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Pendulum - self-levelling gimbal using rods
As my user-name suggests, I'm new to KAP, having been doing this for a little less than a year... so my apologies if I've inadvertently replicated anyone else's designs. I'm putting this here to straighten my ideas in my own mind and hopefully to gain a little feedback for further development.
Before I begin proper, I'd like to set a little terminology re the movement of the rig to keep myself organised.
Yaw, pitch, and roll are described as in the above picture - taken from
The nose of the aeroplane is 0', the pilot's right-hand side or 3-o-clock = 90', the rear of the plane or pilot's 6-o-clock = 180', and the pilot's left hand side or 9-o-clock = 270'.
The kite flies at 0', the kite flier is at 180'.
The aeroplane is the pendulum, and the kite-line angle is ignored in the above.
I've been thinking about pendulum stability for a while, now, and have made a first prototype of a few ideas.
I fly in very light and generally laminar winds at this time of year, and need a lightweight rig. In the picture below, I've used bicycle spokes, bamboo, and copper pipe as those are the materials I have easy access to; kite supplies are strictly mail-order only... mail-order
being a singularly exasperating experience in my part of the world.
An overview - right-click and save for a larger image.
1a is a solid-soldered, square cross made from copper pipe - nothing can move at this part.
Both A-C and B-D are single bicycle spokes @ 30cm long and 2.25mm dia and both pass through 1a, crossing at their central points.
Both A-C and B-D are soldered at all exits from 1a.
A to C is the kite-line hanger. Re the terminology introduction, A is 0' or the "kite end", and C is 180' or the "kite flier's end".
1b is the same as 1a
At points B and D, two further 30cm bike spokes are connected with 2" of coiled wire spring... 1" pushed onto each spoke. The outermost end of each spring-attached spoke is bent at 1" from its end and soldered into 1b.
E-F is a single 30cm spoke, soldered in place exactly as A-C, B-D.
At points E and F, two further 30cm spokes are attached with sections of spring as in points B and D. These spokes pass down to G, where they are held in place under bending tension by being passed through a small section of drilled bamboo.
A-C, E-F, and the bamboo at G are all parallel and vertically aligned.
Ok, now that's out of the way.
B-D is allowed to rotate in pitch ('plane nose = up and down) by the springs, which allows A-C to change angle through around 160'. As A-C is the kite-line hanger, this means the kite line angle movement does not affect the horizontal alignment of E-F or G.
A slight torque is passed into the joints of the 1b cross as the springs turn their attached "downspokes".
On a taut line, yaw is all but eliminated as the B-D spoke cannot move from its square alignment. Neither E-F, nor G can easily be moved from parallel alignment with A-C provided that within the spring joints, the ends of the spokes are pushed to within 2 spring coils of each other.
The pendulum swinging in roll (the airplane wings dipping or rising) is taken care of by the spring connectors at points E and F, so G can swing under points B and D - correcting for roll. A 2m pendulum is attached below G with a small weight at its bottom end. The camera is placed immediately below G at the top of the pendulum.
No progress as yet. The whole pendulum can swing in either direction from the kite to the flier. With a camera pointing to 0' or the nose of the plane, this would give a horizon moving up and down within a photo frame.
A down - aeroplane diving
A up - aeroplane climbing
Roll into point B down - aeroplane left wing down
I'll add further pictures of the pendulum and camera tomorrow.
Perhaps a short video clip showing the movement, even better with the pendulum and camera attached to a kite line (static or on a kite).
I agree. I'd like to see a video of the movement attached to a kite line, static or otherwise. There are a couple of things a kite likes to do that may affect this kind of a setup. It would be nice to see how the suspension reacts.
Something else to keep in the back of your head while you're exploring this, Rob: There was a discussion a while back on damping mechanisms. One that I've been looking at is a damping grease made by Nye Lubricants. They offer a free sample pack with four or five grades of their damping grease, so it might be possible to play with this. I tried their grease in a double row ball bearing pack, but it didn't work that well. The damping grease really wants a plain sleeve bearing: exactly what you have in your design!
So if it looks like the action of the kite, line, and wind excites some mode in your suspension you're not happy with, consider what the effect would be if you damped that pivot.
Cool cool stuff!!
