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arxiv: 2606.03798 · v1 · pith:5LHN3UQAnew · submitted 2026-06-02 · 💻 cs.RO

Optimal Design and Analytical Modeling of a Soft Fin-Ray Effect Gripper Finger Using the Finite Rigid Elements Method

Sara Adeli , Hassan Sayyaadi This is my paper

Pith reviewed 2026-06-28 09:32 UTC · model grok-4.3

classification 💻 cs.RO
keywords soft roboticsfin ray effectgripper fingerfinite rigid elements methoddesign optimizationdeformation modelingagricultural grasping
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The pith

A soft Fin Ray gripper finger with 30 mm length, seven ribs at -15 degrees, 10 mm spacing and 1 mm thickness allows the finite rigid elements method to predict deformation within 3 percent error.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper sets out to create an analytical model and optimal geometry for a soft gripper finger that can grasp delicate items such as tomatoes while supporting later development of force control. It applies the finite rigid elements method to simplify the nonlinear, high-degree-of-freedom behavior of soft materials into a usable analytical form. The design is refined against four performance measures and then checked by both simulation and physical tests. A reader would care because the result supplies a concrete starting point for building controllable soft grippers that avoid damage to fragile objects.

Core claim

The research establishes that the optimal finger configuration of 30 mm length, 10 mm rib spacing, seven ribs angled at -15 degrees, and 1 mm rib thickness, when modeled with the finite rigid elements method, predicts finger deformation with 3 percent error relative to experiment, while a corresponding ANSYS numerical model reaches 2 percent error.

What carries the argument

The Finite Rigid Elements Method (FREM), which breaks the soft finger into rigid segments joined by compliant connections to produce an analytical approximation of large nonlinear deflections.

If this is right

  • The selected geometry meets the four stated criteria and therefore supports gentle grasping of irregular produce.
  • The 3 percent modeling error supplies a usable foundation for building an analytical force controller.
  • The ANSYS model at 2 percent error confirms that the analytical approach is close enough for preliminary design work.
  • The same rib parameters can be used directly in fabrication without further geometric search.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The approach could be tested on other soft materials or rib counts to see whether the same error levels appear.
  • Adding contact sensors to the optimized finger would allow closed-loop force control in real agricultural settings.
  • The rib-angle and spacing choices might transfer to non-gripper soft mechanisms such as compliant arms or adaptive surfaces.

Load-bearing premise

The four optimization criteria of tip displacement, total deflection, stress distribution, and contact force are sufficient to define performance and the finite rigid elements method accurately represents the soft material nonlinearity.

What would settle it

Fabricate the optimal finger, apply a known load at the tip, and measure the actual tip displacement; if the observed error relative to the FREM prediction exceeds 3 percent, the modeling claim does not hold.

read the original abstract

Fin Ray-inspired soft grippers offer a promising solution for gently handling delicate, irregular objects, especially in agriculture. The objective of this research is to design, fabricate, and model a Fin Ray Effect (FRE) soft gripper finger to enable precise force control in future applications. This design aims to gently grasp delicate agricultural products, such as tomatoes, that require both adaptability and accurate force application. To address the inherent challenges of soft robotics, including nonlinear behavior, infinite degrees of freedom, and variable material properties, the Finite Rigid Elements Method (FREM) was employed for modeling. This method preserves analytical accuracy while providing a reliable foundation for the development of a force controller in later stages. A detailed Finite Element Model (FEM) was created using ANSYS, and the analytical results were validated through simulation and experimental testing. The gripper's fingers were optimized based on four key criteria: tip displacement, total deflection, stress distribution, and contact force. The optimal finger configuration includes a length of 30 mm, rib spacing of 10 mm, seven ribs angled at -15 deg, and a rib thickness of 1 mm. Theoretical modeling using the FREM predicted finger deformation with a 3% error, while the ANSYS numerical model achieved 2% error.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The paper claims to design and optimize a soft Fin-Ray Effect gripper finger for delicate objects using the Finite Rigid Elements Method (FREM) for analytical modeling. It reports an optimal configuration (30 mm length, 10 mm rib spacing, seven ribs at -15 deg, 1 mm thickness) based on four criteria (tip displacement, total deflection, stress distribution, contact force). FREM is said to predict deformation with 3% error and ANSYS with 2% error via validation against simulation and experiment.

