FulanoDetailPneumatic Mech
All of the principles mentioned so far can be somewhat applied to the pneumatic system, the difference is that these work with lower compression ratios because unlike liquids, air is compressible. So no matter the pressure you work with, it will always have the same air flow, the difference is that you need to find a balance between pressure and volume of the actuators.
Another problem with pneumatic systems is that the faster the compression, the higher the heat loss, thus, the lower the efficiency.
You can circumvent that by:
- Using multiple stage compressors, compressing the air slowly.
- Using heat exchangers that use the air intake flow to cool down the compressed air in the system, not letting the heat leave the system, and thus, increasing efficiency. But that maintains the system efficiency, not the compressor’s efficiency. You still need to compensate for the heat loss with more air.
Of course, that is assuming piston/diaphragm compressors. I don’t know how axial/centrifugal compressors should work.
I asked ChatGPT:
“Impact of Compression Speed:
Regardless of how quickly the air is compressed, the total heat generated is still proportional to the amount of work done on the gas. Faster compression may not allow sufficient time for heat to dissipate, leading to higher temperatures, but the fundamental relationship between compression and heat generation remains”
You will also need a really good self-cleaning air filter system and a dehumidifier system.
Or you could make a closed loop pneumatic system to avoid both.
But I don’t know how practical that would be.
Should I make a pneumatic mech section?
I mean… I’m already so lost into the sauce, why not?
Diaphragm pneumatic cylinder actuators can reach efficiencies up to 95%, but for some reason I can’t find the efficiency of inelastic pneumatic artificial muscles. They always stay at around 40% to 65%, but never higher, I wonder why…
Source: Amplifying Piston Force Using Fluid‐Induced Tension in Flexible Materials | Request PDF
The idea of all of this is that:
- Diaphragm air compressors and diaphragm air actuators have 95% of efficiency, unlike conventional pneumatic systems with overall efficiencies barely touching 20%.
- By making the pneumatic actuators origami shaped with flexible rubber folds, you essentially turn artificial muscles into diaphragm actuators that will also (supposedly) have 95% efficiency.
- It needs to be really easy to mass-produce at home with as little interference as possible.
- And, well, since pneumatics need to work with such low pressures (4 to 10 bars), maybe you could 3d print everything in whatever size you want. Maybe even using a treadmill 3D printer, since the design is quite flat, but you would need to add triangles or trapezoids at the non-expandable sides.Gas tight 3D-prints (bursts at 116 psi = 8 bar/atm) Making 3D prints actually waterproof How Much Pressure Can a 3D Printed Part Handle? (bursts at 34 bar) Can you 3D print a Pressure Vessel? (bursts at 13 bar) PET-Bottle Airtank by Dionarap - Thingiverse (up to 10 bar) Building a Small and Quiet Air Compressor [4K] (10 bar) 3D Printing Compressed Air Tanks | Hackaday (5 to 6 bar)Are 3D prints water tight? Ultimate Guide to Flexible Filaments for 3D printing (TPU edition)
. — Papiroflexia conceptual avanzada_ Folding...
The idea is to make the actuator in the left figure foldable like in the right picture.
Source: An Origami-Inspired Negative Pressure Folding Actuator Coupling Hardness with Softness
The only grip that I have with this design is that I don’t know if it can be built to work like a filament artificial muscle Artificial Muscles to Mimics the Human Body Motion.
I will never not-mention this stupid thing, will I?
In any manner, I think you could solve this by making the muscle really thin and small.
I will try to solve this with my own 3D model.
Wait a minute, isn’t this just that artificial muscle that I talked about at the beginning of this project?
Source: Modeling and Analysis of a High-Displacement Pneumatic Artificial Muscle With Integrated Sensing
A few other examples of bellow origamis:
Origami-Inspired Soft Pneumatic Actuators: Generalization and Design Optimization
Design and Analysis of a Soft Pneumatic Actuator with Origami Shell Reinforcement
Recent Advances in Design and Actuation of Continuum Robots for Medical Applications
1 - Folding Paper Bellow Triangle Form.
Soft Robot based on Honeycomb Pneumatic Networks
But if you make this origami muscle too thin for filaments, it can become misaligned during contraction. No? How can I make a folding/telescopic radial expanding cylinder?
Sources: https://upcommons.upc.edu/bitstream/handle/2117/114354/Master%27s_Thesis_Victor_Boguny%C3%A0_Piferrer.pdf Design and implementation of origami robot ROS-based SLAM and autonomous navigation | PLOS ONE Reduced-Order Model Description of Origami Stent Built with Waterbomb Pattern 00-Origami Pattern | BioInspired Perception and Robotics … Like this?
Source: Icosahexahedra (polyhedra with 26 faces) The first shape is called “Rhombicuboctahedron”, just pretend that the red line is the folding part that would go inwards. But I have absolutely no idea if it would, and right now in my house there isn’t a single ounce of paper glue, so my brain is absolutely feral.
