# 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 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.

• I do not know the diameter/radius, nor the actuated diameter and radius.

• 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 the equations on this article on researchgate, but I only got negative numbers.

Example:

• ((π(4.97))²(100 ÷ 4 (sin(45))²))(3(1 - 0.11 ÷ 24)² cos(45)²2 - 1)
• -4412.77987695

I got some people saying (in other websites) that I should use the "FPA triangle equation" (the F = P x A or P = F ÷ A), but that are meant for solid hydraulic cylinders. I don't think it would apply for McKibben cylinders, though.

Basically, depending on what number you want to find (Force, Pressure or Area), you can use the equation "F = P x A" or "A = F ÷ P".

The problem is that it is a equation meant for hydraulic solid cylinders, not membrane actuators.

But I tried to use the area of the entire membrane, so I can somewhat calculate the force it will apply.

Accordingly to this cylinder area calculator, if I have a cylinder with 10cm radius and 30cm long, I will have a total area of 2513 cm2 (389.6 in²) applying 60 PSI (0,4 MPa), so I would have a force of 23340 pounds (10586,846 kg).

If it was 5cm radius 30cm length, I would have 1099cm² (170.3 in²).

F = P x A

10200 pounds (4626,6422 kg).

This is the force applied to the area, but the area is the membrane, right? How to translate it to lifting force?​