Encoders 011 - Incremental Encoders - Quadrature & Index

This post continues our discussion of incremental encoders which began in our Encoders 009 post.

One Output - Channel A

In that post, we started with a simple encoder which had a single window in the shape of a slot. We gradually increased the resolution by adding more lines and windows to the encoder’s disk. By the end of the post we showed a typical encoder signal, a square wave output. Let’s call it Channel A. The output went high (+5V) when the encoder’s sensor received light from an LED; and it went low (0V) when a line blocked light from the LED.

Drawing 001: Single Output

The Channel A output waveform looks like this.

Drawing 002: Single Output Waveform

But there’s more to the story. That single output might be fine if you only want to measure distance and speed in one direction, like in a cut-to-length machine.

In many applications, however, motion occurs in two directions: clockwise and counterclockwise, or forward and backward. With a single output channel, you can tell that something in the system is moving-but you can’t tell in which direction the motion is occurring.

A single output has another problem: every cycle looks the same… a line followed by a window… then a line followed by a window… then another line followed by a window… You can’t tell which segment of the disk is aligned with the sensor. You could count cycles from a known starting position-but if the power is turned off and then restored, you’ll lose position information.

These two problems can be solved by adding more output signals.

  • Quadrature Outputs - enable us to determine direction of motion.
  • Index Output - helps us locate a unique position on the encoder disk.

We’ll discuss quadrature first.

Two Outputs: Channel A and Channel B - Quadrature

Let’s begin by adding another LED and photo sensor. (In the drawing, we’ll extend the lines on the encoder disk so that everything fits.)

Drawing 003: Two Outputs - Not Quadrature

Now we have a second output-Channel B. The output from the two signals might look like this.

Drawing 004: Two Outputs - Not Quad - Waveform

We’re making progress, but we can’t determine direction yet. The two signals both rise and fall at the same time. We need a way to change that.

Here’s where the magic happens.

Let’s move the LED and sensor for Channel A over a bit; we’ll shift them a distance of 25% of a full cycle. (That’s one fourth, or one “quadrant” of a cycle-which is where the name “quadrature” comes from.)

Drawing 005: Two Outputs - Quadrature

Now the two output channels look like this.

Drawing 006: Two Outputs - Quadrature - Waveform

As the disk rotates in the clockwise direction, Channel A goes high when its sensor receives light. Then a quarter of a cycle later, Channel B goes high.

As the disk rotates in the counterclockwise direction, after Channel B goes high, one quarter of a cycle later, Channel A will go high.

We can now tell the direction of motion! The commonly used terminology to describe direction is “A leads B for clockwise shaft rotation, B leads A for counterclockwise shaft rotation.”

You also need to know from which end of the shaft we’re viewing the motion. A shaft moving clockwise when viewed from one end would appear to move counterclockwise from the other end! Because each encoder and motor manufacturer may use a different vantage point, ensure that your system follows that same perspective.

Quadrature’s Bonus - Extra Pulses per Revolution (PPR)

We’ve defined resolution as the number of Cycles Per Revolution (CPR) of the encoder disk. Although the number of lines printed on the disk is fixed, with quadrature you can get up to 4 times as many output pulses as the number of lines or windows.

Drawing 007: Resolution Multiplication

This is known as resolution multiplication and can be accomplished with an encoder to counter interface chip such as an LS7183N. As an example, consider an encoder with 100 lines and 100 windows on its disk-a resolution of 100 CPR:

  • x 1 - if we count the rising edge of each Channel A pulse as the disk rotates, we’ll get 100 pulses per revolution (100 PPR). This is the same number as the resolution of 100 CPR, like you would expect if you multiply by 1.
  • x 2 - if we count each rising edge and each falling edge of Channel A, we’ll get 2 pulses per cycle, which adds up to 200 pulses per revolution (200 PPR).
  • x 4 - if we count each rising edge and falling edge of both Channel A and Channel B, we’ll get 4 pulses per cycle, for a total of 400 pulses per revolution (400 PPR).

This technique of resolution multiplication can effectively double or quadruple the resolution of the encoder.

