**5. Discussion**

The obtained numerical results, depicted in Figure 7, allow us to underline the effectiveness of the proposed design algorithm for the considered case of study. Namely, it is considered a biomedical application, where the gear train will operate with very slow and accurate motions. It is worth noting that the main source of dynamic excitation of the geared transmission systems comes from the variability of the meshing stiffness at operating conditions. Consequently, small variations of STE, and thus small values of peak-to-peak (p-p), represent a desired outcome of the design procedure for the considered gear pair.

As reported in the literature [19], reasonable levels of TE peak-to-peak depend on the specific application of the geared system. Two gear pairs that differ in size or in shape can be compared in terms of noise and vibration performance if their STE are expressed in μm [19]. Large values of STE p-p would be permissible on large, slow-speed geared machinery, where the gear noise usually does not represent a significant problem. At the ultra-precision end, a TE of 1 μm p-p could be considered as extremely good.

Focusing the attention on Table 2, the peak-to-peak TE values increase with the applied load, because of the increasing of tooth bending. The highest value is about 73.10 μrad. If the latter is multiplied by the pinion's pitch radius, as reported in Table 1, the maximum peak-to-peak value is obtained at about 0.24 μm. Hence, this value confirms a good vibrational performance and the designed gear pair can be considered as suitable for the specific application for the transmission system of the EasyLap robotic system, where high precision and small footprint are prescribed.

Future developments of the presented algorithm could include:


A 3D printed prototype is shown in Figure 10. This prototype has been successfully mounted at the wrist of the EasyLap operating arm. Figure 11 shows the sterilizable component of the adaptor for standard laparoscopic instruments using the designed couple of small size bevel gears.

**Figure 10.** 3D printed prototypes of the bevel gear pair elements.

**Figure 11.** 3D printed adaptor for traditional surgical instruments using this gear pail.