Sources: Paper Rhombic Pyramids Axially contractable actuator
Sources: [PDF] Pneumatic artificial muscles: Actuators for robotics and automation | Semantic Scholar Paper Half Faceted Sphericons
These pyramids made me think of the Romac pneumatic muscles (right pic), maybe you could make an origami version of them?
Also, how one would 3D print them continuously?
Sources: Characteristic Analysis and Design Optimization of Bubble Artificial Muscles Finite Element Modeling | Soft Robotics Toolkit
These last ones aren’t 3D printable per-se, but they could be easier to mass-produce with an extruder.
Actually, you could make an extruding version of the ROMAC and the spiral one:
Source: Kinematics of a Generalized Class of Pneumatic Artificial Muscles
If you pretend the round parts between the two spiral lines are actually pyramids, and then remove the reverse spiral, you are left with a spiral pyramid that could fold on itself.
The only issue is that it wouldn’t be as easy to calculate as the hexagon ones…
Or maybe not, with the pyramidal ones I can calculate the force required to open up the flat triangle into the actual pyramid shape. But continuous
Like a scissor lift mechanism:
Sources: [PDF] Deriving a Generalized, Actuator Position-Independent Expression for the Force Output of a Scissor Lift | Semantic Scholar Scissor Lift Jack Equations and Loading Calculator
The force it applies is dependent on the initial and final angle, and it uses the most energy the smaller the angle.
For example, according to the calculator itself, if the angle between the two links and the middle were 10º (technically 20º), the tension would be 5 times more than the actual weight. If the angle was 5º (technically 10º), then the tension would be 10 times higher than the actual weight. And in order to make the machine move, you would need an actuator capable of at least that amount of force. At 90º the tension is zero.
So, assuming each square is 5mmx5mm (the area won’t change, only its displacement), it would have 0.25 cm² of area and at 10 bars it would apply around 25 newtons (2kg) of pressure to the area.
Pneumatic Cylinder Force Calculator
Thus, if the fibers were made out of a single pyramid instead, it would be able to lift 5 newtons (0.5kg), but the longer it is, the higher the area, and thus, the higher the force applied.
- Assuming that there are 4 sides of the filament muscle with a pyramid (that can be converted into continuous spirals).
- Thus, for a 1 meter long filament muscle, with pyramids stacked one atop of the other, there would be around 200 pyramids. 200 pyramids x 4 sides = 800 pyramids from the bottom to the top aligned on their axis, but since they fit in between, there would more or less 1.5 times more.
- 800 pyramids x 25 newtons = 20,000 newtons of force, or 2,000kg of force.
- Taking into consideration that the muscles would initially face a reduction of 5 times less strength, then it would be around 4000 newtons or 400 kg of force.
Which is… Impressive and concerning… I can’t possibly expect each filament to output this much force and survive.
So it could be wise to separate the muscles based on the force that they can withstand with as little pressure as possible.
Just 1 bar (10 times reduction in pressure) would still be around 140 kg to 28 kg per strand.
To Be honest, I think I’ve been procrastinating for so long that I think I will just make do with the pneumatic muscles.
I will need to make a treadmill 3D printer and/or an extrusion machine in the shape of the spiral one with a bead extruder so I can use recycled scrap plastics and rubbers.
PP spiral steel wire hose making machine toilet pipe production line - YouTube
Creality CR-30: The INFINITE 3D printer! - YouTube
I could also use a stamping machine to stamp tapes of material with the format of tiny diaphragm cylinders.
Who would guess that those filaments could output such forces all along…
Even though it is this simple, I would’ve never guessed that it would be possible.
By the way, you also need to consider a few losses due to friction and the angle of the pyramids. Depending on the angle, they can output less force. I talked about it more on the 3D modelling of the structure below, but since I’m kinda making all parts at the same time, it can be confusing:
This graph is valid both for structural beams and for ropes.
At the flat angles, you would need 5 times more force (just like the scissor lift calculated showed), so it could also be another source of force-loss.
So:
- ((800 pyramids x 1.5 locking pyramids on eachother x 25 newtons of force) = 30,000 newtons
- 30,000 newtons / 5 times less strength = 6,000 newtons
- 6,000 / 5 times less strength = 1,200 newtons per strand.
- 1200 newtons - 10% to 20% loss due to friction between fibers = 1080 to 960 newtons of output force. Or 1080 to 960 kilograms of force.
- This is assuming that the initial resting angle is 20º degrees at 10 bars of pressure.
- The Hexagonal high displacement artificial muscle would also have a similar output, just since it only has 2 expanding part instead of 4 pyramids, it would output: 25 newtons x 200 actuators for 1 meter long filament x 2 opposed surfaces = 10,000 newtons. Since they would stretch until the cable is almost parallel, then it would lose 5 times the total force as tension. Resulting in 2,000 newtons or 200 kilograms for every filament at 10 bar of pressure.
