Abstract
This study investigates the vibration damping properties of additively manufactured robotic arm components enhanced with optimized infill patterns and resin coatings doped with alumina and silicon carbide. Seven designs, including Voronoi, triangular, and square honeycomb structures at 1 and 2 mm scales, were tested. Modal analysis was performed to evaluate natural frequencies, damping ratios, and damping coefficients. Sample E demonstrated superior damping performance, with the highest damping coefficient (3.2 Ns/m) and ratio (0.18). Sample A represents the unoptimized solid baseline part, while Sample E corresponds to the 2 mm triangular honeycomb design. In contrast, Sample A exhibited the lowest values, indicating inferior vibration control. The Voronoi patterns showed the most significant weight increase post-coating due to their surface area, while triangular honeycomb designs balanced weight and damping performance. These findings highlight the effectiveness of combining advanced materials and designs to enhance robotic arm stability, precision, and longevity. The study provides valuable insights for optimizing robotic components for industrial applications requiring high performance and reliability.
Introduction
In the age of Industry 4.0, robotic arms have become essential tools for optimizing production processes, increasing accuracy, and reducing operational costs. Known for their precision and reliability, these arms are widely utilized in industries such as automotive, aerospace, healthcare, and consumer electronics, transforming assembly lines and driving advancements in automation (Barbosa et al., 2020; Papapaschos et al., 2020). Additive Manufacturing (AM), or 3D printing, has emerged as a key technology in the production of robotic arms, allowing for the creation of intricate geometries that traditional manufacturing cannot achieve (Al Rashid et al., 2021). This versatility allows robotic arm designs to be customized for specific needs, ensuring lightweight and durable performance. However, 3D-printed components often need further treatment to enhance mechanical properties and meet industrial standards (Kristiawan et al., 2021). Coating methods, like applying ceramic powders and resins, improve surface hardness, wear resistance, and longevity, enhancing both performance and durability of components (Attar et al., 2020). These coatings have the dual benefit of increasing the longevity of robotic arms and optimizing their performance through friction reduction and enhanced thermal stability (Agarwala et al., 1996; Nguyen and Lee, 2018; Solomon et al., 2021).
The choice of materials for AM is crucial, as it directly affects the performance and durability of robotic arms. Common materials include polymers like polylactic acid (PLA) and acrylonitrile butadiene styrene (ABS), which are favored for their ease of printing and cost-effectiveness, particularly in prototyping and low-weight applications. Advanced thermoplastics like polyether ether ketone (PEEK) and polyamide (PA) are used in more demanding environments due to their superior strength, chemical resistance, and thermal stability (Krimpenis et al., 2020). Additionally, metals such as titanium, aluminum, and stainless steel are utilized for their excellent strength-to-weight ratios (Costa et al., 2020). Composite materials that combine fibers like carbon or glass with polymers are increasingly popular for their rigidity and low weight (Mick et al., 2019). The careful selection of materials, customized for the unique requirements of robotic applications, plays a crucial role in enhancing the capabilities and dependability of additively built robotic arms (Prianto et al., 2022).
Coating robot arm components with ceramic powders and resin has been shown to significantly improve the performance characteristics of robot arms manufactured using additive manufacturing techniques (Shen et al., 2021). This strategy utilizes the inherent advantages of ceramic coatings, including exceptional hardness, resistance to wear, and thermal stability. These qualities are essential for prolonging the lifespan and ensuring the dependability of robotic arms under challenging operational conditions. Alumina (Al2O3), zirconia (ZrO2), and silicon carbide (SiC) are commonly used ceramic materials for coatings (Smirnov et al., 2022). These materials are chosen for their outstanding mechanical qualities and ability to withstand high temperatures and corrosive environments. In addition, the use of resin coatings, such as epoxy or polyurethane resins, offers an extra level of safeguarding by boosting surface smoothness, decreasing friction, and improving resistance to chemicals (Smirnov et al., 2023). These coatings serve the dual purpose of safeguarding the underlying material and enhancing the dynamic performance of the robotic arms by reducing vibration and suppressing undesired oscillations (Masuda et al., 2019). The utilization of ceramic powders and resin coatings greatly enhances the structural strength and operational effectiveness of additively made robotic arms, rendering them more appropriate for demanding and precise tasks in many industrial domains (Dudek, 2013).