Significance. If the error claims and optimization hold under detailed scrutiny, the work provides a practical analytical modeling route for soft robotic fingers that could support force control in agricultural grippers. The combination of FREM with FEM and physical testing offers a multi-fidelity approach that is potentially useful for design iteration, though its impact depends on the robustness of the reported validation metrics.

major comments (2)
  1. [Abstract] Abstract (validation sentence): The central claim that 'Theoretical modeling using the FREM predicted finger deformation with a 3% error, while the ANSYS numerical model achieved 2% error' is load-bearing for both model validity and the reliability of the subsequent optimization, yet provides no definition of the error metric (e.g., tip-position RMSE, L2 norm over the deformation curve, or force error), no material characterization (hyperelastic constants or strain range), and no experimental protocol details (number of trials, sensor placement, or reference quantity). This prevents assessment of whether the percentages are vs. ANSYS only or vs. physical tests, and whether they capture the nonlinear regime needed for the optimal design.
  2. [Optimization section] Optimization section (criteria and results paragraph): The four optimization criteria are invoked to select the reported optimal parameters, but the manuscript does not specify the weighting scheme, the optimization procedure (e.g., parametric sweep, gradient-based), or quantitative trade-off resolution among tip displacement, deflection, stress, and contact force. Without these, it is impossible to verify that the chosen values (30 mm, 10 mm spacing, -15 deg, 1 mm) are the unique or reproducible optimum under the stated criteria.
minor comments (2)
  1. [Introduction] Notation: The acronym FREM is introduced without an explicit expansion or reference to its prior literature on the first use, which could aid readers unfamiliar with the method.
  2. [Results/Figures] Figure clarity: Stress-distribution and deformation plots would benefit from explicit color-bar scales and axis units to allow quantitative comparison with the reported error values.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive comments. We address each major point below and will revise the manuscript to improve clarity on the validation and optimization details.

read point-by-point responses

  1. Referee: [Abstract] Abstract (validation sentence): The central claim that 'Theoretical modeling using the FREM predicted finger deformation with a 3% error, while the ANSYS numerical model achieved 2% error' is load-bearing for both model validity and the reliability of the subsequent optimization, yet provides no definition of the error metric (e.g., tip-position RMSE, L2 norm over the deformation curve, or force error), no material characterization (hyperelastic constants or strain range), and no experimental protocol details (number of trials, sensor placement, or reference quantity). This prevents assessment of whether the percentages are vs. ANSYS only or vs. physical tests, and whether they capture the nonlinear regime needed for the optimal design.

    Authors: We agree the abstract is too concise and omits key details needed for assessment. The reported errors are mean relative errors versus physical experiments (not ANSYS). In the revised manuscript we will explicitly define the error metric (normalized L2 norm on the deformation curve), add material characterization (hyperelastic constants and strain range from our tests), and describe the experimental protocol (trials, sensors, reference quantities). These details will also be cross-referenced from the methods section. revision: yes

  2. Referee: [Optimization section] Optimization section (criteria and results paragraph): The four optimization criteria are invoked to select the reported optimal parameters, but the manuscript does not specify the weighting scheme, the optimization procedure (e.g., parametric sweep, gradient-based), or quantitative trade-off resolution among tip displacement, deflection, stress, and contact force. Without these, it is impossible to verify that the chosen values (30 mm, 10 mm spacing, -15 deg, 1 mm) are the unique or reproducible optimum under the stated criteria.

