RunRyder - Hoeken's straight line 4-bar linkage

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Main Discussion > Hoeken's straight line 4-bar linkage

Greg McFadden

Key Veteran - Location: Spokane Valley, WA -

So I was talking with a buddy of mine about analizing linkages and I happened across the design for the Hoeken's 4-bar straight line linkage. It intrigued me, so I thought, what better way to learn a bit about linkage math than to analize this (the beauty if the Hoeken is that you get a ~linear output over part of the range of the angular input. but in addition to that, the linear section is also linearly dependednt on the angular input, which is every bit as important as the linear output itself)

so basically this thing looks like this.

Or animated in motion: (open this in a new window, it is a fairly large file)
http://www.physicsninja.com/Hoeken/...e_Linkage42.gif

Now what interested me is that almost linear output portion of the travel path, which, jumping ahead of myself, seems to occur between the input angles 140 degrees and 220 degrees (there is a larger range but as you go outside of that range the real nonlinearity starts to come back.

Various important things as a function of angular position (degrees) of the driving rod.

Now you are probably all bored by now.. but the gist of it is that this would give a rather damn close to linear output to the swashplate if used (granted it may be a bit bulky but I was more interested in the geometry than the bulk at this point in time)

Now anyone who feels like looking over the math, see the following links (If I goofballed anything, tell me please so I can correct it)

http://www.physicsninja.com/Hoeken/...e_Linkage1.html

or for the annotated thing that shows the getting of one set of points
http://www.physicsninja.com/Hoeken/geo/geometry1.html

if you have maple and just want to open the files and run them, here's the links:
http://www.physicsninja.com/Hoeken/geometry.mws
http://www.physicsninja.com/Hoeken/...ine_Linkage.mws

when looking through there... the only thing that has units is the angles. all lengths are ratios based on the shortest linkage lenght.

Now what I still have left to do (not sure when I will get around to this) is to add the math to describe the 3-D link from the output of the 2D device (I forgot to note this... this device MUST be built with only planar freedom, not 3D) to the swashplate. (the math ain't that bad... I just have got to do it.

I strongly suggest lookign through the two HTML files (particularly the whole one) even for those who don't know maple or don't want to look at math since all my graphs are there and it is heavily annotated with my thoughts as I wrote the blasted thing.

but anyways... it was very very interesting to me. If I had an eCCPM ship I might get around to trying to custom one of these setups.

so take a look... I am off to sim it up after putting like 10 hours into this.

-Greg

10-23-2003 07:03 PM

fitenfyr
rrProfessor
Location: Port Orchard, Washington

hmmmm...

Greg,
We need to get you a girlfriend.

Intersting animation. I didn't get how the linkage worked till I saw it.

Jason Stiffey
Fly Fast....Live Slow...

10-23-2003 07:19 PM

HOMEPAGE

Greg McFadden
Key Veteran
Location: Spokane Valley, WA

I'm workin on it!

man... till I started looking into it I never realized how much wierd stuff you can do with only 4 bars linked appropriately... now if I could just figure out how to work backwards... define a path and have program determine geometry... but I suspect that is very very very difficult (and quite possibly impossible without a lot of constraints)

The silence often, of pure innocence persuades, when speaking fails

10-23-2003 07:22 PM

JCadwell
Key Veteran
Location: Richland WA/ Morro Bay, CA

Hey Greg, you have way too much free time

How's that X-Cell coming? Getting close?

Do you really want a linear input to the swash? Since the servo arm is angular, and the swashplate is angular, wouldn't the ideal place for the servo to rotate about be orthoganal to the mainshaft, at a pivot distance equal to the distance from the center of the mainshaft to the swash? Since you subtend an arc with the swashplate when you make an input wouldn't a linear input create an increase in swash deflection as it approached the extremes, rather than a decrease?

Hope things are going well in Minn. The sun is shining here in Cali. Adios.

Thanks, John Cadwell

10-23-2003 07:23 PM

JuanRodriguez
Elite Veteran
Location: Rochester, New York

The angle of the dangle is in direct proportion to the heat of the meat.........

10-23-2003 07:26 PM

Chris Ballard
Senior Heliman
Location: panama city

my thoughts exactly!!!!!!!

if your gonna go.....go all out!

10-23-2003 07:34 PM

Greg McFadden
Key Veteran
Location: Spokane Valley, WA

The x-cell is getting closer.. still waiting to buy electonics.. since I just picked up another one (but it came with a good set of blades so that is how I justify it to myself

)

well. First, to make certain I am being clear on this. when I say this is linear I mean two things not one.

