3.1. The test bench

The station is composed of a 1200 × 1000 × 400 mm rectangular table supported by a frame made of aluminum profiles. The Omron TM5-700 cobot (6 joints; payload 6 kg; reach 700 mm; repeatability ±0.05 mm) and a 400 × 400 × 10 mm aluminum ground plate (surface roughness 0.6 $\mu$ m) were rigidly fixed on the table (Fig. 2(a)). The plate has 169 holes (85 reamed holes for $\phi$ 5 h7 dowel pins and 84 M5 threaded holes) spaced by 30 mm (±0.05 mm), according to a square matrix (Fig. 2(b)). Reamed holes aim to refer to the nominal position of the workpieces to be machined to the center of the base of the cobot; the threaded ones are for assembling the workpieces on the plate (Fig. 2(c)) that simulates the printing plate. In the current study, the expected adhesion of the workpieces to the printing plate was neglected and replaced by the screws, which act as a fixed constraint.

Figure 2. The robotic station: (a) overall view; (b) detail of the aluminum ground plate with reamed (yellow) and threaded (blue) holes; (c) detail of an assembled workpiece to be machined.

With reference to Fig. 3, the developed end-effector (overall mass of 1.605 kg) supports the (1) powered device Dremel® 3000 (maximum rotational speed 33,000 rpm; mass 0.410 kg) for the activation of the (2) HSS cylindrical contouring tool (diameter 6 mm, 16 cutting edges), and a set of three (3) miniature strain gauges load cells HT Sensor Technology TAL 220B (capacity 5 kg; accuracy 0.05% of full scale; rated output 1.0 ± 0.10 mV/V; power supply 3–10 Vdc) with (4) amplifiers Avia Semiconductor HX711 (24 bit ADC; sampling frequency 10–80 SPS; selectable gain 32, 64, and 128; power supply 2.6–5.5 Vdc). Load cells measure the cutting force components along the X, Y, and Z directions. The end-effector structure is made of several parts in steel: (5) for fixing the end-effector to the wrist of the cobot, (6) for the axial support of the tool and the load cells, and (7) for radial support of the tool. An Arduino UNO board (resolution 8 bit; 14 digital input/output; 6 analog inputs; power supply 5 Vdc) acquires the load cells’ signals.

Table I. Material’s bulk mechanical properties in FEAs.

Figure 3. The prototype of the developed end-effector: (a) front view; (b) right view; (c) left view.

3.2. The mechanical design of the end-effector

To check the functionality and the proper stiffness of the conceived end-effector, the mechanical design was supported by finite element analyses (FEAs) developed in the Ansys Workbench® 2024 R2 environment. The 3D geometry of the end-effector was realized by the 3D CAD software Siemens Solid Edge^TM and exported into the FEM code. The modeled parts of the end-effector are the structural elements in steel, the load cells in aluminum, and the axial and radial supports in PLA. All the components are modeled as isotropic materials with the mechanical parameters reported in Table I. Although 3D-printed PLA exhibits anisotropic behavior due to the layer-by-layer manufacturing process, it was modeled as an isotropic material with average bulk mechanical properties [Reference El Mehtedi, Buonadonna, Carta, El Mohtadi, Marongiu, Loi and Aymerich18]. This simplification is commonly adopted in preliminary structural analyses to reduce computational cost, especially when the loading conditions do not induce significant stresses along the weak interlayer direction. Moreover, the parts were printed with 100% infill density to ensure the most homogeneous mechanical behavior. While this approach does not capture the full anisotropic behavior of printed PLA, it provides a reasonable approximation for the global structural response within the scope of this work.