I've only worked on this rig indoors on taut lines to date, but I'll be trying this outdoors tomorrow morning, and will take a video with a kite flying.
Tom - there are no bearings in this frame. The springs grip the spokes tightly and act like universal joints passing movement along connected rods with no slip at all. I think springs made of stronger/larger wire could possibly be effective dampeners. Two of the joints in 1b, both joints in G, and the coils of the springs that are close to their joints share the torque generated by tilting. The pipe joints at 1b to 1a and the joints at G need to be particularly solid to stop them twisting. I used electrical solder to make this model, but maybe silver-solder would be better in further models.
If the planes nose is at 0deg why did you choose the kite to be at 0? Surely wind flows in the plane model from 0 to 180, so for kite and suspension model - flyer is at 0 and kite at 180? Am i missing something?
You're absolutely correct, james.
I guess I was following the aeroplane analogy too closely. I can change the degrees in the original post around if those numbers are more generally understood another way... I was simply setting a standard for possible discussion. Newguyitis, gets me every time.
Here's the pendulum as-is and how it will be flown tomorrow morning. The bamboo at G has been replaced with a soldered rod and a little more copper pipe - the aluminium tube is drilled at just off-centre. I've lowered the camera on the tube for this photo.
The 2 metre pendulum with a counterbalance still gave a slow roll - brainwave during the 2nd beer this afternoon... 2 counterbalances.
For the camera 'holder',
Here's a video made with someone twitching the line a couple of inches and adding the occasional small tug at its lower anchor...
How do I embed YouTube videos here?
Yaw is reduced to a few degrees, which is quickly steadied - roll is greatly diminished - but pitch is still a big problem... when the rig starts to swing from kite to flier, there's nothing stopping it. I think stronger springs at B and D could maybe do it.
Rob - The video is very instructive. Very anxious to see you try this in actual flight.
One thing you may find is that all the pivot axes may benefit from being in one location near the CG instead of two separate locations. If I am watching the video correctly, this seems in evidence for the pitch. If that is not do-able, I agree with Tom that perhaps you may consider a damping mechanism for pitch just to slow reactions down. After all, it is great to have a camera that does not move too quickly/jittery -- kind of the whole idea in getting lots of good photographs (our main objective).
Compliments on your craftsmanship and determination to get this right. There is nothing like the real environment to test things out - that's why even NASA has wind tunnels (not just to verify, but to discover real world interactions).
Aaaaah! Thanks for the clarification regarding the springs. Somehow I missed your diagram where you called that out. (DOH!)
Yeah, on the next rev I think silver solder would stand you in better stead. Electrical solder doesn't make a great structural joint. Still, you've got a safety lanyard (YAAAAY! (I'm a fan of safety lanyards)) so I hope you're going for it this morning. I'm really REALLY eager to see how this flies in the air.
I'm also curious to see how your balanced pendulum works out. I tried something similar a while back with pretty disastrous results. I don't think I had enough of a downward bias on the pendulum, so once it started to rock and roll, it tended to go runaway.
If at all possible, can you make a movie using the camera on this rig? Back when I started trying to make a balanced pendulum rig, Henry Jebe suggested this as a way to see the stability in a rig. It's a really good diagnostic.
Good luck today!
I had a look at your 1st video and it looked like the pendulum was able to move from the flier to the kite easily.
What would happen if you soldered the two top corners instead of them being attached by a spring? I think the rig would then be unable to move in that direction. It would also make it a large object when it came to transporting it!!
In that case, would plastic bendable tubing - like for fuel lines - be stiff enough to stop or lessen the movement?
Good luck with the trials.
It's great to see 'newbies' having new thoughts on our established ways.
Fly High ( and steady)
Sue, if I solder those top two joints, then the rig will be stuck at 90' to the kite line - joints B and D allow the rig to hang from the kite line and point to the ground at a good range of line angles.
And therein lies the rub. If the joints are loose enough to allow the rig to easily hang vertically, then maybe they're too loose to hold the rig stable in pitch.
I did try some fish-tank hose over the springs, but it was too large in diameter, kinked at the corners, and wouldn't easily allow the needed curve in motion. I'll look further for a narrower and smaller-walled tube.