    Authors: We agree the optimization procedure and weighting are not stated explicitly. The process used a parametric sweep in the FREM model with equal weighting of the four criteria; trade-offs were resolved by selecting the parameter set that simultaneously satisfied low stress, adequate contact force, and target deflection ranges. We will revise the optimization section to document the sweep ranges, weighting, and resolution method so the reported optimum can be reproduced. revision: yes

Circularity Check

0 steps flagged

No circularity: modeling validated externally and optimization uses independent criteria

full rationale

The paper introduces FREM for analytical modeling of the soft finger, reports validation against ANSYS FEM simulation and experimental testing (with stated 3% and 2% errors), and performs optimization over four explicit performance criteria (tip displacement, total deflection, stress distribution, contact force). No derivation step reduces by construction to a fitted parameter renamed as prediction, no self-citation chain is invoked for uniqueness or ansatz, and the central claims rest on external benchmarks rather than internal redefinition. The error figures are presented as comparison outcomes, not tautological outputs.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Based solely on the abstract, the work relies on standard assumptions of finite element discretization and material modeling for soft robotics; no free parameters or invented entities are explicitly introduced beyond the design variables optimized.

axioms (1)
  • domain assumption Finite Rigid Elements Method accurately approximates nonlinear soft material deformation for gripper analysis
    Invoked to justify use of FREM over traditional methods for handling infinite degrees of freedom.

pith-pipeline@v0.9.1-grok · 5760 in / 1209 out tokens · 24759 ms · 2026-06-28T09:32:34.857693+00:00 · methodology

discussion (0)

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Reference graph

Works this paper leans on

31 extracted references · 28 canonical work pages

  1. [1]

    Research on effects of different internal structures on the grasping performance of Fin Ray soft grippers,

    J. Yao, Y. Fang, and L. Li, “Research on effects of different internal structures on the grasping performance of Fin Ray soft grippers,” Robotica, vol. 41, no. 6, pp. 1762–1777, 2023, doi: 10.1017/s0263574723000139

    work page doi:10.1017/s0263574723000139 2023

  2. [2]

    Optimising Soft Fin Ray Robotic Fingers using Finite Element Analysis to Reduce Object Slippage,

    J. Emerson and K. Elgeneidy, “Optimising Soft Fin Ray Robotic Fingers using Finite Element Analysis to Reduce Object Slippage,” UKRAS20 Conf. “Robots into real world” Proc., vol. 3, no. April, pp. 43 –45, 2020, doi: 10.31256/dy2bn4p

    work page doi:10.31256/dy2bn4p 2020

  3. [3]

    Characterising 3D-printed soft fin ray robotic fingers with layer jamming capability for delicate grasping,

    K. Elgeneidy, P. Lightbody, S. Pearson, and G. Neumann, “Characterising 3D-printed soft fin ray robotic fingers with layer jamming capability for delicate grasping,” RoboSoft 2019 - 2019 IEEE Int. Conf. Soft Robot., pp. 143–148, 2019, doi: 10.1109/ROBOSOFT.2019.8722715

    work page doi:10.1109/robosoft.2019.8722715 2019

  4. [4]

    Design and Testing of Fin Ray Soft Gripper’s Finger,

    V. S. P, V. S. Raj, and S. G. Varshan, “Design and Testing of Fin Ray Soft Gripper’s Finger,” Int. Res. J. Eng. Technol., pp. 237–250, 2023, [Online]. Available: www.irjet.net

    2023

  5. [5]

    Learning Optimal Fin -Ray Finger Design for Soft Grasping,

    Z. Deng and M. Li, “Learning Optimal Fin -Ray Finger Design for Soft Grasping,” Front. Robot. AI, vol. 7, 2021, doi: 10.3389/frobt.2020.590076

    work page doi:10.3389/frobt.2020.590076 2021

  6. [6]

