Authored by Dr. James F. Young, Electrical & Computer Engineering Department, Rice University.
(Originally published here. See copyright notice at end of article.)
This chapter introduces several types of motors commonly used in robotic and related applications.
DC motors are inexpensive, small, and powerful motors that are widely used. Gear-train reductions are typically needed to reduce the speed and increase the torque output of the motor.
Stepper motors, also called actuators, do not rotate continuously, but turn in fixed increments, and resist a change in their fixed positions. They require special driving circuits to apply the correct sequence of currents to their multiple coils. They are commonly used in robotics, particular in mechanisms that perform linear positioning, such as floppy and hard disk drive head motors and X-Y tables.
Servo motors are used for angular positioning. The output shaft of a servo does not rotate freely as do the shafts of DC motors, but rather is made to seek a particular angular position under electronic control. In effect, a servo motor is a combination of a DC motor, a shaft position sensor, and a feedback circuit. A servo motor also usually includes a built-in gear-train and is capable of delivering high torques directly.
DC motors are widely used in robotics because of their small size and high energy output. They are excellent for powering the drive wheels of a mobile robot as well as powering other mechanical assemblies.
Ratings and Specifications
Several characteristics are important in selecting a DC motor. The first two are its input ratings that specify the electrical characteristics of the motor.
If batteries are the source of power for the motor, low operating voltages are desirable because fewer cells are needed to obtain the specified voltage. However, the electronics to drive motors are typically more efficient at higher voltages. Typical DC motors may operate on as few as 1.5 Volts or up to 100 Volts or more. Roboticists often use motors that operate on 6, 12, or 24 volts because most robots are battery powered, and batteries are typically available with these values.
The ideal motor would produce a great deal of power while requiring a minimum of current. However, the current rating (in conjunction with the voltage rating) is usually a good indication of the power output capacity of a motor. The power input (current times voltage) is a good indicator of the mechanical power output. Also, a given motor draws more current as it delivers more output torque. Thus current ratings are often given when the motor is stalled. At this point it is drawing the maximum amount of current and applying maximum torque. A low voltage (e.g., 12 Volt or less) DC motor may draw from 100 mA to several amperes at stall, depending on its design.
The next three ratings describe the motor's output characteristics:
Usually this is specified as the speed in rotations per minute (RPM) of the motor when it is unloaded, or running freely, at its specified operating voltage. Typical DC motors run at speeds from one to twenty thousand RPM. Motor speed can be measured easily by mounting a disk or LEGO pulley wheel with one hole on the motor, and using a slotted optical switch and oscilloscope to measure the time between the switch openings.
The torque of a motor is the rotary force produced on its output shaft. When a motor is stalled it is producing the maximum amount of torque that it can produce. Hence the torque rating is usually taken when the motor has stalled and is called the stall torque. The motor torque is measured in ounce-inches (in the English system) or Newton-meters (metric). The torque of small electric motors is often given in milli-Newton-meters (mN-m) or 1/1000 of a N-m. A rating of one ounce-inch means that the motor is exerting a tangential force of one ounce at a radius of one inch from the center of its shaft. Torque ratings may vary from less than one ounce-inch to several dozen ounce-inches for large motors.
The power of a motor is the product of its speed and torque. The power output is greatest at about half way between the unloaded speed (maximum speed, no torque) and the stalled state (maximum torque, no speed). The output power in watts is about (torque) x (rpm) / 9.57.
Measuring Motor Torque
|Figure 1. Experiment to Measure Motor Torque.|
A simple experiment can be performed to determine the torque rating of a small hobby motor. All that is needed is a motor to be measured, a power supply for the motor, a piece of thread, a mass of known weight, a table, and a ruler. The mass is attached to one end of the thread. The other end of the thread is attached to the motor shaft so that when the motor turns the thread will be wound around the motor shaft. The motor shaft must be long enough to wind the thread like a bobbin.
The motor is put near the edge of a table with the mass hanging over the edge, as illustrated in Figure 1. When the motor is powered it will begin winding up the thread and lifting the mass. At first this will be an easy task because the moment arm required to lift the mass is small -- the radius of the motor shaft. But soon, the thread will wind around the shaft, increasing the radius at which the force is applied to lift the mass. Eventually, the motor will stall. At this point, the radius of the thread bobbin should be measured. The torque rating of the motor is this radius times amount of mass that caused the stall.
Alternatively, a small gear and long beam can be mounted on the motor shaft, and a small scale (such as a postage scale) calibrated in grams can be used to measure the force produced by the stalled motor at the end of the lever resting on the scale. The torque in mN-m is given by (force in grams) x (lever length in cm) x (0.09807). The stall current can be measured at the same time. The measurement must be made quickly (1 second) because the large current will heat the motor winding, increasing its resistance, and significantly lowering the current and torque.
Figure 2 shows a relative comparison of several small motors.
|Figure 2. DC Motor Comparison.|
Speed, Torque, and Gear Reduction
It was mentioned earlier that the power delivered by a motor is the product of its speed and the torque at which the speed is applied. If one measures this power over the full range of operating speeds -- from unloaded full speed to stall -- one gets a bell-shaped curve of motor power output.
When unloaded, the motor is running at full speed, but at zero torque, thus producing zero power. Conversely, when stalled, the motor is producing its maximum torque output, but at zero speed -- also producing zero power! Hence the maximum power output must lie somewhere in between, at about one-half of the maximum speed and of the maximum torque.
A typical DC motor operates at speeds that are far too high to be useful, and at torques that are far too low. Gear reduction is the standard method by which a motor is made useful.
