes DC motors useful and ubiquitous.

Control of Motors Control of Motors Motors require more battery power

(i.e., more current) than electronics E.g., 5 milliamps for the 68HC11

processor v. 100 milliamps - 1 amp for a small DC motor).

Typically, specialized circuitry is required

H-bridges and pulse-width modulation are used

Servo Motors Servo Motors It is sometimes necessary to move a

motor to a specific position. DC motors are not built for this

purpose, but servo motors are. Servo motors are adapted DC motors,

with the following additions: some gear reduction a position sensor for the motor shaft an electronic circuit that controls the

motor's operation

Uses of Servo Motors Uses of Servo Motors

What is used to sense shaft position?

Servos are used to adjust steering in RC (radio-controlled) cars and wing position in RC airplanes.

The job of a servo motor is to position the motor shaft; most have their movement reduced to 180 degrees.

Why? This is sufficient for a full range of positions.

Control of Servo Motors Control of Servo Motors

The motor is driven with a waveform that specifies the desired angular position of the shaft within that range.

The waveform is given as a series of pulses, within a pulse-width modulated signal.

Pulse-width modulation is using the width (i.e., length) of the pulse to specify the control value for the motor.

Pulse-Width Modulation Pulse-Width Modulation

The exact width/length of the pulse is critical, and cannot be sloppy.

Otherwise the motor can jitter or go beyond its mechanical limit and break.

In contrast, the duration between the pulses is not critical at all.

It should be consistent, but there can be noise on the order of milliseconds without any problems for the motor.

Why?

Noise in Modulation Noise in Modulation When no pulse arrives, the motor

does not move, it simply stops. As long as the pulse gives the motor

sufficient time to turn to the proper position, additional time does not hurt it.

On the other hand, if the duration of the pulse is incorrect, the motor turns by an incorrect amount, so it reaches the wrong position.