- At the moment I’m assuming I’m correct, but something is telling me that I’m overlooking an aspect of it…
- It can’t be this simple, right…?
I asked both ChatGPT and DeepSeek and both agreed that I’m correct.
In fact they argued that reducing the strength by 5 more than once was incorrect.
Meaning that the correct thing was 6,000 newtons per strand.
If Romac artificial muscles were so good, then why no one uses them?
I “asked around” (aka: I’ve made a post on physics forums) to see if the math is correct, but I doubt anyone will even give a dang about this…
Solid state hydraulic pump:
Also, if you used hydraulics, you could raise the pressure while not requiring any complex pumping and tubing, such as using a pascal lever/hydraulic tool holder:
The screw moves with high force, small distance and the contraction is low force and longer distance.
However, its practicality would depend on the amount of fluid that would be required to be displaced.
A single telescopic cylinder muscle would have 1.5 liters, while all of the others would be: 1.5 x 82 = 123 liters. Increasing the pressure decreases the amount of fluid required for displacement.
It also puts hydraulic actuators on a different perspective…
Both hydraulic and pneumatics can work continuously, but only hydraulics are incompressible, requiring less fluids to work with. But still requiring a lot of fluids flowing.
Taking into consideration that every 200 actuator filaments there will be around 0.22 liters of working fluid, if you multiply by the whole 82 bundles of muscles:
82 x 0.22 = 18.04 liters in total or 18.04 liters of water to work with.
I could even use linear voice coils/solenoids in order to push syringes, making them work as pumps.
Solid State Compressors:
Since I would need such low pressures and such fast flowing working fluid (hydraulic or pneumatic), I was also wondering about solid state compressors.
Thermoacoustics and Laser Propulsion can generate shock waves that can compress air, maybe I could use these to compressor air without a gigantic compressor unit.
Or a more practical approach would be diaphragm voice coils.
But there is something that actually caught my attention that could be relevant for this:
The Most Exciting PC Hardware in YEARS. - Frore AirJet Cooler
Take A Lab Tour Of This Solid-State Cooling Tech
This 1mm-Thin Chip Cools In Tiny Places
This solid state air cooler works with a moving membrane that pumps air like a caterpillar insect moving.
Source: Amazing new electric boat motor based on fish fins - Plugboats
Magnetohydrodynamic levitation for high-performance flexible pumps | PNAS Steel Heart- Artificial Heart Prototype (these pumps works more like a heart, like in the gif, but without a voice-coil)
Acoustic and Thermoacoustic Jet Propulsion
You could also use that for hydraulic pumping.
The exact composition and inner-workings of the membrane are a secret, but you could use electromagnets just as well:
Polymer-Based MEMS Electromagnetic Actuator for Biomedical Application: A Review
Design and Fabrication of a Novel Micro Electromagnetic Actuator
(PDF) Focal tunable liquid lens integrated with an electromagnetic actuator
Ultrafast small-scale soft electromagnetic robots | Research Communities by Springer Nature
Electromagnetic actuator and integrated actuator and fluid flow control valve - Eureka | Patsnap
Control System Hardware Design, Analysis and Characterization of Electromagnetic Diaphragm Pump
Anyway, taking this idea and the pneumatic cylinder calculator:
Pneumatic Cylinder Force Calculator
A voice coil with a flat plate of 30cm would need at least 700 newtons of force per stroke to compress the air to 10 KPa above ambient pressure.
Assuming it has a stroke of 1 mm and a frequency of 200 to 300 hertz (according to ChatGPT), it would be able to displace 70.69 cm³ or 0.07 Liters for every stroke, a maximum of 14 to 21 liters per second. THus, with a total of 840 liters per minute.
Volume of a Cylinder Calculator
I would need around:
191,070 liters per minute of airflow / 840 liters per minute = 227.4
Around 230 of those 30cm wide voice coils…
Not taking into consideration their length, size of tubing etc.
Evaporative Coolant Pneumatic Mech:
Now that I thought about this a little more, the idea of using the evaporation of coolant to pressurize the actuators in the pneumatic mech should not depend on the cooling rate and efficiency of the cooler.
I kept worrying about removing heat as fast as possible in order to turn the coolant into liquid to avoid using compressors, inherently using compressors to keep everything cooled down.
Like I discovered while talking about energy generation: cooling is the inverse of heat engines (aka combustion engines), thus, it has an efficiency equal to them.
Cooling is the inverse of heat engines (aka combustion engines), thus, it has an efficiency equal to them.
Thus², it can’t really be that efficient IF you use the cooling process to turn it into a liquid.
However, if you use pressure alone to turn the coolant into liquid, it is not so dissimilar to an air pressure tank. The only difference is that the pneumatic working gas is stored in the liquid form.
