Economizers–The Physics of Linkage Systems

In the post before the previous, I was discussing an economizer performance problem in a facility we worked with as a class in Monterey California.  One of the problems was related to the mechanics of motion in the linkage system serving the economizer dampers.  The branch of physics that deals with this is called kinematics and if you are out there working on machinery, you probably are developing and understanding of the topic via trial and error if nothing else.


The links below will jump you to major topics in the post that follows.  A Back to Contents link at the end of each section will bring you back here.

A Hands-on Control System Learning Opportunity

Every year at the Pacific Energy Center, we teach a class call Control Systems, Design, Performance and Commissioning Issues.   A highlight of the class is that for the afternoon portion of it, we do a number of  lab sessions that attempt to solidify the class topics with a bit of practical experience including working with 4-20 ma current loops and position sensitivity and thermal lag

current loop

… working with a functioning pneumatically controlled VAV box …

Shortridge and the VAV demonstrator

… working with control system logic using Eikon for Educators

software (2)

… understanding how loads on actuators can impact the way they sequence

sequencing (2)  sequencing (3)

… and to my point here, how linkage systems work.

pneumatic damper control (1)

pneumatic damper control

We are doing the class in about a week and I was working on a lab guide that supported the linkage system session a bit with images from one of the SketchUp Models that I use in class these days.  In doing that, I realized that if I made the lab guide a blog post, it might be helpful to others who were not involved with the class.  So here we go.

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Using SketchUp To Work with the Model Used in the Blog Post

You don’t have to use SketchUp to be able to learn from this blog post.  But if you wanted to explore the model behind the images in the post a bit more, you will find a version of it located on my Google Drive.

Bear in mind that my models are typically works in progress.   For instance, pipes are not insulated, control sensors may not have conduits hooked up to them, chillers may only have chilled water piping, hangers and supports are missing, etc.

Eventually I plan to address all of that.  But if I make a model available for use with a blog post, or use it in class, I do it with the belief that the detail that is there is sufficient for the point I am trying to make with it.  All of that means that you need to use them with a bit of “Imagineering” and that there could be a few details that are not quite right. But hopefully, they are useful tools to help you understand the topic I am discussing.

SketchUp Basics

You can download the free version of SketchUp by going to and following the directions there.  The free version is called “SketchUp Make” and you access it by selecting that you want to use SketchUp for educational purposes. There is a version for Windows based PCs and a version for MACs.  Once you have downloaded and installed it, you can learn the basics about how to move around inside a model by taking a look at one or more of these YouTube video tutorials.

  •  and will show you how to make a basic 3D model along with how to orbit and zoom around inside SketchUp.  This video will simply reinforce some of the ideas that show up in the other two videos and will also show you how to get started if you are intrigued by 3D modeling and want to give it a try yourself.  It really is pretty easy to pick up the basic skills and start building your own models.
  • will show you the basics of navigation in SketchUp, which is all you really need to know if you just want to look around in a model.
  • will show you how to measure distances in SketchUp, which will make one of the exercises we might do a bit easier.

An even deeper resource is the SketchUp YouTube Channel, illustrated below:


If you page down a bit, you come to a number of tutorials on basic functions if you are interested in knowing other things besides the basics you need to know to get around in the model.


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A Few Basics About Working With the Model

What follows are images taken from a SketchUp Model of a heat recovery AHU that I developed to support a project and some classes.  This is also the model where the images in the blog post come from.


If you elect to use the model while you are reading this, there are “Scenes” saved in the model that will index it to some of the images.  When you select a scene, the model will go from where ever you are in terms of the view, layer status, etc. to a saved perspective which includes rotations, zooms, and turning off layers to make certain parts of the model more visible. So if you want to explore one of the images in greater detail, you may find it desirable to select the scene associated with it as a starting point.

You can access the scenes via the tabs across the top of the workspace or by opening up the “Scene Manager” window. It may be helpful to turn on the “Layer Manager” so you can turn layers on and off. All of this is illustrated below in the three figures that follow.