    A 3D -printed fin ray effect inspired soft robotic gripper with force feedback,

    Y. Yang, K. Jin, H. Zhu, G. Song, H. Lu, and L. Kang, “A 3D -printed fin ray effect inspired soft robotic gripper with force feedback,” Micromachines, vol. 12, no. 10, 2021, doi: 10.3390/mi12101141

    work page doi:10.3390/mi12101141 2021

  7. [7]

    A Universal Soft Gripper with the Optimized Fin Ray Finger,

    J. H. Shin, J. G. Park, D. Il Kim, and H. S. Yoon, “A Universal Soft Gripper with the Optimized Fin Ray Finger,” Int. J. Precis. Eng. Manuf. - Green Technol., vol. 8, no. 3, pp. 889 –899, 2021, doi: 10.1007/s40684 -021- 00348-1

    work page doi:10.1007/s40684 2021

  8. [8]

    Structural optimization method of a finray finger for the best wrapping of object,

    J. Suder, Z. Bobovský, J. Mlotek, M. Vocetka, P. Oščádal, and Z. Zeman, “Structural optimization method of a finray finger for the best wrapping of object,” Appl. Sci., vol. 11, no. 9, 2021, doi: 10.3390/app11093858

    work page doi:10.3390/app11093858 2021

  9. [9]

    Analysis of flexible end-effector for geometric conformity in reconfigurable assembly systems: Testing geometric structure of grasping mechanism for object adaptibility,

    C. I. Basson, G. Bright, and A. J. Walker, “Analysis of flexible end-effector for geometric conformity in reconfigurable assembly systems: Testing geometric structure of grasping mechanism for object adaptibility,” 2017 Pattern Recognit. Assoc. South Afric a Robot. Mechatronics Int. Conf. PRASA-RobMech 2017, vol. 2018 -Janua, pp. 92 –97, 2017, doi: 10.110...

    work page doi:10.1109/robomech.2017.8261129 2017

  10. [10]

    A Soft Gripper Design for Apple Harvesting with Force Feedback and Fruit Slip Detection,

    K. Chen et al., “A Soft Gripper Design for Apple Harvesting with Force Feedback and Fruit Slip Detection,” Agric., vol. 12, no. 11, 2022, doi: 10.3390/agriculture12111802

    work page doi:10.3390/agriculture12111802 2022

  11. [11]

    Fin Ray Crossbeam Angles for Efficient Foot Design for Energy‐Efficient Robot Locomotion,

    P. Manoonpong et al., “Fin Ray Crossbeam Angles for Efficient Foot Design for Energy‐Efficient Robot Locomotion,” Adv. Intell. Syst., vol. 4, no. 1, 2022, doi: 10.1002/aisy.202100133

    work page doi:10.1002/aisy.202100133 2022

  12. [12]

    Fin Ray gripper for handling of high temperature hybrid forging objects,

    C. V. Ince, J. Geggier, and A. Raatz, “Fin Ray gripper for handling of high temperature hybrid forging objects,” Procedia CIRP, vol. 106, no. March, pp. 114–119, 2022, doi: 10.1016/j.procir.2022.02.164

    work page doi:10.1016/j.procir.2022.02.164 2022

  13. [13]

    Scalable Simulation-Guided Compliant Tactile Finger Design,

    Y. Ma, A. Agarwal, S. Q. Liu, W. Yuan, and E. H. Adelson, “Scalable Simulation-Guided Compliant Tactile Finger Design,” 2024 IEEE 7th Int. Conf. Soft Robot. RoboSoft 2024, pp. 1068 –1074, 2024, doi: 10.1109/RoboSoft60065.2024.10521969

    work page doi:10.1109/robosoft60065.2024.10521969 2024

  14. [14]

    A Deep Learning Method for Vision Based Force Prediction of a Soft Fin Ray Gripper Using Simulation Data,

    D. De Barrie, M. Pandya, H. Pandya, M. Hanheide, and K. Elgeneidy, “A Deep Learning Method for Vision Based Force Prediction of a Soft Fin Ray Gripper Using Simulation Data,” Front. Robot. AI, vol. 8, no. May, pp. 1–15, 2021, doi: 10.3389/frobt.2021.631371

    work page doi:10.3389/frobt.2021.631371 2021

  15. [15]