Post-processing coatings applied to polymer parts produced by Fused Deposition Modeling (FDM) are commonly used to enhance surface quality, mechanical properties, and environmental resistance. Due to the layered nature of FDM, polymer parts often exhibit rough surfaces and mechanical weaknesses (Jiang and Kobayashi, 2005). Various coating techniques improve part performance, including primer, spray, electroplating, dip coating, and surface fillers. Common materials used are polyurethane, epoxy, nickel, chrome, and Teflon. These coatings reduce surface roughness and enhance appearance (Elumalai et al., 2024). As a result, post-processing coatings are a crucial step in achieving higher performance and longer lifespan, particularly for industrial and consumer products, thereby playing a significant role in the broader application of additive manufacturing technologies. Lattice structures used in FDM additive manufacturing, like octahedral, tetrahedral, Voronoi, cubic, diamond, gyroid, truss, honeycomb, Schwarz D, and rhombic dodecahedron, are valued for their lightweight, durable, and energy-absorbing qualities (Abou-Ali et al., 2022). Key design criteria for lattice structures include cell size, geometry, material selection, and infill density. These structures offer significant weight savings while maintaining mechanical performance, benefiting industries like aerospace and automotive (Aloyaydi et al., 2020). Optimization of these lattice structures is often achieved using advanced methods such as topology optimization and genetic algorithms, which refine the geometry and infill density to maximize performance under specific loading conditions.
The modal analysis and vibration analysis conducted on parts produced by FDM (Fused Deposition Modeling) additive manufacturing provide concrete findings while evaluating the dynamic properties and vibration damping capabilities of the parts (Palmieri et al., 2022). These studies were carried out using accelerometers and laser Doppler vibrometers to vibrate the parts at specific frequency ranges and measure their responses (Belter and Dollar, 2015). For instance, the first natural frequency of a part made from PLA material was determined to be 148 Hz, with a vibration amplitude of 0.048 mm at this frequency. After applying an epoxy coating to the same part, the first natural frequency increased to 169 Hz, and the vibration amplitude decreased to 0.029 mm. This change indicates that the coating process increased the vibration damping capability by 39%. Similarly, the first natural frequency of a part made from ABS material was found to be 130 Hz; after epoxy coating, this frequency increased to 145 Hz, and the vibration amplitude decreased from 0.052 to 0.033 mm, showing an improvement of 37%. When examining the damping ratios, it was found that the damping ratio for PLA parts increased from 0.02 in the uncoated state to 0.035 after epoxy coating, representing a 75% increase in damping ratio. For ABS parts, the damping ratio increased from 0.018 in the uncoated state to 0.032 after coating, showing a 78% improvement. In conclusion, the modal and vibration analyses of parts produced by FDM demonstrate with concrete data that coating processes significantly enhance the dynamic performance and vibration damping capacity of these parts (Chalgham et al., 2021). These findings provide critical information for developing more durable and efficient products in industrial applications (Nguyen et al., 2022).
The importance of vibration analysis in robotic arms is paramount for ensuring their precision, stability, and longevity (Alshihabi et al., 2025b; Badkoobehhezaveh et al., 2022). Vibrations can significantly impact the performance and accuracy of robotic arms, leading to motion errors, increased wear, and potential failure of components. For instance, a study on a 5-DOF long-reach robotic arm demonstrated that the first six natural frequencies ranged from 4.4 to 41.6 Hz, and managing these vibrations was crucial for maintaining operational stability and accuracy in farm applications (Li et al., 2022). The study utilized finite element analysis (FEA) and experimental modal analysis to emphasize the importance of vibration control in extending a robotic arm’s lifespan. Research on vibration prediction based on elastic joint dynamics modeling revealed that joint flexibility could lead to significant vibrations at the end effector, causing motion errors. A method combining the internal transfer function of the drive system with external excitation parameter identification demonstrated how effective vibration prediction and mitigation strategies enhance robotic reliability. Additionally, a six-axis robotic arm study highlighted the need for accurate vibration and noise measurement methods across different axes (Cernohlavek et al., 2023). These findings underline the importance of continuous monitoring and adjustment to maintain optimal performance across different operational scenarios. Composite structures made from resin and ceramic powders have diverse industrial applications. These composites provide enhanced mechanical strength, insulation, wear resistance, and thermal stability, making them suitable for demanding conditions (Cheng et al., 2022). Composite materials in robotic systems enhance durability and performance. Ceramic powders provide hardness and wear resistance, while the resin matrix adds flexibility. Epoxy resin composites with Al2O3 ceramic powders improve the lifespan of robotic joints and parts (Wang et al., 2023). The ceramic-reinforced resin coating was applied to enhance surface hardness, increase stiffness, and improve vibration damping by reducing amplitude decay times during modal excitation.
