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- 1. Lecture Outline <ul><li>DC motors </li></ul><ul><ul><li>inefficiencies, operating voltage and current, stall voltage and current and torque </li></ul></ul><ul><ul><li>current and work of a motor </li></ul></ul><ul><li>Gearing gear ratios </li></ul><ul><ul><li>gearing up and down </li></ul></ul><ul><ul><li>combining gears </li></ul></ul><ul><li>Pulse width modulation </li></ul><ul><li>Servo motors </li></ul>
- 2. Definition of Actuator <ul><li>An actuator is the actual mechanism that enables the effector to execute an action. </li></ul><ul><li>E.g, electric motors, hydraulic or pneumatic cylinders, pumps… </li></ul><ul><li>Actuators and effectors are not the same thing. </li></ul><ul><li>Incorrectly thought of the same; “whatever makes the robot act” </li></ul>
- 3. DC Motors <ul><li>The most common actuator in mobile robotics is the direct current (DC) motor </li></ul><ul><li>Advantages: simple, cheap, various sizes and packages. </li></ul><ul><li>DC motors convert electrical into mechanical energy </li></ul><ul><li>How? </li></ul>
- 4. How DC Motors Work <ul><li>DC motors consist of permanent magnets with loops of wire inside </li></ul><ul><li>When current is applied, the wire loops generate a magnetic field, which reacts against the outside field of the static magnets </li></ul><ul><li>The interaction of the fields produces the movement of the shaft/armature </li></ul><ul><li>=> Electromagnetic energy becomes motion </li></ul>
- 5. Motor Inefficiency <ul><li>As any physical system, DC motors are not perfectly efficient . </li></ul><ul><li>The energy is not converted perfectly. Some is wasted as heat generated by friction of mechanical parts. </li></ul><ul><li>Inefficiencies are minimized in well-designed (more expensive) motors, and their efficiency can be high. </li></ul><ul><li>How high? </li></ul>
- 6. Level of Efficiency <ul><li>Good DC motors can be made to be efficient in the 90th percentile . </li></ul><ul><li>Cheap DC motors can be as low as 50%. </li></ul><ul><li>Other types of effectors, such as miniature electrostatic motors, may have much lower efficiencies still. </li></ul>
- 7. Operating Voltage <ul><li>A motor requires a power source within its operating voltage , i.e., the recommended voltage range for best efficiency of the motor. </li></ul><ul><li>Lower voltages will (usually) turn the motor, but will provide less power. </li></ul><ul><li>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) </li></ul>
- 8. Current and Work <ul><li>When constant voltage is applied, a DC motor draws current in the amount proportional to the work it is doing . </li></ul><ul><li>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. </li></ul><ul><li>The reason is the resistance to the motor motion introduced by the wall. </li></ul>
- 9. Stall Current <ul><li>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. </li></ul><ul><li>The stall current of the motor is the most current it can draw at its specified voltage. </li></ul>
- 10. Torque at the Motor Shaft <ul><li>Within a motor's operating current range, the more current is used, the more torque or rotational force is produced at the shaft. </li></ul><ul><li>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. </li></ul>
- 11. Stall Torque <ul><li>Besides stall current, a motor also has its stall torque. </li></ul><ul><li>Stall torque is the amount of rotational force produced when the motor is stalled at its operating voltage . </li></ul>
- 12. Power of a Motor <ul><li>The amount of power a motor generates is the product of the shaft's rotational velocity and its torque. </li></ul><ul><li>If there is no load on the shaft, i.e., the motor is spinning freely , then the rotational velocity is the highest </li></ul><ul><li>but the torque is 0 , since nothing is being driven by the motor. </li></ul><ul><li>The output power, then, is also 0 . </li></ul>
- 13. Free Spinning and Stalling <ul><li>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 . </li></ul><ul><li>Between free spinning and stalling, the motor does useful work, and the produced power has a characteristic parabolic relationship </li></ul><ul><li>A motor produces the most power in the middle of its performance range . </li></ul>
- 14. Speed and Torque <ul><li>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). </li></ul><ul><li>This puts DC motors in the high-speed but low-torque category (compared to some other actuators). </li></ul><ul><li>How often do you need to drive something very light that rotates very fast (besides a fan) ? </li></ul>
- 15. Motors and Robots <ul><li>DC motors are best at high speed and low torque . </li></ul><ul><li>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. </li></ul><ul><li>As a result, the performance of a DC motor typically needs to be adjusted . </li></ul><ul><li>How? </li></ul>
- 16. Gearing <ul><li>Gears are used to alter the output torque of a motor. </li></ul><ul><li>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. </li></ul><ul><li>This is the underlying law behind gearing mechanisms. </li></ul>
- 17. Gear Radii and Force/Torque <ul><li>By combining gears with different radii, we can manipulate the amount of force/torque the mechanism generates. </li></ul><ul><li>The relationship between the radii and the resulting torque is well defined </li></ul><ul><li>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. </li></ul>