We’ve used quadrature to solve the direction of rotation problem, with an added bonus of enhanced resolution. Now, if we could just figure out where we are within that rotation…

A Third Output - the Index Channel

Let’s go back to the drawing board one last time, and add a solid ring with only one window. We’ll also add another LED and light sensor to detect that window.

Drawing 008: Three Outputs - Index

This thin window occupies its own track on the disk. The window is called an Index, and its output is a third channel called the Index Channel. (It’s sometimes called the registration marker or Z channel-where Z might stand for “zero position” aka the home location.)

Here’s what the outputs look like.

Drawing 009: Three Outputs - Index Waveform

As the encoder disk rotates, the Index Channel will change its output to high in precisely one position. It is common for a system to use this known position to perform a homing move upon powering up, or after an unexpected power cycle. You can also use the index to count rotations of a disk for an application with multiple turns.

That completes our introduction to incremental encoders. In a future blog post, Encoders 013, we’ll discuss absolute encoders, look at their output waveforms, and make some comparisons with incremental encoders.

It is my goal to make this blog as informative, engaging and as accurate as possible. If you ever have some additional or contrary information, please contact me directly and I will be glad to make any appropriate corrections in a future post. Previous Post


Written by Steve Mathis
Director of Customer Relations & Marketing

"My goal at US Digital is to work with the excellent teams here to contribute to the success of our customers by eliminating pain points and making it easy for them to do business with us."

Encoders 010 - Encoder Applications - Encoders Used on Mobile Robots

My plan for these posts has been to focus on technical concepts in posts released on the 2nd Tuesday of the month and focus on real world applications in posts released on the 4th Tuesday of the month. I’ll continue that pattern with today’s post and discuss the exciting application of Encoders Used on Mobile Robots.

Years ago, the world of science fiction promised us we would all have robots in our future. With the help of books from authors like Isaac Asimov and movies like Star Wars, we envisioned robots which could move about freely, communicate with us, and help us in many ways (Star Wars); or sometimes scare the living daylights out of us (Terminator).

When the first robots arrived in real life a few decades ago, they were very different than we imagined. They didn’t walk on two legs, or even four legs. They were industrial robots, firmly mounted on a pedestal, and they stayed in one place as they drilled holes, welded or painted.

Industrial robots have been great for automating manufacturing tasks—but where are those mobile robots that move around on their own and interact with us in our daily lives? Where are the science fiction robots?

Guess what—they’re here! And they rely on encoders to help them function.

A company named Savioke (pronounced SAVVY-oak) has developed their Relay robot to help in hospitality, medical and other settings.

Savioke robots in action

The robot is shaped like a tall cylinder. It can move throughout a hotel or hospital, navigating on its own and even calling for an elevator when necessary. The robot has a lid on top that opens to reveal a cargo compartment. Items for delivery are placed inside the compartment, and the robot rolls away to make the delivery.

If a guest in a hotel forgets their toothbrush or razor, they can call the front desk and the Relay robot can deliver a replacement for the forgotten item within minutes.

In a hospital, a nurse can draw a blood sample, place it in the Relay’s cargo bin, and the robot will quickly deliver the sample to the lab for analysis.

Savioke uses encoders on the drive wheels, to accurately sense and measure the distance the robot travels. They also use an encoder on the lid, to sense the angle of the lid when it opens.

By the way, an interesting book called The Sprint Book has a section that discusses an experiment Savioke performed in a real hotel with actual guests. The company worried about the reaction unsuspecting humans might have when they opened their doors to discover a robot outside. The short answer: humans loved it! Many guests even took selfies with the robot. (Amazon’s free “Look Inside” preview of the book includes the section about the experiment.)

Mobile robots are becoming popular in retail stores, too. Badger Technologies developed a mobile robot to monitor hazards in grocery stores like spills. They’ve continued to add features; Badger’s latest model roams store aisles and scans shelves for depleted inventory, misplaced items or incorrect price tags. Badger uses encoders on the drives that move the robot.

“Yes,” you say, “those are mobile robots. But they move by rolling. Where are the exciting science fiction robots? The ones that walk on their own two – or four, or six – legs?”

