# Studies regarding the Use of Pneumatic Muscles in Precise Positioning Systems
## 2 Materials and Methods
### Pneumatic Muscle Principle  
The pneumatic muscle is a system that involves the contraction of a membrane, and works on a principle similar to that of human muscle. It ensures movement by changing its geometric shape when placed under pressure. Consisting of an elastomer tube reinforced with aramid fibers (synthetic fibers), the pneumatic muscle contracts rapidly and exerts pulling forces when supplied with pressurized air. As compressed air enters the muscle, a traction force is developed that works along the longitudinal axis, and the muscle is shortened in proportion to the increase in the internal pressure. The contraction reduces the length of the muscle by up to 25% of the initial value in the unloaded state. The pneumatic muscle achieves a maximum force as soon as the contraction begins, with the developed force being zero at the end of the stroke. The working diagram of the pneumatic muscle can be seen in Figure 2b. According to [32], pneumatic muscles are able to reproduce movements that closely mimic the kinematics, speed, strength, and refinement of natural muscles. The characteristics of pneumatic actuators have been investigated by many researchers, and some research findings have been achieved. The dynamic model was proposed in [33], \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Value** \\ \hline Length & 100 mm \\ Diameter & 10 mm \\ Maximum working pressure & 8 bar \\ Axial contraction & Max. 20 mm \\ Force that can be generated & Max. 492 N \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Characteristics of the investigated pneumatic muscle. \begin{table}
\begin{tabular}{c c} \hline \hline
**Component** & **Characteristics** \\ \hline Pressure control valve with manometer & The pressure gauge displays the pressure in the pneumatic circuit within 0–10 bar \\  & Power supply 15–30 V dc \\ The analog pressure sensor & Analog output 0–10 V dc \\  & Pressure measuring range 0–10 bar \\ On-off directional valve & Pressure range 0–8 bar \\  & Maximum flow: 60 L/min (ANR) \\ Displacement sensor & Linear potentiometer, 200 mm stroke \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Components and characteristics of the experimental setup. Figure 2: Pneumatic muscle. (**a**) Picture; (**b**) working diagram. which included the processes of contraction upon inflation and deflation of a pneumatic actuator. In addition, the best fitting parameters were determined by utilizing the least square linear regression method in [34] to depict the hysteresis phenomenon. Similar work can also be found in [35]. Due to their construction, pneumatic muscles develop a nonlinear and hysteretic behavior. An example is the hysteresis of axial contraction-pressure dependence, which is presented in this research. The occurrence of the hysteresis phenomenon is well-known for pneumatic muscles, therefore, tracking the control performance of it is difficult. Some possible causes of hysteresis in the functioning of pneumatic muscles are friction between fibers, friction between fibers and rubber tube, conical deformation of the rubber tube at its end, and the stretching of rubber tube due to increased volume [26; 31]. The actuation of an artificial muscle is made by means of compressed air, which is introduced or extracted from it. Although it is possible to design a muscle to function in depression, in most cases, these actuators function in overpressure, according to [1] and [32]. This is because the compressed air supply is easier to achieve, and, on the other hand, much more energy can be transmitted through overpressure than through depression. Feeding a pneumatic muscle with compressed air allows it to move a load in a certain direction. Once the air supply is interrupted (it is removed from the muscles), the load is moved in the opposite direction (Figure 2b). The mode of operation of a pneumatic muscle can be observed by performing two experiments (Figure 3), according to [32; 36]. In both cases, the muscle is fixed at one end and a mass load (\(M\)) is attached to the other end.