The flapping foil propulsion drive based on Cardan gear mechanism

[Victor R]

As Google's AI says:
Flapping foil propulsion is a bio-inspired method that generates thrust by oscillating a submerged hydrofoil through a fluid. Unlike traditional rotating screw propellers, flapping foils generates thrust through a tightly synchronized mix of linear translating (heave) and rotating (pitch) oscillations.
If this combined motions are driven by internal electric motors or mechanical linkages, it is called Active (mechanized) propulsion.
The pitch motion typically lags approximately 90 degrees behind the heave motion to maintain an optimal angle of attack during the stroke.
Multi-Functional Action: Serves simultaneously as a propulsor and steering rudder.
Flapping foil propulsion drive can also be used to convert the kinetic energy of the surrounding flow into electrical energy to power on-board systems, for example on a sailing yacht (power generation).
Engineers face high mechanical complexity in building the joint linkages required for continuous dual-axis oscillation.

I found this complexity interesting to solve, so I propose for discussion one of the possible propulsion and steering drive design for discussion.

In short, in the proposed drive, fin is driven by a single motor via two synchronized and linked mechanisms. One of these mechanisms performs the fin's reciprocating motion, while the other ensures its angular oscillation. An angular shift is introduced between the rotations of the shafts of these mechanisms, which determines the amplitude of the fin's angular oscillation.
This scheme is quite practical and is used, for example, in patents:
1. Propulsion mechanism employing flapping foils
2. Apparatus for oscillating a foil in a fluid

The proposed drive uses a Cardan gear mechanism, which is less bulky in comparison with the traditional crank-rod or Scotch yoke mechanism.

AI says: The Cardan gear mechanism (named after 16th-century mathematician Girolamo Cardano) is a brilliant engineering setup that converts continuous rotary motion into precise straight-line (linear) motion without requiring sliding tracks or extra linkages.
File:Cardan Gear linear movement packed vertical.svg - Wikimedia Commons https://commons.wikimedia.org/wiki/File:Cardan_Gear_linear_movement_packed_vertical.svg

The movement of the fin is shown in the animation:


The diagrams to compare the sizes of different mechanisms for the same range of fin motion:
- Cardan gear mechanism,
- Scotch yoke mechanism,
- Slider crank mechanism,
- Crank and rocker mechanism.


I'll be glad to tell more about the details and features of this design:

 

[philSweet]

Are you looking at human power levels of less than 1 horsepower, or are you considering higher power applications? Because their are serious issues with the cost and weight of a cardan gear systems used for power delivery. That's why the Watts linkage and grasshopper/Russel/Evans linkage predominated. Also, there are no provisions for carrying the thrust and bending loads in your mechanical mock-up.

Using the cardan gear for the pitch control rod is reasonable. The throw and clocking can be easily adjusted at the gear, but it's not as versatile as a cam follower system that allows complete control of the angle of attack at any point in the cycle. But this should be slaved to a better push-pull blade drive run from a grasshopper linkage or similar. Better than any of those is a simple chain loop running constantly around two sprockets. This has constant transverse speed, controllable acceleration at either end, and you get a free reduction gear out of it. A bit agricultural, but very effective. They sell all manner of special chain links for attaching things. Look up K1 roller chain links.

Before worrying about the drive linkage, get the statics and dynamics of the problem solved and design the bearing systems and load paths. You also need to compute the angle of attack profile that minimizes induced drag and accommodate forward and reverse operation. That can get a bit tricky for oscillating motion if you aren't using the chain loop, but it has been solved. If you look at the Voith drive, for instance, they handle most of these problems by using multiple vanes that are quite short, and they don't worry about trying to have linear motion.

You really need to sit down and do a full power and efficiency analysis for the system. What is the cyclic hydrodynamic performance and what is the average thrust/drag ratio for your implementation. I'd be surprised if you can get to 5. In front of that, what are the drive line losses - 30%, 40%? What is the average transverse speed of the blade and what is the ratio of transverse speed to target ship speed? Have you looked at how yulohs work? they have been around for a long time and are pretty darn good both from a mechanical and a hydrodynamic perspective. Do you understand that having the blade canted at 45 degrees doesn't really matter once the boat is moving, and the thrust can be sent up the shaft. You can pin the end of the handle to a cam track and really control the angle of attack profile. The Japanese Ro oar enters at even a finer angle - like 25 degrees. I suspect either of these hacked out of a small tree by a 12-year-old with an adz would beat yours in efficiency. It's really hard to beat a thousand years of applied practice. And it may take a lifetime to figure out why it's so hard.

Presenting the Amazing Pedyuloh https://smallcraftadvisor.substack.com/p/presenting-the-amazing-pedyuloh

Ro - the Japanese Sculling Oar — Douglas Brooks Boatbuilding https://www.douglasbrooksboatbuilding.com/ro-the-japanese-sculling-oar

There has been a century-long debate over whether a scull with single leading edge beats a yuloh with two leading edges. There is the matter of achieving reverse. Setting that aside and just looking at going forward, the energy and dwell-time needed to pivot the scull is generally thought to loose more than what the yuloh looses with its compromised foil shape. But this conclusion usually applies to people power, where arm and wrist power looses to leg and back power. If you really set about optimizing control of the sweep motion, I think the scull might be the more versatile unit (and maybe can go in reverse). But if we are talking about a fixed mechanical sweep pattern, I'd go with the yuloh because its simpler to implement and no-one has shown me the scull is better.