Researchers have been busy developing the capabilities of robots that walk, sometimes called “legged robots.” It hasn’t always been easy. This video from a few years ago shows researchers at the University of Michigan, plagued by an intermittent failure of what turned out to be an encoder interface board.

Engineers have been making steady progress. Students at Stanford are developing their cute “Doggo” robot, which can walk on four legs and even do backflips.

Doggo the robot

You can see Doggo go through its moves in this video:

The students designed Doggo to be open source. Anybody can download the plans and build their own Doggo robot.

The link for the Bill of Material (BOM) shows that Doggo uses 8 encoders and 8 motors. Each motor has an encoder used to track the motor angle.

The trend in legged mobile robots seems to be for development to start in university research laboratories. As researchers gain knowledge, they start spinoff companies, and then eventually team up with industrial partners for broader sales distribution.

Agility Robotics, located in Albany, Oregon is a good example. One of the co-founders is also a professor at Oregon State University. Agility developed the “Cassie” robot, a two-legged walking robot.

Agility Robotics Cassie robot

Cassie’s legs utilize encoders on their joints, to measure the joint angle, as detailed in this video and technical paper from researchers at the University of Michigan.

Agility Robotics’ YouTube channel has more videos of Cassie walking, like this one.

Agility’s next step was to add a torso and arms – and probably more encoders – mounted above Cassie’s hips and legs. They call their new robot Digit, and just a few weeks ago Ford Motor Company announced that it was teaming up with Agility Robotics to explore integrating Digit with Ford’s self-driving vehicles. The plan is to deliver packages straight to a customer’s doorstep, with Digit stepping over obstacles and climbing staircases along the way.

Among many others, CNN reported the story about Ford and Agility, and explained that Amazon and FedEx are also developing delivery robots—but those are rolling robots, and can’t climb stairs as well as Digit. Those robots also require that the customer unload the package from the robot. Digit, on the other hand, can drop off the package all by itself if no one is home.

The trend is clear: those sci-fi robots you’ve been wondering about are definitely coming. They might already be in your grocery store, and before long you could get a text message saying that your pizza is at your front door—delivered by a mobile robot, every inch of its progress monitored by its encoders.

It is my goal to make this blog as informative, engaging and as accurate as possible. If you ever have some additional or contrary information, please contact me directly and I will be glad to make any appropriate corrections in a future post. Previous Post


Written by Steve Mathis
Director of Customer Relations & Marketing

"My goal at US Digital is to work with the excellent teams here to contribute to the success of our customers by eliminating pain points and making it easy for them to do business with us."

Encoders 009 - Introduction to Incremental Encoders

This post continues our discussion of the various classifications of encoders identified previously

Form of Output

One of the most common classifications used for encoders is whether their architecture is incremental or absolute in design. This refers to the type of output the encoder emits, or what information is being provided by the encoder. This post will begin our discussion of incremental output and our future post will continue that discussion. Later, we'll have a discussion of absolute encoder output and make some comparisons between incremental and absolute encoders.

Incremental Output

The most common encoders are incremental encoders, for two main reasons. First, the information supplied by an incremental encoder is sufficient for most applications. The second reason is just a matter of economics and simplicity: it is much more cost effective to manufacture an incremental encoder than an absolute encoder.

Incremental Output

A very rudimentary form of an incremental encoder is shown above. It only involves a disk with one slot, an LED, and a photo detector. The detector provides an output each time it "sees" the LED.

The first piece of information that can be determined by an incremental encoder's output is distance. As the above disk rotates, each time the slot is aligned with the LED and detector, the detector produces an output. The disk has rotated through an angle of 360 mechanical degrees. A controller can use this information to calculate distance traveled in a system.

World's Largest Encoder'

The "encoder & controller" represented by the picture shown above is a reconstruction of an odometer made over 2,200 years ago. Each time the cart's wheels rotate, a pin on the axle engages a cog on a system of cogwheels that keep track of total distance traveled.


