On the integration of strain gauges in an additive manufactured prosthetic phalanx

On the integration of strain gauges in an additive manufactured prosthetic phalanx Alice Giovannetti, Flavio Napoleoni, Stefano Revello, Marco Controzzi The Biorobotics Institute Scuola Superiore Sant’Anna Pisa, Italy {alice.giovannetti, flavio.napoleoni, stefano.revello, marco.controzzi}@santannapisa.it Abstract— Lack of tactile feedback remains a major limitation in prosthetics, restricting manipulation accuracy and increasing cognitive effort during daily activities. For this reason, modern artificial hands must be endowed with force or tactile sensors. A key question is whether additive manufacturing plastic structure can themselves host load sensing elements. Here we investigate the integration of semiconductor strain gauges into an additively manufactured proximal phalanx of a prosthetic finger as a structural sensing approach for force estimation. We propose a methodological framework to identify the optimal sensor configuration, ensuring independence from the contact point as well as robustness to finger posture variations. The phalanx was further refined with cavities that concentrate strain in the sensing regions, enhancing measurement sensitivity and overall system effectiveness. Finite element simulations guided the structural optimization and assessed sensor performance under representative loads. Simulation results demonstrate that the introduction of cavities can increase strain sensitivity by a factor of up to 2.5, while reducing crosstalk between sensing axes and improving robustness across different grasp types. This confirms that structural modifications enabled by additive manufacturing can significantly enhance the effectiveness of embedded strainbased sensing. Ongoing efforts focus on the experimental validation, with the potential to establish structural additive manufacturing sensing as a potential solution for affordable, personalized prosthetic hands with integrated tactile feedback. Keywords— prosthetic hand, strain gauge, optimized sensor design, multi-axis force sensing, Additive Manufacturing I. INTRODUCTION The development of advanced prosthetic hands has significantly improved dexterity and functional performance over the past decades. However, one of the major limitations that still characterizes state-of-the-art prostheses is the lack of reliable tactile feedback [1]. While myoelectric control strategies have enabled more natural and versatile actuation of artificial fingers, the absence of sensory information inhibits the user from perceiving external stimuli such as contact, force distribution or slippage, ultimately reducing manipulation accuracy and increasing cognitive effort during daily activities [2]. Restoring real-time, natural sensory feedback is therefore essential to enhance functional outcomes and user acceptance [3]. To overcome this limitation, extensive research has been dedicated to the integration of sensing systems into artificial fingers. Different approaches have been proposed in literature [4][5], including FSRs for normal force detection, capacitive sensors for pressure distribution, and optical or multimodal sensors. Nevertheless, one of the primary challenges remains the physical integration of such sensors into prosthetic fingers. The stringent requirements [2] of reduced weight, compact dimensions and mechanical robustness often limit the feasibility of embedding tactile sensors directly into the fingertip. For these reasons, several studies have also proposed indirect sensing approaches [6], in which sensors are housed within the structural components of the prosthesis rather than at the contact surface, allowing measurements of internal strain correlated with external loading conditions. At the same time, the design of modern prostheses increasingly demands lightweight, compact, and customizable solutions to ensure comfort and adaptability to individual users. Additive manufacturing provides a unique opportunity to address these requirements, combining high geometric flexibility, enabling the fabrication of complex structures, with a high degree of product personalization, particularly advantageous in developing cost-effective, patient-specific solutions. In addition, the use of polymerbased materials further contributes to meeting these stringent criteria, owing to their intrinsic lightness and versatility. Within this framework, the present study specifically addresses the question of whether additively manufactured plastic phalanges can act as structural substrates for loadsensing elements, thereby combining mechanical functionality and sensing capability in a unified design. To address this challenge, we propose the direct integration of semiconductor strain gauges into the polymer-based phalangeal structure of the prosthetic finger as a reliable approach. This solution offers high sensitivity, compactness, and structural compatibility, enabling the monitoring of localized strain with minimal impact on weight and geometry. The methodological framework guiding the optimal strain gauge configuration is detailed, alongside the optimization of the phalanx’s structural design to enhance sensor performance and ensure accurate force estimation during grasping. Finite element simulations were carried out to support the design process and establish a solid basis for experimental validation. II. MATERIALS AND METHODS A. MIA hand Finger and sensor location The hand used for this study is a modified version of the MIA hand [7], now commercialized by Prensilia SRL. The finger consists of a proximal and a distal phalanx connected through an interphalangeal joint -Figure 1 (A)-. This