This study focuses on the experimental modal analysis of additively manufactured robotic arms enhanced with optimized infill patterns and coated with ceramic-reinforced resin. By examining their dynamic characteristics, including natural frequencies, mode shapes, and damping behavior, the research aims to support the development of more stable and reliable robotic arm designs for demanding operational environments. Although extensive work exists on AM components and coating-based performance improvement, the combined influence of topology-optimized infill architectures and ceramic-resin coatings on modal behavior remains largely unexplored. Prior studies typically analyze coatings or internal structures in isolation. The present work fills this gap by experimentally evaluating how various optimized infill geometries respond after ceramic–resin coating, offering a novel integrated approach to improving robotic arm stability. This provides new insight into the coupled effects of design strategy and surface reinforcement on damping, rigidity, and overall dynamic performance.
Materials and methods
In our study, focusing on a six-jointed open-source robotic arm named Thor, we selected the limb that experiences the highest load and applied topology optimization to its design. This optimized design process involved manufacturing the component using three different infill methods across two distinct sizes, resulting in a total of six samples. The technical drawing of this part can be seen in Figure 1.
Technical drawing of optimized part (mm).
The aim was to evaluate the effects of different infill patterns and sizes on the structural performance through topology optimization. While the focus of this study was on the component experiencing the highest load, the selected infill patterns are expected to influence other components similarly under comparable load conditions. The infill patterns were chosen for their structural enhancement capabilities, and their effects are likely consistent across different geometries due to their inherent design characteristics. The component’s lattice structures were categorized into three types: Voronoi, triangular honeycomb, and square honeycomb configurations, each examined at 1 and 2 mm scales. The Voronoi structures were produced with varying point counts and rib dimensions. For instance, the Voronoi 1 mm sample had a point count of 100 with a rib height of 2.6 mm and a rib thickness of 1 mm, whereas the Voronoi 2 mm sample had a point count of 50 and a rib thickness of 2 mm. Triangular honeycomb structures were characterized by specific cell counts. The 1 mm triangular honeycomb featured 25 U cells and 20 V cells, while the 2 mm version had 21 U cells and 6 V cells. Similarly, the square honeycomb structures were detailed with 28 U cells and 20 V cells for the 1 mm scale and 14 U cells and 10 V cells for the 2 mm scale. This detailed numeric analysis provided insights into the structural integrity and performance enhancements achieved through topology optimization. By comparing these configurations, we systematically assessed the mechanical properties and optimization outcomes, leading to a comprehensive understanding of how design parameters and infill methods influence the overall performance of additively manufactured parts. The Voronoi pattern is an irregular, stochastic structure offering high surface area and complex rib arrangements, while the triangular honeycomb follows an ordered, load-efficient geometry known for stiffness and stability. The square honeycomb pattern uses orthogonal ribs that provide balanced stiffness and consistent directional behavior. These differences directly influence coating adhesion, mass distribution, and vibration response. Figure 2 illustrates the topology-optimized designs for the selected limb of the robotic arm, showcasing the different infill patterns: Voronoi, triangular honeycomb, and square honeycomb. This detailed numeric analysis provided insights into the structural integrity and performance enhancements achieved through topology optimization. By comparing these configurations, we systematically assessed the mechanical properties and optimization outcomes, leading to a comprehensive understanding of how design parameters and infill methods influence the overall performance of additively manufactured parts.
Design optimization sub-features and lattice structures.
The manufacturing of all specimens was performed using Fused Deposition Modeling and the process parameters were carefully controlled to ensure high print quality and uniform mechanical behavior as summarized in Table 1. All parts were printed using a Creality Ender-3 S1 FDM printer (Shenzhen Creality 3D Technology Co., Ltd., China). To verify the reliability of the experimental results, a minimum of three samples was produced and tested for each design configuration, and the measurements showed a maximum deviation of 7% from the average values which confirms the repeatability and stability of the fabrication process. All printing conditions including thermal settings, layer specifications, motion parameters, retraction configuration, and build-plate adhesion strategy were standardized across every print so that any differences observed during modal testing could be attributed solely to the design variations rather than inconsistencies in manufacturing.
