## 2 Design of Pneutrunk Module  
As can be seen in Figure 1, the redundant manipulator PneuTrunk is a cascade type manipulator constructed out of parallel platform modules ordered in series. The number of modules depends on the required degrees of freedom. One module, shown in Figure 2, consists of two duraluminium plates connected by an universal joint and three evenly spaced pneumatic bellows. The tilt angles between the top and the bottom plates are measured by two potentiometric rotation sensors, placed in such a way that the axis of the universal joint is colinear with both axes of the sensors and the \(y\) sensor axis is always  
Figure 1: CAD model of PneuTrunk.  
parallel to the bottom plate and the \(x\) sensor axis is always parallel to the top plate. The pneumatic actuators are off-the-shelve Dunlop 2 3/4 \(\times\) 3 bellows. The pressure in the pneumatic bellows is controlled by three separate electro-pneumatic pressure controllers SMC ITV1050-31F20. In our experience, these controllers have little lag and no discernible overshoot. All tubing is of inner diameter of 6 mm to eliminate the effects of tubing diameter on the dynamic behavior of the bellows. The module is controlled by a B&R PLC type 4 PPC70-0702-20B and was programmed using B&R Automation studio version 4.9.  
The maximum operating pressure for one bellow is 7 bar, but to prevent damage to the system and especially the universal joint, the allowable pressure range is set to 0-5 bar. The \(x\)-axis is oriented towards the center of one bellows. The asymmetric layout of the bellows with respect to the axes \(x\) and \(y\) in combination with the mechanical limits of the bellows themselves, causes the rotational extremes around both axis to be different, as can be seen in Table 1.  
It is expected that the module will be driven only by positive pressure. This has important implications when designing the control algorithm for such a device. While the extension of one bellows is facilitated by simply supplying pressure, compression is achieved by applying external forces that predominantly originate from the extension of one or both remaining bellows. This fact is also the reason why the minimum number of pneumatic bellows is three. Coincidentally, because the module only has two degrees of freedom, this design is inherently overactuated. This causes one posture of the module to be reachable by an infinite number of bellows input pressure combinations and, in theory, giving the system the ability to change its stiffness without changing the posture. This was taken into account when designing the control algorithm for one module.  
The flow of information and energy is visualized in Figure 3. The whole system is simple and contains only the necessary components. It could be argued that adding a center closed 2/2 valve between each bellows and its corresponding electropneumatic pressure controllers could give the system the ability to pneumatically lock the bellows extension, improving the systems positioning performance. Unfortunately, this would also complicate the system and its regulation, introducing other challenges and distracting from the aim of this paper.  
\begin{table}
\begin{tabular}{c c c} \hline \hline  & **Tilt [deg]** & **Tilt [deg]** \\ \hline axis & min & max \\ y & \(-\)24.4 & 16.6 \\ x & \(-\)21.2 & 20 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Tilt extremes.  
Figure 2: One module of the manipulator PneuTrunk and top sketch of the module. Letters G, B, Y denote the center-points of the bellows.