articulation allows for more natural finger motion, enabling both palm and pad grips, ensures better alignment with human trajectories and improves grip stability. Among the two, the proximal phalanx represents a suitable candidate for sensor integration, as it is a key element responsible in load This work was Funded by the European Union - Next Generation EU and supported by the Italian Ministry of University and Research (MUR) in the frame of the programme PRIN 2022 (Avviso DD 104 del 02/02/22) Piano Nazionale di Ripresa e Resilienza (PNRR) – Missione 4 Componente 2, ‘‘Dalla ricerca all’impresa’’ Investimento 1.1, ‘‘Fondo per il Programma Nazionale di Ricerca e Progetti di Rilevante Interesse Nazionale (PRIN), project title ‘‘Calliope: lattiCe bAsed uLtra Light SensOrized upper limb ProsthEsis’’, grant number 2022PRHZM3 - CUP J53D23002380001 (CUP University of Pisa unit I53D23001840006). Link to the website of the project: https://www.calliope-hand.it/ 2025 I-RIM Conference October 17-19, Rome, Italy ISBN: 9788894580570 10.5281/zenodo.17629804 173 transmission during grasping and it can therefore provide valuable information on external interactions. Placing the sensors proximally not only broadens the range of detectable grasping conditions, by enabling the measurement of forces transmitted along the entire finger but also reduces the risk of damage or accidental impacts, thereby improving overall sensor robustness and reliability. Moreover, internal loads in this component are comparatively higher during the grasping (in particular using contact at the fingertips), enhancing measurement sensitivity. To design the sensor configuration, the frequency of occurrence of grasp types and their associated forces, considering both magnitude and direction, was first analysed. Here we refer to the two principal loading planes (the sagittal and coronal planes) and to the force magnitudes found in literature [8]. Furthermore, according to the classification and analysis of daily grasping activities reported in [9] (for a total of 4,700 daily grasps) 2,538 (54%) involve forces acting primarily in the sagittal plane, while 825 (17%) are associated with the coronal plane. Accordingly to the magnitude of the involved loads and the material of the finger, semiconductor strain gauges were identified as the most appropriate sensing solution. Their high sensitivity allows reliable detection of the relatively low loads, while their favourable dynamic response is adequate to follow the rapid force variations occurring during daily grasping activities [10]. In addition, their lightweight and ease of integration facilitate seamless embedding within the phalanx structure. To instrument each loading plane, two bar semiconductor strain gauges are planned for installation per plane, with signal acquisition implemented via a half-bridge Wheatstone circuit. This choice reflects a trade-off between minimizing the number of sensors per load axis, simplifying assembly complexity and controlling overall costs, while providing adequate measurement accuracy for the intended application. B. Comparison and choice of the sensors arrangements Several sensor arrangements were theoretically assessed and compared. The expected output of each configuration was evaluated through theoretical strain analysis, with the objective of selecting a layout capable of estimating the forces acting at the level of the proximal phalanx independently of the specific point of load application. By combining this information with the recorded finger posture of the prosthetic hand, forces at the fingertip during grasping can be inferred. For simplicity, the analyzed configurations as shown in Figure 1 (B) are presented for the sagittal plane (yz plane), which is predominantly involved in daily grasping activities, and the subsequent discussion refers to this plane. This section details each case, highlighting the placement of sensors on the proximal phalanx and their corresponding Wheatstone bridge connections, the resulting output and the associated advantages and limitations. Configuration B-1 - Figure 1 (B)- places two strain gauges on the dorsal surface of the proximal phalanx, aligned with its longitudinal axis in the sagittal plane. This location corresponds to the region of maximum strain under sagittal bending and simultaneously to the neutral axis for bending in the coronal plane, allowing forces acting along different axes to be decoupled. The strain gauges are connected in adjacent arms of a half Wheatstone bridge circuit, yielding an output proportional to the strain difference: 𝑉𝑜𝑢𝑡 ∝ (𝜀1− 𝜀2) 𝑉𝑖𝑛 () where Vout is the differential output voltage of the Wheatstone bridge, Vin is the bridge supply voltage, and ε1 and ε2 denote the strains measured at the respective sensor positions (ε1 at the more proximal position and ε2 at the more distal). Theoretical strain evaluation shows that this difference depends only on the sagittal-plane force Fy and the sensors’ spacing l and it is independent of the fingertip contact point, as expressed in (2): |𝜀1− 𝜀2|=𝐹𝑦 𝑙 𝑦 𝐸 𝐼𝑥 (2) where E is the Young’s modulus, y is the distance of the sensing fiber from the neutral axis and Ix is the second moment of area about the transverse axis of the cross-section. Thus, Configuration B-1 allows reliable measurement of sagittalplane forces at the proximal phalanx while remaining insensitive to variations in the fingertip contact point. In Configuration B-2 (Figure 1 (B)) the strain gauges are placed on opposite surfaces of the proximal phalanx, on the dorsal and palmar surfaces respectively, while keeping their alignment along the longitudinal axis. With the half-bridge Wheatstone connection as