FDM printing parameters.
In this study, we explored the enhancement of additively manufactured components through the application of a resin composite coating, focusing on parts optimized using topology optimization techniques. The components were fabricated using three distinct infill patterns—Voronoi, triangular honeycomb, and square honeycomb—each at two different scales, 1 and 2 mm. After the topology optimization, these components were coated with a resin composite comprising polyester mixed with ceramic powders, specifically aluminum oxide (Al2O3) and silicon carbide (SiC). The purpose of this coating was to improve the mechanical properties and durability of the parts by leveraging the strengths of the ceramic materials. Material and design choices play a pivotal role in the long-term durability and maintenance of robotic arms. The integration of optimized infill patterns and coatings, as seen in this study, contributes to enhancing the mechanical robustness of the components, reducing the likelihood of failure under repeated loads. The use of ceramic-enhanced resin coatings not only improves surface hardness but also protects against environmental wear and chemical exposure, which are common challenges in industrial settings. These enhancements result in lower maintenance requirements and extended service intervals, which are crucial for reducing downtime and operational costs in industrial robotics. To strengthen the lattice structures and improve vibration damping, the components were coated using a resin-filling technique. Rather than applying the coating only to external surfaces, the polyester–ceramic mixture was poured directly into the internal lattice volume of each part. This method allowed the resin to penetrate through openings in the infill geometry and completely fill the interconnected cavities, ensuring uniform reinforcement throughout the internal structure. The pouring process continued until the entire internal volume was saturated and excess resin flowed from the outlets, confirming full coverage.
After filling, each component was rotated manually for several minutes to promote even distribution and to prevent resin pooling inside the cavities. The parts were then left to cure at ambient room temperature for 24 h, allowing the polyester matrix to solidify around the ceramic particles (Al2O3 and SiC). Because this technique fills the lattice rather than only coating external surfaces, minor variations in local thickness are possible; however, visual inspection confirmed consistent internal saturation across all samples.
Table 2 details the composition of the resin mixture applied to each type of component. The resin consisted of a base polyester mixed with aluminum oxide and silicon carbide powders, each constituting 5% of the total weight of the resin mixture. This uniform distribution aimed to provide a consistent enhancement across all parts, ensuring comparability in performance results. The table below presents the specific proportions of the resin and ceramic powders used in coating each type of component. Each row represents a different infill pattern and scale, detailing the percentage by weight of the polyester resin and the ceramic powders (aluminum oxide and silicon carbide) used.
Composition of resin and ceramic powder mixtures applied to topologically optimized components.
The image in Figure 3 shows various topologically optimized parts after being coated with resin composite.
Coated topologically optimized parts with various infill patterns and scales.
Each part is labeled according to its infill pattern and scale: Part A is the original body without any infill pattern, serving as a control sample. Part B has a Voronoi pattern with a 1 mm scale. Part C features a Voronoi pattern with a 2 mm scale. Part D incorporates a triangular honeycomb pattern with a 1 mm scale. Part E presents a triangular honeycomb pattern with a 2 mm scale. Part F shows a square honeycomb pattern with a 1 mm scale. Part G includes a square honeycomb pattern with a 2 mm scale. These coated components display the different infill patterns used in the study, showcasing the visual and structural differences between the various configurations. The resin coating, visible in the image, enhances the overall robustness of the parts by leveraging the mechanical properties of the incorporated ceramic powders. This comprehensive approach allows for a detailed comparison of how different infill patterns and scales affect the performance of additively manufactured components when reinforced with a ceramic-enhanced resin. The natural frequency (often denoted as ωn) of a vibrating or oscillating system depends on the characteristics of that system. For a simple harmonic oscillator, like a mass-spring system or a pendulum, the equation for the natural frequency is shown in equation (1). where w n represents the natural frequency. k is the stiffness or spring constant of the system. m is the mass of the object or system.
As shown in equation (2). which is a formula used to calculate the damping ratio (ξ) of a vibrating or oscillating system, given the excitation frequencies (ω1 and ω2) and the natural frequency (ωn) of the system. This formula represents the damping ratio in a simplified form, which is based on the difference between the excitation frequencies and the natural frequency, normalized by twice the natural frequency.
The damping coefficient quantifies the damping in a system and is used in the context of second-order linear systems to describe the relationship between damping, mass, damping ratio, and natural frequency. The damping coefficient (c) in a vibrating or oscillating system can be calculated using the formula that’s shown in equation (3). where c represents the damping coefficient. m is the mass of the system. ξ is the damping ratio. ωn is the natural frequency of the system.