Thus, using a coolant for pneumatic systems can be efficient.
In fact, it would be way lighter and compact, since 1 liter of water can be turned into 1500 liters of water, the coolant would result in the same thing. With a smaller and thus, lighter pressurized tank.
The issue is: coolant gases can be very expensive in high quantities (and nobody sells R-11 anymore, which would be the ideal coolant for this, since it boils at 23ºC [which would allow for liquefaction at room temperature by using radiators]).
For some F*CKing reason, all of the online sales for gas coolants only shows the weight, not the pressure, nor liters.
There are fluids that boil at ambient temperature, but all of them are either flammable or toxic or both.
The displacement of a single filament of high displacement hexagonal pneumatic muscle with 0.25 cm² of area would be around 4.91 cm³ (I will round it up to 5 just for the sake of simplicity).
Volume of a Cylinder Calculator
So, 100 times less pressure than 10 bar, requires 100 times more air = 500 cm³. Which would be 0.5 liters maximum.
So, 0.5 liters x (((4 bundles for biceps and triceps in each arm + 12 bundles in each shoulder)x5 times more muscles for 3000 kg force) + 6 bundles on torso + (12 bundles in both legs + 8 bundles on each foot)x15 more muscles for 9000 kg force) = 193 liters of air in total.
0.5(((4+12)5)+6+((12+8)15)) = 193
A conventional bicycle tire compressor compresses 15 liters of air per minute with 60 watts with a maximum 250 Psi of pressure.
Thus, I would need around 15 of these, requiring a maximum of 15 x 60 = 900 watts.
Compressed air loses pressure when you open it, requiring more air to compensate. Assuming double the pressure, thus, double the air flow, finally, double the energy consumption = 1800 watts = 2.4 horsepower.
That is for one actuation only on the entire body with all muscles actuating at once.
1800 watts x 10 hours = 18,000 watts = 64,800,000 joules or around 1.5 liters of gasoline.
There is something wrong…
If you add the numbers to a horsepower calculator, or 1000 kilogram-meter of torque times 300 rotations per minute = 314.2 kilowatts = 421.3 horsepower
I must be miscalculating something… And I can’t figure out what. Even if you replaced the thing for hydraulics, the result wouldn’t change much…
Now I’m McFucking losing it my guy.
Wait, I did use a cylinder volume calculator, what if I use a rectangle 5mm by 5mm by 5mm?
… It gave 0.125 cm³ of volume, around 5 times lower volume than the previous calculation. Resulting in 5 times less energy required. Or 0.6 horsepower.😐
Actually, the force output of each individual cell wouldn’t be added. However, if it was a single long hexagonal filament muscle, then it would have this output force.
And the distance of contraction wouldn’t change, so it would only lift a few millimeters, so you would need to increase the distance of contraction proportional to the distance of contraction.
So I would need to have thousands of parallel filaments to compensate for the distance.
So: 3000 kg / 2.5kg of force per filament = 1200 parallel filaments.
1200 parallel filaments x 200 cubes per 1 meter of filament x 0.125 cm³ = 30,000 cm³ or 30 liters of air.
Increasing its pressure from ambient pressure (100 KPa) by 0.1 bar (10 KPa) would require 3 liters of air, or 33 liters in total.
NOW we are talking.
You can’t break the laws of physics.
So, taking the first equation again:
33(((4+12)5)+6+((12+8)15)) = 12,738 liters of air.
Of course, that is assuming that all muscles actuate at same time at maximum capacity, which wouldn’t happen.
4 to 5 less liters in total, so 3,184.5 to 2,547.6 liters PER ACTUATION.
Assuming 4 to 5 actuations per second, then:
3184.5 liters x 60 seconds = 191,070 liters per minute of airflow.
Taking a conventional bicycle compressor: 191,070 LPM / 15 LPM = 12,738 12,738 compressors x 60 watts = 764,280 watts or 1019.04 horsepower.
Taking a proper 95% efficient diaphragm air compressor could reduce the energy input to around 9 times, or 84,920 watts or 113 watts.
… But that is one third of the value, then it should be around that value also.
764.2 kilowatts / 314.2 kilowatts = 2.43220878421
So, 100% efficiency / 2.43220878421 = 41.1% efficiency
Thus, the 95% efficient air compressor would have an increase in efficiency around 2.3 times maximum. And as such, decrease the energy cost from 764.2 kilowatts to 332.2 kilowatts or 443 horsepower.
Even so, you would need 12,738 times the airflow of that 60 watt compressor, which may be a really daunting task.
… Or maybe not:
The first fan has 1000 CFM at 200 watts, the second 420 CFM at 42 watts,
I keep posting these pictures everywhere in the document (like, 3 times), but 1000 CFM = 28,316 liters per minute.
