Compliant element design for shape-adaptive linkage-driven prosthetic fingers

Compliant element design for shape-adaptive linkage-driven prosthetic fingers 1st Ludovica Nini CREO Lab UCBM di Roma 00128 Rome, Italy [email protected] 1st Lucia Tontini CREO Lab UCBM di Roma 00128 Rome, Italy [email protected] 2ndNevio L. Tagliamonte CREO Lab UCBM di Roma 00128 Rome, Italy [email protected] 3rd Loredana Zollo CREO Lab UCBM di Roma 00128 Rome, Italy [email protected] 4rd Fabrizio Taffoni1 CREO Lab UCBM di Roma 00128 Rome, Italy f.taf[email protected] Abstract—Few linkage-driven devices achieve finger Shape Adaptivity (SA) because of the difficulties in providing enough degrees of freedom during grasping without increasing the overall encumbrance. This work proposes a method to provide fourbar linkage fingers with SA by substituting one rigid link with a compliant element. Compliance was obtained by inserting into a Nylon rigid link a compliant domain in TPU 95A using Additive Manufacturing (AM) Multi-material printing. Different interlocking interfaces and printing parameters were tested to optimise link compliance. Compression tests identified the best parameter combination, and cyclic tests confirmed the stable behaviour of TPU. These results enable the development of linkage-driven prosthetic fingers with SA, overcoming current limitations. Index Terms—Compliant elements, Multi-Material Printing, prosthetic fingers, shape-adaptivity. I. INTRODUCTION Human fingers intrinsically adapt their shape to the geometry of grasped objects, distributing contact forces to enhance stability and maximize grip strength. Replicating this behaviour is essential for prosthetic fingers to achieve stable and functional grasps. An effective implementation of Shape Adaptivity (SA) [1], i.e. the capability of distal phalanges to continue flexion after the proximal phalanx contacts the object (Fig. 1), ensures the presence of multiple contact points replicating human behaviour. Prosthetic fingers are typically Fig. 1. SA of a robotic finger composed of two revolute joints and two phalanges (P h1and P h2). a) Initial configuration. b) Free flexion of the P h1. c) SA during object interaction enables the possibility to flex P h2 when P h1is locked in contact with the object. cable or linkage-driven. Cable-driven devices provide limited This work was funded by the Istituto Nazionale per l’Assicurazione contro gli Infortuni sul Lavoro (INAIL) within the 3D-AID and 3Daid++ project, CUP: E59E19001460005 and C83C23001060001. grasping forces but guarantee SA. Although linkage-driven devices exert higher forces, compliant elements must be added to perform SA since the number of Degrees of Freedom (DoFs) during interaction has to be increased [1]. The insertion of compliant components is challenging due to the limited prosthetic finger volume. This work proposes a novel workflow for the design and manufacturing of 3D-printed compliant components, enabling SA in linkage-driven prosthetic fingers without requiring additional components. II. MATERIALS AND METHOD A four-bar linkage was identified as the target mechanism for the finger design (as in the Vincent and Bebionic hands [2]). Two links represent finger phalanges, one the palm, and the last one is a further link that couples phalanges (L1). The mechanism presents 1 DoF, so its movement stops when it contacts the object. If L1is manufactured to be compliant, a further DoF is enabled during grasping, ensuring SA. A multi-material 3D printing (MMP) approach was selected to fabricate this link, using Fused Deposition Modelling (FDM) technology. Three domains were identified: two rigid to transmit forces between phalanges and one soft to ensure link compression and distal phalanx flexion after first contact with the object. A Finite Element Analysis (FEA) was used to determine the stress distribution and select the position of the interfaces between the two domains. Strong interfacial bonds are essential to prevent detachment under load. Thus, adhesion properties were optimised by selecting materials with compatible bed and extrusor printing temperatures (Fig. 2.a). Nylon was selected for the rigid domains and TPU 95A for the compliant one. Furthermore, compliance was maximized by exploring interlocking interfaces with different geometries between the materials (Fig. 2.b) in addition to different printing parameters for the compliant domain, such as infill percentage (40%, 60%, 80%, 100%) and patterns (Fig. 2.c). Rigid domains were