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Setting the Stage

Opposed vs. Parallel Blade Action

This video clip gives a quick overview of the parts of a damper and illustrates the difference between parallel and opposed blade damper action.  Note that there is not sound (other than the amusing but potentially “too much” intro and ending that I added).  The key point is to illustrate the parts of a typical damper and the difference between opposed and parallel blade action.

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Damper, Actuator, and Linkage System Nomenclature

The image below is a repeat from the other blog post where I was discussing linkage system kinematics, but I thought it would be good to insert it so we all are on the same page about what I am calling things as we go forward.


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Details About the Damper Assembly We Will Be Working With

The damper actuator in the foreground in the picture rotates 90° to go through its full stroke, moving the blades on the damper it is connected to via the linkage system between it and the drive blade on the damper assembly. The damper actuator rotates its crank arm clockwise when it is commanded to open the damper and counter clock-wise when it is commanded to close the damper. For all intents and purposes, the torque delivered to the crank-arm by the actuator output shaft is uniform through the entire stroke. It is in the fully closed position in the image above.

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Identifying Opposed Blade Damper Action By Inspection

One of the points of the linkage lab is that if you think about the physical relationships between crank arms, links, etc. you can often figure out how the linkage system will move and how the device it is attached to works. To illustrate this, we will use images from the model to figure out if the damper that is being controlled by the orange actuator is an opposed blade or parallel blade damper.

The video clip in the previous section illustrated this by moving the blades.  But sometimes in the field, the system you are looking at is steady state, meaning the dampers are not moving.  And, you may not  be able to upset the system (change a set point, cycle it off and then back on, etc.) to observe the damper action if the loads it serves can not tolerate a deviation from normal.  So, it can be handy to be able to figure out the type of damper action that is associated with an assembly by inspecting the linkage system vs. observing the damper blades in action.

Let’s start by figuring out which way the damper blade rotates when the actuator shaft rotates clockwise. To do that, I am going to insert a transparent reference plane into the picture that will let me draw circles and lines on it to represent the path various components will take.

If I were to replace the ball joint on the actuator crank arm with a pencil that could draw on the reference plane, I would discover that as the actuator rotated clockwise, the pencil would draw a circle around the centerline of the actuator output shaft, as illustrated below.

Kinematics 03

Similarly, the ball joint on the blade clip would also draw a circle as the blade rotated.

Kinematics 04

If we add a direction arrow to the actuator image and recognize that it will pull the damper blade clip along with it as it rotates, we discover that rotating the actuator shaft clockwise will cause the blade clip on the drive blade of the actuator to rotate counter clockwise.

Kinematics 06

If we flip to look at the other side of the damper frame, where we can see the damper linkage system that is installed between the various blades, we can start to understand how the counter clockwise blade clip rotation will cause the other blades of the damper to move.

As a starting point, we have to recognize that since we are now looking at the system from behind, relative to the perspective in the image above (in other words, we are now looking at the back of the mounting bracket) the rotation of the blade clip (the tip of it is just visible above the damper frame to the left and below the mounting bracket) will be clockwise simply because we are looking at it from the other side. That is indicated by the green arrow in the figure below.

Opposed Linkage 02

The drive blade would also cause the links attached to it to move in the direction indicated below by the straight green arrows.

Opposed Linkage 03

This, in turn, would cause the other blades connected directly to the linkage to rotate in the same direction as the drive blade, as indicated by the blue arrows below. Note how the links only connect to every other blade.

Opposed Linkage 04

Finally, the reversing links (the ones with the bend in them) would transmit the motion to the remaining blades as indicated by the blue straight arrows below.

Opposed Linkage 05

The motion of the reversing links will cause every other blade to rotate in the opposite direction from the one adjacent to it (because they are connected to every other blade;  nothing magic), thus, opposed blade action, as illustrated by the red arrows below.

Opposed Linkage 06

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Identifying Parallel Blade Damper Action By Inspection

A parallel blade damper is a bit simpler. The one I will use in this example is a direct drive damper, meaning the actuator output is clamped directly to a shaft extension from the drive blade on the damper. The drive blade shaft centerline is the same line as the actuator output coupling centerline. In the image below, you can see the damper shaft extension extending through the actuator (the orange box) with the actuator output coupling clamped to it.