 

[Skip Johnson]

If you make an AD style sculling oar with a nice high aspect ratio blade out of unidirectional fiberglass there's the added benefit of the slight blade flex adding a little kick in the transition at the end of a stroke.

 

[Victor R]

Are you looking at human power levels of less than 1 horsepower..

Hi! Thanks for the interesting links and comments.

The drive is assumed to be 400-watt electric motor, nor human- or horse-powered .
At this point, this is just a concept, not a production-ready design, so only minimal kinematic calculations have been made. I hope the mechanism will withstand a fin oscillation frequency of up to 3 Hz, which corresponds to an average fin speed of approximately 2 m/s.

I've corrected the link to the mechanism animation, which wasn't working before. I think it shows that the drive is, so to speak, a mechanism for executing fin movements similar to the vertical blade of a yulos oar.

The mechanism allows for the adjustment of the fin's angular oscillation amplitude to match the flow speed. It is also possible to change the direction of thrust for steering, including reversing, without the chassis rotation. It is allowed to switch from thrust to drag mode for braking.

All of these possibilities would be difficult to combine without using a Cardan gear mechanism, so I did not consider lever mechanisms for converting rotation into reciprocating motion. The compactness of a Cardan gear mechanism is also important.
For the same reasons of compactness, this mechanism has already been used to drive flapping wings in radio-controlled ornithopter models.
Cardan gear mechanism of the ornithopter models EV1 to EV6.

 

[gonzo]

Are there any advantages compared to a propeller or is this an academic exercise?

 

[Victor R]

Are there any advantages compared to a propeller or is this an academic exercise?

In theory, the drive should work similarly to the Voith Schneider Propeller.
We'll see what happens after construction is completed.

 

[gonzo]

What theory is the claim based on? Propellers are universally used because of their proven efficiency.

 

[Victor R]

What theory is the claim based on? Propellers are universally used because of their proven efficiency.

There are many theoretical studies; here's one review:
Flapping Foil-Based Propulsion and Power Generation: A Comprehensive Review
Practical implementations are fewer, such as the O-foil: O-foil promotion

I'm not looking to outperform the propeller, I'm just trying to test the drive idea, mostly out of curiosity.
By the way, the screw did not immediately become what it is now, and I suspect that this happened due to someone’s curiosity.

 

[philSweet]

The story goes that it happened when an old auger-style propeller used to get riverboats over strainers broke apart, and the little remaining screw bit actually worked better in open water.

 

[gonzo]

That is the correct story. An accident and an observant person.

 

[Victor R]

Are there any advantages compared to a propeller or is this an academic exercise?

To change the direction of a propeller's thrust, it must be placed in a rotating chassis to create an azipod. A fin propulsor has the ability to change thrust direction built right into its functionality.
To change the direction of thrust within small limits for steering, it is sufficient to change the average angle of fin oscillation during its movement cycle, as described in the article:
Forces on oscillating foils for propulsion and maneuvering (4. Maneuvering with an oscillating foil, 4.1. Pitch bias):

But this drive utilizes a different method: rotating the plane in which the fin's reciprocating motion occurs. Moreover, the Cardan gear allows this to be accomplished by simply rotating the central pinion; a rotating chassis is not required.
Therefore, I think it is more logical to compare the drive not with a regular propeller, but with a Voight-Schneider propeller.

 

[Skip Johnson]

@Victor R thanks for the article, it puts some academic rigor to an approach that I've been cogitating on for a while.

 

[gonzo]

To change the direction of a propeller's thrust, it must be placed in a rotating chassis to create an azipod

The common method is a gear box. The second common are propellers with reversible blades.

 

[Horton HCCI]

I think I can see the potential gain in efficiency from having more foil area in contact with the water (a larger "actuator disk"). And I think, perhaps akin to the idea of a high-bypass-ratio turbofan or turboprop vs. a turbojet, the idea of moving more fluid more slowly favors something needing a lot of torque.

This suggests to me possible applications as a ship maneuvering system, as with a Voith-Schneider unit. My understading is that, unlike a gearbox or reversible blades, things like a Voith-Schneider or perhaps Victor's idea are more akin to thrust vectoring, like an F-22 or an outboard. Tighter maneuvering in a small area, in other words. Or maybe something driving something very heavy rather slowly over flat water, like a tugboat or a river barge or ferry.
--
What I don't understand, Victor, is your aversion to rails. Yes, they add an unsightly transverse frame, which is draggy, particularly if underwater. But doesn't your mechanism trace the same transverse path in any event? Let its motion trace out an invisible rectangle in a transverse plane. Just put rails above and below. How is it different?

I think, especially if you use a rail above and below, with considerable separation, you'd have a lot more support and wouldn't need to cantilever your entire mechanism off a single attachment point. This might let you use a lighter structure overall. My current design does this. It also staggers the upper and lower track, which I think (?) also adds stability and maybe strength. See attached.

 

[Skip Johnson]

The "actuator disk" for an underwater oscillating foil I believe is defined by the span of the foil times the width (heave) of the foil travel perpendicular to the crafts forward motion.
There's a lot of fiendishly little devils in the details which are addressed in the article referenced above.