The following settings were adopted in the model: automatic meshing with element size less than 3.0 mm (118,241 nodes and 71,389 elements), acceptable since an average skewness of 0.28; all tetrahedral elements; a fixed constraint at the flange attached to the wrist of the cobot (green-colored Fixed Support as shown in Fig. 4(a) to fix all nodes preventing motion); X, Y, and Z components of a concentrated remote force (simulating the cutting force) acting at the tip of the cutting tool (colored force vectors F, Fig. 4(a)) applied as a ramp force in the range (−4.0 to 4.0) N in the simulated time interval 0–1 s; a mass of 0.410 kg concentrated at the center of gravity of the Dremel (yellow point m, Fig. 4(a)); gravitational effects was included (standard earth gravity); bonded contacts among the load cells and the structural parts to represent the parts as rigidly connected, preventing any slip or detachment, while also reducing computational cost; nonlinear analysis by the Newton–Raphson method; auto time stepping controlled by the program. The applied forces are higher than the current experimental ones, as shown in Section 4. Several simulations were conducted to evaluate the total displacement for different values of the remote force components. Examples of the total displacement results are shown in Fig. 4(b) (F_x = −4.0 N, F_y = 4.0 N, and F_z = 0.0 N), and Fig. 4(c) (F_x = −2.0 N, F_y = 3.0 N, and F_z = 2.0 N). The maximum values of the deformation equal to 0.036 and 0.071 mm are comparable with the cobot repeatability (±0.05 mm), confirming that the end-effector stiffness is suitable for the purpose.

Figure 4. The numerical model of the end-effector: (a) mesh, fixed support (in green), remote force components (colored arrows F), and concentrated mass (point m in yellow); (b) the resulting total displacement in [mm] for F_x = −4.0 N, F_y = 4.0 N, and F_z = 0.0 N; (c) the resulting total displacement in [mm] for F_x = -2.0 N, F_y = 3.0 N, and F_z = 2.0 N.

3.3. Ground plate calibration

The ground plate calibration was necessary to find the current spatial orientation of the plate, refer its position to the cobot base reference system, and modify the 3D CAD model to adapt the tool path. The center of the ground plate was placed within the cobot workspace, slightly far from its boundary surface, at 500 mm from the center of the base of the cobot, along the -Y reference direction. An end-effector made of a mechanical dial test indicator (measurement range 0-10 mm, resolution ±0.01 mm) and its support (Fig. 5(a)) was assembled and mounted at the wrist of the cobot. Hence, by a procedure required by RoboDK® (Fig. 5(b)), three points of the upper surface of the plate were detected to build a virtual plane corresponding to the existing one. Finally, by manual control of the cobot, the coordinates of all the centers of the holes of the plate were acquired and imported into Solid Edge^TM and RoboDK® to create the virtual plate equipped with all the holes and referred to the cobot reference system.

Figure 5. The plate calibration procedure: (a) detail of the dial test indicator for detecting significant points; (b) detail of the RoboDK® interface for the plate calibration.

3.4. TCP calibration

The self-learning procedure [Reference Siciliano, Villani and Oriolo32] in TMFlow^TM identifies the TCP coordinates. It consists of positioning the center of the contouring tool’s lower surface in six poses and maintaining contact with the same object at the same point. The tip of a pin rigidly mounted in the center of the ground plate was used as the object. The software defines the position of the TCP with respect to the robot flange to compensate for it in subsequent movements. This phase is fundamental to ensure that the contouring machining tasks are not compromised. Fig. 6(a–f) shows the six points acquired. Later, the local reference system (placed at the center of the wrist of the cobot) was rotated to be aligned with the cobot reference system. Finally, the goodness of the calibration was verified by rotating the cobot around the TCP, demonstrating its stability without relative motion between the tip of the pin and the center of the contouring tool (see Video S1). Results are reported in Table II and added in RoboDK® for the tool path planning.

Table II. TCP calibration results.

Figure 6. TCP self-learning procedure: (a) first pose; (b) second pose; (c) third pose; (d) fourth pose; (e) fifth pose; (f) sixth pose.