Parallel Linkage 01

If you were to remove the actuator (the orange colored box), you would expose the shaft extension assembly, which you see in the next figure.

Parallel Linkage 02

If you remove the shaft extension assembly you can see the parallel blade damper linkage. Note how all of the blades are connected to the same link vs. the opposed blade damper, which only had every other blade connected to the straight link and also had reversing links.

Parallel Linkage 03

When the actuator rotates the drive blade (the left-most blade in this illustration), as illustrated by the green arrow below …

Parallel Linkage 04

… the linkage transmits that motion to the other blades, as indicated by the straight green arrow in the picture below.

Parallel Linkage 05

That, in turn, causes the other blades to rotate in the same direction as the drive blade, creating a parallel blade action as illustrated by the blue arrows below.

Parallel Linkage 06

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The Force Available Varies with the Stroke

To some extent, this part of the post repeats what was in the previous post.  But I have a few more details and illustrations to share at this point.   In any case, it is important to remember that the torque from the actuator shaft shows up as a vector that is applied perpendicular to a line from the center of the shaft to the center of the ball joint. as illustrated by the purple arrow below.


Not all of that force will be available to the link connecting the crank arm with the blade clip.  To understand that, you need to remember what you learned about vectors in physics or math class.

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Vectors;  Physical Parameters with  Magnitude and Direction

One way to think about a vector is to think about the difference between speed and velocity.   If I were to tell you I was in an airplane going 528 miles per hour as I type this, that would tell you something, but not everything you need to know to understand my situation.  You don’t know if:

  • I am going 528 mph straight down (hopefully not), or
  • I am going 528 mph straight up (not likely for long in a 757,which is what I am in, but quite possible in an F-15), or
  • I am going 528 mph over Michigan or California or Oregon.
  • I am going 528 mph due North, due South or any direction in-between

But if I told you I was going 528 mph level over Bismarck, South Dakota at 32,000 feet on a heading of 285° relative to true magnetic north, I have given you my velocity (speed with a direction) and you would know exactly where I was.  You would even be able to figure out where I would end up after a given period of time if things continued as they were.

If this was my 757 …


… (I know, it couldn’t be because the gear is down and the flaps are out, which would be a disaster at 528 mph, but it’s a cool picture of the plane in plan view so I used it), one way to think of its velocity is that it is traveling on a course of 285° relative to true north at 528 mph, like this.

imagen In other words, the plane is traveling West North West at a speed of 528 mph.   But you could also think of it as traveling West pretty fast, but at a speed somewhat less than 528 mph while it concurrently traveled North at a modest speed relative to 528 mph, like this.


Because North and West are 90° apart, the red arrow and the blue arrow make a right triangle with the purple arrow and you can use trigonometry to come up with an exact value for “pretty fast” and “modest speed”, like this.


So, in moving West North West at 528 mph, my Boeing 757 could be thought of as moving west at 510 mph while at the same time, moving North at 137 mph.

This might be a good time to ask if you know what snake is the most feared of all snakes by airline pilots?

(Page down for the answer)

It’s the Boeing constrictor.

Ba Ba Da Bing, Ba Da Da Boom

All of this levity is brought to you at no additional cost, and I am here all week folks (longer probably) (I hope).

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Trig in the Context of our Damper Actuator

My point here is not to teach trig;  rather it is to demonstrate that you can break a vector down into components by using trigonometric principles.

That means we could use those principles to break our purple arrow …

Kinematics 07

… into two components, one that runs along the centerline of the link (the blue arrow in the image below) and one perpendicular to that (the red arrow).

Kinematics 08

It’s the force represented by the blue arrow that will be available to rotate the damper blade that is connected to the other end of the link by the blade clip.   The force represented by the red arrow will be of no use in moving the damper blade and will actually try to bend and loosen up the linkage.

It’s also important to recognize that as the actuator rotates, the angle between the linkage rod and the line joining the centerline of the actuator shaft with the centerline of the ball joint will change.


