Choosing a Motor and Gearing Combination - Revision history

Lynch: /* Basics of Power Transmission */

2007-01-04T15:10:16Z

Basics of Power Transmission

Lynch: /* Basics of Power Transmission */

2007-01-03T00:32:50Z

Basics of Power Transmission

Lynch: /* Basics of Power Transmission */

2007-01-03T00:32:07Z

Basics of Power Transmission

Lynch: /* Choosing a Motor and Gearing Combination */

2006-12-27T15:20:59Z

Choosing a Motor and Gearing Combination

Lynch: /* Choosing a Motor and Gearing Combination */

2006-12-27T15:18:31Z

Choosing a Motor and Gearing Combination

Lynch at 15:15, 27 December 2006

2006-12-27T15:15:30Z

Lynch at 15:14, 27 December 2006

2006-12-27T15:14:56Z

Lynch: /* Choosing a Motor and Gearing Combination */

2006-12-27T13:25:00Z

Choosing a Motor and Gearing Combination

Lynch: /* Choosing a motor and gearing combination */

2006-12-27T13:22:47Z

Choosing a motor and gearing combination

Lynch at 13:18, 27 December 2006

2006-12-27T13:18:55Z

@@ Line 57: / Line 57: @@
 In practice, transmissions are not 100% efficient at transmitting power.  Some
-power is lost due to friction.  Gearboxes usually have an associated
+power is lost due to friction.  Gearboxes have an associated
-efficiency <math>\eta</math>, such that the torque output of the gearbox is actually
+efficiency <math>\eta < 1</math>, such that <math>P_{out} = \eta P_{in}</math>.
-<math>\tau_{out} = \eta \tau_{in}</math>.  The efficiencies of gearboxes attached
+Since the gear exactly enforces the speed relationship <math>\omega_{out} = \omega_{in}/G</math>, this means
+that the torque output of the gearbox is actually
+<math>\tau_{out} = \eta G \tau_{in}</math>.  The efficiencies of gearboxes attached
 to each other is obtained by multiplying the individual efficiencies.
 Gearboxes with large gear ratios are usually obtained by having several

@@ Line 24: / Line 24: @@
 <center>
-<math>\tau_{out} = G \tau_{in}</math>
+<math>\tau_{out} = G \tau_{in}\,</math>
 </center>

@@ Line 10: / Line 10: @@
 of the transmission performs the lower speed, higher torque motion that
 we want (e.g., motion of a wheel, robot joint, etc.).  The transmission
-could be built of belts and pulleys, gears, or other elements, and the
+can be built of belts and pulleys, gears, or other elements, and the
 output motion of the transmission can be rotational or linear.  Here, let's
 consider the case of a rotational output motion where the output speed
@@ Line 81: / Line 81: @@
 backdrivability.  A motor+gearbox is '''backdrivable''' if it is possible to rotate the output of the gearbox while the motor is off.  Some gear types make it nearly impossible to backdrive.  Sometimes you want the system to be backdrivable, so a human can physically manipulate it, for example.  Other times you don't:  for example, you might want the system to hold its position without brakes or power, even under gravity.  Backdrivability is a qualitative property.  Of two systems using the same type of gearing, the one with the smaller gear ratio is usually more backdrivable.
 Finally, gearboxes usually come with specifications on the maximum speed allowable at the input shaft and the maximum torque allowable at the output shaft.
 ==Choosing a Motor and Gearing Combination==

@@ Line 115: / Line 115: @@
 are most efficient at converting electrical power to mechanical power
 at high speeds.  On the other hand, gearboxes with larger gear ratios
-generally have lower efficiency than gearboxes with smaller gear ratios,
+generally have lower efficiency than gearboxes with smaller gear ratios.
+Don't worry about efficiency in converting electrical to mechanical power
-so you probably don't want to worry about this criterion except for sophisticated
+unless it is a critical issue for you.
-designs.
 <li> Some of the mechanical power created by a motor goes to accelerate the rotor
@@ Line 128: / Line 128: @@
 </center>
-This is called '''inertia matching'''.  This is only an issue for
+This is called '''inertia matching'''.  Again, this is only an issue for
 more sophisticated designs.
 </ul>

