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Midland Helicopters . HeliProz . ZoomsHobbies

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Main Discussion > Linear Servo travel analysis
 
 
Augusto
rrAdvertiser
Location: San Diego, CA

Adam,

I'm switching between using -20% and not using it. I feel I can adapt to either one. I tried -20% only because Jason told me to try it when I went to the freestyle 3D school and I liked it for certain things but I'm used to the no expo response for others.

Semi,

You are correct about the swashplate links having a circular movement around the swashplate ball. The thing is that compared to the servo arm radius, the swashplate behaves practically like a slider crank. That's due to the fact that a +/- 60 degrees at the servo gives +/- 6 degrees at the swashplate. I did the math for it but I didn't want to post it here because those are really much more complicated equations than the ones I posted. When you do the calculations you end up with a less pronounced expo for the correction but it's still an expo.

Avant Aurora Ultimate
02-21-2002 09:34 AM
 
 
SemiArticulate
Veteran
Location: On Location

If you want to model the swash I think you will find it easier to model it as a grashof crank-rocker. The servo will be the Rocker pivot and the last link will represent cyclic tilt of the swash. But, swash tilt will end up as a small angel again by the time you get to the pitch.

S=length of the shortest link
L=Length of the longest link
P=Length of one remaining link
Q=length of other remaining link

if S+L<=P+Q then it is grashof and at least one link could make a full revolution. Else if its not true then its called non-grashof and no link can make a full revolution. That does not matter in this case because you are bound by the travel of the servo. It will matter as far as the equations used to solve it. Without measuring, I would guess S+L
02-21-2002 10:27 AM
 
 
Raptor_killer
Heliman
Location: Atkinson, NH

Wonder if my thumbs work in a linear fashion. Nope, they look like bellcranks. How do I make those linear? What about the tranmitter gimbals.


02-21-2002 04:22 PM
 
 
SemiArticulate
Veteran
Location: On Location

Raptor_killer, your thumbs look like bellcranks? I'd get that checked. Is your brain sending PCM of PPM? Mine glitches and causes near crashes.

furyflyer, I am using mechanical desktop 6. They include the power pack now. You can extrude along any path and the thread utility is pretty nice. Plus if I want a bolt, nut, snap ring, etc. then I just click on it and the part will be drawn in 3D as a parametric feature. I have not tried Inventor. It supposed to be better suited for the parametric 3D but does not have the vast 2D options or file support. I think since most of what I do is parametric 3D then I would like Inventor better. MD is great stuff, I love not having to draw out 2D views anymore and making adjustments without redrawing everything. With the 3rd party add-ons, it could about do my job for me.
02-21-2002 11:17 PM
 
 
Augusto
rrAdvertiser
Location: San Diego, CA

Semi,

Yes it does comply with the Grashof Linkages condition for a crank-rocker linkage. Applying a vector sum of all the linkages and the line between the two centers and equallying it to zero together with the equation for the angles you can get a system of two vector equations with two variables the servo arm angle and the swashplate arm angle. Solving the system you get the Grashof equations where a is the servo arm, b is the pushrod , c is the swashplate ball link to center of rotation distance and d the distance between the two center of rotations. Theta2 is the servo angle and theta4 is the swashplate angle.



Using the Grashof equations if you calculate the angular travel from a smaller servo arm you get something like this:


Even though in this case the effect is less pronounced than the slider one you can still see the non-linearity and in the yellow curve the correction is still very similar to a small expo.

I also agree with you that the complete model would require the pitch movement as well. I would also include the rotation out of plane from the swashplate and make it a 3D model.
I'm not familiar with the program you mentioned. Do you have a website for it?

Augusto

Avant Aurora Ultimate
02-21-2002 11:29 PM
 
 
SemiArticulate
Veteran
Location: On Location

Yes thats the solution for the swash cyclic for one servo. Theta4 will give two solutions of course. The larger value being invalid in this case because it would mean the links would be crossed. You can see why I was so emphatic about the model.