That means that the force available to the link rod varies as the damper strokes.  In this particular arrangement, the maximum force through the link rod occurs at about mid-stroke because that is the point where the torque vector (the purple arrow) will itself be perpendicular to the line from the centerline of the actuator shaft to the centerline of the ball joint as illustrated by the semi-transparent crank arm in the image below.

Kinematics 10

Notice also that the linkage rod and blade clip are an arrangement that is similar to the damper crank arm and linkage rod.  But at the actuator end of  the system, angular motion (movement in a circle) is being converted to linear motion.  At the damper  blade end of the system, the opposite is happening; i.e. the linear motion of the link is being converted to angular motion.

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Linkage Systems Have A Lot of Adjustability

If you think about it a bit, you will realize that there are all sorts of things you can move and adjust in the linkage system we have been using as an example.  Specifically, you could adjust:

  • The crank radius for the actuator crank arm and its ball joint
  • The crank radius for the damper clip and its ball joint
  • The angle of the actuator crank arm at the start of the stroke, which would allow you to maximum force to maximize it at a particular point in the stroke, like the beginning or the end or the middle.
  • The length of the link rod
  • The position of the damper blade clip on the damper blade relative to the damper blade shaft centerline

All of those adjustments will have an impact on how the damper assembly will work.

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Maximum Torque = Maximum Break-Away Force

Given our discovery that the maximum amount of torque was available from the current arrangement with the actuator at mid stroke, we may want to set the system up to start the stroke with the crank arm in that position relative to the torque vector.  That would maximize the break-away force available to start the damper moving, which could be important if the damper had been in the closed position for a while and a layer of dirt and grime had built up on the blade seals, linkage, and bearings.  Or, we may need to break the dampers loose against a high pressure difference at the beginning of the stroke.

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Maximum Torque = Maximum Actuating Force

Of course, since (we hope) economizer dampers are always on the move in an effort to deliver the desired mixed air temperature as outdoor air and return air conditions change, we may not be as worried about the break-away torque as we would be concerned about being sure the dampers could move against all of the flow and pressure drop conditions encountered during normal operation.   It could be that the maximum actuating force would be required at some intermediate position vs. the beginning or end of stroke.

Maximum Torque = Maximum Sealing Force

For many applications, including economizers, we might also be concerned about making sure the damper blade seals were fully compressed at the beginning or end of stroke.

If you read the fine print in damper specification sheets, you will discover that the leakage specs have a torque requirement associated with them.


For a large damper, the inch pounds per square foot metric can add up and on more than one occasion, when selecting an actuator, the torque required to meet the leakage spec has been the governing factor for the selection rather than the torque required to actuate the damper.

Achieving the rated leakage spec can be important for a number of reasons.  For instance, in a cold climate or a hot and humid one, we may want to make sure the outdoor air dampers sealed tightly when the system was off to prevent infiltration of unconditioned outdoor air, which could freeze a coil in extremely cold weather, or cause condensation problems on start-up in a hot and humid climate.

Similarly, if the return dampers did not fully seal with the system in operation, leakage through them could compromise the ability of an economizer cycle to deliver free cooling.  In other words, if we had a system that wanted to make 57°F mixed air, in a perfect world, up to and including the time when it was 57°F outside, you would be able to deliver.

But if the return dampers did not seal and leaked 10%-15% (I’ve measured those rates and higher), then the mixed air temperature would actually end up being between 59 and 60°F instead of 57°F.  As a result, a system with an integrated economizer would be running mechanical cooling when it did not need to do that.  In a mild environment like, for instance, San Francisco, that could mean there were over 2,400 hours a year when the system would be using mechanical cooling when it would not  have needed to do that if the return dampers had sealed tight.

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Adjusting the Position of the Crank Arm at the Start of the Stroke

To maximize the force available from the linkage system at a particular point in the stroke, we would need to adjust the crank arm so that at the point of interest, the toque vector acted directly down the linkage rode, a condition which happens at about mid stroke in the system in the illustration we have been using (i.e. the purple arrow associated with the transparent crank arm image below).