I asked chatGPT:
“Conventional fans (like a typical 1000 CFM model) are designed to move large volumes of air at low static pressures. In practice, such fans usually develop only on the order of 0.25–0.5 inches of water column (in H₂O) of static pressure—roughly 60–125 Pa (0.06–0.125 kPa). This is far less than a few kilopascals (1 kPa = 1000 Pa).
In other words, a “few kilopascals” is about 10–20 times higher than what you’d normally see from a conventional fan in HVAC applications. Only specialized, high–static–pressure designs (like some centrifugal blowers) can generate pressures on the order of 1–3 kPa.
For example, many HVAC systems specify fan performance in terms of inches water gauge. A conventional fan rated at 1000 CFM might be measured at around 0.15–0.5 in H₂O, which converts to roughly 37–125 Pa—demonstrating that conventional fans are low–pressure, high–volume devices.
Fan Basics: Air Flow, Static Pressure, and Impedance
The 3 Fan Laws and Fan Curve Charts | HVAC Know It All “
200 watts x 100 times more pressure = 20,000 watts 191,070 LPM / 28,316 LPM = 6.74777510948
20,000 x 6.74777510948 = 134,955.5 watts
… Now I’m confused again since the perfect case scenario with 100% efficiency would be 764 kilowatts…
I went for another and:
7000 CFM = ~ 200,000 LPM
10 kpa / Static pressure 4 pa = 2500 2500 x 7.5 horsepower = 18,750 horsepower = 14,062,500 watts
More realistic, but still terrible.
10,000/540 = 18.5
24000 m³/h = 400,000 LPM
3 kw x 18.5 = 55.5 kw
What am I doing wrong…?
Pneumatic Cylinder Airflow Calculator
According to this calculator, I would need 0.0003 LPM for a single 5x5x5mm cylinder (let’s pretend it is the hexagonal muscle) in order to actuate 1 time per second.
3000 kg / 2.5 kg = 1,200 parallel actuators 0.0003 x 1200 = 0.36 LPM for a single actuator 0.36x(((4+12)5)+6+((12+8)15)) = 138.96 LPM
I didn’t add the force, which would need to be around 0.1 more times more liters per minute, since air is compressible.
138.96 x 1.1 = 152.856 LPM
I guess it would be easier to calculate and predict by using hydraulics…
This one says I would need 3 liters for a 5x5x5mm cylinder at 0.1 bar pressure with a force of 0.25 newtons.
30,000 newtons / 0.25 newtons = 120,000 parallel muscles 120,000 x 3 liters = 360,000 liters 360,000 x 60 seconds = 21,600,000 LPM 21,600,000x(((4+12)5)+6+((12+8)15)) = 8,337,600,000 LPM 8,337,600,000 LPM / 400,000 LPM of the fan mentioned above = 20844000 20844000 x 3.3 kilowatts = 68,785,200
I would need to take into consideration the extra 200 muscles for the 1 meter long filaments, but at this point, it is just insane.
What I’m gonna do is pretend that the cylinder in the filament muscles is a flat, wide, telescopic cylinder that has a stroke length of 30cm with X bar of pressure and 1 meter of length.
Like this.
So: 0.25 cm² of area x 200 = 50 cm² This would be a circle, and thus, a cylinder with 79.79mm of diameter.
With an actuation velocity of 2 m/s, 300mm of stroke I would need 600 LPM and a total volume of 1.5 liters.
600 LPM x (((4+12)5)+6+((12+8)15)) = 231,600 LPM of fluid flow in total assuming using fluids (incompressible).
With 10 bars using fluids, this one would output 600 kg of force. At 60 Bars, 3000kg. At 180 bars, 9000kg
If I were to mass 3D-print this muscle, I would try to make something like in the image below. Then break it where I need, plug in the holes and attach a rope.
With 0.1 bar, a single flat telescopic muscle would output 50 newtons (5kg) of force.
If it is using pneumatics: 3000 kg / 5 kg = 600 actuators required 600 actuators x 600 liters per minute of fluid flow = 3600 LPM 3600 LPM x (((4+12)5)+6+((12+8)15)) number of actuators in the mech = 1,389,600 LPM Assuming that I’m using that ducted fan mentioned previously:
138,960,000 LPM / 400,000 LPM = 347.4 extra fans 3.3 kilowatts x 347.4 extra fans = 1146.42 kilowatts.
That is, assuming all of the actuators actuate at same time, but since ¼ to ⅕ of them wouldn’t even be working, then you could reduce the total energy required to around 250,000 to 200,000 watts.
Well, before I used too much RPM value, that’s why it stayed in 765,000 watts for the electric motor, but if you just recall it in the electric motor part, I modelled them to be in the 100kw to 300kw range for human-speed velocity. So this is still inside that mark. I bet that the inefficiencies related to hydraulics and pneumatics (such as heating when compressed) and the fan not being 99% efficient is going to increase the energy cost.
Now you can change from telescopic cylinders to the hexagonal muscles and that’s it.