It's already an unwieldy contraption as it's 30cm square and about 60/70cm tall... I'll be adapting a final, working design for easier portability.
Tom, no wind today.
The leaves on the trees were twitching for short periods, but nothing strong enough for a long enough time that would lift any of my kites. Windy all week and then a flop on the day. It'll be next weekend before I get the chance to get out and about again. I'll take a look at video, thanks.
I dug out some bicycle brake-cable sleeves this afternoon - they're basically just long, coiled springs covered with a black plastic jacket - and I'll be trying those out in any free time I have this week as they're a fair amount stronger than the springs I've used so far. They also have a very thin, plastic, inner sleeve that may or may not accept lubrication depending on their diameter re various bike spokes. Possible sleeve bearing and possible placement for a dampening oil/grease if I can use differing spoke diameters in a single joint.
Certain lubes can swell the inner lining on a bike cable, providing even more friction if you need it :-(
Just tried it - they're WAAAAY too strong.
new guy, I can sympathize. It's been gusting over 30kts here for the last couple of weeks. Last weekend I went down to the beach to fly my Nighthawk in what honestly was something of a grudge match against the weather. But I didn't fly a camera. This weekend? Still howling.
Be patient with your tests. Better to have to wait for a real answer than force it and lose your rig. Hang in there.
Rob - Hopefully you will get a chance to test soon in a calmer wind.
If the pitch problem persists, perhaps adding a damped joint in another axis would help where the pendulum is joined now (errr...that is not very clear) as framed in in this image:
It is not going to be easy to solder or braze, but something like this
help with the pitch --
I really do like the fact that your pendulum is counterbalanced and believe you are on the right track for sure.
Man you guys sure make me appreciate my simple aspirations and expectations.
But I keep reading these threads
@ AerialLensGuy, I made a quick and very dirty version of that and it works.
It levels in roll very well, but the pendulum within a pendulum introduces even more pitch than before as the pendulums' forces battle for balance... I think it will take some careful calculation to find a balance point as at the moment the double pendulum seems chaotic in its movement. Sometimes the period "wavelengths" cancel out in opposition and the camera is very steady for a second, then they get into sync and the camera pitches unexpectedly sharply, although smoothly.
benedict - the video shows there's a new "problem" with a fast, almost vibratory, movement in yaw, which I think is related to a possibly harmonic oscillation in the kite line... I'm using around a 15 foot length of line tied tightly between 2 very solid anchors and I think a wave of some sort is travelling back and forth along the line and producing a force acting in parallel with the kite-line and affecting yaw through the framework around joint 1a to the B to D bar... the ends of this bar wobble in a yaw at the kite-line angle, although I'm pretty sure they haven't before and shouldn't be able to - the line is tight.
I think that a shorter cross-bar at B to D would reduce this problem as the leverage that the B to D bar can pass down through the 1b joint is quite high, but I'll leave it as-is until I've seen the results flying outdoors. Maybe tomorrow.
Wow - you do work quickly. Those are great observations.
Somewhere in these threads there is a very good discussion, complete with videos, showing the double pendulum idea and the finding that it generally is not as stable as hoped. The term used in the discussion is "thwarted" pendulums. I am sorry but I need to leave at the moment or would find the discussion link myself.
Anyway, since now you have a complete set of axes in one "trapeze" frame (excuse my terminology), perhaps you can exclude one of the two frames thus giving one pendulum frame containing the internal counterbalanced pendulum as you now have? In other words, just get rid of the top frame maybe. I hope that makes some sense. Worth a try?
If I remove the top frame, I'll be introducing contact between the line and the frame at higher line angles - I think the lower frame is too close to the line as it is as I fly fleds and deltas...
I took a look around with the search function and came up with these...
I'll look into the thwarting pendulum over the next week and see how it might be applied to what I've got here.
There's a lot of good info from benedict at the second link regarding "pan axis" wobble. If I may add to that... what I've noticed very clearly is that the wobble in what I've called "yaw" is a force that passes up and down the line, rather like a single ripple on water but bouncing and returning. It can clearly be seen passing through the rig then moving on and returning - the wobble visibly increases and diminishes as it passes.
SteamPunk pendulum V2 is now up and working indoors, here.
Yaw is gone, with the exception of an occasional, very much reduced, "pan axis / yaw" wobble.