manufactured with cubic infill at 100%. The desired L1compression was estimated by simulating adaptive grasps of objects with different diameters (from 55.0 to 75.0 mm), positioned with their centre of mass aligned with the metacarpal joint and locked in contact with the palm. Evaluated compression ranged between 0.0 and 3.9 mm, so the target was set at 4.0 mm. Five specimens (Fig. 3.a) for each 2025 I-RIM Conference October 17-19, Rome, Italy ISBN: 9788894580570 10.5281/zenodo.17629772 141 Fig. 2. a) Extrusor and build plate printing temperatures of the most used FDM filaments; b) interlocking interfaces; c) compliant infill patterns. (Adapted from [3]) Fig. 3. a) Positioning of the specimen into the clamps. The axis of the link connecting the centre of the two holes (blue dash-dotted line) is vertically aligned. Detailed view of specimen extremities designed to increase the clamped surface area to avoid slippage during tests; b) Compression tests; c) Cyclic tests. (Adapted from [3]) combination were manufactured with MMP and subjected to compression tests (Fig. 3.b) at the Instron Universal Testing machine to identify the parameter combination that guarantees the softer behaviour. A three-way ANOVA was performed to exclude those combinations that require a significantly higher force to reach the target compression. A new batch with the best parameter combination was subjected to cyclic tests up to 0.2 true strain to precondition the TPU, followed by cycles up to 0.1 true strain (4 mm-compression) to verify repeatable stress–strain behaviour (Fig. 3.c) [3]. III. RESULTS AND DISCUSSION Compression test results (Fig. 4) indicate that the rectangular interlocking interface with a Cross 3D infill pattern at 40% exhibited the softest mechanical response among the tested configurations. The jigsaw interface resulted in significantly stiffer specimens, especially with a Cross pattern, whereas the T-shaped interface exhibited poorer adhesion due to stress concentrations that led to detachment. The concentric infill pattern produced the stiffest specimens at high infill percentages, resulting in tightly packed rings that enhanced rigidity. Fig. 4. Compression force results. The combination exhibiting the softest behaviour is highlighted with a dashed black square. The mark (**) indicates manufacturing combinations with forces significantly different from the target (p < 0.01). (Sourced from [3]) Specimens subjected to cyclic tests (Fig. 3.c) exhibited higher stiffness during the first cycle and gradually softened until the fourth one, after which a stable behaviour was established. In the first test, the standard deviation (std) associated with the average curve calculated over the last seven cycles was less than 3%, verifying the stable behaviour of the TPU despite the presence of hysteresis. In the second test, the std associated with the average curve calculated over all ten cycles was less than 3%. Preconditioning during the first loading–unloading test ensured stable behaviour of the specimens in the subsequent test, conducted up to 0.1 true strain. IV. CONCLUSIONS The work presented a novel workflow to design compliant components via MMP to enable SA in linkage-driven prosthetic fingers. Statistical analysis confirmed that the combination of a rectangular interlocking interface, 40% of infill, and a Cross 3D pattern resulted in significantly more compliant specimens. The stable behaviour of the TPU was confirmed during a loading-unloading test conducted after preconditioning. The hysteresis observed during cyclic tests results from the viscoelastic behaviour of TPU, which dissipates energy while reorganising its internal fibres. This leads to a slower return of the link to its original length during unloading and, in the case of active unloading, requires more energy than during the loading phase. However, specimen behaviour in the prosthetic finger can be considered repeatable. These results pave the way to the development of linkagedriven AM prosthetic fingers with SA behaviour, overcoming limitations of current solutions. REFERENCES [1] M. C. Carrozza et al., “The spring hand: Development of a selfadaptive prosthesis for restoring natural grasping,” Autonomous Robots, 2004. [2] J. T. Belter et al., “Mechanical design and performance specifications of anthropomorphic prosthetic hands: A review,” JRRD, 2013. [3] L. Nini et al., “Design of compliant components in linkagedriven prosthetic fingers: A multi-material printing-based method,” IEEE Access, 2024. 142