A second piece of information which can be determined by an incremental encoder's output is velocity, or speed of movement - the encoder essentially acts as a tachometer. As the disk in our first drawing above rotates, each time the slot is aligned with the LED and detector, the detector produces an output. The number of outputs in a minute would be the RPM or speed of the disk.

Although in the rudimentary drawing of an encoder at the beginning of this post you will be able to determine if a full rotation has taken place, for most of the 360 degrees, movement can take place without that movement being reported. The disk rotates without a change in output until the slot is reached.

Disk Model

To resolve that issue, a disk can be used with multiple slots as is shown in the picture above from a blog post by Aditya Prasad. Please note in this specific design, it would work as shown with an optical sensor or with a magnetic sensor as described earlier in the same post.

Now with 15 slots and 15 teeth, the optical sensor will provide an output while the disk turns through 12 mechanical degrees and a slot is in front of the sensor. During the next 12 degrees, a tooth will block the light, and the optical sensor will provide no output.

Sensor Drawing

Most applications require an output when the movement is much less than 12 degrees so disks are made with much finer increments. The technical term used to define the size of increments used is resolution. We will discuss resolution in more detail in a future post but for now, we will define it as the number of outputs provided by the encoder based on the number of lines or windows on the disk.

Mmmm, pie!

To illustrate the resolution in everyday (or at least Thanksgiving Day) terms, think of resolution as the size of the pieces of a pie. Neither high resolution nor low resolution is better but the resolution should match the need. Speaking of pies, if one is extremely hungry, the pie on the left would be the best choice. However, if one is trying to limit their caloric intake, other than not eating the pie at all, a smaller piece would be the best choice.


All of the illustrations and examples have been focused on a single output as is further illustrated in the above drawing. The drawing is indicative of what that single output might look like on an oscilloscope. The bottom of the drawing represents an output of zero volts. The top of the drawing represents an output of five volts. The complete drawing is showing the changes in output or cycles as the disk rotates. When the sensor sees the LED, the output goes high (5 volts); when the disk via the line prevents the sensor from seeing the LED, the output goes low (0 volts).

One complete electrical cycle starts when the output goes high and ends just before it goes high again. One electrical cycle is 360 electrical degrees. For every mechanical revolution, the number of electrical cycles will be equivalent to the resolution or lines and windows on the disk.

The specification for resolution is CPR which stands for Cycles Per Revolution. An encoder with 512 CPR will have 512 lines and windows on the disk and, of course, produce a high and low output 512 times for each rotation of the disk.

NOTE: Unfortunately, there are some vendors who use the term CPR to mean counts per revolution which, depending on the vendor, that number can be twice as many or four times as many as the resolution. This will be discussed in more detail in a future post.


One drawback with incremental encoders is that with power cycling, there is no memory as to where the disk is, as all of the lines and windows on the disk are identical. If you have ever been lost, you know this feeling where your surroundings might look the same in every direction. Essentially the position of the disk in relation to the sensor is lost. We will show in our next post how we can use a search operation, like the search dogs shown above, to figure out where the disk is in its rotation.

Although we are able to calculate both distance moved and velocity from a single encoder output, one other piece of information provided by incremental encoders is direction of travel. Our future post will continue this discussion and explain how direction can be determined.

It is my goal to make this blog as informative, engaging and as accurate as possible. If you ever have some additional or contrary information, please contact me directly and I will be glad to make any appropriate corrections in a future post. Previous Post

Source for photo detector graphic - reviseomatic.org
Tachometer image source - boschperformance.com
Image source for ancient odometer - commons.wikimedia.org
Source for slotted disk on motor - technlab.blogspot.com
Pumpkin pie image source #1 - finecooking.com
Pumpkin pie image source #2 - bettycrocker.com
Image source for search dog team - vsar.org

Written by Steve Mathis
Director of Customer Relations & Marketing

"My goal at US Digital is to work with the excellent teams here to contribute to the success of our customers by eliminating pain points and making it easy for them to do business with us."

Encoders 008 - The Strange History of the Industries from which Encoders Evolved

What do these have in common?

What do an organ, a black widow spider, and a scale have in common?