The logarithmic decrement (Λ) is a formula used to describe the rate at which the amplitude of a damped oscillatory system decreases. It is typically expressed in terms of the damping ratio (ξ) of the system. The formula for logarithmic decrement is shown in equation (4).
The damped period of an oscillatory system is typically expressed in terms of the angular frequency of the damped oscillation (ωd). The formula for the damped period is given in equation (5). where Td is the Damped period and ωd is the Angular frequency of the damped oscillation.
Eigenvalue approaches were used in the calculations of the modal analysis according to equation (6). [M] is mass matrix and [K] is stiffness matrix.
This study employs modal analysis to evaluate the vibrational characteristics of the additively manufactured robotic arm, focusing on how different infill patterns and coatings influence its dynamic performance. The schematic representation (Figure 4) in the visual illustrates how modal analysis of a structure is conducted. In this technique, specific points (a, b, and c) on the structure are subjected to a known force using an impulse hammer, and the resulting vibrations induced by this force are measured using an accelerometer placed at a fixed point on the structure. The data from the accelerometer is transferred to a data recorder and subsequently analyzed by the SignalCalc software. Isolation foam is employed to mitigate the influence of environmental vibrations on the measurements. This system furnishes critical data by analyzing the responses of the structure at different frequencies, thereby facilitating the optimization of vibration performance on the structure.
Experimental setup of modal analysis.
Excitation at points a, b, and c was used to ensure full modal coverage by capturing direction-dependent responses and reducing the risk of missing local mode shapes. Different impact positions improve accuracy by exciting different modal characteristics.
Results and discussions
In this study, measurements were conducted on samples with various infill patterns designed for robotic arm applications. Figure 5 demonstrates the effects of the coating process on the weight of the samples. and how these effects vary according to design features. During this process, the weights of each sample before and after coating were recorded, and the obtained data were used to analyze the contribution of surface area and infill pattern to the weight increase. The results show that the post-coating weights vary significantly according to the infill pattern and scale, which is critical for understanding how the coating affects material usage and performance in robotic arm designs. The findings provide important data for optimizing infill patterns and coating processes. The reported values represent the averages of multiple tests, and the maximum observed deviation from the mean was 7%. This limited variation supports the consistency and reliability of the results obtained in this study.
Weight comparison table before and after coating.
The table presents the weights of seven distinct samples before and after coating, highlighting significant variations in weight gain. Initially, the lightest sample was Voronoi 1 mm (B) at 113.94 g, whereas the heaviest was the Original Part (A) at 161.32 g. After coating, Voronoi 2 mm (C) reached the highest weight of 210.203 g, while Square Honeycomb 1 mm (F) was the lightest at 166.475 g post-coating. The Voronoi patterns demonstrated the most substantial weight increases, with Voronoi 1 mm (B) and 2 mm (C) exhibiting 73.66% and 68.96% increases, respectively, indicating a high surface area for coating adherence. Triangular Honeycomb patterns showed moderate weight increases of around 25.7% and 25.98% for 1 mm (D) and 2 mm (E) scales, respectively. Square Honeycomb patterns had a notable increase, with 1 mm (F) at 41.06% and 2 mm (G) at 37.37%, suggesting efficient coating absorption. The Original Part (A), serving as a control, had a weight increase of 16.94%, providing a baseline for comparison. These findings underscore the impact of infill patterns and scales on the weight gain due to coating, essential for optimizing material usage and structural performance in additive manufacturing. The research was carried out to understand the vibrational behavior of the robotic arms. (A-G) from vibration tests under six sensor and impact positions (AB, AC, BA, BC, CA, CB). The study analyzes vibration absorption and damping performance of various infill patterns and materials for robotic arm applications. Comparing damping times and peak amplitudes helps identify optimal configurations for improved design and durability. Based on the observed performance of the infill patterns, it is expected that similar structural benefits would be observed in other components of the robotic arm when subjected to comparable load conditions. However, variations in performance may occur due to geometry-specific factors, which emphasizes the need for further studies to evaluate these patterns across different components to fully understand their geometry-dependent impacts.