The working model software can be found at:
http://www.krev.com/
It has changed hands since I last used it. I have version 1.0 but it does not work with the latest version of MD I have. It can work as stand alone but I don't like its interface. There is another program by the same group called Working Model 2D that is very good and easy to use. I would bet it is pretty affordable. The 3D version was over $8000 dollars at the time. I bought it as a student (student price) and it still cost me $500. The latest and greatest version is now called MSC.visualNastran 4D 2002. I'll try to get my Working model 2D working and model the crank-rocker this weekend. I'll try to post the video it makes. I think you would like it.
02-22-2002 12:30 AM
 
 
rsilvers
Senior Heliman
Location: Marshfield, MA

Even if you do a computer-radio correction, you are still losing precision to due the finite nature of servo steps.

But what about this linear output servo arm?

http://www.x-cellrchelicopters.com/newproducts.htm
04-07-2002 11:29 PM
HOMEPAGE  
 
 
SemiArticulate
Veteran
Location: On Location

I forgot all about this. I think i'm suposed to post some pictures since I can't get it to give me video that works. I'll try to generate a computer model of the MA servo arm also. Just from looking at it, it does not really wind my watch. There is even some argument as to what the point of it is. The website claims that it makes the output from the servo "linear". Some say that its only purpose is to keep the rod up against the tail boom. The first reason does not seem technically correct and the second reason, well I don't care what the rod is doing as long as the gyro and tail rotor are happy. For linearity, you need the output angle (pitch) to be some constant fraction or multiple of the input (servo). The MA product takes the servo angle and converts it to motion along a single axis. The problem is that the other end at the tail rotor does not move along this path. For the MA product to really be linear you would need another such mechanism on the other end to convert the straight line motion back to to the angle and then you are right back where you started. The only benefit of doing all that would be to make the control rod stay up against the tail boom. So it seems to make the output less linear and not more for the same reasons that a slider-crank is less linear and not more. But I think I can make a computer model of it, so that is what I will try to do and we can look at the actual numbers. I don't have one so I am going by the photo and what I remember at the Jamboree. So the model may need to be corrected once or twice after I post it. I'll try to post it by next weekend as I have a stack of problems I need to get under control first.
04-08-2002 12:07 AM
 
 
kyoshokamper
Senior Heliman
Location: HOUSTON, TX, U.S.A.

great topic coloepter!

I have walked away from many linearity conversations due the lack of detail, substance and definition. In other words I felt it was hopeless to continue. But not today!

There 3 types of very confusing linearity conversations that seem to persist and when woven together can throughly confuse even the most technical of pilots and obviously we have many very technical guys.

1. The relationship between stick input and stick output as with jr 8103 wherein 50% in and 50% out shows on both the throttle and pitch curves. When the two numbers match, you are referred to has having a linear curve. But the actual result is strictly dependent on a critically accurate set up with equal atv settings on both sides of travel and perfect 90 degree at neutral with no mechanical trim input, no subtrim input and no electronically mixed input so that the picture is absolutely clear.

2. The relationship between the servo wheel input and the output of the pushrod is only linear while at 90 degrees and gradually gets less and less linear the further away one moves from 90 degrees in either direction. The definition of linear here means a 1:1 relationship of movement into the servo wheel and out to the pushrod. For instance consider a perfectly set up 90 degrees to the pushrod for an elevator wherein 1 degree of movement results in 1cm movement in the pushrod. If perfect the same 1 degree movement in the opposite should result in the opposite 1cm movement in the pushrod. But 20 degrees movement will not result in 20 cm of movement in the pushrod in either direction because the nature of the conversion of circular motion to linear (opps theres that word again) motion is not constant because the more movement that you input the closer the pushrod gets to the center of both the drive and driven parts!

3.
04-08-2002 07:35 AM
HOMEPAGE  
 
 
kyoshokamper
Senior Heliman
Location: HOUSTON, TX, U.S.A.

great topic coloepter!