In any manner, I don’t think that a single super wide telescopic hexagon muscle pulling 600kg is that reliable.
I would need to find a sweet-spot between those thin filaments and its wide counter-part.
The first pressing issue, however, is that there is absolutely no way that I can solve the problem of the airflow.
347.4 f*cking extra fans! One of those is 80cm wide!
Even though it is doable, how the hell will I transport 138,960,000 liters per minute of air without a gigantic windmill?!
50,000,000 CFM
This one has 1 million CFM Source: Axial fans | Chart Industries
I mean, I know that you don’t actually need to move 50 million CFM, only that you need a certain amount of air to move at that speed. But how do you convert liters per minute of fluid flow to meter second?
Well, you would need this calculator:
First I need to calculate the specific amount of air that needs to be moved, then the cross-section of the pipe.
And now that I thought about it, I did something wrong.
I used the “(((4+12)5)+6+((12+8)15))” thingie. It has 5 and 15 instead because it was the number based on a specific set, but I oversaw that.
The actual number of muscles would be “4+12+6+((12+8)3) = 82” because the legs would need to be 3 times stronger than the arms.
So, for the pneumatic 0.1 bar:
3000 kg / 5 kg = 600 actuators required
600 actuators x 600 liters per minute of fluid flow = 3600 LPM
3600 LPM x 82 = 295,200
295,200 x 1.1 bar = 324,720 LPM
So, the fan uses 3300 watts for 400,000 liters per minute at around 540 pa.
So: 10,000/540 = 18.5
18.5 x 3.3 kw = 45,833 watts
Now I’m confused again…
600 lpm for a 50cm² area cylinder with 80 mm of diameter and 300mm of stroke.
at 0.1 bar = 5kg of force
3000/5 = 600
600 LPM x 600 actuators = 360,000
360,000 x 82 actuators = 29,520,000 LPM
29520000 / 5 (since not every muscle will contract) = 5,904,000 LPm
5,904,000 / 400,000 = 14.76
14.76 x 3.3 kilowatts = 48,700 watts = 36 horsepower.
Also, using the issue of the ropes being at an specific angle and lowering the overall strength even more: 36 x 5 = 180 horsepower = 135,000 watts
Taking the pressure the fan produces: 560 pascals
Since 0.1 bar = 10,000 pascals / 560 pascals = 17.8571428571
17.8571428571 x 36 hp = 642.8 hp in total or 482,142
Again…?
29,520,000 LPM x 5 due to rope angle / 400,000 LPM of the industrial fan = 369
369 x 3.3 = 1217.7 kilowatts in total
Well, inputting 3000kg at 2 m/s in a kinetic energy calculator gives around 6000 joules.
joule second = watt second
So the maximum absolute efficiency of this system would consume 6000 watts?
I tried again:
300 kilowatts x 82 actuators = 24,600,000 watts = 32,800 horsepower
600 LPM x 600 actuators = 360,000
360,000 x 82 actuators = 29,520,000 LPM
29,520,000 lpm / 400,000 lpm = 73.8
73.8 x 3.3 kilowatts = 243.54 kilowatts = 324.72 horsepower.
Since 0.1 bar = 10,000 pascals
10,000 / 560 = 17.8571428571
17.8571428571 x 324.72 = 5,798.57 hp in total
If you take the fact that ropes suffer 5 times more tensiel strength around 170º degrees of angle, then you would need 5 times more energy:
5,798.57 x 5 = 28,992.8
Obviously, both values would be different anyway due to differences and inefficiencies, but the pneumatic one should at least be slightly higher than the second equation; An actuator that requires less horsepower to rotate a mechanical arm with 400 horsepower seems to break the laws of physics to me, but I don't know what I did wrong...
Maybe this slight difference is due to differences in different laws of physics being used? One is about fluid physics, for example. And both of the systems are simplified versions.
But… Even if you don’t have the cable into consideration. It would still be just 5,798 horsepower…
Even if you doubled the pressure with the fan to keep everything from losing pressure, it would still be too low.
Well, I asked ChatGPT and DeepSeek to attempt to calculate how much a cylinder with 57mm of diameter, 100mm of travel, 0.1 bar of pressure, 25 newtons of output force with both compressor and actuator with 95% of efficiency and both agreed in similar numbers around 3 joules.
So, assuming I want to lift 30,000 newtons (3 tons), I would get:
30,000 / 25 = 1200 parallel cylinders (not necessarily arranged as fibers/filaments).
1200 x 3 joules = 3600 joules.
That for a single actuation of a single actuator.
1 / 5 = 0.2 or 5 actuations per second.
3600 x 5 = 18000 joules
18,000 joules x 60 seconds x 60 minutes = 6,4800,000 joules = 18,000 watt-hours.
18,000 wh x 82 actuators in total = 1,476,000 watt-hours
1476000 / 5 since not every actuator will be working = 295,200 watt-hours.
