# Design and Control of a Pneumatic Muscle Servo Drive Applied to a 6-DoF Parallel Manipulator
## 2 Materials and Methods
### Comparison with Commercial Muscles  
For the purposes of pneumatic muscle research, a research setup was developed. A comprehensive description of it can be found in [1]. Below are the most important details and the appearance of the developed setup (Figure 2). The setup allows for conducting research on both a single muscle (4) and a pair of muscles working in opposition, connected by a toothed belt gear (3) with a pitch diameter \(dp=63.66\) mm. An absolute optical encoder (2) with a resolution of 16 bits per revolution is mounted on the setup. Additionally, the setup is equipped with Parker Tecno Plus pressure servo valves (5) for supplying the muscles with working fluid. Furthermore, the setup is equipped with two tensortic force sensors (6) with a range of 2 kN. To apply the desired force load to the muscles, the setup is equipped with an electric servo drive with a precision planetary gearbox. This drive allows for loading a single muscle with a maximum force of \(F=2.792\) kN. Using the described setup, a comparison was made between the developed pneumatic muscles and Festo's DMSP muscles. Models with similar nominal diameters were selected. Figure 2: Diagram and actual view of the research setup. To achieve this, a family of isobaric static characteristics was determined as the relationship between relative shortening and the force \(F\) generated by the muscle for various constant values of internal pressure \(p\). Figures 3 and 4 depict selected isobaric characteristics of the developed muscle and Festo's DMSP-20-120 muscle. Solid lines represent the characteristics of the developed muscle, while dashed lines represent the characteristics of the Festo muscle. A family of isometric characteristics was also determined, i.e., the relationship between the force \(F\) generated by the muscle and the internal pressure \(p\), for several constant muscle shortenings. Figures 5 and 6 depict the isometric characteristics of the developed muscle and Festo's DMSP-20-120 muscle. Solid lines represent the characteristics of the developed muscle, while dashed lines represent the characteristics of the Festo muscle. Analyzing the results presented in Figures 3 and 4, it was noticed that the maximum absolute shortening of the developed muscle at the operating point \(p=0.6\) MPa and \(F=50\) N is \(x=109.4\) mm, corresponding to a relative shortening of 31.28%. Meanwhile, the maximum absolute shortening of the Festo muscle at the same operating point is \(x=27.7\) mm, corresponding to a relative shortening of 23.08%. Comparing both muscles, it was observed that the difference between the relative shortening of the developed muscle and the Festo muscle varies from \(-1.19\)% to 13.21% depending on the operating point. Analyzing the research results presented in Figures 5 and 6, it can be noticed that the maximum force generated by the developed muscle at the operating point \(x=0\) mm, \(p=0.6\) MPa is \(F=1201.22\) N. Meanwhile, the maximum force generated by the Festo muscle at the same operating point is \(F=936.73\) N. The difference between the force  
Figure 4: Selected isobaric characteristics of the compared muscles in the range from 0.4 MPa to 0.6 MPa. Figure 3: Selected isobaric characteristics of the compared muscles in the range from 0.1 MPa to 0.3 MPa. generated by the developed muscle and the Festo DMSP-20-120 muscle varies from 6.88 N to 395.28 N, depending on the operating point. The above data favor the developed muscle. However, it was observed that the static characteristics of the proprietary muscle are more nonlinear than those of the Festo muscle. Furthermore, considering the internal construction of both muscles, it is expected that the Festo muscle will be more resistant to mechanical damage and have greater overall durability. However, the Festo muscle lacks one feature crucial for the mentioned application. The proprietary muscle can be pretensioned, meaning its shortening can reach a negative value. This will have a significant impact on the manipulator's design.