According to the findings in Figure 6, seven different samples labeled A, B, C, D, E, F, and G show the acceleration–time curves obtained from vibration tests under six sensor and impact positions (AB, AC, BA, BC, CA, and CB). In the AB, AC, and CA positions, the acceleration signals decay to near zero within approximately 0.045–0.055 s for all samples, indicating faster damping and higher vibration absorption capability. In contrast, in the BA position the oscillations persist for a longer duration, with several samples maintaining noticeable acceleration up to about 0.08–0.10 s, which reflects weaker damping performance in this loading direction. The BC and CB positions show intermediate behavior, where the acceleration responses typically settle between 0.05 and 0.07 s, representing moderate damping performance.
Acceleration-time curves of all samples under various sensor and impact positions.
Peak acceleration values also show clear differences among samples. In the BA position, sample F exhibits the highest initial peak acceleration, reaching values close to 250–300 m per second squared, indicating the largest vibrational response and the weakest resistance to impact. In other positions, peak accelerations across all samples generally remain below 80 m per second squared, suggesting better initial vibration absorption. Among the evaluated samples, sample G consistently shows shorter decay times across most positions, indicating superior damping behavior, while sample F displays the highest peak amplitudes and slower decay, confirming its relatively poor vibration control performance. Figure 7 presents the frequency-magnitude curves from vibration tests conducted on seven different samples labeled A, B, C, D, E, F, and G. The analysis focuses on identifying the highest magnitude values and the corresponding natural frequencies for each sample. This study aims to understand how infill patterns and material properties affect the vibration performance and rigidity of the samples.
Frequency-magnitude analysis of vibration tests for all samples.
Based on the data in Figure 7, the frequency-magnitude curves obtained from vibration tests of seven different samples labeled A, B, C, D, E, F, and G were analyzed. The analysis reveals the highest magnitude values of the samples and the frequencies (natural frequencies) at which these magnitudes occur. Sample A showed a magnitude of approximately 0.15 m/s2/N at a frequency of about 150 Hz in the AB position. Sample B showed a magnitude of approximately 0.2 m/s2/N at a frequency of about 100 Hz in the AC position. Sample C showed a magnitude of approximately 0.25 m/s2/N at a frequency of about 200 Hz in the AB position. Sample D showed a magnitude of approximately 0.35 m/s2/N at a frequency of about 300 Hz in the BA position. Sample E showed a magnitude of approximately 0.3 m/s2/N at a frequency of about 100 Hz in the CB position. Sample F showed a magnitude of approximately 0.25 m/s2/N at a frequency of about 250 Hz in the BC position. Sample G showed a magnitude of approximately 0.15 m/s2/N at a frequency of about 200 Hz in the CA position. It can be inferred that samples with lower natural frequencies possess lower rigidity and lower spring constants, whereas samples with higher natural frequencies exhibit greater stiffness and structural rigidity. In the BA position, Sample D showed the highest magnitude (0.35 m/s2/N), indicating that this sample produced more vibration and has lower rigidity compared to the others. The highest natural frequency was generally observed in Sample D (300 Hz), while the lowest frequency was observed in Sample B (100 Hz). In a similar study where PLA parts were manufactured with FDM and tested for vibration modal analysis, it was found that the best natural frequency value was 81.745, while in this study, the natural frequencies were observed on two peaks with the best peak being at 227.5 Hz in sample A (Zhang et al., 2019). The best-performing samples are characterized by low magnitudes and high natural frequencies, while the worst performance is exhibited by Sample D, with high magnitudes and low frequencies. This analysis provides critical data for understanding the impact of infill patterns and material properties on vibration performance. The differences in dynamic behavior between the infill geometries can be explained by their underlying structural mechanisms. Voronoi structures contain irregular cell distributions with non-uniform rib thicknesses, resulting in discontinuous load paths and locally flexible regions that reduce stiffness and lead to moderate damping ratios. In contrast, the triangular honeycomb pattern forms highly efficient interconnected triangular cells, which are known to maximize rigidity through stable three-point load transfer and distribute stresses more evenly along the lattice walls. This geometry therefore exhibits higher natural frequencies and superior damping performance, as observed in Sample E. The square honeycomb pattern provides orthogonal rib networks that offer balanced but less efficient stiffness compared to the triangular layout, producing intermediate natural frequencies and damping ratios. These geometric characteristics govern the way vibrational energy propagates through the structure, explaining the observed trends in stiffness, damping ratio, and overall modal response.