To reduce that wobble, I removed the B to D bar in the above photo and hung rods directly from 1a; the top section between 1a and 1b is now a long rectangle hanging by a short side - neither short side is soldered and both can pivot. I cross-braced the rectangle twice with springs to dampen the pivots at both top and bottom by pulling the rods quite hard into the pipe ends at the bends. No rods are soldered into 1b - all rods can pivot, there. No springs are used as pivots in this version - all pivots are sleeve bearings; I think the springs were adding to the yaw wobble effect.
Pitch is heavily damped and comes under total control to rest within 2 or 3 swing cycles, even after a hefty tug on the line. The pendulum shaft above the circular gimbal rubs along between 2 springs set between the rods making up the lower triangle giving friction the opportunity to do its business.
Roll is back again over the whole height of the rig - pretty obvious why. A 2 metre pendulum slows that, but it needs work to fix it.
2 out of 3 ain't bad, I suppose. Will keep at it.
I've done some more experiments with that "other avenue". The damping grease is effective, but how much damping force it applies depends on a couple of things. The damping force goes up linearly with the radius of the sleeve bearing. It also goes up with the length of the sleeve bearing. The damping force is inversely proportional to the gap between the shaft and bearing in the sleeve bearing, though, so tight fits are better than loose fits.
Read between the lines, and you can see why packing that double row ball bearing cartridge with damping grease wasn't all that effective. Not bad for really small loads (Gopro on a short pendulum), but nowhere near enough to hit critical damping on a full sized KAP rig on a 1m+ pendulum. But you can also see why it might not be a bad route to try on an arrangement like yours, albeit with different pivots.
But from what you wrote, it looks like you've already got decent damping force. 2-3 swings isn't critically damped, but it's not bad at all. I'd move forward with what you've got rather than introduce new stuff.
As far as yaw damping, this can be as simple as decoupling the rig from the pendulum with an additional pivot, and damping that joint somehow. Damping grease, silly putty, a relatively high friction fit in the joint, whatever.
On the source of yaw, you've got one source nailed: standing waves on the kite line. Here's where lab testing and real world testing differ, though. Depending on the kite you're using, that standing wave may never damp down. Some kites are prone to generating standing waves on the line in given wind ranges. The other source is a varying wind load on the rig. I know the last time I mentioned vortex shedding on a KAP rig, it wasn't well-received. But I've seen this now on my 4x5 box camera, my DSLR rig, and my A650 rig before I added the Ho/Ver axis. Once a Picavet rig starts oscillating in yaw because of vortex shedding, it doesn't tend to stop unless the wind conditions change.
But as you said, 2 out of 3 ain't bad! If you get decent wind, get this sucker in the air and shoot some video. That'll let you know how well the damping is working in those two axes, and may give you some hints about the third.
Hey, Rob, haven't heard from you in a while. I'm curious if you've made any more progress on your damping pendulum.
I'm working on a different approach, but it's all theory and CAD drawings so far. It looks like it should damp like nuts in pitch while facing in the direction of the kite line, and should do a decent job of damping in yaw. It's roll about the kite line that's the real bugaboo, of course.
But! I think I might have found something of use: Years ago Robert Oppenheimer's brother, Frank, built a cool exhibit for the Exploratorium. It was two coupled pendulums (pendulae?) [Edit: fixing the remaining spellings, courtesy of wayback] It was used to demonstrate momentum transfer. Start one pendulum swinging with the other standing still, and eventually all the angular momentum transfers to the other pendulum. Then the process reverses itself. Neat stuff.
Frank Oppenheimer's exhibit used two equal length pendula, and had free-pivoting bearings at every pivot point. BUT! What if you used two unequal pendula, coupled at a damped axis that's oriented parallel to the kite line. One pendulum takes on the job of suspending the KAP rig. The other one holds a dummy weight, and is of a length such that the fundamental frequency isn't a harmonic of the first pendulum.
As the rig swings around the kite line, the damped pivot will take energy out of the system as heat. And since the two pendula have different fundamental frequencies, they shouldn't reinforce each other's motion. If anything (and this is the whole point!) they should basically funnel energy into the damped pivot.