I have walked away from many linearity conversations due the lack of detail, substance and definition. In other words I felt it was hopeless to continue. But not today!

There 3 types of very confusing linearity conversations that seem to persist and when woven together can throughly confuse even the most technical of pilots and obviously we have many very technical guys.

1. The relationship between stick input and stick output as with jr 8103 wherein 50% in and 50% out shows on both the throttle and pitch curves. When the two numbers match, you are referred to has having a linear curve. But the actual result is strictly dependent on a critically accurate set up with equal atv settings on both sides of travel and perfect 90 degree at neutral with no mechanical trim input, no subtrim input and no electronically mixed input so that the picture is absolutely clear.

2. The relationship between the servo wheel input and the output of the pushrod is only linear while at 90 degrees and gradually gets less and less linear the further away one moves from 90 degrees in either direction. The definition of linear here means a 1:1 relationship of movement into the servo wheel and out to the pushrod. For instance consider a perfectly set up 90 degrees to the pushrod for an elevator wherein 1 degree of movement results in 1cm movement in the pushrod. If perfect the same 1 degree movement in the opposite should result in the opposite 1cm movement in the pushrod. But 20 degrees movement will not result in 20 cm of movement in the pushrod in either direction because the nature of the conversion of circular motion to linear (opps theres that word again) motion is not constant because the more movement that you input the closer the pushrod gets to the center of both the drive and driven parts!

3. The relationship between the sticks and the pushrod movement is what most believe that they are reffering to when linearity is mentioned. I believe that coleopter's point is that the differences between actual stick movement and actual pushrod movement are small and easily compensated for with today's electronics. My point with regard to ccpm is that linear servos would not solve the problem because the motors are the same and the same matching problems that are experienced with the best digital and coreless servos would crop up on the proposed linears. Until you have an electronic output matching system linked between all 3 or 4 ccpm servos, you will never completely cancel interaction naturally and without mixing because no 2 servos are exactaly the same under varing loads and consistently over their entire 60 degree designed operating range!
04-08-2002 07:47 AM
HOMEPAGE  
 
 
Steve Campbell
Elite Veteran
Location: Baton Rouge, LA

Whew! Heady stuff. What a great job of presenting one's ideas and backing them up with solid theory. I have learned much from this thread.

Semi-Articulate, I agree with you in regards to the usefulness of the MA "linear output" gadget on a tail rotor. I installed it, played with it, looked at it, then realized that the linear output was going to another bellcrank on the tail...

Tell you what, though; it is just the ticket for the elevator pushrod on a plank that has split elevators and a "Y" pushrod. When using such a set-up, the slight rotary off-set induced by a normal servo arm can introduce a bit of differential into the elevator response on one side. The bigger the model, the more this effect is seen. This MA gadget fixes that.

I was glad to discover this, as it means I didn't waste twenty bucks...

Steve
04-08-2002 02:09 PM
 
 
Jared
Heliman
Location: Hickory NC

Outside the box?

What about servos that are linear to start with? Is there some mathematical reason that these won't work, or are the limitations merely temporary?

Here are the indoor versions:
http://www.microrc.com/Servos.htm#LS24
04-08-2002 03:07 PM
HOMEPAGE  
 
 
steve9534
Key Veteran
Location: yakima, wa.

Linear servos

I've looked at this a couple of times now, and it looks to me as if you're answering the wrong question. The primary difficulty I see with CCPM is that the cyclic rate changes as the collective position changes. This is because the position of the servo arms vary over an approximately 45 degree range as the collective is moved up and down. A cyclic input at full collective with the servo arm at 65-70 degrees to the pushrod will produce less movement at the swashplate and the blades, than an equivalent cyclic input at mid stick with the servo arm at 90 degrees to the pushrod. A linear servo would eliminate this inequity, as would a program that varied the cyclic travel as the collective was moved. As far as I'm aware, no presently available radio system has this capability. The exponential function will reduce the non-linearity in a standard mixing setup, but will not resolve the problem mentioned above. Hope this helps, Steve.
04-08-2002 04:08 PM
 
 
Phil Cole
Veteran
Location: Redwood City CA

ECCPM Correction Mixes

Steve,

I think you could do it with a 9Z.