Still too little energy, something must be amiss.
Maybe that’s not the issue, maybe it is something like electro steam:
Even though the efficiency of converting water to steam electrically is 99%, the amount of heat that it makes is completely based on the amount of heat it can absorb and carry, so it ends up requiring waaay more energy than electric motors.
I’ve found the culprit: the calculator itself
I tested other calculators and they gave at least 1000 times smaller numbers than the one I used.
So, with the new results:
Assuming 0.25 cm² of area with a diameter of around 0.56 cm, 10,000 pascals of pressure and 50mm of stroke length, I would have 0.0009 liters per cube, 0.19 newtons of force and 1.6493 liters per minute of fluid flow to make it actuate at a linear speed of 1.4 m/s.
30,000 newtons / 0.19 newtons = 157,894.8 cubes in total 157,894.736842 / 200 cubes per meter = 789.5 parallel filament artificial muscles.
157,894.8 cubes x 1.65 liters per minute = 260,526 liters per minute of airflow for a single bundle of filament artificial muscles to contract.
260526 x 82 bundles = 21,363,166 LPM 21,363,166 LPM / 5 since not all muscles would be actuated at same time = 4,272,633.288 LPM
4,272,633.288 LPM / 400,000 LPM of the industrial fan = 10.68158322 3.3 kw x 10.68158322 = 35,249 watts.
How…?
ChatGPT & DeepSeek said:
“The error comes in when you try to “convert” that force into a rotating lever system. In that step you appear to have taken the instantaneous force (or the speed of free air expansion) and applied it as if the cylinder could continuously deliver the full static force at a very high angular velocity. In reality, the cylinder’s energy is limited by its stroke—force multiplied by the stroke length—and the piston can only move so fast. When you then use this to calculate torque and RPM, you’re effectively “creating” extra power that isn’t there.”
10 kpa at 350 watts and 850 lpm
200,000 lpm / 850 = 235.294117647
350 x 235.294117647 = 82,353 watts. Still lower than 300 kw…
Probably this is a sign that I should just give up on this project.
Everything that I calculate is incorrect…
I just wish someone with actual expertise could give me a hand.
When asking around I still didn’t get the answer, but someone suggested taking the volume of the initial state and subtracting it by the volume of the compressed state. On top of that, they also suggested doubling that value since in pneumatics you can only apply a constant force if the actuator is fully actuated. From the initial flow of air to the final state, the air works like a spring being released.
So, again, assuming 5mm of width, 5mm of length and 50mm of height when expanded, 5mm when contracted I would have:
- Actuated: 1250mm³ Rectracted: 250mm³ Volume Calculator
- 1250mm³ - 250mm³ = 1000mm³ 1000mm³ = 0.001 liters
- 0.001 liters x 1.1 bars (if I multiply by 0.1 bars it will decrease volume even though you are adding 0.1) = 0.0011 liters
I asked ChatGPT just to be sure:
“We can solve this using the ideal gas law under the assumption of an isothermal process. In a fixed-volume container, the pressure is directly proportional to the number of moles of gas. In other words, if you add a certain fraction of the initial moles, you increase the pressure by the same fraction (assuming temperature is constant).
Let’s assume that initially the container is at atmospheric pressure, approximately 101.3 kPa. The ideal gas law tells us:
n = P·V/(R·T)
If the container’s volume is V = 0.001 L and you want to increase the pressure by ΔP = 10 kPa, then the additional moles you need are proportional to ΔP. In fact, the fractional increase in moles is
Δn/n = ΔP/P₍atm₎ = 10/101.3 ≈ 0.0987.
If you’re adding air at atmospheric pressure (101.3 kPa), then the volume of air (at atmospheric conditions) that supplies these extra moles is given by the same fraction of the container’s original volume:
V_added = V × (ΔP/P₍atm₎) = 0.001 L × (10 kPa/101.3 kPa) ≈ 0.001 L × 0.0987 ≈ 9.87×10⁻⁵ L
So, you need to add approximately 9.87×10⁻⁵ liters (about 0.1 mL) of air at atmospheric pressure to increase the pressure by 10 kPa in a 0.001-liter container.”
- 0.001 liters + 0.0000987 = 0.0010987 liters Which would be the same thing as multiplying 0.001 x 1.1 = 0.0011 liters
- So, converting this to a pneumatic cylinder by taking the area of 25mm² and taking the diameter of what that would be: 5.642mm of diameter. Area Calculator
- Using the correct cylinder calculators: 0.25 newtons Piston Cylinder Pressure and Diameter to Force Calculator Pneumatic Cylinder Force Calculator
- So, assuming parallel actuators in a 1 meter long filament fiber: 5mm/1000mm = 200 actuators
- 200 actuators x 0.25 newtons = 50 newtons = 5 kilograms
- 200 actuators x 0.0011 liters = 0.22 liters to fully actuate all 200 actuators.
