# Grasp Analysis for the Robot-Based Manipulation of Pre-Assembled Cables with Electrical Connectors
## 3 Methodology
### Contact Modeling and Grasp Force Estimation
Therefore, it is evaluated whether the opposite of the external disturbance lies within the GWS. If this is the case, the grasp can withstand this external disturbance [11]. Fourth, the required grasp force for a given external disturbance is estimated for each surface pair inspired by [33]. For this purpose, the GWS is built for a grasp force of 1 Newton (N) as a basis. For each WP, the associated cable wrench and further wrenches (e.g., the mating force at the end of the task) are referenced to the EC coordinate system (see Figure 5), and superimposed. Each of these WPs is then evaluated individually. Inspired  
Figure 5: Example of a high-voltage plug ([[https://www.te.com/deu-de/product-4-2103015-1.html](https://www.te.com/deu-de/product-4-2103015-1.html)]([https://www.te.com/deu-de/product-4-2103015-1.html](https://www.te.com/deu-de/product-4-2103015-1.html)), accessed on 9 February 2023). Its CAD data (left) is used to derive different surface pairs, as shown in the middle (surface pair 1) and on the right (surface pair 2). On the left, the convention of this work for the coordinate system of the plug of the EC (white, EC) and the cable-connector-interface (orange, CCI) are shown. by [10, 33, 34], if the opposite of the external disturbance does not lie within the GWS, the latter is scaled until this is the case. In order to scale the GWS, its intersection with the external disturbance has to be calculated. The GWS is bounded by several surfaces. Figure 6 shows a visualization of the GWSs of the two surface pairs introduced in Figure 5.  
A single surface of the GWS is defined by a six-dimensional surface normal and its distance from the origin. For each of these surfaces, the scalar product is used to check whether it is intersected by the external disturbance. For each intersection, the proportion of the external disturbance is determined at which it intersects the surface. For the surface with the smallest proportion, the reciprocal of this proportion represents the scaling factor of the GWS. The external disturbance now reaches exactly to the boundary surface of the scaled GWS. The corresponding required grasp force can then be derived from the scaled GWS. After determining the required grasp force for every surface pair and every WP, the course of the required grasp force over the trajectories can be depicted. With this course, a user has the main information to decide on a gripper basis and a surface pair. In addition, adjustments to the trajectories can be carried out if avoidable load peaks result from the cable deformation. Figure 6: Exemplary representation of the convex hull of the GWSs of surface pair 1 (black) and surface pair 2 (blue) of the EC shown in Figure 5 with respect to the coordinate system EC, a grasp force of 1 N, and a friction coefficient of 0.5. For visualization purposes, (**a**,**c**) show the force components \(F_{x}\), \(F_{y}\), and \(F_{z}\) of the six-dimensional GWS projected into the three-dimensional space. Analogously, (**b**,**d**) show the projection of the three torque components \(T_{x}\), \(T_{y}\), and \(T_{z}\).