Kinematics 10

You adjust the position of the crank arm relative to the damper shaft by loosening the two nuts on the U-bolt that claps the crank arm to the damper shaft, driving the actuator to the desired position, say the beginning of the stroke for example and then rotating the crank arm to the position you want at that point in the stroke.  Then, you tighten the nuts on the U-bolt back up.

Of course, if you did not want this movement to impact the position of the damper blade at the beginning of the actuator stroke, you might have to lengthen the or shorten linkage rod so that the damper remained closed with the actuator crank arm in the desired position.

For the sake of discussion, lets say we decided to set up the actuator in our example to start its stroke with the maximum force available;  i.e. we set it up so the crank arm is in the position of the transparent crank arm in  the image above and lengthen the linkage rod so that the damper is held closed with the crank arm in that position.

If you analyze the kinematics like we have been doing in this blog post, you might discover that by the end of the stroke, there is very little torque applied to the link and that most of the actuators force is simply trying to bend and loosen up things.  In some instances, you may even discover that the linkage system binds up before the end of the stroke because the linkage rod runs into the damper shaft if it extends past the actuator or the linkage rod or crank arm run into the air handling unit casing or some similar obstruction.

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Adjusting Crank Radius

One of the other things we could adjust is the distance between the actuator shaft centerline and ball joint centerline.  You simply loosen the clamping nut and slide the ball joint up and down the slot in the crank arm.  Of course, some crank arms may not have slots, only a couple of holes, which limit your options a bit.  There could be a reason for that, as you will discover if you read on.

At first consideration, you may decide that it is best to put the ball joint as far out the crank arm as possible.  After all, the further out you go, the more mechanical advantage you have.  But it also means that the linear displacement of the ball joint over the course of the stroke will be longer.  So, in a confined area, a large crank radius could result in the crank arm running into something like the air handling unit casing before it completed its stroke.

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Force is Not the Only Thing that Varies with Stroke

In the example, our focus has been on centerline drive actuators, but all of these issues will come up with a piston style actuator too, which is typically a pneumatic actuator.  But that is not always true.  For example here is an electric actuator that moves a shaft back and forth, just like a piston actuator.

AHU2 CHW valve

Its also worth noting that electric/electronic actuators are the only form of centerline drive actuator.  Here is a pneumatic one.


In any case, if you think about piston type actuators in the context of kinematics, you will discover at least two additional contingencies.

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Something’s Got To Give

One thi8ng that’s got to give is that since the shaft on the actuator has to move in a straight line (by virtue of the design of the actuator) while the end of the shaft must follow an arc if it is hooked up to a crank arm,  then something has to pivot someplace.  Otherwise, the actuator shaft will bend or bind up.

There are two common ways to deal with this.  One is to mount the actuator so that the entire actuator can pivot, like this example.


Notice how the entire actuator can pivot around the mounting pin at the back.

The other is to mount the actuator rigidly and put a pivot in the output shaft, like this example.


Note that there is a ball joint on the end of the shaft.

Either way, the force available will vary over the course of the stroke, as we have discussed.  But the relationship for the first actuator will be different from that for the second actuator if you analyze the details.

Percent Stroke May Not Equal Percent Blade Rotation

The other thing that happens, because the shaft is moving in a straight line relative to the actuator but also follows an arc due to the motion of the ball joint on the crank arm is that the relationship between shaft extension and damper blade rotation is not linear.   In other words, if an actuator had a 4 inch stroke and you were using that stroke to move a damper blade 90°, 1 inch of stroke would not always give you 22.5° (90° divided by 4) of blade rotation.


Not a huge difference but something to be aware of.  If you really want to get into it, then the following geometric relationships may be of value to you.  The first one lets you calculate a number of useful parameters given what you might know about an actuator and the results you are trying to deliver.


The second lets you compare the ultimate displacement produced by a given linkage arrangement with the path that the system travels on its way there.


The Relationship Between Motion in an Arc and Motion in a Straight Line

In the illustration I am using for the blog post, full stroke on the actuator is 90° of rotation.  In a perfect world, we would like the 90° of actuator rotation to turn into 90° of damper blade rotation.  To get that to happen, there are a number  of fairly specific dimensions that need to be set up in the system.

