Lecture Outline

1. 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

2. 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”

3. 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?

4. 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

5. 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?

6. 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.

7. 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)

8. 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.

9. 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.

10. 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.

11. 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.

12. 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.

13. 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.

14. 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)?

15. 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?

16. 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.

17. 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.

18. 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.

19. 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

20. 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.

21. 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

22. 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?

23. 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.

24. 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.

25. 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.

26. 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

27. 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

28. 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.

29. 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.

30. 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?

31. 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.