2. 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

3. 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”

4. 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?

5. 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

6. 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?

7. 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.

8. 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)

9. 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.

10. 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.

11. 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.

12. 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.

13. 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.

14. 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.

15. 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) ?

16. 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?

17. 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.

18. 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.

19. 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.

20. 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

21. 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.

22. 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

23. 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?

24. Gear Teeth  The 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.

25. 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.

26. 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.

27. 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

28. 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

29. 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.

30. 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.

31. 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?

32. 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.