# How to calculate the dimensions of a McKibben actuator based on the force you want it to apply?

I intend on design and build a McKibben hydraulic muscle that can lift 5 tons by itself, it won't be attached to a human or anything like that.

I tried to search for methods to calculate the amount of force and pressures required for this type of soft actuator, but it seems these equations are too complex for me, because I couldn't get results besides error messages on the calculators.

I have the intention to build it with the following specifications:

• The artificial muscle will lift 5 tons.

• The amount of pressure inside the artificial muscles will range from 0.4 MPa to 1 MPa.

• The length I intend to make it 30 cm long, I do not know which will be the actuated length. But I will work under the assumption of 20% of contraction, since this is the most common percentage.

• I do not know the unactuated diameter/radius, but searching a little about McKibben actuators, I came to observe that normally these increase the diameter more or less in 30-40%

• The inner bladder and the outer expandable sleeve are meant to be made of Aramid fabric and fibers.

• Both connections in both ends of the soft actuator are meant to be made out of steel.

The hydraulic fluid will be conventional hydraulic oil with a density of 0.9 g/ml.

I tried equations I found on multiple articles and asked around for help, but no one was able to help me.

In this question on WorldBuilding an answer was given showing an equation with the answer that the artificial muscle should be 14cm in diameter and 30cm long.

However, when I tried said equation again with the same diameter/radius and got totally different numbers, the values in newtons were in the millions. The equation needs the values on KPa, millimetres and Newtons.

I tried the equation without the R (radius) value on a scientific calculator and the answer for the radius was ~4mm.

I don't know very well what I did wrong, but I do think that maybe the equation isn't quite right.

This equation was made on this online scientific calculator.

I just want to correct myself: the equation above is incorrect, but even though I made the correct equation later, it still gave me results totally different from the answer in the question I talked about (with newtons still on the millions).

• This gives you some idea: engineering.stackexchange.com/a/51311/10902 Dec 11, 2022 at 14:07
• @SolarMike My apologies, but that didn't give me any ideas. As the question says: I don't see how the force generated by a hydraulic cylinder can be used to calculate the acuation force of a McKibben membrane acuator. Dec 11, 2022 at 15:04
• It's a "lever"... you can make the actuation force as small as you like but other things get bigger in exchange. Basic mechanics... Dec 11, 2022 at 15:45
• @SolarMike I do not understand, how a Membrane Actuator is a lever? Could you write an answer explaining it? Dec 11, 2022 at 17:23
• $\sin$ and $\cos$ use radians, so you have to either convert the degrees into radians or use the degree option. That means the second calculation should be correct. Dec 13, 2022 at 20:12