## Materials and Methods
### Image Analysis Software  
A semi-automatic software has been implemented in Matlab according to the following steps. 1. At first, it is important to find the Instant Center of Rotation (ICR) of the DUT comb-drive. Considering the image that corresponds to 0 V (both for OPS and for LTM systems), four point are manually selected (a, a', b, b' and c, c', d, d') on the edges of the comb-drive and the ICR has been found as the intersection of the two lines (Figure 6). 2. The second step regards the manual selection of a particular Region Of Interest (ROI) on the same image considered previously. The identified ROI is characterized by a particular pixel pattern, which is compared with subsequent images (that correspond to 2 V, 4 V,..., 28 V for OPS and 2 V, 4 V,..., 24 V for LTM) to identify where this pattern is located. This procedure is carried out through a template-matching algorithm, which identifies for each image the coordinates of the point corresponding to the center of gravity (COG) of the ROI. This point corresponds to one of the three vertices of the triangle necessary to identify the angular aperture of the device comb-drive. The comb-drive has a static part fixed to the structure of the MEMS device and a mobile part. The ROI has been chosen on the mobile part of the microgripper comb-drive (Figure 7). Figure 6: Two images of the microgripper comb-drive acquired by optical profilometer (a) and microscope (b), respectively. The first and second above described steps of the implemented software are the only ones in which the manual selection of an operator is necessary to properly select points on the images and the positions and dimensions of the ROI. The following ones have been automated. 3. As shown in Figure 8, the automatic part of the implemented software considers the coordinates of the following three points on the images: * The most distant point from the ICR on the fixed part of the comb-drive (a); * The ICR of the comb-drive (b); * The center of the ROI (c); The first two points remain fixed for all the following images, under the hypothesis of no deformation due to the movement of the comb-drive, while the only point, whose coordinates change for each considered image, is the center of the ROI. 4. These three points determine a triangle, where the vertex ICR corresponds to the angular opening \(\alpha\) of the comb-drive. With reference to Figure 9, points \(a\), \(b\) and \(c\) are considered to be the vertices of an isosceles triangle, where \[\alpha=2\arcsin\left(\frac{A}{B}\right)\] (1) with \(A=\frac{\overline{\alpha}}{2}\) and \(B=\overline{cb}\). Using a template matching algorithm, a match is found between the coordinates of the center of the selected ROI on the first image (i.e., that corresponds to 0 V supply) and on all the subsequent images. Through this operation the in-house software detects the new coordinates of the ROI center of gravity (ROIGC) for each subsequent image and therefore for each applied voltage. The ROIGC changes its coordinates and, consequently, it changes also the shape of the corresponding triangle and the angular aperture of the DUT comb-drive, depending on the different voltage supply. 5. The angular displacement is obtained from the comb-drive angular aperture at each voltage value. Figure 7: Manual selection of a particular region of the image (ROI), to find its center of gravity (COG) on OPS image (**a**) and on LTM image (**b**). The above described software can be used with any type of image. For example, in this study two sets of images have been considered, acquired by the optical profilometer and the light microscope, respectively. The limit associated with this type of analysis is that the procedure provides a first semi-automatic part, which must be carried out by the operator.