I haven't worked out all the physics yet. Initially I though it wouldn't matter where the damped pivot was, but in doing a back of the envelope calculation, it looks like the performance of the system depends heavily on where that pivot lives.
I honestly think the easiest way to try this is to just try it. I'm still a good way off from testing my damped pendulum idea, but if this idea makes sense and you're interested in trying it, I'm curious to see what you get.
Hope your experiments are going well! I can't wait to see wobble-free night time panoramic KAP.
P.S. At one extreme, where the pivot point of the second pendulum is located at the bottom of the first, this looks exactly like Christian's double pendulum. The big difference is that the rotation axis of the second pendulum is 90 degrees to the axis of the first.
Thanks, wayback! I fixed all but the first instance.
Good ideas, there - give me a few days to think on them and see what jumps out.
I'm still figuring mine... here's the latest step.
I went back to the first frame and added a crossbar to the top of the pendulum at 90' to the kiteline, then allowed it to pivot in roll. What this crossbar does is swing at a different frequency to that of the main pendulum and tap that pendulum into a vertical alignment / rest state in roll by transferring pendulum momentum into an upward "bump" movement of the crossbar - ie, during natural swings, the rubber washer is moving up when the crossbar is moving down, and when the 2 meet, the crossbar is bounced upward and the pendulum swing reduced.
It also controls well the
*ed movements made by the standing wave in the kiteline and hugely reduces the yaw wobble that was present in the camera. I'll be looking to frame construction improvements and different masses on the crossbar to remove the rest of that.
This system has the much the same efficiency as the spring I used as a roll damper previously; with a 1.7m total height pendulum it will calm an approximate 1.5m roll swing to a 10cm or so movement at the bottom of the pendulum in 3 to 4 swing cycles. With no damping, for the same reduction to happen "naturally" generally takes 12 to 13 cycles.
It's a little early for giving parameters as it's only been working a few days and is only on it's 2nd generation, but I'm tentatively suggesting some details.
1. The period of both crossbar and pendulum needs tuning until the swing of the pendulum is at a frequency that allows rubber washer to tap the crossbar at moments that will reduce the pendulum's swing and not increase it. The crossbar is like a metronome in its regularity when the pendulum is held still - I trimmed the pendulum length to suit that. I haven't removed sync'd hits entirely yet, but seem to have removed them from the larger, initial swings - after the 3rd and 4th swing cycle there's very little energy left in the pendulum and syncing up at that point or later doesn't currently look to be a problem.
2. The distance between the top of the rubber washer and the crossbar needs to be carefully set. The crossbar must be able to swing freely, but too large a distance here will allow the main pendulum to swing unimpeded, and too little will allow the pendulum to "push" the crossbar... the goal is to have the 2 parts meet during a natural cycle and transfer pendulum momentum into the crossbar by bumping it upward.
3. The camera must be placed as high as possible, tight under the gimbal.
4. The crossbar must be perfectly horizontally balanced at rest. I used magnets as it's easy to move them and add/change the weights there, but a weight on a threaded screw would give better control.
I'm really happy with this solution as it's clean, simple and elegant to watch. It's a little dark here for a video - will sort one out tomorrow when there's better light.
I'll be sticking with tuning this system and adding another, similar crossbar parallel to the kiteline for pitch control.
As an aside, I'll also be looking at using 2 read arm bearings set up in in 2 parallel pendulums hanging from / integral with the gimbal. The pendulums to be connected with a weighted crossbar through the bearings, and with the camera placed onto the bar in the gap between pendulums. If I can get this working, I think it would give a very stable camera platform, but a perhaps a faux "photographic stability" as the camera would be stable in pitch, yaw, and roll, but would still be moving in space - no good for night-time. That's for later though as I'll be looking at the current setup first.
Compliments on that split/locking part of the pendulum that lets you adjust up or down securely. I do not know what you choose to call it, but I love the elegance, effectiveness, and simplicity.
IMHO That is really quite brilliant!
W00t!! Looks like you beat me to the idea in the first place. Your counter-balanced crossbar is a nice (better, in my mind) variation of what I had in mind.