Classic Ultrasound Machine

It has always been intriguing to me how companies came into existence. US Digital's founding is an exclamation to the saying - "necessity is the mother of invention". David Madore, the founder of US Digital, worked at the time as a design engineer for a medical ultrasound imaging company. The equipment had many knobs on the front panel for potentiometers. The company wanted to upgrade the design to use optical encoders to improve operation. In doing research they could not find a good source suitable for the application. The ones they found were overpriced, had long lead times and poor specifications. In 1980, David Madore, made his first encoder to meet this need. And as they say, the rest is history.

Parlor Organ

BEI's history dates back to the 1800's. Many of us have heard of Baldwin pianos or organs but are unaware of how they fit in with encoders. Dwight Hamilton Baldwin was a minister and a singing teacher in schools who also opened a music store in Cincinnati, Ohio in 1862. Instead of just distributing the keyboard instruments, he set out to make "the best piano that could be built". World War II interrupted their operation as the company participated in making wings and other aircraft parts. A more detailed account of their history is available if you are interested.

Glass Disks

After the war, Baldwin started using electronics in the development of keyboard instruments. The goal was to use this technology in an organ to replicate the sound of pipe organs in European cathedrals. The engineers at Baldwin came up with a way to use optically encoded glass discs to reproduce the organ tones. The codewheel transcribed the original organ tones into etched glass - in opaque and transparent segments so that when the disk turned, it created an alternating pattern of light and dark. Photodiodes were used to translate this into an electronic signal (sound familiar?) which was processed and amplified to create the tones and harmonics desired.

Sidebar - this development by Baldwin was not the first use of photo-electricity with a spinning glass disk to create musical tones. This was done as early as the 1920's in France, Austria, Russia, Germany, and the USA.

In 1951 the U.S. Army Signal Corp contracted with Baldwin to develop optical encoders, realizing that the company's technology could help in the pointing and tracking for radar antennas. In 1955 Baldwin made their first experimental optical encoder. In 1962, Baldwin's research resulted in an 18-bit optical encoder which was the first optical encoder used in space. The following year, they produced the first optical encoder with an LED light source which was used in space as was highlighted in our post, "Who Made the First Optical Encoder". That same year the electronics division was incorporated as Baldwin Electronics, Inc., hence the name, BEI.


The Gurley enterprise was established in 1845 but changed to W. & L. E. Gurley in 1852 as the brothers, William and Lewis, both engineering graduates of Prensselaer Polytechnic Institute in New York teamed up to create products with technical innovations. The Gurley brothers had many different interests but most related in one way or another to measuring things - from electrical current to pressure, to weights and distances and angles. In their factory the brothers created different departments, with each department making different components and then final assembly taking place in still another department after all components had been made.

Crosshair Drawings

The area of technology by Gurley which is of most interest to those of us in the encoder field is the surveying field and their designing of theodolites - an optical instrument used for measuring angles. The crosshairs used in the late 1800's for these surveying tools was the spider web filament from a black widow spider. The spider web filament was impregnated into the glass of their surveying instrument eyepieces. Gurley and other surveying equipment companies, actually had black widow spiders in their employment to provide them with the material they needed to create the crosshairs.


This technology was also used in the war effort in both world wars. One of the numerous industries developed in the US following the bombing of Pearl Harbor was the special defense plants or spider ranches supplying the spider silk for everything from bomber sights to periscopes and telescopes. The next time you think about complaining about your coworker, remember to be thankful it isn't a black widow spider.

Gurley was an early adopter of photolithography to transition from the use of spider webs. This new method provided for chrome patterns on the glass which not only was a superior method but provided a relief from the literally toxic work environment. This technology was offered as a service to others and in fact, according to Martin Gordinier of Gurley, they created the first encoder disk for Dr. Gray - famously known for the development of the Gray code used on encoder disks. After selling encoder disks to many firms, Gurley started producing their own encoders in the 1950's.

Etching examples

Wilhelm Heidenhain founded his company in 1889. It began as a metal etching factory. The company etched templates, signs, graduations, and scales. Heidenhain's enterprise was destroyed in World War II and the Dr. Johannes Heidenhain Company was founded in Traunreut by Wilhelm Heidenhain's son in 1948.


