Mechanism for directly converting rotation into large amplitude mechanical waves in flexible (planar) sheets.

I have always been fascinated by waves. Ocean waves in particular have a primordial power, efficiency and calm that is unmatched by any other type of movement.

I have also been fascinated and challenged to find a device to efficiently generate a moving wave surface. A device like that could extract energy from ocean waves, push a boat along, locomote like a fish or snake, or provide a massaging surface to sit or lie on. A search of patents and literature on this subject reveals very little. The devices that are proposed are so complex and unwieldy that it is easy to see why none of them have emerged in practical products and devices.

Several types of wave generating devices have been patented. United States Patent No. 3,981,612 issued to Bunger et al is directed to a wave generating apparatus using a set of rollers mounted on a carriage that is driven along a set of rails. A flexible sheet is secured at the ends of a frame and as the carriage is driven along the rails, the roller displaces the sheet upwardly so that a wave motion is produced along the sheet. This device is quite bulky and is only able to produce one displacement wave for only one set of rollers.

United States Patent No. 4,915,584 issued to Kashubara discloses a device for converting fluid flow into mechanical motion using an airfoil movable within a vertical track. As air flows over the air foil, the foil moves vertically up or down in the vertical track thereby transmitting movement to a set of crank arms, thereby rotating an axle which is attached at the ends to the two crank arms.

United States Patent No. 4,465,941 issued to Wilson et al is directed to a water engine for converting water flow into other types of mechanical energy. Water flowing toward one side of the device engages a set of butterfly valves and a wheeled carriage is pushed along the frame of the barrage.

United States Patent No. 3,620,651 issued to Hufton discloses a fluid flow apparatus that may operate as a pump or motor. The device includes several flexible sheets driven in oscillatory motion by a bulky crank assembly.

What all of these earlier pioneers missed is that there is an aspect of waves that can be exploited to give rise to a much simpler mechanism. Let me explain.

If you put a buoy on the surface of the ocean, interesting things happen as a wave passes below it. (Buoy oh buoy Figure 1) The first observation is that it more or less stays in place. It does move up and down and side to side of course, but it moves around the same point. The water underneath does the same, as you would expect since it is the movement of the water that lifts and rocks the buoy. The buoy will also rock back and forth, tipping one way and then the other as the wave passes by. If you were to take a series of photos and overlay them on top of each other you would see a progression of positions of the buoy that repeated with every passing wave. The position that the buoy takes at its base as it moves from one moment to the next is its locus of movement at the wave surface This locus looks like a flattened circle with large up and down and very small side to side movement. The buoy also tilts and the angle that it makes on the water is called the slope.

Now the next thing that we might notice, is that the top of the buoy seems to move around a lot more than the bottom. The bottom moves a little side to side but higher up the buoy moves a lot more because it rocks from its base, much like a metronome, as it simultaneously bobs up and down. Now, if we look at the middle of the buoy, it describes a locus of motion where the back and forth motion is about the same as the up and down motion, and at the top of the tall buoy shown (Fig 1), the side to side movement is even greater than its up and down motion.

What is also amazing about waves is that they travel through materials transmitting rather than losing energy. It’s almost as if a wave movement is how materials like to flow or flex of their own accord or even transmit information and energy with minimal loss. That could also be the clue as to why it only takes 1/100 of the power of a light bulb to push a wave through a flexible sheet the size of a bed or why a machine like that can last almost forever! But more about that later. I’m getting ahead of myself.

If we put dots on the buoy from top to bottom and we look at what each of the dots do, then we would see a rather interesting pattern.(Fig. 1) At the bottom, the buoy moves up and down a lot, and side to side, very little. A bit further up, the side to side motion increases. As we move higher and higher, the side to side movement gets larger and larger At a certain point, part way up the buoy, the up and down movement is equal to the back and forth motion and, at this point, the locus of movement is almost circular. Remember that the locus is what you get if you connect all the positions that a point on the buoy moves through in its cycle.