Use a CTL mix, with the collective stick as the control input, and mix the two cyclics back to themselves. The CTL curve is only 7 points, so it you have a funky pitch curve you won't be able to match it exactly. But it'll be better than nothing.

I've already done this to mix out the aileron to elevator interaction when the collective is off centre.
04-08-2002 07:50 PM
 
 
ed vega
Key Veteran
Location: nyc, queens

just a stones throw .. reading what mike mas had indicated on the march/april complimentary issue .. a dedicated heli servo going forward .. both linear and rotary : D
04-08-2002 07:54 PM
 
 
cerberus
Senior Heliman
Location: Southeast Louisiana

...Very interesting...

$to_be || !($to_be); $that = $the_question;
04-08-2002 08:29 PM
HOMEPAGE  
 
 
steve9534
Key Veteran
Location: yakima, wa.

Mixing

Phil;
Thanks for the kind reply. I don't own a 9Z, but have had a little chance to play with one and the solution you describe sounds like it would work. Whether it's worth the trouble is another question...
Ed;
I'm not sure exactly what you're trying to say, but am curious if you ever get back to PR, and if so, where do you fly? My wife's family is there and we try to get in a trip every year or so. Steve.
04-08-2002 10:37 PM
 
 
SemiArticulate
Veteran
Location: On Location

steve9534,

If I understand you correcty, I think you have a good idea but there might be a few implementation problems. In order for the computer radio to know how to move the swash with linear servos, it needs to know exactly where they are positioned. So all eccpm systems would either need to be standard or the radio would need to provide the user the ability to enter the manufactures coordinates for the blind end and the rod end. The technical term for the swash would be the "End-effector" as far as the equations were concerned because now you talking about a robotic manipulator. That is probably ideal anyway because the radio could be programmed with the spatial descriptions and transformations to handle it nearly perfectly (with enough computer power). I guess you could also argue the same for standard servos. If they were modeled correctly in the radio software, they could also eliminate these problems. That would seem simple to just tell futaba and JR to have the ability to model that. But say you have a 120 degree ccpm system and each ball link is equally spaced. You need to tell each linear servo how far to extend to control both the cyclic and the swash. If you add cyclic then add collective, the travel of the three servos during the collective input will not be equal. If you are not using cyclic but add collective all three servos could extend the same distance but the motion could not be linear if you want the collective to be linear. The reason for that is nothing exotic, its just a^2+b^2=c^2. c being the distance between points of the linear servo. Your pitch is still rotational so the linear servos are going to need to create a movement that follows that path. In other words, a major pain in the ass for the programmer. If anyone wants to tackle it there is a pretty good book called "Introduction to Robotics, Mechanics and Control" by John J. Craig. Warning: this is a real robotics book. The name "Radio Shack" can not be found in this book. But if you want to know about "jacobians in the force domain" then it is the book for you. I know I sure the hell don't want to know about it . The book is heavy reading.

I don't know what the radio is telling the servos in the ccpm setup. Maybe they are doing the math right but are planning on some ideal servo setup that is not being followed by some of the manufacturers. There is also the practical argument that if people are flying them the way they are now and are happy, then who cares about any of this. But it is nice to look and see if and how the truth measures up with the hype.

I don't mean to keep rambling but there is also another point that Heli_Gal mentioned in another thread about an article that Mike Mas wrote. I did not read the article but I think I understand what Heli_Gal is saying. The control for these servos arrives in a line of pulses or series of codes one servo at a time. That whole pcm and ppm thing. So for a ccpm system, the last servo does not know its position until the second one does which does not know until the first one does. So if you want to be picky (as I know some of you can ) you can't really have a perfect eccpm system unless the servos can all be told what to do at the same time. Without that, there will technically always be interaction.