3.5. Mechanical decoupling of the load cells: the cross-talk check

The load cells’ mechanical assembly and decoupling were evaluated before the cutting tasks were executed. Forces along the X–Y–Z directions were acquired by loading the contouring tool in the +X, −X, +Y, −Y, and +Z, −Z directions. Loads were manually applied by a laboratory spring dynamometer. The results, plotted in Fig. 7, show how the load cells are mechanically decoupled. For a maximum load of ±6 N along X, maximum force components of ±0.19 N along Y and ±0.38 N along Z were detected. Instead, for a force of ±7 N along Y, maximum force components of ±0.42 N along X and ±0.44 N along Z were detected. Finally, for a force of ±6 N along Z, maximum force components along X and Y of at most ±0.45 N and ±0.29 N, respectively, were detected. A not-perfect alignment of the dynamometer could justify the force components along the perpendicular directions of the applied force during the test execution. Results revealed that the unexpected forces are lower than 7.5% of the applied ones. For this reason, the three load cells were considered mechanically decoupled, with negligible cross-talk. Hence, the three-load cell system was considered suitable for the purpose.

Table III. Cutting parameters adopted in the experimental activity.

Figure 7. Cross-talk between load cells by loading: (a) the first cell along +X and −X direction; (b) the second cell along +Y and −Y direction; (c) the third cell along +Z and −Z direction.

4.1. Evaluation of the surface roughness

Surface roughness measurements were carried out using the Leica M205A stereo zoom microscope, which provides optical magnification ranging from 7.8x to 160x and high-resolution imaging (around 1 µm). Average surface roughness values were extracted using the Leica Map®, which allows for the calculation of standard roughness parameters from the images obtained by a stereo microscope and provides accurate visualization of the surface morphology, as shown in Fig. 9. Raw workpieces show an average roughness (R_a ) of about 23 $\mu$ m. Hence, preliminary tests were conducted to evaluate which climb or up-cut contouring machining mode could improve the surface roughness. Fig. 9 shows the results for two tests conducted at ω, f _rate and c _depth equal to 33,000 rpm, 4 mm/s, and 0.4 mm, respectively. The best resulting surface roughness is 110.04 $\mu$ m for the climb contouring and 6.43 $\mu$ m for the up-cut contouring. The latter provides the best surface finishing, as found in the literature [Reference El Mehtedi, Buonadonna, Carta, El Mohtadi, Marongiu, Loi and Aymerich18], and was then adopted as a contouring machining mode in the following. The extracted surface’s height (y coordinates) was measured along the profile (x coordinates) shown in blue in Fig. 9. The examined profiles are reported in the same figures.

Table V reports some surface roughness values achieved from the twelve contoured surfaces for different combinations of the cutting parameters. The highest roughness value is 6.43 $\mu$ m for c _depth and f _rate equal to 0.4 mm and 4 mm/s, while the lowest is 1.52 $\mu$ m for c _depth and f _rate set to 0.1 mm and 1 mm/s. The last combination was adopted for machining the profiles.

Table V. Up-cut contouring roughness results for different combinations of cutting parameters.

Figure 9. Roughness results. Surface color map, 3D view of the extracted surface, and the examined profile for (a) climb contouring and (b) up-cut contouring.

4.2. Evaluation of the cutting forces

The load cells described in Section 3.1 acquired cutting forces during each test. The behavior of the forces is shown in Fig. 10, while the maximum forces along the X, Y, and Z axes are reported in Table VI to enhance the result clarity. The maximum measured value of one force component is about 1.0 N; the maximum absolute value of the force is about 1.1 N. The latter is lower than the adhesion force between the printing plate and the workpiece [Reference Płaczek33], suggesting that the proposed contouring machining robotic task avoids the detachment of the workpiece from the printing plate. Moreover, the maximum absolute value of the force is lower than the payload of the cobot. This item demonstrates that a cobot, more cost-effective and compact than an industrial robot, is a valid device within a new generation of large 3D printers. The higher f _rate and c _depth result in higher cutting forces because the single tooth of the tool must remove more material per unit time. The cutting forces on the planar machined surfaces are constant since the c _depth is kept constant. However, there are increases or decreases, especially at the beginning or end of contouring, due to the presence of more or less material to be removed, respectively. As expected, the cutting force along the Z-direction is almost zero due to the peripheral contouring task. In the same direction, a force of at most 0.1 N is recorded for a c _depth of 0.4 mm, as the tool teeth also lightly work in front contouring.