Now this location on the buoy that moves in a (pseudo)circle is very useful, because at this point we could attach one end of a crank and the crank would be driven around in a circle (the locus) every time a wave came by. We could even attach a motor or generator at this point and the motion of the wave would drive the crank and this motor one full revolution every time a wave passed by. This could be valuable if we wanted to exchange energy between a wave and a rotating machine. This location is very important. We’ll first of all say that it is the preferred crank location since cranks usually go around in circles and because, at that point, the locus is as close as we can get to a circle. Furthermore we’ll give this point a name because we will refer to it often and we don’t want to confuse it with any other location. Let’s call it the “Power point” since it is the best location to take power in or out of the wave. Finally, we could choose another position, other than the Power point as an attachment point, and the mechanism can still be made to work, (with a rotary cam, for example, but not with a simple crank) however it would not operate as smoothly.

Now there are other very interesting aspects to these movements that are worth noting. First of all, the point on the buoy that follows this almost circular locus goes around the same Power point for a fairly wide range of different wave amplitudes. In other words, as the wave gets bigger, the up and down motion increases but so does the back and forth movement so the diameter of the movement locus (and crank length) increase, but the Power point stays put. The next observation is that as the locus gets larger, it gets more eccentric and starts to look more and more like an egg locus rather than a circle and our crank will have increasing difficulty turning smoothly through this without some tricks we could play. The locus is not actually an egg shape, but I haven’t thought of a better or more accurate description of it, so I’ll just call it an egg locus. You’ll have to remember that what I mean is that it is an odd shape, much like an egg since it is symmetric about one axis only. Now cranks don’t usually lengthen or shorten on their own, so we would need to have our crank connected through a sliding pin or rotating cam if we wanted to get the crank to adjust to different amplitudes automatically, and accommodate the less than perfect circular movement for larger amplitudes, or something like that. I haven’t explored any of these options so I can not advise of one best or preferred approach, or how well they would work.

Another awkward thing happens as the wave gets larger; the crank attachment point on the buoy moves slower around the bottom end of the egg locus than the top half. If you think that moving through a non circular locus is difficult, it gets even harder for our poor crank to speed up and slow down, unless of course we build in another little trick. As it turns out, nature is on our side once more because what plagues engineers the most when they couple two rotating shafts together with inexpensive couplings, is that they don’t operate very smoothly. They speed up and slow down through portions of their cycle and this can get quite pronounced when the shafts are misaligned by any significant amount. But one man’s poison is another man’s feast because it is precisely this error that can help our crank keep pace with the eccentric loco locus even as the waves surge larger. Once again, until this area gets explored, the solution may change.

Ah, but we are not yet finished with our observations. There is unfortunately one circumstance under which the Power point also moves as the wave changes its profile. Alas, when the length of the wave changes, so does the position of the circular locus, so much so that varying the wavelength requires us to raise or lower the Power point proportionately. It would probably need a sewing machine company to figure out how to put all these elements together reliably in one mechanism, but it would be a sight to behold, a mechanism that moved through an egg shaped cam, a sliding crank, a cheap coupling and a rod that lengthened. It could vary with both the amplitude and wavelength while it was running! Ah, it would be so much fun to see it, rather than simply imagining it! A bird in the hand is worth two in the brain!

And now, of course, we need to say a bit more about the slope. You will recall that this is the amount of rock or angular displacement of the buoy. As it turns out, this takes care of itself since the buoy sits flat to the water and accordingly, follows the slope of the wave exactly as the buoy moves through its loci.

A small mathematical digression is in order here. There are some people who believe that when you observe that there is a simple equality between measurements in nature, then there is a rather important connection between the two. Well, strange as it may seem, when the wave gets to be the shape of an ideal wave (a Sine wave), then the distance travelled along the egg shaped locus, around the Power point, is exactly equal to the wavelength. If you move the Power point ever so slightly, the equality no longer holds. There must be a simple and rather elegant formula in there somewhere. I certainly think that this fact is significant and lends support to the notion that this locus, and the Power point it moves around, is very special and unique.