Figure 8 displays the damping ratio and damping coefficient data for seven different samples labeled A, B, C, D, E, F, and G obtained from vibration tests. The analysis shows that sample E has the highest average damping coefficient and damping ratio values, indicating superior vibration damping performance. Conversely, sample A exhibits the lowest values, demonstrating the least effective damping capabilities.
Analysis of damping ratios and damping coefficients.
Figure 8 presents the damping ratio and damping coefficient data obtained from vibration tests of seven different samples labeled A, B, C, D, E, F, and G. According to the analysis, the highest average damping coefficient value is 3.2 Ns/m, belonging to sample E. Sample E shows the best performance in terms of damping coefficient. Sample G has an average value of 3.0 Ns/m, approximately 6.25% lower than sample E. Among the other samples, sample D ranks third with 2.8 Ns/m, 12.5% lower than sample E. Samples F, C, B, and A have values of 2.5, 2.0, 2.2, and 1.5 Ns/m, respectively. Sample A has the lowest average damping coefficient value, performing 53.13% lower compared to sample E. In terms of damping ratio, the highest average value is 0.18, belonging to sample E. Sample E again shows the best performance in terms of damping ratio. Sample D has an average damping ratio of 0.15, 16.67% lower than sample E. Samples F, B, C, and A have values of 0.13, 0.12, 0.10, and 0.05, respectively. Sample A has the lowest average damping ratio value, performing 72.22% lower compared to sample E. In a similar study where PLA parts were manufactured with FDM and tested for vibration modal analysis, it was found that the damping ratio value was 0.055, while in this study, the max damping ratio value was 0.18 in sample E (Öteyaka et al., 2022). High damping coefficient and damping ratio values indicate that the samples can more effectively dampen vibrations and dissipate energy quickly. A high damping ratio means the sample can quickly reduce vibration amplitudes, leading to a more stable and quiet performance. A high damping coefficient indicates the sample’s capacity to absorb more energy and control vibrations, enhancing the durability of structures under impact or sudden load changes. The best-performing samples are those with high damping coefficient and damping ratio values, such as samples G and E in terms of damping coefficient, and samples E and D in terms of damping ratio. These samples possess the material and design properties preferred for optimizing vibration performance in structures. To properly interpret the damping behavior, it is important to distinguish between improvements driven by mass or stiffness changes and those resulting from true material damping. Heavier samples inherently exhibit reduced vibration amplitudes due to inertial effects, whereas stiffer geometries shift natural frequencies upward and decrease resonance response. For this reason, the damping trends were interpreted qualitatively in relation to each sample’s measured mass and corresponding natural frequency rather than relying on absolute values alone. When considered relative to these structural parameters, the superior performance of Sample E cannot be attributed solely to mass increase but reflects enhanced material damping provided by the ceramic-filled resin and the efficient load redistribution produced by its triangular honeycomb geometry. This qualitative normalization provides a clearer distinction between mass- or stiffness-induced damping and true coating-induced damping behavior.
Samples with high damping ratio and damping coefficient offer more reliable performance, especially in sensitive and critical applications, extending the lifespan of structures and reducing maintenance costs. Figure 9 presents the damped period (Td) values obtained from vibration tests of seven different samples labeled A, B, C, D, E, F, and G. The left graph illustrates the Td values at the first natural frequency, with the x-axis representing the damped period and the y-axis representing the test codes. The right graph displays the Td values at the second natural frequency, with a similar axis setup, allowing for a comparative analysis of the damping performance across different frequencies.
Analysis of damped period (Td) values at first and second natural frequencies.
In Figure 9, the damped period (Td) values obtained from vibration tests of seven different samples labeled A, B, C, D, E, F, and G are analyzed. A lower damped period (Td) indicates faster attenuation of vibration cycles, meaning the sample dissipates vibrational energy more efficiently and therefore has superior damping capability. According to the analysis, at the first natural frequency, the highest average damped period values are 0.16 s for samples A, C, and G. These samples dampen the incoming impact over longer repetitive time intervals, exhibiting lower damping performance. The lowest average damped period value is 0.12 s for sample D, indicating that sample D dampens vibrations more quickly and effectively. Samples A, C, and G have a 33% higher damped period value compared to sample D, which significantly shows their lower vibration control performance compared to sample D. In the right graph, which shows the second natural frequency, all samples exhibit nearly the same damped period values. This indicates that at the second natural frequency, the damping performances of the samples are quite close to each other, and the differences in material or design do not create significant differences in damping capacity at this frequency range. This homogeneity suggests that the second natural frequency minimizes the performance differences between the samples and equalizes their damping capacities within this frequency range. Samples with higher damped period values dampen the incoming impact over longer repetitive time intervals, meaning lower vibration control. The superior damping capability observed in sample D is particularly significant for real-world robotic arm applications, as it directly enhances the stability and performance of the arm in dynamic environments. High damping reduces the amplitude of vibrations, which is crucial in tasks requiring precision and control, such as pick-and-place operations, welding, and medical procedures. By minimizing oscillations, robotic arms can achieve greater accuracy, reduce wear on joints and actuators, and improve the overall operational lifespan of the system. This makes the damping properties of the design not just a theoretical advantage but a critical factor in practical, high-performance applications.