Table VI. Maximum cutting force for different cutting parameter combinations in X, Y, and Z directions.

Figure 10. Cutting forces during tests for the c _depth of: (a) 0.1 mm; (b) 0.2 mm; (c) 0.4 mm.

A modal test was performed to verify the main factor that allows achieving a low-vibration environment by identifying the natural frequencies of the machining system. Specifically, a SIEMENS SPM50 SCADAS system was employed to acquire signals from the modal hammer (ENDEVCO MODEL 2302-5, sensitivity 1.14 mV/N, frequency range up to 8 kHz) and the triaxial accelerometer (TLD356A32, sensitivity 10.2 mV/m/s², measurement range ± 50 g, frequency range 1 ÷ 4000 Hz). The frequency response function was obtained by exciting the system along the X, Y, and Z directions, using an impulse excitation provided by the instrumented hammer, and measuring the acceleration on the end effector: five averages for each FRF were used. The resulting dynamic compliances are shown in Fig. 11(a).

Figure 11. (a) X (blue solid line), Y (black solid line), and Z (red solid line) dynamic compliances as a function of frequency; (b) PSD of accelerations for a contouring task with c _depth = 0.4 mm and f _rate = 4 mm/s.

The Power Spectral Density (PSD) of the accelerometer signal was analyzed during contouring operations under the most critical conditions, with a c _depth of 0.4 mm and a f _rate of 4 mm/s. The dynamic compliance is quite low above 300 Hz. Furthermore, the modal density (the number of modes in a frequency band) is also low, and the resonant peaks are well damped. This ensures that the vibrations of the end effector will remain low if the excitation spectrum is above 300 Hz, as expected for this machining operation. This is confirmed by observing Fig. 11(b), which shows that the excitation frequency associated with the specified contouring task is around 474 Hz.

In addition, Fig. 12 shows the behavior of the joint angles over time at the maximum c _depth value (0.4 mm) and several f_rate values. Cutting forces do not generate joint vibrations (see details of some joints in the [0, 2] s time window in Fig. 12), showing that the overall stiffness of the cobot is suitable for the expected task. This experimental evidence confirms that the cutting operations are far from resonance peaks, thereby preventing vibration amplification. As a result, the system maintains stable dynamic behavior, directly contributing to achieving a smooth surface finishing with low roughness, as illustrated in Fig. 9.

Figure 12. Cobot’s joints for c _depth = 0.4 mm and f _rate: (a) 1 mm/s; (b) 2 mm/s; (c) 3 mm/s; (d) 4 mm/s.

4.3. Validating contouring machining tests

The toolpath planning procedure was improved to compensate for the mismatch between the workpiece’s nominal and current dimensions and orientations. To overcome this issue, a code was developed in the TMFlow^TM environment to adapt the planned tool path to the real workpiece. The code algorithm expects a first step in which the robot moves to where the workpiece is placed (following the RoboDK® script file instructions). Hence, with the integrated robot 5MP color camera, the robot recognizes the position and orientation of the workpiece in the X–Y plane and adapts the planned tool path to the current orientation. Then, by a touch-stop operation, the robot vertically moves along the Z-axis to identify the workpiece’s current height, adjusts the Z height of the planned tool path, and moves the contouring tool to the starting point of the overall adapted tool path.

Figure 13(a,b) show the stage when the cobot is recognizing the orientation of the workpiece and when it is recognized, respectively (see Video S3). The blue arrows indicate the current positioning and orientation of the workpiece, and the red arrows refer to the nominal ones. A detail of the touch-stop operation is shown in Fig. 13(c).

Figure 13. Contouring trajectory compensation: (a) vision job during the orientation recognition of the workpiece; (b) vision job of the recognized orientation of the workpiece; (c) a detail of the touch-stop operation.

Three representative workpieces with circular, dodecagon, and curvilinear profiles were adopted to validate the contouring machining tasks. Fig. 14 shows the CAD model and the tool path (in green) with the relative recorded cutting forces and the joint angles of the cobot. Each test was conducted at a f _rate set to 1 mm/s and c _depth equal to 0.1 mm. The forces are consistent with those expected from the previously described tests: each force component is within the range ±0.3 N. The angular positions of the joints show that no vibrations are induced in the joints. The dimension measurement demonstrated the effectiveness of the tasks.