@@ Line 110: / Line 110: @@
 to choose a larger motor to meet this specification.
-<li> You can further optimize your design for maximum efficiency at converting
+<li> You can further optimize your design for maximum efficiency in converting
 electrical power to mechanical power, to
 save on electrical power for battery-powered robots.  Motors usually

@@ Line 39: / Line 39: @@
 since the ideal gearbox neither adds nor subtracts power.  If the speed <math>\omega</math>
-is measured in radians per second, and the torque is measured in Newton-meters, then the units for power are Watts.
+is measured in radians per second, and the torque <math>\tau</math> is measured in Newton-meters, then the units for power are Watts.
 In terms of the speed-torque curve above, a gearbox has the effect of

@@ Line 100: / Line 100: @@
 <li> Once you have chosen a motor, choose a gearbox for the motor so that the speed+torque combinations you want from it (including the maximum
 speed and maximum torque you need) are under the
-speed-torque curve of the motor+gearbox combination.
+speed-torque curve of the motor+gearbox combination.  Also make sure the gearbox output shaft maximum torque specification is sufficient.
 <li> Motors should not be run for long periods of time at stall, as they are likely to overheat, as explained in [[Brushed DC Motor Theory|Brushed DC Motor Theory]].  It is

@@ Line 102: / Line 102: @@
 speed-torque curve of the motor+gearbox combination.
-<li> Motors should not be run for long periods of time at stall, as they are likely to overheat, as explained in the previous section.  It is
+<li> Motors should not be run for long periods of time at stall, as they are likely to overheat, as explained in [[Brushed DC Motor Theory|Brushed DC Motor Theory]].  It is
 fine if they intermittently stall.  The allowable continuous operation
 region of the speed-torque curve depends on the thermal characteristics

@@ Line 1: / Line 1: @@
 ''You should be familiar with [[Brushed DC Motor Theory|DC motor speed-torque curves]] before reading this page.''
+==Basics of Power Transmission==
 For most robotics and mechatronics applications, DC motors run at speeds
@@ Line 22: / Line 24: @@
 <center>
-<math>\omega_{out} = \frac{\omega_{in}}{G}</math>
+<math>\tau_{out} = G \tau_{in}</math>
 </center>
 <center>
-<math>\tau_{out} = G \tau_{in}</math>
+<math>\omega_{out} = \frac{\omega_{in}}{G}</math>
 </center>
@@ Line 51: / Line 53: @@
 shaft of gearbox 1 is connected to the input shaft of gearbox 2, the
 total gear ratio from the input of gearbox 1 to the output of gearbox 2
-is <math>G_{total} = G_1 G_2</math>.
+is <math>G_{total} = G_1 G_2</math>.  Gearboxes can achieve gear ratios of several hundred, often by chaining multiple sets of gears.
 In practice, transmissions are not 100% efficient at transmitting power.  Some
@@ Line 73: / Line 75: @@
 be large (a few degrees) in cheap gears, much lower in precision
 gears, and nearly zero for certain gear technologies (e.g.,
-harmonic drive gears).
+harmonic drive gears).  See the [[Gears|Gears]] page.
+One other issue to keep in mind with gearboxes is
+backdrivability.  A motor+gearbox is '''backdrivable''' if it is possible to rotate the output of the gearbox while the motor is off.  Some gear types make it nearly impossible to backdrive.  Sometimes you want the system to be backdrivable, so a human can physically manipulate it, for example.  Other times you don't:  for example, you might want the system to hold its position without brakes or power, even under gravity.  Backdrivability is a qualitative property.  Of two systems using the same type of gearing, the one with the smaller gear ratio is usually more backdrivable.
+Finally, gearboxes usually come with specifications on the maximum speed allowable at the input shaft and the maximum torque allowable at the output shaft.
+==Choosing a Motor and Gearing Combination==
 To choose a motor and gearbox appropriate for your application,