## 3 Results and Discussions
### The Results Obtained for the Five Point-Generating Trajectories  
We started from the generating mechanism from Figure 11. The ABM-generating element (Figure 19) was further added, an element jointed with AB. The MD element is connected by a rotation joint in M, describing a circle through D. The arrows indicate points that trace circles. These circles  
Figure 16: Aesthetic image (k = 120).  
Figure 17: Aesthetic image (k = 270).  
Figure 15: Aesthetic image (k = 90).  
Figure 18: Aesthetic image (k = 300).  
are the trajectories generated by the five driving elements articulated in the driving joints A, B, C, D, and M.  
Computer simulations were performed for the trajectories generated by the mechanism of Figure 19. The research regarding the mechanism trajectories was made for different values of the geometric parameter--the angle k. A single variable design, the geometrical parameter defined by the angle k of the rhombus ABCD, was considered.  
In Figure 20, we show the image obtained for k = 60 degrees, which is much more complex than the one in Figure 5. It can be seen that the image in Figure 20 has 19 circles of equal radius and 30 petals resulting from the intersection of the circles. In Figure 21, the successive positions of the rhombus and the BM element are presented, and in Figure 22, the MD side from Figure 19 is also presented.  
Figure 27: Image for k = 70.  
Figure 28: Aesthetic image for k = 90.  
Figure 25: Aesthetic image for k = 30.  
Figure 26: Aesthetic image for k = 45.  
Figure 27: Image for k = 70.  
Figure 28: Aesthetic image for k = 90.  
The images shown in Figures 20 and 23-31 were also generated using a Gwbasic program, created for the mechanism given in Figure 19, based on the mathematical relationships (6-10). For example, the program for generating the image given in Figure 20 is presented in Appendix A.  
From the presented results it can be observed that the gear mechanism with five trajectory-generating elements is capable of generating an identical image to the Flower of Life with 19 circles, as shown in Figure 20. We also obtained images similar to the Flower of Life, such as those in Figures 14 and 25. They look like flowers with circular corolla and have geometry based on repetitive elements, such as the Flower of Life petals, but differently arranged. Furthermore, we can observe that the mechanisms proposed in the work can generate other images with complex geometry, with symmetry, with beauty, and with many repetitive elements, which is promising for aesthetic purposes.  
In the newly created mechanisms, there are several variable parameters, so that the families of images formed based on several circles arranged according to certain rules can be obtained. Several trajectories were simulated, by the variation of a single geometrical parameter of the mechanisms--the angle k of the rhombus ABCD. For both mechanisms, with four and five trajectory-generating  
Figure 31: Image for k = 270.  
Figure 29: Aesthetic image for k = 120.  
elements, at small values of the angle k of the rhombus mechanism (k = 10, k = 20), images with more complex geometry resulted. Also, by comparing the images obtained with the mechanisms in Figures 11 and 19, the mechanism with several trajectory generating elements (the case of the five-point trajectory-generating mechanism) could draw more complex images, with a very large number of circles. The research can be extended, for example, by changing other variable geometric parameters of the mechanisms and thus interesting geometry images can be obtained.