## 3 Results and Discussion
### Results of the Analysis of Moments in the Kinematic Pairs of the CPM Positioner  
In order to research to optimise the links of a CPM multibody mechanism using the Generative Design method, it is necessary to divide the mechanism into individual links, which are then optimised as separate components. The input parameters for such studies, in addition to knowledge of the geometry, are of course the values of the forces or moments and other constraints to be taken into account in the optimisation. To determine the parameters to be used for the simulation in Creo Parametric, a preliminary study of the dynamics was carried out using the Rigid Dynamics toolbox of ANSYS Workbench. Analyses included kinematic pairs \(A^{\prime}\), \(B^{\prime}\), \(C^{\prime}\), \(D^{\prime}\), and \(E^{\prime}\). They involved determining the values of the moments in each pair, in the \(X\), \(Y\), and \(Z\) axes, during the working movement of the mechanism in ROM. Figure 6 shows the results of determining the values of the torques in the \(X\), \(Y\), and \(Z\) axes of the kinematic pair \(A^{\prime}\) in ROM. Only the maximum values of these torques will be important from a Generative Design optimisation point of view. These investigations determined the following maximum values: in the \(X\)-axis, the maximum torque is 2.7042 \(\times\) 10\({}^{-14}\) Nm; in the \(Y\)-axis, it is 8.0357 \(\times\) 10\({}^{-14}\) Nm; and in the \(Z\)-axis, it is \(-\)1.0565 \(\times\) 10\({}^{-14}\) Nm. The maximum value of the total moment, in this case, is 2.8503 \(\times\) 10\({}^{-8}\) Nm. The results obtained indicate that the kinematic pair in question does not practically transfer the torques induced by the motion of the drive link connected to the actuator. Figure 5: Results of the kinematics analysis of the \(E^{\prime}\) kinematic pair (position, velocity, and acceleration in a range of motion) and the graphical representation of the path of movement. Figure 7 shows the results of determining the values of the torques in the \(X\), \(Y\), and \(Z\) axes of the kinematic pair \(B^{\prime}\). These tests determined the following maximum values: in the \(X\)-axis, the maximum torque is 68.788 Nm; in the \(Y\)-axis, it is 1.0039 Nm; and in the \(Z\)-axis, it is 59.215 Nm. The maximum value of the total moment in this case is 90.691 Nm. Figure 8 shows the results of determining the torque values in the \(X\), \(Y\), and \(Z\) axes of the \(C^{\prime}\) kinematic pair. These tests determined the following maximum values: in the \(X\)-axis, the maximum torque is 68.117 Nm; in the \(Y\)-axis, it is 5.4788 \(\times\) 10\({}^{-2}\) Nm; and in the \(Z\)-axis, it is 8.6341 \(\times\) 10\({}^{-14}\) Nm. The maximum value of the total moment, in this case, is 68.791 Nm. Figure 6: Graphs of torques in the X-, Y-, and \(Z\)-axes in \(A^{\prime}\) kinematics pair in a range of motion. Figure 7: Graphs of torques in the X-, Y-, and \(Z\)-axes in \(B^{\prime}\) kinematics pair in a range of motion. Figure 9 shows the results of determining the values of the torques in the \(X\), \(Y\), and \(Z\) axes of the \(D^{\prime}\) kinematic pair. Through these tests, the following maximum values were axes of the \(D^{\prime}\) kinematic pair. Through these tests, the following maximum values were determined during the movement of the mechanism, i.e., in the \(X\)-axis, the maximum torque is 65.596 Nm; in the \(Y\)-axis, it is 54.671 Nm; and in the \(Z\)-axis, it is 7.2349 \(\times\) 10\({}^{-14}\) Nm. In this case, the maximum value of the total torque is 66.023 Nm. The knowledge about these torques is in addition to optimising the links of the CPM motion apparatus. It also makes it possible to determine the parameters of the pins connecting links 2, 3, and 4, which were omitted from the analysis when simplifying the geometry prepared for the numerical analysis. Figure 10 shows the results of determining the torque values in the \(X\)-, \(Y\)-, and \(Z\)- axes of the kinematic pair \(E^{\prime}\).