The motor shaft is fitted with a gear of small radius that meshes with a gear of large radius. The motor's gear must revolve several times into order to cause the large gear to revolve once. The speed of rotation is thus decreased, but overall power is preserved (except for losses due to friction) and therefore the torque must increase. By ganging together several stages of this gear reduction, a strong torque can be produced at the final stage.
The challenge when designing a high-performance gear reduction for a competitive robot is to determine the amount of reduction that will allow the motor to operate at highest efficiency. If the normal operating speed of a motor/gear-train assembly is faster than the peak efficiency point, the gear-train will be able to accelerate quickly, but will not be operating at peak efficiency once it has reached the maximum velocity. Remember that the wheel is part of the drive train and gearing, and its size, the velocity desired, the motor characteristics, and other factors all effect the optimum gear ratio. While calculations can provide a guide (see the Quick Links page on gear ratios), experimentation is necessary to determine the best gear-train.
Pulse Width Modulation
Pulse width modulation (PWM) is a technique for reducing the amount of power delivered to a DC motor. Instead of reducing the voltage operating the motor (which would reduce its power), the motor's power supply is rapidly switched on and off. The percentage of time that the power is on determines the percentage of full operating power that is accomplished. This type of motor speed control is easier to implement with digital circuitry. It is typically used in mechanical systems that will not need to be operated at full power all of the time.
|Figure 3. Example of Several Pulse Width Modulation Waveforms.|
Figure 3 illustrates this concept, showing pulse width modulation signals to operate a motor at 75%, 50%, and 25% of the full power potential.
A wide range of frequencies could be used for the pulse width modulation signal.
A PWM waveform consisting of eight bits, each of which may be on or off, is used to control the motor. Every 1/1000 of a second, a control bit determines whether the motor is enabled or disabled. Every 1/125 of second the waveform is repeated. Therefore, the control bit make 8 checks per cycle, meaning the PWM waveform may be adjusted to eight power levels between off and full on. This provides eight motor speeds.
The shaft of a stepper motor moves between discrete rotary positions typically separated by a few degrees. Because of this precise position controllability, stepper motors are excellent for applications that require high positioning accuracy. Stepper motors are used in X-Y scanners, plotters, and machine tools, floppy and hard disk drive head positioning, computer printer head positioning, and numerous other applications.
Stepper motors have several electromagnetic coils that must be powered sequentially to make the motor turn, or step, from one position, to the next. By reversing the order that the coils are powered, a stepper motor can be made to reverse direction. The rate at which the coils are respectively energized determines the velocity of the motor up to a physical limit. Typical stepper motors have two or four coils.
Stepper Motor Control
One type of stepper motor has two sets of three wires: power, and two control/ground lines. The power wire is simply connected to a power supply.
The two control/ground signals are alternately grounded for a brief period. This series of pulses thus steps the motor to the desired position of the shaft. Each pulse pair represents one step command. The length of a pulse in time does not correspond to any angular position. The pulses must simply be long enough to cause the motor coil to actuate. Special circuitry or software must be used to drive the stepper motors.
Servo motors incorporate several components into one device package:
- a small DC motor;
- a gear reduction drive for torque increase;
- an electronic shaft position sensing and control circuit.
The output shaft of a servo motor does not rotate freely, but rather is commanded to move to a particular angular position. The electronic sensing and control circuitry -- the servo feedback control loop -- drives the motor to move the shaft to the commanded position. If the position is outside the range of movement of the shaft, or if the resisting torque on the shaft is too great, the motor will continue trying to attain the commanded position.
Servo Motor Control
A servo motor has three wires: power, ground, and control. The power and ground wires are simply connected to a power supply. Most servo motors operate from five volts.
The control signal consists of a series of pulses that indicate the desired position of the shaft. Each pulse represents one position command. The length of a pulse in time corresponds to the angular position. Typical pulse times range from 0.7 to 2.0 milliseconds for the full range of travel of a servo shaft. Most servo shafts have a 180 degree range of rotation. The control pulse must repeat every 20 milliseconds.
First through sixth editions, copyright © 1994-1999 by John K. Bennett;
Seventh edition, August 2000, copyright © 2000 by James F. Young;
Rice University, Houston, Texas
Permission is hereby granted to reproduce and to distribute verbatim copies of this document in whole or in part, provided that no fee is collected for its distribution (other than reasonable reproduction costs) and provided that this copyright notice is included.
Other than verbatim copies with copyright notice intact, no part of this document may be reproduced in any form without written permission of the author. For example, the right to make derivative works based on this document is not granted, and requires written consent.
Substantial portions of this document are derived from The 6.270 Robot Builder's Guide, Copyright © 1992 by Fred G. Martin, with the permission of the author. Please see the Acknowledgements for additional contributors and information.
The M.I.T. Department of Electrical Engineering and Computer Science and the M.I.T. Media Laboratory, who sponsored the development of the original 6.270 class technology, have agreed to unrestricted and free distribution of the robotics technology described in the course documentation for the 6.270 class, including their printed circuit board artwork and software programming environment. The Department of Electrical Engineering and the George R. Brown School of Engineering at Rice University have agreed to similar unrestricted distribution of the ELEC 201 class technology developed at Rice. While the material has not been placed in the public domain (it is still copyrighted), this means that any individual or organization can use the material for whatever purposes they desire. Our mutual hope is that people will use this work in the spirit of GNU software, which is distributed freely and is supported largely by a community of interested users. Corrections and suggestions for improvement are most welcome.
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