I honestly don't think that letting the camera translate while keeping it from rotating is a bad thing. If you think about how much rotation it takes to produce a 1 pixel blur in an image, it's not much. But if you think about how much translation it takes to get a 1 pixel parallax shift in an image with a reasonable amount of altitude and subject distance, it's actually quite a lot. I'd be happy to let my camera translate a fair bit if I could guarantee it wouldn't be rotating much at all.
I can't wait to see a video of this arrangement in the air. I REALLY can't wait to see a video from the camera mounted on this in the air!
P.S. It's not mine to name, but looking at the arrangement, "Highwire" is what comes to mind.
Bear with me, Tom.. life's getting in the way.
Will sort a video out when I've the time.
in Gizmag. Pretty thought provoking, yes?
HAHAHAHA! Rob, I can bear with you. Trust me. I feel bad about the number of times I've posted ideas or CAD renderings here in the forums, only to abandon the idea completely because life got in the way. You're leagues ahead of where I usually am on projects. Take your time.
That MojoFloCam is a pretty piece of engineering! I just can't help thinking that between the KAP world and the migration of the consumer camera world into higher quality video, we're on the cusp of something phenomenal.
Not abandoned, Tom.
Cambodia is currently restructuring its power grid and dealing with the annual peak demand from the mid dry season. Day long power cuts and random half-day and night-time cuts are playing havoc with working schedules here. When its on, it's a mad dash to get things done, and when it's off, there's not much can be done besides sweat - the temperature's in the mid to high 30s and humidity's variable to 80%... not pleasant without fans or aircon.
Add in fixing a failed starter motor on my truck, sourcing a small generator for my classroom, wiring said room for a 12v lighting and power take-off circuit and it's been a busy week.
AerialLensGuy - that's exactly where I'm headed... even down to the orientation of the crossbars. I don't have the ground connection of the hand and thumb, though. Their website says they have a patent pending... aaaaaarghh!
I've sent a brief note through their website feedback form - could be interesting if they'd like to give some input, here.
Depends on what they're claiming in their patent. If it's the crossbar system, I've got prior art on that.
(Imagine that crossbar attached to the vertical bar poking out of the gimbal where that screw is sticking out.)
I don't have the orthogonal lower crossbar, so if that's what they're patenting then they've got me. Anyway, for the sake of experimentation patents don't mean a lot. Just means you can't produce and sell stuff that violates their patent. I wouldn't sweat it.
One Idea I had for some time...
How about using counterweights filled with (viscous) liquid?
Just take two eggs, one raw and one boiled for 10 minutes, and try to spin them on a table. Notice how much quicker raw egg stops rotating.
I think that's a really good idea, actually!
It's similar to the idea of a tuned mass damper. The idea with a TMD is that you have a mass suspended in a damper. The spring constant and damping of the damper are tuned to the mass so that vibrations below a particular frequency are absorbed by the damper. These are used on everything from bows for competition archery to buildings.
With the raw egg, the egg goo is both the mass and the damper. And it damps like NUTS! Good idea!
My idea was/is to make a counterweighted pendulum with additional elastic pivot (piece of tubing) just above camera cradle and with counterweight made from some plastic bottle with baffles inserted to increase liquid resistance.
Seb - I think you and Tom are on to something. A stroke of genius. The whole idea of the tuned mass damper - whether a gooey fluid or purely mechanical - is very elegant and can be very effective.
is where Scott Armitage demonstrates a simple mechanical type to help control oscillations on a whole rig. The damper is not pretty, but I bet the images from the camera will be. Please continue the great thoughts.
Time for some wrapping-up of this idea for me. I'm leaving this idea as open for whosoever would like to develop it further - if anyone would like to do so... I've no time for it and can't see that changing.
The rigs were stripped and scavenged for parts very recently, and a duo of JudoBots have emerged, phoenix-like, from their remains.
Tom, here's a good use for hard-drive read-arm bearings... the kids love this one.
Thanks to all for your input here.
That's cool, Rob! I love the hydraulic actuators. I wanna see a video of fight night!
First observed fight
Assessment of weaknesses - design of possible strengthening solutions
Guy lines added to the boys' machine after watching the above video - easy as it has an "H" footprint with the arm arcing in the upper half of the H. The girl's machine has an "X" footprint with the arm arcing northwest to southeast... stabilising solution yet to be reached.
Further work to be done as and when these kids figure it out...
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