A) Linear travel (or close enough)
B) a one unit change in angle gives a change in the linear direction of some constant multiplied by the angle.
I.E. x=constant*Angle

the reason the second is important is that at extreme servo throws, a 1 unit change in angle gives the same linear change as a 1 unit change when the servo is centered. that is one of the primary things we dial out with expo, is that. this basically removes that concern.

now when you hook this widget to the swash you get nonlinearity on the swash due to the 3D nature of the linkage. but what this gets you is (on a eccpm machine) when you are at high collective and the swash is level, the servos are all far away from center.

now with the stock setup if you want to turn one way or another, some of the servos will move towards their regions of increased sensitivity, some towards regions of less, so you don't get say right swash angle, you get right with a little in another direction. (this can be dialed out electronically, I think)

with this, the servos no longer have that off center sensitivity change. you still get nonlinearity at the swash but that nonlinearity no longer changes with your collective stick position, making it much easier to dial out without complicated mixes)

at least I think I explained that well enough., but it is clearer in my head than I can write

The silence often, of pure innocence persuades, when speaking fails

10-23-2003 07:35 PM

Greg McFadden
Key Veteran
Location: Spokane Valley, WA

maybe. maybe not. I do not know. I don't think that they can get rid of the effective phase change as a function of collective position (I might be wrong, but I don't see how they could do that).

but yeah. thanks for the reply. if i goofed anywhere I want to know (I did this primarily to teach myself about geometric techniques for solving these problems and this one, as it may have some practical use seemed to peek my interest.)

10-23-2003 07:49 PM

KC
Elite Veteran
Location: WA

Greg, you've really been thinking about this stuff lately! heh heh.

It looks pretty cool, linear numchucks? I'm too lazy for this one, does the linear travel occur at a constant rate with one of these too?

phase changes? long p-rod direct CCPM laid out as close to what JCad was saying, ulitmate control configuration, simple and eloquent, most precise set up for the weight and the mind!

only problem with that, you probably already realize, is that theres little things that prevent it from being done to a current machine, like a big main gear in the way or that you have to go about 9:1 or more on the p-rods so you can space the servos as close to the mainshaft as possible.

Micro servos would make this the set up (shorter p-rods closer to the main shaft, conventional engine / drivetrain layouts could be retained) only when micro servo geartrains are improved.....I think that's the future of r/c helicopter controls, too bad I can't put a patent on it

most swashes are about 25-30mm lever arms so that would mean 8-10" long p-rod! but it could be done to some degree with a Caliber, Graupner or Vario, using 20mm servo wheels with high success. just have to line up the servos very carefully.

10-23-2003 09:12 PM

HOMEPAGE

Greg McFadden
Key Veteran
Location: Spokane Valley, WA

yes. constant rate if you have a constant angular velocity on the input. and yes the geometric constraints on this widget make it a bit more labor intensive to get to actually fit... the other actual construction caveot is that it must be a planar device meaning that you couldn't just make this out of some rod and ball links. Each axis would have to be a bearing to make sure it stays planar. (I was more interested in doing the math than building one right off anyways. I think it could be fit on an x-cell ship but it might take (would take) a bit of creativity... might actually be easier to do with an older stack frames than a fury but again that is something for later on. I just found it interesting that something this neat could come out of 4 bits of rod

also, you wouldn't have to drive the driving rod directly off the servo. a properly set up push-pull link between that and the servo would work and retain linearity.

and for those of you who want evidence that heli's actually exist here

10-23-2003 09:35 PM

G.Man
rrProfessor
Location: Northants, but soon to be Nicosia, Cyprus

trouble is with the exception of collective, the swashplate has circular not linear travel....

If your servo - bellcrank input and bellcrank output - swashplate all have the same radius the degrees of movement in will be the same as the degrees of movement out... therefore linear..

Don't Email me as I wont reply - PM Only (spam countermeasures)

10-23-2003 09:45 PM

S.Peterson
Heliman
Location: Sun Prairie, WI

Greg

This site

http://www.cedarville.edu/dept/eg/k...pdf/ccpagef.htm

is the only one I have been able to find on the net to analize coupler curves (the motion defined by the output of a 4 bar linkage).

I have not spent much time playing with it but it may help.

