## 4 Application
### Empirical Predictive Models  
The last step for fully solving the vector loop equations is to determine the resulting joint clearance \(c_{ij}\) for the clearance vector \(\vec{c_{ij}}\) and the geometric deviation of the linkages \(L_{j}\), respectively their tolerances, to consider the influence of the process parameters on the motion accuracy of the regarded mechanism by _empirical predictive models_ (see Section 3.2). For determining the most significant parameters influencing the accuracy of 3D-printed mechanisms, preliminary studies were conducted. Findings coincide with related researches concerning this topic, as the build orientation along the Z-axis, the layer height, the seam style and the part's geometry have a major impact on geometric deviations of 3D-printed parts [15, 43]. As a result, the following process parameters and a varying part geometry are considered for gathering the training data (see Figure 8). Further process parameters, viz. extrusion temperature, extrusion speed and ambient temperature are predefined as they are automatically chosen by the used FDM machine Stratasys F370 itself for the used material ABS and thus cannot be varied or controlled by the operator. The part geometry, viz. the size of pin and hole and the linkage length also plays a major role and must therefore be taken into account for gathering the training data. Hence the nominal geometry of the parts is varied in the DoE using the highest, the smallest and a mean value of the linkage lengths presented in Table 1. For gathering the training data for the predictive models, following parameters and factor levels were chosen for the full-factorial DoE (see Table 2). Figure 8: Schematic representation of the considered process parameters and the part geometry for manufacturing non-assembly mechanisms via FDM. Figure 7: Resulting joint forces for one revolution of the 8-bar mechanism simulated in MSC ADAMS for joint clearance \(c=0.4\) mm. After 3D-printing a total number of 288 test specimens according to the defined DoE, including 12 repeat tests and non-destructively removing the support structures, they were digitalised by a GOM ATOS 12M scanner and the geometric deviations are determined using GOM Inspect software. For evaluating the geometric part deviations, three part characteristics were measured, the diameter of pin and hole to determine the resulting clearance and the axis of the linkages to determine the dimensional length deviation, that is, the tolerance values. In total, 288 data points for each training data set were acquired and stored in.csv-files, which are subsequently used as the input values for training the predictive models. Figure 9 shows examples of the 3D-printed non-assembly test specimens after printing before the support structures were dissolved non-destructively in a subsequent cleaning process. Before the test data is suitable for training the predictive models, the data is randomised. This randomisation is based on a random swapping of the input variables and is particularly advisable when using full-factorial DoE since the parameters are mostly sorted mathematically and thus approximations are always determined for certain data groups but not for the entire testing space [37]. Due to their good model adaption, GP and SVM were chosen as ML techniques since they provide a suitable method for the prediction of geometric part deviations resulting from the FDM process, especially for smaller data sets [44]. For building up the predictive models, the functionality of MATLAB 2019a was utilised. After the input variables have been defined, the training data is randomised according to a predefined distribution. In this process, 20% of the training data is kept out in order to subsequently evaluate the forecast quality of the models based on the calculation of the CoP. The predictive models are then generated based on the training data set. For the application, two different predictive models are required.