## 2 Materials and Methods
### Design of the Adaptive Clamping Device  
The presented schemes of the clamping situation and the gap measurement (see Figure 1a) must be implemented in a single setup with the force measurement and the mechanical actuators (see Figure 1b) to obtain an adaptive clamping device for laser beam welding in butt joint configuration. This requires both mechanical engineering and automation engineering to ensure all functionalities and to enable the manipulation of the process by means of a closed-loop control. The design of the system is shown in the following. Figure 2 shows the fixture design as complete rig with six-axis robot and processing head in perspective view. The clamping device allowed to weld samples with a length up to 500 mm in butt joint configuration and different sheet thicknesses up to 3 mm. The fixed clamping of sheet 1 by clamping jaws 3 was realized by two pneumatic Festo linear swing clamps CLR-25-20-L-P-A, each one realizing a clamping force of approx. 230 N at 6 bar of air pressure. The chosen design ensured a determined clamping situation without using a continuous bar as single clamping jaw. In contrast, clamping jaw 4 was designed as a continuous bar to ensure the movement of sheet 2 in the y-direction while limiting the movement in z-direction to 0.1 mm. It should be noted that the moveability of sheet 2 was limited to the y-direction only if the actuators and load cells were connected to it, otherwise the sheet can move freely in the x-y plane. The continuous bar also protected sensors and actuators against spatters from the welding process. The top view shows the arrangement of sensors and actuators along sheet 2. Sensors and actuators were color-coded based on the schematic figure in Section 2.2. The uniform distribution along the sheet ensures information about the entire weld seam length. In the context of this paper, the sensor positions were implemented in the positions given in Section 2.2 for welding sheets with a length of 300 mm but can be further relocated to other positions for realizing welds up to 500 mm in length. Figure 1: Schematic figure of the clamping situation and position of sensors and actuators (dimensions in millimeter): (**a**) Gap measurement via inductive probes IP1-3; (**b**) Linear actuators LA1-2 and force measurement via load cells LC1-2. An exemplarily detailed view on sensor and actuator integration is provided by Figure 3 for inductive probe IP2 and linear actuator LA1 with the associated load cell LC1. A prismatic centering in a V-groove ensured the position of each inductive probe along x-direction due to its rotationally symmetric housing. A clamp joint set the position in y-direction that enabled the measurement of the inductive probes against the sheet edge position utilizing a connector clamped to the sheet edge. The measured displacement is representative for the resulting joint gap in the butt joint [15,16]. The movability of the sheet in the y-direction was ensured for this purpose which is why a gap of 0.1 mm between clamping jaw (c) and sheet (d) was realized. Each linear actuator was lined up with a linear guide and a load cell which is shown for LA1 and LC1 in Figure 3. The linear guide was based on a plain bearing and acted as connecting element between linear actuator and load cell. The load cell was screw joint to the linear guide and an additional connecting element that contained two thrust screws with thrust heads that created a force-fit joint between sheet (d) and the linear actuator and the load cell. The connection between sheet (d) and the sensors and actuators limited its moveability in x-direction. Figure 2: Design of the adaptive clamping device in perspective and top view. Figure 4 shows the realized adaptive clamping device in the laser welding setup. In addition to the design shown before, a high-speed camera (see Section 2.1) was included to provide further information on the forming gap between both sheets and to prove the validity of the clamping concept (sheet 1) fixed, sheet 2) moveable in y-direction).