in Configuration 1, the output corresponds to the differential strain (1), which in this case equals twice the strain induced by sagittal plane bending Mx: |𝜀1− 𝜀2|= 2 𝑀𝑥 𝑦 𝐸 𝐼𝑥 () As a result, the bridge output increases by a factor of two compared with Configuration 1, enhancing sensitivity to fingertip forces. Nonetheless, the output remains directly dependent on the bending moment, varying with the fingertip contact location and thus precluding direct estimation of the applied force without further information. In addition, the placement of a sensor on the palmar surface exposes it to a higher risk of damage during grasping. Reconfiguring the strain gauge connections in opposite arms of the Wheatstone bridge yields an alternative sensor arrangement, (this configuration is not shown in Figure 1 (B)). Here, the bridge output corresponds to the sum of the sensor strains: 𝑉𝑜𝑢𝑡 ∝ (𝜀1+ 𝜀2) 𝑉𝑖𝑛 () This arrangement cancels the contribution of the bendinginduced strain, which exhibits equal magnitude but opposite sign on the two sensors, leaving the output primarily sensitive to the normal stress transmitted to the proximal phalanx, N, as indicated in (5): Figure 1 (A) CAD model of an articulated finger of the modified MIA hand with proximal and distal phalanxes. (B) Possible strain gauges configurations. 174 |𝜀1+ 𝜀2|= 2 𝑁 𝐸 𝐴 () where A is the cross-sectional area of the proximal phalanx. The magnitude of this normal component depends on the finger posture, and it is markedly reduced when the distal phalanx is extended, leading to a configuration-dependent variation in overall measurement sensitivity. Finally, Configuration B-3 (Figure 1 (B)) provides a variant sensor arrangement designed to capture strain associated with shear in the proximal phalanx. Inspired by shear load cell designs, the sensors are placed on the lateral (interdigit) surface of the phalanx, oriented at ±45° to the longitudinal axis, in the region of maximum shear strain and along the neutral axis for sagittal-plane bending. When connected in adjacent arms of the Wheatstone bridge, the bridge output, according to (1), is proportional to the strain difference, given by: |𝜀1− 𝜀2|=𝐹𝑦 𝜅𝑠 𝐴 𝐺 () where G is the shear modulus and 𝜅 is the shear correction factor. This configuration exhibits lower sensitivity for a given tangential force (Fy), and a non-zero output might arise from a bending moment (My) associated with lateral grasping, reflecting partial decoupling between the sensing axes. Based on the above considerations, to obtain a sensing system that can distinguish between contributions of forces acting on different planes while providing a fingertip force estimate independent of the contact point, Configuration 1 proves to be the most suitable choice. Unlike the other arrangements, which either introduce dependence on the point of application or result in reduced sensitivity, this configuration ensures robustness in the force estimation process, remaining unaffected by finger posture. Moreover, the possibility of integrating all sensors and electronic components on the same surface further enhances its implementation efficiency, facilitating both assembly and system integration. The same rationale can be applied to the measurement of forces in the coronal plane. Specifically, the system can be complemented with two additional strain gauges placed on the lateral (interdigit) surface, aligned with the longitudinal axis. With this extension, the system is capable of independently monitoring forces in both sagittal and coronal planes, thereby enabling discrimination between different types of grasps during functional tasks. C. Optimal structural design of the phalanx Building upon the selected sensor configuration, the structural design of the proximal phalanx was optimized through geometric modifications, including cavities, to induce localized strain concentrations in the area of sensor placement, inspired by the design principles adopted in single-point load cells. Cavities increase strain sensitivity by locally reducing stiffness and concentrating the deformation in the sensing region, where the gauges are positioned. Such localization enhances the resolution of the measurement and promotes repeatability and stability, as the strain consistently develops within the same defined area. In addition, the cavities mechanically decouple the sensing zone from boundary effects and parasitic load components. The adjacent, stiffer regions act as filters that limit the transmission of bending and torsional moments to the sensitive area, enabling the strain gauges to operate under a deformation state closer to pure bending, thereby improving the robustness and reproducibility of the measurement system. Accordingly, the proximal phalanx has been modified to include two strategically positioned cavities, each intended to improve the performance of sensor systems monitoring forces along specific planes. A lateral through-cavity targets the sensors on the dorsal surface, responsible for measuring forces in the sagittal plane, while a dorsal cavity is designed to increase the response of the sensors on the lateral surface, tasked with measuring forces in the coronal plane. Different geometrical configurations of the cavities were considered, including ovaloid shapes and designs consisting of two holes connected by a slit, as illustrated in Figure 2 (A). From a manufacturing perspective, the use of additive manufacturing ensures full geometric flexibility in defining these shapes, overcoming the constraints typically imposed by conventional subtractive or molding processes. The cavity design was guided by stress concentration theory [11], which models openings as equivalent