At the actuator end of things, the ball joint and link attached to it will move from point A to point B as illustrated below.


The path taken by the ball joint will be an arc between those two points with a radius, in this case, of 4-1/2 inches.


If we do a little basic math we will discover:


In other words, as the actuator strokes, the ball joint follows a curved line that is just a little over 7 inches long.

By the end of the stroke, the ball joint is displaced from its starting point along a straight line connecting the two points.


That line is the hypotenuse of a 4.5 inches isosceles triangle (I’m starting to sound like the scarecrow from The Wizard of Oz) and we can calculate its length using the Pythagorean Theorem.

The sum of the squares of the sides of a right triangle is equal to the square of the hypotenuse.

Mathematically, that looks like this …


… and if you solve that equation for our situation, you end up concluding that the length of the line between point A and B is 6.36 inches.

Converting Motion in a Straight Line Back Into Motion on a Circle

Since the ball joint on the actuator crank arm is physically connected to the ball joint on the damper blade clip by a rod, if the crank arm ball joint moves 6.36 inches, then the damper blade clip ball joint will move 6.36 inches.


That means that at the damper blade end of the linkage, we need to set the ball joint to damper shaft centerline radius such that a displacement of 6.36 inches will produce 90° of damper blade rotation.  In other words, the radius there needs to be 4.5 inches also.

But it is important to realize that the slot in the damper blade clip is not the same as the slot in the crank arm on the actuator because the centerline of the slot in the blade clip does not pass through the damper shaft centerline.  That means that the radius we are talking about is not a line that is parallel to the slot in the blade clip.


Notice that the red dashed line is not parallel to the blade clip slot.

If what I am trying to say is not clear from the preceding picture, this view from the other end of the damper (looking at the opposite side of the actuator mounting plate) but with the frame and mounting plate removed may help you understand.

Kinematics 10

Note how the red line, which is parallel to the slot in the blade clip, does not go through the centerline of the damper shaft, which is the square rod that the link is attached to.  The green line does and if you were setting up the linkage using measurements, that is the line you would need to be referencing for your radius measurement.

Think about doing all of this through an access panel inside a space that is about 2 feet high and 4 feet wide with actuator mounting brackets with sharp corners in the vicinity, the pointy end of sheet metal screws sticking out here and there, etc.

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The Bottom Line

It is important to recognize that while I framed up this discussion in the context of a linkage system serving an economizer, the kinematics we have discussed will apply to any linkage system.   It doesn’t really matter if the linkage serves an economizer, a face and bypass damper, or a three-way butterfly valve.  And it doesn’t really matter if the actuator is pneumatic or electric or electronic.

Also recognize that relationships I have illustrated are fairly specific to the geometry of the linkage system.  For instance, if I set the system up to start the stroke with the link rod perpendicular to the damper blade clip and the link rod was actually the output shaft of a pneumatic actuator that was mounted with a pivot at the back, then all of the numbers change.

When I first realized all of this, I did a bunch of math and developed the following table, which may be useful as a bottom line on everything.


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The point of all of this is that something that seems simple upon first encounter is actually pretty complicated.  In a given linkage system, there are a lot of subtleties that need to be taken into account when setting it up if you want it to provide the motion and force required by the application. Some of these subtleties may not be recognized by an service technician or installer, especially if they are pressed for time.

There-in lies the opportunity.  Specifically, by recognizing them, you may be able to make an adjustment to a linkage system and, for instance, make an economizer that was dysfunctional become functional, just like the team working on the system I was discussing in the previous post did.

And, if you share what you have come to understand with the people working on the systems day to day, then you have planted a seed that will yield benefits beyond the project where the subject came up.  To some extent, I am hoping that is what I have done here.  And that, of course, is just the offspring of the seeds my mentors planted in me.


David Sellers
Senior Engineer – Facility Dynamics Engineering

Click here for a recent index to previous posts

This entry was posted in Air Handling Systems, Controls, Economizers, Pneumatic Controls. Bookmark the permalink.

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