Stu

10-23-2003 09:51 PM

Greg McFadden
Key Veteran
Location: Spokane Valley, WA

Galifrey you would be right if the belcrank axes were directly underneath the axes of the swashplate and the arm connecting to the swash was planar with the equivalent arm created by drawing a line from the swash ball link to its axis. but since this is not the case, the 3D aspects come into play since your pushrod now can tilt not only in the X-Y axes but also in Z. [edit] as I just figured out , as soon as you take an eccpm moving swash into account even with the planar stuff Galifrey was talking about, the nonlinearity comes back... can't believe I messed that one up... the upside is the hoeken linkage math is coming along well... more posted shortly[/edit oct 28]

Well, I did goof on this picture, so I fixed it. Even if you mount things right under the main mast you still get nonlinearity. the new albeit clutterd picture will help. you will have to clear out your browsers cache to be able to see the new picture

if it were like this

so when you go to try to solve the geometry you run into solving sphere intersections instead of circular intersections. needless to say, even with my geekishness I draw the line there.

but back to another bit.

doing a little math, with 60 degrees of throw from neutral on the driving arm, to get ~27.5 mm linear throw the driving arm would need to be 10mm long. interresting.

The silence often, of pure innocence persuades, when speaking fails

10-23-2003 09:58 PM

G.Man
rrProfessor
Location: Northants, but soon to be Nicosia, Cyprus

Fair point greg...

I had forgotten they were offset compared to the swash...

hmmm

That gives me an idea for a bevel gear servo bellcrank...

AW CRAP

My head just exploded

Don't Email me as I wont reply - PM Only (spam countermeasures)

10-23-2003 10:09 PM

Greg McFadden
Key Veteran
Location: Spokane Valley, WA

interesting... bevel (poof, head explodes, math limit for day reached.. resetting universe)

10-23-2003 10:14 PM

G.Man
rrProfessor
Location: Northants, but soon to be Nicosia, Cyprus

yeah reefer alcohol and physics not a good combo

Don't Email me as I wont reply - PM Only (spam countermeasures)

10-23-2003 11:25 PM

smudge
Senior Heliman
Location: Wiltshire, UK

Parallel linkage

James Watt, the steam engine engineer made a parallel linkage in about 1782. This was designed to replace the slide which held the piston in parrallel with the cylinder.

He had to design the linkage because another engineer claimed that the slide mechanism was a proprietry design, would not allow it to be used on Watts' engines.

Watts' linkage probably does not work for our purposes though, because it is not constant velocity, like the Hoeken linkage.

10-24-2003 09:57 AM

KC
Elite Veteran
Location: WA

"and for those of you who want evidence that heli's actually exist here"

LOL that looked my old dorm room.

10-24-2003 09:39 PM

HOMEPAGE

Greg McFadden

Key Veteran - Location: Spokane Valley, WA -

ok, so you were all probably hoping that I'd be really bored of this by now... you would be wrong (maniacle laughter

) so I finally got through doing the static force and moment analysis on this widget. so here are some graphs. (just for reference 66.7 Newtons is about 15 pounds, and if you have a 1 inch moment arm (about what my xl ship has below the swash) that gives ~239oz-inches of holding torque required of course this means that if you hae 3 servos attached to the swash they can deal with 45 pounds on said swash... but this was my benchmark overkill as it may be)

but as I promissed here are the charts.

take this one and multiply the y axis by the length of the shortest arm in meters and by the applied force in newtons and it will then spit out ounce inches of holding torque required

or this one has some input values for a 10mm shortest arm (remember that we are only interested in the region between 120 and 240 degrees)

now you may be wondering, like I was after looking at my very very crude comparison... where is the downside besides the complexity... well here it is.

Forces on the two fixed position posts. (y direction only, i forgot to plot x)

this is for the fixed post at the driving (shortest) rod. the y forces on the other fixed post are the inverse of this. keep in mind this is in units of force/applied force at the output.

so the torque is doing quite well comparitively but the forces on these fixed points are large, requiring that the servo not be used as one of them (not a problem at all)

10-28-2003 08:37 PM

JCadwell
Key Veteran
Location: Richland WA/ Morro Bay, CA

Oooohhh that one graph looks like a preeeeetttyyy rainbow.

You'll have to give me a call after 6 tonight Greg. We'll do some bench racing.

Thanks, John Cadwell

10-28-2003 10:30 PM

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Main Discussion > Hoeken's straight line 4-bar linkage

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