As previously mentioned, in a similar study where PLA parts were manufactured using FDM and tested for vibration modal analysis, the best natural frequency value was found to be 81.745 Hz. In this study, however, the natural frequencies were observed at two peaks, with the best peak reaching 227.5 Hz in sample A (Zhang et al., 2019). Similarly, the damping ratio value in the previous study was found to be 0.055, whereas in this study, the maximum damping ratio value was 0.18 in sample E. These results demonstrate the improvements achieved in this study (Öteyaka et al., 2022). As reported in prior studies, ceramic-filled coatings increase surface rigidity and shift resonance frequencies due to enhanced structural damping (Augsburg et al., 2004). Likewise, optimized lattice architectures alter mass distribution and stiffness pathways, which directly influence modal parameters (Alshihabi et al., 2025a). These findings align with the trends observed in our samples.
Despite the valuable insights gained from this study, there are several limitations that must be acknowledged. One of the primary limitations is the variability in the coating application process, which may result in inconsistencies in coating thickness and uniformity across different samples. These variations could affect the mechanical properties and vibrational performance of the coated components. Additionally, the experimental setup used in this study may not fully replicate real-world operational conditions, such as variable loading scenarios, environmental factors, and long-term wear effects. These factors could influence the accuracy and generalizability of the results, highlighting the need for further investigations.
Conclusions
In this study, a topology-optimized limb of the six-joint Thor robotic arm was manufactured using three infill patterns—Voronoi, triangular honeycomb, and square honeycomb—each produced at 1 and 2 mm scales. These configurations correspond to Sample A (Original part), Sample B (Voronoi 1 mm), Sample C (Voronoi 2 mm), Sample D (Triangular Honeycomb 1 mm), Sample E (Triangular Honeycomb 2 mm), Sample F (Square Honeycomb 1 mm), and Sample G (Square Honeycomb 2 mm). All samples were subsequently coated with a polyester resin reinforced with aluminum oxide and silicon carbide.
The key findings of this study are as follows. The Voronoi-based designs (B and C) showed the highest weight increase after coating due to their large surface area. Sample E (Triangular Honeycomb 2 mm) achieved the best vibration performance, exhibiting the highest damping coefficient (3.2 Ns/m) and damping ratio (0.18). Sample A, the unoptimized baseline, showed the lowest damping values. Samples A, C, and G displayed the largest damped period values (0.16 s), indicating weaker damping performance, while Sample D demonstrated the shortest damped period (0.12 s). Sample D also recorded the highest vibration magnitude (0.35 m/s2/N) at the first natural frequency, confirming its lower rigidity relative to the other coated designs.
These findings confirm that combining optimized infill architectures with ceramic-reinforced resin coatings can significantly enhance the dynamic stability of additively manufactured robotic components. The results provide a clear framework for selecting infill patterns and coating strategies to improve vibration performance in robotic arms.
Future research may investigate multi-material additive manufacturing, alternative ceramic–resin formulations, and adaptive or gradient infill structures to further improve vibration attenuation and stiffness-to-weight performance. Examining additional robotic arm components under varying load cases and real-world operating conditions would also help generalize the findings and support the development of more durable and precise robotic systems.
Footnotes
Acknowledgements
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Funding
The authors received no financial support for the research, authorship, and/or publication of this article.
Declaration of conflicting interests
The authors declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.
Data availability statement
The data that support the findings of this study are available upon reasonable request.
Declaration of generative AI and AI-assistedtechnologies in the writing process
During the preparation of this work the author(s) used ChatGPT in order to improve language and readability. After using this tool/service, the author(s) reviewed and edited the content as needed and take(s) full responsibility for the content of the publication.