    PINN -Ray: A Physics -Informed Neural Network to Model Soft Robotic Fin-Ray Fingers

    X. Wang et al., “PINN -Ray: A Physics -Informed Neural Network to Model Soft Robotic Fin-Ray Fingers”

  16. [16]

    Physics -Informed Recurrent Neural Networks for Soft Pneumatic Actuators,

    W. Sun, N. Akashi, Y. Kuniyoshi, and K. Nakajima, “Physics -Informed Recurrent Neural Networks for Soft Pneumatic Actuators,” IEEE Robot. Autom. Lett., vol. 7, no. 3, pp. 6862 –6869, Jul. 2022, doi: 10.1109/LRA.2022.3178496

    work page doi:10.1109/lra.2022.3178496 2022

  17. [17]

    A Neural Network Based Dynamic Control Method for Soft Pneumatic Actuator with Symmetrical Chambers,

    Y. Li, Y. Cao, and F. Jia, “A Neural Network Based Dynamic Control Method for Soft Pneumatic Actuator with Symmetrical Chambers,” Actuators, vol. 10, no. 6, p. 112, May 2021, doi: 10.3390/act10060112

    work page doi:10.3390/act10060112 2021

  18. [18]

    Wehbeh and I

    J. Z. Zhang et al., “Sim2Real for Soft Robotic Fish via Differentiable Simulation,” in 2022 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), IEEE, Oct. 2022, pp. 12598 –12605. doi: 10.1109/IROS47612.2022.9981338

    work page doi:10.1109/iros47612.2022.9981338 2022

  19. [19]

    Incremental Machine Learning for Soft Pneumatic Actuators with Symmetrical Chambers,

    Y. Kozhubaev, E. Ovchinnikova, I. Viacheslav, and S. Krotova, “Incremental Machine Learning for Soft Pneumatic Actuators with Symmetrical Chambers,” Symmetry (Basel)., vol. 15, no. 6, p. 1206, Jun. 2023, doi: 10.3390/sym15061206

    work page doi:10.3390/sym15061206 2023

  20. [20]

    Modeling and performance analysis of a trapezoidal section beam for soft robotic fingers using the fin ray effect,

    J. Yao, P. Wang, S. Guo, and Y. Fang, “Modeling and performance analysis of a trapezoidal section beam for soft robotic fingers using the fin ray effect,” Mech. Mach. Theory, vol. 199, no. January, p. 105673, 2024, doi: 10.1016/j.mechmachtheory.2024.105673

    work page doi:10.1016/j.mechmachtheory.2024.105673 2024

  21. [21]

    Discrete Cosserat Approach for Closed -Chain Soft Robots : Application to the Fin-Ray Finger,

    C. Armanini et al., “Discrete Cosserat Approach for Closed -Chain Soft Robots : Application to the Fin-Ray Finger,” pp. 1–16, 2021

    2021

  22. [22]

    Intrinsic Contact Sensing and Object Perception of an Adaptive Fin -Ray Gripper Integrating Compact Deflection Sensors,

    G. Chen et al., “Intrinsic Contact Sensing and Object Perception of an Adaptive Fin -Ray Gripper Integrating Compact Deflection Sensors,” IEEE Trans. Robot., vol. 39, no. 6, pp. 4482 –4499, 2023, doi: 10.1109/TRO.2023.3311610

    work page doi:10.1109/tro.2023.3311610 2023

  23. [23]

    Modeling and analysis of soft robotic fingers using the fin ray effect,

    X. Shan, “Modeling and analysis of soft robotic fingers using the fin ray effect,” pp. 1–20, 2020, doi: 10.1177/0278364920913926

    work page doi:10.1177/0278364920913926 2020

  24. [24]