I think that we have probably said enough about our solitary buoy. I think that he deserves a bit of company. So I’d like to bring in a few more. Now buoys can drift a bit in any kind of swell, so I am going to put a floating sheet over the water and attach the buoys to the sheet so that they can’t blow or slide off. We now have a flexible raft that takes on the exact shape of the wave below it with our buoys happily bobbing around on top. To make things a bit simpler, we’ll arrange the buoys so that they are all the same distance apart, inline, and some simple fraction of the wavelength. I’m being selfish here because I like to have a bit of order and buoys all going in different directions are a bit hard for me to deal with. You see, if any two buoys are at exactly the same position on one wave following the other, then, like synchronised swimmers, they will move exactly the same way. In fact, you could connect these buoys up with a rigid beam to the same relative point hinged on the buoy, and the beam would not affect or disturb either buoy in its motion. It makes sense (actually I need to make things simple in order to keep them that way!) that we would also make that connection point coincide with the Power point. Remember, that’s the point that produces the egg locus that is as close to circular that loco loci get. Also, if the beams were thin enough, the beams could bend with the flexible sheet allowing the direction of the wave to change and be asymmetric. Asymmetric means flatter with a longer wavelength on one side and shorter wavelength and higher amplitudes on the other. (Fig 2) Anyway, I’m moving fast again so let me slow down a bit.

So, by having our buoys separated by one wavelength, they move identically one wavelength apart. They are in phase, as a mathematician or engineer would say, moving synchronously through identical loci separated by one wavelength. Now the other buoys can be placed consistently between the two we just talked about and they too will move synchronously one wavelength apart. But because they are sitting at different points along the wave from the ones next to them, they are out of phase with the others. In other words, they bob up and down just like the others but they are either ahead or behind the others as they move. Now of course we can put any number of buoys between each other and therefore end up with any number of beams we could connect between the buoys synchronous with each other. Or, to keep it simple, just have two or three beams and divide the interval between buoys to half or a third of a wavelength respectively. We need to have as many beams as we have divisions of the wavelength between buoys. If we divide the wavelength in three preferably equal intervals, then we will need three beams to interconnect those buoys that are in phase with each other.

Now we have order! Being on the same wavelength is certain to buoy the spirit! And another thing as well. Now that they buoys are all dancing the same tune to the same beam connecting them, each beam is going through exactly the same locus anywhere along its length. So we can attach our motor or generator anywhere along the beam and drive or be driven by several of the buoys at once. Handy huh? That’s not even the end of it! Nature has yielded us another opportunity! All these beams rotate around each other at every point along them out of phase with each other. You can connect all the beams together through one crankshaft, attached at different phase angles, at any point along their lengths! Engineers will love it because they can put power in or take it out wherever they want at a single location, to all of the buoys and beams at the same time! Wow!

Well wow is maybe more accurate. As it turns out, the nirvana we thought we achieved above is only available under simple circumstances, such as for example, when the waves are relatively shallow and when they are consistent from one to the next. This is a rather rigid set of circumstances. Remember that when the wavelength gets bigger, the locus gets eggier (less and less round) and the loci start needing those tricks we talked about. For deeper waves, the beams are no longer offset from each other by a fixed angle and they don’t rotate at a constant speed so it isn’t possible to hook them up to a common crankshaft without getting the wave all bent out of shape. And we couldn’t have that happen, could we? It’s time to go back to the sewing machine company to make those loco loci dance to the same tune, or the same crankshaft for that matter, assuming that they can. And while they’re at it, they can figure out how to alter the phase angles between successive crank positions to accommodate varying wavelengths and flexible beams. Or, keeping it simple, drive every crank point independently, and the wave can do as it wants.

Oh, I almost forgot, once you have all this fancy set of buoys hooked up to beams connected to a single crankshaft, wherever you want to put it, you can get rid of the water because the mechanism will keep the shape of the wave and if you turn the motor, the wave moves forward and when you turn it backwards, the wave moves backwards and if you push on the wave surface, the motor turns like a generator which is how you get power! And unlike water that stays in one plane, the mechanism can follow any contour, such as the profile of an ergonomic chair. Not bad huh?

And of course there are all sorts of variations we can build on this common theme. For example, if we stick a rod through a hole in a barrier, by rotating one end in an arc, the opposite end also rotates with the point at the barrier pivoting.. This would enable us to transmit a wave through a barrier with the motor on one side and the wave on the other and build a mechanical Manta Ray. The oceans will never be the same!

Thanks for you attention. You now know more about waves than you ever wanted to!

By John Saringer

March 10th 1999