- Like I said before, you need to take into equilibrium the pressure vessel and the actuators. IF you have 2 chambers, one with high pressure and another with lower pressure and open a valve connecting both, you will get an equilibrium. So, 0.22 liters x 2 = 0.44
- 3000 kilograms of actuation force / 5 kilograms of actuation force by the actuators = 600 parallel filaments
- 600 parallel filaments x 0.44 liters = 2640 liters
- Even though the actuators can lift all of this weight, they are in parallel, thus, you need to increase their length to compensate for the lack of actuation length/stroke. Assuming that the actuation is around half of the length of the pneumatic cylinder, around 25mm, I would need: 100mm of travel / 25mm = 4 200mm of travel / 25mm = 8
- Thus, 2640 x 8 = 21,120 liters per minute.
- fan with 400,000 liters per minute with 560 pascals and 3.3 kilowatts 10,000 pascals / 560 pascals = 17.8571428571 3.3 kw x 17.8571428571 = 58.928 kilowatts
- Since pneumatics needs to stay in equilibrium, I need to multiply it by 2 58.928 x 2 = 117,856
- 400,000 / 21,120 liters per minute = 18.9393939394 times less energy
- 117,856 watts / 18.9393939394 times less energy = 6,222.7 watts
Even though I did everything right this time, it still got 6 kilowatts… If I apply this muscle with 3000kg of actuation strength to a lever with the load arm 3 times longer than the effort arm, it will lift something with a force of 1000kg. Given that a mechanical arm moving at 300 RPM and 10,000 newton meters, it would require 300 kilowatts.
Just now I received answers from people in physics forums and the like.
They also reached the same result of around 6000 joules.
But the expansion of the actuator would make that super fast, faster than 300 rpm.
Wouldn’t that mean that I’m breaking the laws of physics?
I asked ChatGPT and DeepSeek agreed that I’m not breaking the laws of physics…
But wait a minute, I’m confused because the air is working like a spring.
Then I should use the math (aka asking ChatGPT/DeepSeek to do it for me) for a spring.
“No—it doesn’t violate any physical law. A lever with a 3:1 mechanical advantage simply “trades” force (or torque) for displacement. In our example, the compressed spring stores about 736 J of energy (using:
E=21FmaxX,
with 𝐹 max ≈ 29 430 F max ≈29430 N and 𝑥 = 0.05 x=0.05 m). When you use a lever that multiplies the force (or torque) by 3, the output angular displacement is proportionally reduced so that the total work done (torque multiplied by angular displacement) remains equal to the 736 J stored in the spring. Also, when people refer to “several hundreds of kilowatts,” they’re talking about power—that is, energy delivered per unit time. If you release 736 J very rapidly, the instantaneous power (in kilowatts) can be high, but the total energy remains limited to 736 J. In short, mechanical advantage and rapid energy delivery don’t create extra energy—they just change how that energy is applied. Conservation of energy is fully respected, so no laws of physics are broken”
I was just being stupid, it seems I’m actually correct…?
This may also be relevant for electrical motors…
I always calculated them as using their energy constantly, not in a few bursts of contraction, like in this case.
So… I need 6,222.7 watts to fully actuate a single muscle continuously… Which won’t continuously actuate…
So hydraulics and pneumatics are viable…
Well, my apologies, but I won’t be working with these actuators anymore.
I did have the intention of 3D modeling every idea I had for the joy of it, but I’ve been procrastinating for 5 months now.
So I’ve decided to simply skip all other ideas and focus on just one.
And in this case, I’m focusing on electromagnetic artificial muscles.
Well, I tried to focus on electromagnetic coils and I ended up procrastinating anyway.
So I should at least give this a try.
… Do I…?
Source:The Research on Soft Pneumatic Actuators in Italy: Design Solutions and Applications
You can just mold the artificial muscles as the shape of a sphere, I just used the origami as an easier way of calculating the force and fluid flow required.
Just shape the spheres to dimensions similar to what I calculated and that’s it.
The only difference is that you would need to make a spiral instead of spheres in series.
You/I can use an extruder die for that.
DIY CLAY EXTRUDER HOLLOW DIE- create a hollow die for making tubes
Timothy Pottery Clay Extruder Die Making
Clay Pottery Extruder Hollow Dies
Handle Extruder + Dies - Top Pottery Tools
Well, the least I can do is attempt on 3D model an extruder die within the dimensions I previously calculated the hexagonal bellow:
Guess what? I couldn’t do it either, the 3D model gets all messed up no matter what I toggle.
And there goes all the little confidence I had on finishing this project…
Now it worked for some reason. Partially, because for some reason² when I tried to make a higher resolution version it got weird too.
Oh. Now I get it.
In any manner, I think the best course of action would be to 3D print the spiral, then make a mold out of silicone rubber, remove the plastic and then extrude.
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