# How to calculate the torque of pneumatic rotary vane actuators?

In a development by Festo (BionicCobot), a rotary pneumatic actuator was used.

It is also similar to Kinetrol vane pneumatic actuators.

I have a question what is the formula for the torque of such an actuator depending on the pressure.

And are there any restrictions on the angle of rotation of such a drive?

I can't really answer any questions on the Festo as they're not showing much in the videos. The yellow fellah is much simpler.

I have a question what is the formula for the torque of such an actuator depending on the pressure.

Torque is force by distance so in this case I suspect that you'll have to do an integral. Let's assume that the vane has constant width, $$w$$, minimum radius, $$R_1$$ and maximum radius, $$r_2$$. Pressure is $$P$$ (and is force per unit area in your chosen units).

$$T = \int^{R_2}_{R_1}Pwr\ dr = Pw\int^{R_2}_{R_1}r\ dr$$

If my maths is correct so far this shoult work out as

$$T = \frac {Pw}{2}(R_2^2 - R_1^2)$$

And are there any restrictions on the angle of rotation of such a drive?

Yes. The yellow fellah is restricted to 90° as the vane will bump into the casting. The Festo unit will have similar restrictions.

• Are there any restrictions on the angle of rotation if you design a custom vane actuator? I mean that the actuator will work if its rotation angle is 270 degrees? Commented Apr 23, 2023 at 15:25
• None other than it can't go full ircle. It'd say that about 330° would be the max. Any further and you're making a motor. The most common application for these vane actuators is for rotating ball valves which only require 0° to 90° to go from fully closed to fully open. Commented Apr 23, 2023 at 15:40
• Ok, thanks. Commented Apr 23, 2023 at 15:50