Ok, I'll shut up now.
04-09-2002 12:23 AM
 
 
steve9534
Key Veteran
Location: yakima, wa.

CCPM

Semi-articulate;
I'm not sure I understand your point, and it seems clear you didn't understand mine. In an ECCPM setup, as you call it, the individual servos movements are obviously divided between cyclic and collective functions. As the collective endpoints are reached the servo arms will be at some degree of offset, or to say it another way, some angle other than 90 degrees with respect to their pushrods. Cyclic inputs will now be less effective because a given rotational output of the servo arm will result in less linear travel of the pushrod than when the collective is in the middle of it's range.
I'm sorry, I don't know how to indicate this more clearly, but a simpler way to understand it might be to imagine that the collective travel of the servos was 180 degrees. If that were the case, then the cyclic travel would still be at it's maximum in the center of the collective travel, but would diminish to 0 as the servos reach full collective throw and the servos output shaft, the servo arm, and the pushrod all are aligned with each other and any movement of the output arm would be perpendicular to the desired direction of travel. The same principal applies to a less drastic degree in any ECCPM setup that uses rotary servos. Linear servos should resolve this problem because the linear output for any given cyclic input would not vary, regardless of the position that the servo was in to begin with. Even if the servo was near the end of it's travel with full + or - collective the linear cyclic output should be the same for any given input, something that is not the case with a rotary output servo. Thanks for your thoughts. Steve.
04-09-2002 03:09 AM
 
 
SemiArticulate
Veteran
Location: On Location

"In an ECCPM setup, as you call it, the individual servos movements are obviously divided between cyclic and collective functions."

No, that is MCCPM. The freya, raptor, etc. are ccpm systems. CCPM just means collective cyclic pitch mixing. So basically if your swash moves up and down to control collective, it is ccpm. MCCPM is not the issue. They are among the best control systems. ECCPM is where the servos all act together to control both cyclic and collective. On 120 degree ECCPM, you can't make a cyclic input without changing all three servos. You can't make a collective input without changing all three servos. You also need to change all three for combinations of the two. If you give it forward cyclic, the front servo pulls down and the two toward the back must move up a little or you will reduce collective. Now I fully agree that if you exhaust the travel of the servo for any function, you will affect the travel of the other functions. That is a design issue. The thing about linear servos is that nothing else on the heli moves in a straight line. Just like Steve Campbell2 pointed out about the tail. The rotating servos lead to rotating parts. So if you want to put a linear servo on the swash, its output can not be "linear". We are using the word "linear" two different ways. One being moving along straight line, the other describing the relationship of the ouput. For example, lets say you want to tilt a swash one degree per second with a hydraulic cylinder. The hydraulic cylinder can only move in a straight line but pivots at the rod end and blind end. The rod end is attached to the swash, the blind end is attached to the frame. In order for the swash to rotate one degree per second the change in the length of the cyclinder can not be fixed. Its rate of change will be different (non-linear). Now put two more on the swash 120 degrees apart and have them not only change the cyclic but also the collective. The mathematical model would probably not be very difficult but it gets more difficult when you realize that not every company will want to stick the servos in the same exact spot with the same size swash. That is the rub. So if you want the best ECCPM system in the world, you would have an accurate math model for the specific machine and servos and you would send all three servos their commands at the exact same time. While your at it, you should also account for the transit time of each servo to ensure no interaction while the servos are moving. But now we are getting silly. With MCCPM, when each servo has a dedicated funtion, you should not have to worry about interaction. If you have any, it is the fault of the design. What I don't like about ECCPM is that if you have control interaction it is supposedly your fault because you set it up. I however think there may be other things to blame.
04-09-2002 04:27 AM
 
 
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