Figure 14. Validating test results. Workpiece geometry, cutting forces, and cobot joint angles for different profiles: (a) circular; (b) dodecagon; (c) curvilinear.

4.4. Discussion and comparison with related works

The developed end-effector was tested to validate no cross-talk between the load cells, allowing for independent cutting force measurement along the X, Y, and Z directions. Accurate calibration of the plane and TCP ensured precise tool alignment between simulations and real-world paths. Additionally, contouring operations were adapted to the current position and orientation of the workpiece using vision jobs and touch stops. The absence of observable vibrations in the cobot joints (Figs. 11, 14) provides experimental evidence of the cobot’s mechanical stability during contouring tasks. In the same way, Fig. 12 demonstrates that the modal density and the dynamic compliance along X, Y, and Z, around the excitation frequency (around 474 Hz) during the contouring task, are relatively low. This indicates that the end-effector exhibits sufficient damping and avoids resonance within the frequency range excited during machining. This behavior confirms that the end-effector and the cobot have enough stiffness for contouring operations. If the end-effector or cobot joints lacked adequate stiffness, the experimental data would be expected to show increased surface roughness or noticeable force oscillations. Since no such effects were observed, the tool can be considered effective and reliable for the intended application.

To evaluate the effectiveness of the proposed system, a comparative analysis was conducted with recent studies involving CNC machines, industrial robots, and cobots in machining operations, as summarized in Table VII. In ref. [Reference Lalegani Dezaki, Mohd Ariffin and Ismail17], a CNC machine was employed to process PLA material, like the approach adopted in this study. Although this work achieved a lower surface roughness of 0.36 $\mu$ m compared to the 1.52 $\mu$ m obtained in this study, the system presented here is more cost-effective, compact, and flexible. This topic highlights a significant trade-off between surface quality and system complexity. Studies refs. [Reference El Mehtedi, Buonadonna, Carta, El Mohtadi, Marongiu, Loi and Aymerich18, Reference El Mehtedi, Buonadonna, El Mohtadi, Loi, Aymerich and Carta19] also investigated CNC milling of PLA, but the cutting parameters and tools adopted led to surface roughness values of approximately 2.10  $\mu$ m, higher than those achieved with the proposed system. These results reinforce the effectiveness of the present approach, which performs favorably even when compared to more established CNC technologies working on the same material. In ref. [Reference Iglesias, Sebastiàn and Enrique23], an industrial robot was adopted for various manufacturing tasks, including cutting, contouring, and drilling. However, the study does not report quantitative data regarding cutting forces or surface roughness, which limits direct comparison with this work. The study focuses more on the robot’s operational versatility rather than its precision or stability. In the same field, a comprehensive literature review [Reference Makulavičius, Petkevičius, Rožėnė, Dzedzickis and Bučinskas25] discusses the limitations of using industrial robots in certain machining operations, particularly regarding the material removal rate. Other studies have employed cobots in different machining contexts. For instance, ref. [Reference Perez-Ubeda, Gutiérrez, Stanisic and Lluch-Cerezo24] presents milling operations on resin-based materials, while ref. [Reference Yuzhang. and Qingsong26] investigates the use of a cobot for polishing steel. In the latter, a force control system was implemented to ensure accurate path tracking over complex geometries, demonstrating advancements in adaptive contact-based processes. In the present study, the use of vision-based and touch-stop compensation allowed adjustment of the tool path according to the current position and orientation of the workpiece, an approach rarely addressed in the literature. Combined with a rigid and mechanically stable end-effector, these strategies enabled low-vibration operations and consistent surface quality under low-force conditions typical of polymer machining. Overall, the proposed system distinguishes itself in performance and balanced adaptability, accuracy, and cost integration. This approach effectively bridges the gap between high-end CNC machines and more accessible robotic solutions for contouring 3D-printed MEX components.