Design Realization lecture 20 John Canny 10/30/03 Last time  Real-time programming This time  Mechanics – Physics and Motors Review of physics  Newton’s law for translation: F = m a F in Newtons, m in kg, a in m/s 2 .  Acceleration a = dv / dt  Kinetic energy E = ½ m v 2 E in Joules, m in kg, v in m/s. Physics of translation  Momentum p = m v and so F = dp / dt  In the absence of force, momentum is conserved.  Momentum conservation implies energy conservation. Physics of rotation  Rotation is more complex; Euler’s equation: T = I α + ω x I ω T (torque) in N-m, ω in radians/sec, α in radians/sec 2 , I in kg-m 2 , α = d ω / dt  I is a 3x3 matrix, not necessarily diagonal.  If T = 0, then I α = - ω x I ω which is usually non-zero. So α is non-zero, ω changes with time, and the object wobbles. Physics of rotation  Angular momentum is q = I ω  The rotation equation simplifies to T = dq / dt because dq/dt = I d ω /dt + dI/dt ω = I α + ω x I ω  So even though an object wobbles when there is no external force, the angular momentum is conserved: q = I ω Physics of rotation  Kinetic energy of rotation is ½ ω T I ω  In the absence of external torque, kinetic energy of rotation is conserved.  But angular momentum conservation does not imply energy conservation. Work  Work done by a force = F x (Joules) where x is the distance (m) through which the force acts.  Work done by a torque = T θ (Joules) Power  Power is rate of doing work.  Power of a force = F v (Watts).  Power of a torque = T ω (Watts).  Power often expressed in horsepower = 746 Watts [...]... cheap, high-power, high torque, simplest are 3-phase  Speed up to 7200 rpm: speed ~ 7200 / # “poles” of the motor  Induction motors are brushless (no contacts between moving and fixed parts) Hi reliability  Efficiency high: 5 0-9 5 % Single-phase AC Motors  Single-phase (induction) motors – operate from normal AC current (one phase) Household appliances  Single-phase motors use a variety of tricks to... Single-phase motors (AC) Synchronous motors  The first two are highly controllable, and usually what you would use in an application But we quickly review the others 3-phase AC  Three or four wires that carry the same voltage at 3 equally-spaced phases:  Single phase AC requires two wires (only 1/3 the current or power of 3-phase) AC induction Motors  Induction motors – simple, cheap, high-power,... efficiency (20% - 50%)  Gears decrease precision (due to backlash)  Reduction gear train is normally not backdriveable (can’t use for “force control”) DC torque motors  Some high-end motors are available for direct drive servo or force applications (no gears)  They have low speed (a few rpm), high precision (with servo-ing), and moderate torque  Typically have large diameter vs length, and use rare-earth... machine: Step angle: 1.8° Voltage: 3.2 V Holding torque: 0.97 N-m Rotor inertia: 250 g-cm2 Weight: 1.32 lb (0.6 Kg.) Length: 2.13" (54 mm) Power output = 3W  Precision stepper motor: 0.02° /step, 1 rpm, 3W DC Motor example          V = 12 volts Max Current = 4 A Max Power Out = 25 W Max efficiency = 74% Max speed = 3500 rpm Max torque = 1.4 N-m Weight = 1.4 lbs Forward or reverse (brushed) Many DC... normal AC current (one phase) Household appliances  Single-phase motors use a variety of tricks to start, then transition to induction motor behavior  Efficiency lower: 2 5-6 0%  Often very low starting torque Synchronous AC Motors  Designed to turn in synchronization with the AC frequency E.g turntable motors  Low to very high power  Efficiency ?? DC Motors  DC motor types:  DC Brush motor  “DC”... and some large XY robots True Linear movement        There are some true linear magnetic drives BEI-Kimco voice coils: Up to 1” travel 100 lbf > 10 g acceleration 6 lbs weight 500 Hz corner frequency  Used for precision vibration control Summary  AC motors are good for inexpensive high-power applications where fine control isnt needed  DC motors provide a range of performance:  DC brush:... precision is possible without reduction gearing by using many rotor teeth  Can also “microstep” by activating both coils at once Driving Stepper Motors  Note: signals to the stepper motor are binary, on-off values (not PWM)  In principle easy: activate poles as A B C D A… or A D C B A…Steps are fixed size, so no need to sense the angle! (open loop control) Driving Stepper Motors  But in practice,... DC brush: versatile, “servo” motor, high speed, torque  DC brushless: speed/toque depend on electronics  Stepper: simple control signals, variable speed/accuracy without gearing, lower power  Direct-drive (torque) motors, expensive, lower torque  Linear actuation via drives, or voice coils . Design Realization lecture 20 John Canny 10/30/03 Last time  Real-time programming This time  Mechanics – Physics and Motors . in N-m, ω in radians/sec, α in radians/sec 2 , I in kg-m 2 , α = d ω / dt  I is a 3x3 matrix, not necessarily diagonal.  If T = 0, then I α = - ω x I ω which is usually non-zero reliability.  Efficiency high: 5 0-9 5 % Single-phase AC Motors  Single-phase (induction) motors – operate from normal AC current (one phase). Household appliances.  Single-phase motors use a variety