## 2 Materials and Methods
### Experimental Setup and Design  
#### 2.1.1 Identification of Relevant Control Element Parameters  
To investigate how the control elements can be adapted to VR, a workshop with drillers and experts in usability and VR identified factors that could influence positioning accuracy, time required for positioning tasks, user experience, and workload. Drillers control the drilling process on offshore rigs and are experts in operating joysticks and rotary controls. Table 2 lists the identified factors that were examined in this study. In addition, the experts defined value ranges in which the factors vary. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameter** & **Recommended Value** & **Recommended Value** \\  & **[PERSON]**[36] & **[PERSON]**[35] \\ \hline Diameter & 40–50 mm & \(\geq\)30 mm \\ Number of detent pos. & 25–35 & 8–24 \\ Torque & 30–40 mNm & 200–700 mNm \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Recommendations for the design of rotary controls. The **angular resolution** factor describes the sensitivity of the rotary control. With an angular resolution of 5\({}^{\circ}\)/value (\(-\)), the rotary control must be turned by 5\({}^{\circ}\) such that the value displayed on the screen changes by 1. The **inclination** of the control element describes the angle between the control element and table (refer to Figure 2: inclination 0\({}^{\circ}\)). Rotary controls with knurling, without knurling (cylinder), and with toggles were tested. In addition, the **diameter** of the control elements was varied. \begin{table}
\begin{tabular}{c c c c} \hline \hline  & **Factor** & \(-\) & \(+\) \\ \hline \multirow{4}{*}{**Sampling**} & \multirow{4}{*}{**Sampling**} & Angular resolution & 5\({}^{\circ}\)/Value & 45\({}^{\circ}\)/Value \\  & & Diameter & 20 mm & 110 mm \\  & & Inclination & 0\({}^{\circ}\) & 90\({}^{\circ}\) \\  & & Shape & Knurling/Toggle/Cylinder \\ \hline \multirow{4}{*}{**Sampling**} & \multirow{4}{*}{**Sampling**} & Max. angle of deflection & 10\({}^{\circ}\) & 45\({}^{\circ}\) \\  & & Max. positioning & 2.5\%/s & 12\%/s \\  & & speed & Size \\  & & (vertical/horizontal) & 15/7 cm & 32/17 cm \\  & & Angular resolution & 3-Stage & linear \\  & & Visual feedback & Yes & No \\  & & Shape & Vertical & Horizontal \\ \hline \multirow{4}{*}{**Sampling**} & \multirow{4}{*}{**Sampling**} & Haptic feedback & Yes & No \\  & & Acoustic feedback & Yes & No \\ \cline{1-1}  & & Hand visualization & Yes & No \\ \cline{1-1}  & & Position of the & Sitting & Standing \\ \cline{1-1}  & & participant & VR environment & Table & Crane \\ \cline{1-1}  & & Input device used & HTC Vive & Valve Index \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Identified factors that could influence the operation and subjective perception of users. Figure 1: Overview of the methodological approach. The maximum **deflection angle** was varied to examine the joystic. For example, the joystick could be deflected forward or backward by a maximum of 45\({}^{\circ}\) (+) from the zero position (perpendicular to the table). The factor **max. positioning speed** describes the maximum possible rate of change in the maximum deflection of the joystick. The factor **angular resolution** describes the ratio of the deflection angle to the change in the displayed value of the bar graph. With a linear angular resolution (+), the change in the positioning value is proportional to the deflection angle. With a three-stage angular resolution (-), three angular ranges are defined, in which the change in the positioning value is the same. A joystick with a vertical handle (cf. Figure 2. left) and a joystick with a horizontal handle, such as that used as an aircraft thrust lever, were tested. The **size** of the joystick was tested on three levels. In addition to the extreme values shown in Table 2, a medium size was tested (vertical: 23.5 cm; horizontal: 12 cm). In addition, the **visual feedback** was varied.