- 18. Example of Gearing <ul><li>Suppose Gear1 with radius r1 turns with torque t1, generating a force of t1/r1 perpendicular to its circumference. </li></ul><ul><li>If we mesh it with Gear2, with r2, which generates t2/r2, then t1/r1 = t2/r2 </li></ul><ul><li>To get the torque generated by Gear2, we get: t2 = t1 r2/r1 </li></ul><ul><li>If r2 > r1, we get a bigger number, if r1 > r2, we get a smaller number. </li></ul>
- 19. Gearing Law for Torque <ul><li>If the output gear is larger than the input gear, the torque increases. </li></ul><ul><li>If the output gear is smaller than the input gear, the torque decreases. </li></ul><ul><li>=> Gearing up increases torque </li></ul><ul><li>=> Gearing down decreases torque </li></ul>
- 20. The Effect on Speed <ul><li>When gears are combined, there is also an effect on the output speed. </li></ul><ul><li>To measure speed we are interested in the circumference of the gear, C= 2 pi r. </li></ul><ul><li>If the circumference of Gear1 is twice that of Gear2, then Gear2 must turn twice for each full rotation of Gear1. </li></ul><ul><li>=> Gear2 must turn twice as fast to keep up with Gear1. </li></ul>
- 21. Gearing Law for Speed <ul><li>If the output gear is larger than the input gear, the speed decreases. </li></ul><ul><li>If the output gear is smaller than the input gear, the speed increases. </li></ul><ul><li>=> Gearing up decreases speed </li></ul><ul><li>=> Gearing down increases speed </li></ul>
- 22. Exchanging Speed for Torque <ul><li>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. </li></ul><ul><li>Gears are used in DC motors (which are fast and have low torque) to trade off extra speed for additional torque. </li></ul><ul><li>How? </li></ul>
- 23. Gear Teeth <ul><li>The speed/torque tradeoff is achieved through the numbers of gear teeth </li></ul><ul><li>Gear teeth must mesh well. </li></ul><ul><li>Any looseness produces backlash , the ability for a mechanism to move back & forth within the teeth, without turning the whole gear. </li></ul><ul><li>Reducing backlash requires tight meshing between the gear teeth, which, in turn, increases friction . </li></ul>
- 24. Gear Reduction Example <ul><li>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 </li></ul><ul><li>E.g., a small gear can have 8 teeth, and the large one 24 teeth </li></ul><ul><li>=> We have slowed down the large gear by 3 and have tripled its torque. </li></ul>
- 25. Gears in Series <ul><li>Gears can be organized in series, in order to multiply their effect. </li></ul><ul><li>Gears in series can save space </li></ul><ul><li>Multiplying gear reduction is the underlying mechanism that makes DC motors useful and ubiquitous. </li></ul>
- 26. Control of Motors <ul><li>Motors require more battery power (i.e., more current ) than electronics </li></ul><ul><li>E.g., 5 milliamps for the 68HC11 processor v. 100 milliamps - 1 amp for a small DC motor). </li></ul><ul><li>Typically, specialized circuitry is required </li></ul><ul><li>H-bridges and pulse-width modulation are used </li></ul>
- 27. Servo Motors <ul><li>It is sometimes necessary to move a motor to a specific position. </li></ul><ul><li>DC motors are not built for this purpose, but servo motors are. </li></ul><ul><li>Servo motors are adapted DC motors, with the following additions: </li></ul><ul><ul><li>some gear reduction </li></ul></ul><ul><ul><li>a position sensor for the motor shaft </li></ul></ul><ul><ul><li>an electronic circuit that controls the motor's operation </li></ul></ul>
- 28. Uses of Servo Motors <ul><li>What is used to sense shaft position? </li></ul><ul><li>Servos are used to adjust steering in RC (radio-controlled) cars and wing position in RC airplanes. </li></ul><ul><li>The job of a servo motor is to position the motor shaft; most have their movement reduced to 180 degrees . </li></ul><ul><li>Why? This is sufficient for a full range of positions. </li></ul>
- 29. Control of Servo Motors <ul><li>The motor is driven with a waveform that specifies the desired angular position of the shaft within that range. </li></ul><ul><li>The waveform is given as a series of pulses , within a pulse-width modulated signal. </li></ul><ul><li>Pulse-width modulation is using the width (i.e., length) of the pulse to specify the control value for the motor. </li></ul>
- 30. Pulse-Width Modulation <ul><li>The exact width/length of the pulse is critical, and cannot be sloppy. </li></ul><ul><li>Otherwise the motor can jitter or go beyond its mechanical limit and break. </li></ul><ul><li>In contrast, the duration between the pulses is not critical at all. </li></ul><ul><li>It should be consistent, but there can be noise on the order of milliseconds without any problems for the motor. </li></ul><ul><li>Why? </li></ul>
- 31. Noise in Modulation <ul><li>When no pulse arrives, the motor does not move, it simply stops. </li></ul><ul><li>As long as the pulse gives the motor sufficient time to turn to the proper position, additional time does not hurt it. </li></ul><ul><li>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. </li></ul>

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