ellipses defined by their major and minor axes. Finite element simulations (ANSYS Mechanical APDL) were performed iteratively to assess the effects of these structural modifications on sensor output with the goal of maximizing strain capture while maintaining the mechanical integrity of the proximal phalanx. The analyses explored both changes in ellipse dimensions and modifications of the internal cavity geometry. The former directly influenced strain amplification at the sensor location, whereas the latter affected local stress concentration around the cavity, potentially reducing material strength. Consequently, the configuration A-3 shown in Figure 2 (A) was selected, as it limits excessive stress within the cavity region compared to the other geometries and preserves the structural integrity of the polymeric material. Moreover, dimensional differentiation was implemented between the dorsal and lateral cavities. The dorsal cavity, located more proximally and thus subjected to higher transmitted loads, was reduced to mitigate local stress concentrations; conversely, the lateral cavity was elongated by approximately 10% to enhance sensitivity along the sagittal plane, the primary direction of loading during daily activities. The final phalanx design, along with the corresponding prototype, is presented in Figure 2 (B) and (C). Finally, sensor outputs were simulated under multiple load configurations, both with and without structural cavities, for various grasp types. The analysis was based on strain values extracted from the finite element simulations and compared across configurations. Three case studies were considered: an extended finger subjected to a 20 N load (load case 1), a pinch Figure 2 (A) Cavity configurations designed to generate local strain concentration, all referenced to the same equivalent ellipse. (B) Optimized CAD model of the proximal phalanx with differentiated cavities, showing strain gauge placement on the dorsal (blue) and lateral (red) surfaces. (C) Prototype. 175 grasp under a 50 N load (load case 2), and a lateral grasp under a 40 N load (load case 3). III. RESULTS The results are summarized in TABLE I, reporting the differential strain measured by sensors on dorsal surface and on the lateral surface of the proximal phalanx, fabricated via SLA 3D printing using Rigid10K resin (Formlabs). The material exhibited a Young’s modulus of 9.5 GPa, as assessed through a tensile testing campaign conducted with the universal testing machine [12], considering the thermal cycle required for sensor installation. The introduction of the proposed cavities led to an increase in sensitivity by a factor of approximately 2 for forces applied in the sagittal plane and about 2.5 for those applied in the coronal plane. In addition, the cavities enhanced the robustness of force detection by (theoretically) reducing relative crosstalk errors. It is worth noting, however, that, in load cases 1 and 2, corresponding to forces applied along the sagittal plane, slightly elevated crosstalk errors were observed. This phenomenon is due to an inclination of the neutral axis relative to sagittal plane bending on the order of 5°, depending on the specific load configuration. Considering the limited magnitude of this effect and its variability with loading conditions, the lateral sensor positioning was maintained to preserve simplicity of alignment and ease of assembly. TABLE I: Simulated sensor readings and relative crosstalk error for different proximal phalanx designs (with and without cavities) under realistic grasp configurations. Load case Strain gauge differential output readings Configurations |ε1 – ε2|dorsala |ε1 – ε2|lateralb Crosstalk error Load case 1 (extended finger, 20N) Without cavities 285μm/m 48 μm/m 17% With cavities 560μm/m 71μm/m 13% Load case 2 (pinch grip, 50N) Without cavities 478μm/m 65μm/m 14% With cavities 992μm/m 86μm/m 9% Load case 3 (lateral grip, 40N) Without cavities 14μm/m 221μm/m 6% With cavities 17μm/m 552μm/m 3% a. Differential strain measured by the strain gauges mounted on the dorsal surface of the phalanx. b. Differential strain measured by the strain gauges mounted on the lateral surface of the phalanx. IV. CONCLUSION AND FUTURE WORKS The integration of semiconductor strain gauges within the proximal phalanx, combined with strategically designed structural cavities, provides an effective approach for enhancing tactile sensing in prosthetic fingers. Specifically, the proposed sensor configuration consists of two bar semiconductor strain gauges applied on the dorsal surface, aligned with the longitudinal axis of the phalanx, and two additional strain gauges positioned on the lateral interdigit surface with the same alignment; the signals from these sensors are acquired via two independent half-bridge Wheatstone circuits. This arrangement would enable the detection of grasping forces in combination with finger posture, without requiring prior knowledge of the exact contact location or force application point. In addition, the dual independent sensing system allows forces applied along the sagittal and coronal planes to be measured separately, thus supporting the distinction between different grasp types. Moreover, the optimized cavity design, inspired by load-cell principles and enabled by the geometric adaptability of additive manufacturing, has proven effectiveness in concentrating strain in the sensing regions, thereby improving both sensitivity and measurement reliability. The numerical analyses demonstrated an increase in sensitivity, together with reduced crosstalk and improved robustness against variations in loading conditions. 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