One revolutionary advancement was the development of the diadur process in 1950 which enabled them to apply very fine structures of chromium on glass. In 1952 Heidenhain used the diadur process to create optical position measuring devices for machine tools. That same year they introduced their first optical linear and angle encoders for machine tools. It was in 1961 that Heidenhain produced its first photoelectric incremental rotary encoder for position feedback (10,000 lines).

It is my goal to make this blog as informative, engaging and as accurate as possible. If you ever have some additional or contrary information, please contact me directly and I will be glad to make any appropriate corrections in a future post. Previous Post

Organ picture source - 120years.net
Black widow spider image - nationalgeographic.com
Source for scale picture - heidenhain.com
Ultrasound machine image - ob-ultrasound.net
Glass disk imagery - 120years.net
Theodolite image - Etsy.com
Cross hair imagery source - surveyhistory.org
Source for bombsight image - masseyaero.org
Classic Baldwin Organ photo - patternsofink.blogspot.com

Written by Steve Mathis
Director of Customer Relations & Marketing

"My goal at US Digital is to work with the excellent teams here to contribute to the success of our customers by eliminating pain points and making it easy for them to do business with us."

Encoders 007 - Encoders: Mechanical Configurations

US Digital Product Family

We will continue in this post going through the various classification of encoders which were identified in my earlier post.

Mechanical Configurations

Mechanical configurations include differences based on whether the encoder comes with a shaft or will be installed onto an existing shaft. There are also different configurations based on the size of the motor, the required IP rating, and other environmental conditions.

Mechanical configurations

Motor feedback encoders may contain their own bearings, or they may use an existing bearing set such as that found on the tail shaft of a servo motor. The best configuration option to use is a function of the stability of the shaft/bearings to which the encoder is attached. Feedback encoders with bearings are typically used when the application shaft has a significant amount of axial or radial run out (eccentricity or vibration). The use of a shafted encoder with a motor will require some sort of flexible member, either a flexible shaft coupling or flexible body mount, to allow mechanical compliance with the application shaft operating irregularities.

Kit Encoder example

Modular encoders, also referred to as encoder kits, don’t contain their own internal shaft. They are assembled from components supplied by the encoder manufacturer and are designed to be attached to the tail shaft and end bell of the motor. These encoders rely on a mechanically stable motor shaft, as the shaft is responsible for holding the encoder’s internal rotating code wheel in a precise location relative to the encoder’s sensing module. For these applications, motor manufacturers put a considerable amount of effort in designing high-performance motors with very stable shaft/bearing assemblies. Because the modular design does not add the expense of the extra set of bearings that a motor feedback encoder does, modular encoders offer one of the most cost effective feedback solutions.

Modular encoders

When using a kit style encoder, another mechanical consideration is the size of the motor. Most encoder manufacturers supply a motor/encoder compatibility chart based on the motor size. It is recommended to use such a chart, like the one below, to help identify the appropriate encoder model.

Spec table sample
IP65 Rated encoder

Another mechanical configuration relates to environmental conditions. If the encoder will be installed in an environment that is subject to excessive dust and/or moisture, encoders are available with various IP ratings to meet those requirements. Magnetic and capacitive encoders would also be a potential candidate to meet some environmental concerns.

Modular encoders

Finally, there are many applications of encoders where they are inherently protected from physical contact. However, other encoders are located where they might be contacted by a person or object, therefore, requiring more physical protection. The above housing is machined from solid aluminum to provide the kind of protection needed in such an application.


If you are afraid of spiders, you might want to skip our next post which is scheduled for May 28th.

It is my goal to make this blog as informative, engaging and as accurate as possible. If you ever have some additional or contrary information, please contact me directly and I will be glad to make any appropriate corrections in a future post. Previous Post

Written by Steve Mathis
Director of Customer Relations & Marketing

"My goal at US Digital is to work with the excellent teams here to contribute to the success of our customers by eliminating pain points and making it easy for them to do business with us."

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