    Soft Robots Modeling: A Structured Overview,

    F. R. C. Armanini, F. Boyer, A. T. Mathew, C. Duriez, “Soft Robots Modeling: A Structured Overview,” IEEE Trans. Robot., vol. 39, 2023, doi: 10.1109/TRO.2022.3231360

    work page doi:10.1109/tro.2022.3231360 2023

  25. [25]

    Statics and Dynamics of Continuum Robots Based on Cosserat Rods and Optimal Control Theories,

    M. A. F. Boyer, V. Lebastard, F. Candelier, F. Renda, “Statics and Dynamics of Continuum Robots Based on Cosserat Rods and Optimal Control Theories,” IEEE Trans. Robot., vol. 39, 2023, doi: 10.1109/TRO.2022.3226112

    work page doi:10.1109/tro.2022.3226112 2023

  26. [26]

    Modeling and prototyping of a soft closed -chain modular gripper,

    M. Anwar, T. Al Khawli, I. Hussain, D. Gan, and F. Renda, “Modeling and prototyping of a soft closed -chain modular gripper,” 2019, doi: 10.1108/IR-09-2018-0180

    work page doi:10.1108/ir-09-2018-0180 2019

  27. [27]

    Analytical Modeling and Design of Generalized PneuNet Soft Actuators with Three -Dimensional Deformations,

    X. Z. G. Gu, D. Wang, L. Ge, “Analytical Modeling and Design of Generalized PneuNet Soft Actuators with Three -Dimensional Deformations,” Soft Robot, vol. 8, 2021, doi: 10.1089/soro.2020.0039. 8 7 6 5 4 3 2 1 Link -0.03 -0.083 -0.237 -0.315 0.026 0.052 0.08 0.205 Experiment -0.03 -0.085 -0.242 -0.318 0.026 0.052 0.079 0.209 Theory -0.03 -0.084 -0.241 -0.3...

    work page doi:10.1089/soro.2020.0039 2021

  28. [28]

    Behavior Analysis of Biomimetic Soft Bending Actuators in Free Motion and Contact,

    M. Hadi, N. Ghalati, S. Akbari, H. Ghafarirad, and M. Zareinejad, “Behavior Analysis of Biomimetic Soft Bending Actuators in Free Motion and Contact,” J. Bionic Eng., vol. 20, no. 3, pp. 967 –981, 2023, doi: 10.1007/s42235-022-00322-w

    work page doi:10.1007/s42235-022-00322-w 2023

  29. [29]

    Evaluation of engineering properties for waste control of tomato during harvesting and postharvesting,

    A. Jahanbakhshi, V. Rasooli Sharabiani, K. Heidarbeigi, M. Kaveh, and E. Taghinezhad, “Evaluation of engineering properties for waste control of tomato during harvesting and postharvesting,” Food Sci. Nutr., vol. 7, no. 4, pp. 1473–1481, Apr. 2019, doi: 10.1002/fsn3.986

    work page doi:10.1002/fsn3.986 2019

  30. [30]

    Book Review: Introduction to Robotics: Mechanics and Control,

    A. Renfrew, “Book Review: Introduction to Robotics: Mechanics and Control,” Int. J. Electr. Eng. Educ., vol. 41, no. 4, pp. 388–388, 2004, doi: 10.7227/ijeee.41.4.11

    work page doi:10.7227/ijeee.41.4.11 2004

  31. [31]

    Learning-Based Optoelectronically Innervated Tactile Finger for Rigid -Soft Interactive Grasping,

    L. Yang, X. Han, W. Guo, F. Wan, J. Pan, and C. Song, “Learning-Based Optoelectronically Innervated Tactile Finger for Rigid -Soft Interactive Grasping,” IEEE Robot. Autom. Lett., vol. 6, no. 2, pp. 3817–3824, Apr. 2021, doi: 10.1109/LRA.2021.3065186

    work page doi:10.1109/lra.2021.3065186 2021