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

This paper presents the optimal design and analytical modeling of a Fin-Ray-inspired soft gripper finger for delicate agricultural handling, utilizing the Finite Rigid Elements Method to achieve high-accuracy force control and validated through ANSYS simulations and experimental testing.

The Gist

Imagine trying to pick up a ripe, juicy tomato with a robot hand. If the hand is made of stiff metal, it will crush the fruit. If it's too floppy, it won't hold it at all. This paper describes how the authors built and figured out the "brain" for a special kind of robot finger that solves this problem by mimicking the inside of a fish fin.

Here is a breakdown of their work in simple terms:

1. The Inspiration: A Fish Fin

The robot finger is based on the Fin Ray Effect. Think about the inside of a fish's tail fin. It has a soft outer skin but a skeleton inside made of small, angled ribs. When you push on the side of a fish fin, it doesn't just bend away; it actually curves around whatever is pushing it, hugging the object tightly. The authors wanted a robot finger that does the same thing: it wraps gently around irregular shapes like tomatoes without squishing them.

2. The Challenge: Predicting the Unpredictable

Soft robots are tricky to design because they are made of squishy materials (in this case, a flexible plastic called TPU). Unlike a rigid metal arm, a soft finger can bend in infinite ways. It's like trying to predict exactly how a wet noodle will flop when you poke it.

To solve this, the authors needed a way to do the math without getting bogged down in super-complex calculations that take hours to run. They used two main tools:

• The "Virtual Lego" Method (FREM): They broke the soft finger down into a chain of small, stiff blocks connected by tiny springs and dampers (like shock absorbers). This is the Finite Rigid Elements Method. It's like pretending a flexible snake is actually a chain of rigid links connected by hinges. This makes the math much faster and easier to solve, which is great for teaching a robot how to move in real-time.
• The "Super-Powerful Simulator" (ANSYS): They also used a heavy-duty computer simulation that looks at the material at a microscopic level to see exactly how it stretches and bends. This is their "gold standard" for checking if their "Virtual Lego" math is correct.

3. The Experiment: Finding the Perfect Shape

The authors didn't just guess the shape of the finger; they ran thousands of virtual tests to find the "Goldilocks" zone—not too stiff, not too floppy. They tweaked four main things:

• Width: How wide the finger is.
• Rib Spacing: How far apart the internal "bones" are.
• Rib Angle: The tilt of those internal bones.
• Rib Thickness: How thick those bones are.

The Winning Recipe:
They found that the best finger had:

• A width of 30 mm (about the width of a large thumb).
• Ribs spaced 10 mm apart.
• Ribs angled at -15 degrees (tilted slightly backward).
• Ribs that were 1 mm thick.

This specific combination allowed the finger to bend just enough to wrap around a tomato while applying the perfect amount of gentle pressure.

4. The Results: How Well Did It Work?

They built a real 3D-printed finger and tested it against their computer models.

• The "Virtual Lego" (FREM) model was surprisingly accurate, predicting how the finger would bend with only a 3% error.
• The "Super-Powerful Simulator" (ANSYS) was even more precise, with only a 2% error.

The real-world test confirmed that the finger could handle the delicate task of grasping without crushing. The math models they created are now ready to be used as the "brain" for a controller that can automatically adjust how hard the robot squeezes, ensuring it never hurts the fruit.

Summary

In short, the authors took a fish fin, turned it into a 3D-printed robot finger, and used a clever mix of "chain-link" math and heavy-duty computer simulation to figure out exactly how to build it. They proved that you can predict how a soft, squishy robot will behave with high accuracy, paving the way for robots that can harvest delicate crops without damaging them.

Technical Summary

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

Problem Statement
Soft robotic grippers are essential for the gentle manipulation of delicate, irregular objects, particularly in agricultural applications such as harvesting tomatoes. However, the inherent challenges of soft robotics—specifically nonlinear material behavior, infinite degrees of freedom, and variable material properties—complicate the development of precise force control strategies. While Finite Element Analysis (FEM) offers high accuracy, it is often computationally expensive for real-time control. Conversely, purely data-driven or simplified theoretical models may lack the necessary interpretability or accuracy for reliable dynamic control. This research addresses the need for a design and modeling framework that balances analytical accuracy with computational efficiency to enable precise force control in soft grippers.

Methodology
The study employed a three-pronged approach involving design optimization, analytical modeling, and experimental validation:

1. Design and Fabrication:

   • A Fin Ray Effect (FRE) gripper finger was designed using a trapezoidal longitudinal beam structure with internal ribs.
   • The finger was fabricated from Thermoplastic Polyurethane (TPU 95A) via 3D printing.
   • A parametric study was conducted using ANSYS Workbench (Static Structural module) to optimize four geometric variables: finger width, rib spacing, rib angle, and rib thickness.
   • Performance was evaluated based on four criteria: tip displacement (X and Y directions), total deflection, stress distribution, and contact force.

2. Analytical Modeling (Finite Rigid Elements Method - FREM):

   • To address the challenges of soft robot modeling, the authors developed a dynamic model using the Finite Rigid Elements Method.
   • The flexible finger was discretized into rigid elements connected by torsional springs and dampers, reducing the system to a finite number of degrees of freedom (8 DOF).
   • The model utilized the Denavit-Hartenberg (DH) convention for kinematic description and the Newton-Euler method to derive governing dynamic equations.
   • Assumptions included planar motion, negligible torsion/longitudinal stretching, and quasi-static equilibrium where inertial effects were disregarded in favor of force and moment balance.
   • Stiffness and damping coefficients were distributed parabolically along the finger, with higher values near the base and lower values near the tip.

3. Experimental Validation:

   • A testbed was constructed featuring a motorized base, a uniaxial bending load cell, and an encoder.
   • Motion data were captured via high-speed video (60 fps) and processed using image analysis (Tracker software) to extract link angles.
   • Motor torque was calibrated using current measurements (INA219 sensor), and contact forces were measured directly.
   • Experimental data were used to validate both the FREM theoretical model and the ANSYS numerical simulations.

Key Results

• Optimal Design Parameters: The parametric analysis identified the optimal configuration as a finger width of 30 mm, rib spacing of 10 mm, rib angle of -15°, and rib thickness of 1 mm. This configuration yielded a maximum contact force of approximately 9.88 N, with tip displacements of 1.43 mm (X) and 0.05 mm (Y), and a total deformation of 21.86 mm. The -15° angle and 1 mm thickness provided the best balance of flexibility, stiffness, and structural integrity.
• Model Accuracy:
  • ANSYS FEM: The numerical simulation predicted finger deformation with a 2% error compared to experimental results.
  • FREM Analytical Model: The theoretical model predicted deformation with a 3% error.
  • While the FEM approach offered higher precision in capturing stress and strain distributions, the FREM model successfully captured the overall deformation trends and link rotations with sufficient accuracy for control applications.
• Dynamic Behavior: The study confirmed that bending behavior shifts from linear at low loads (4 N) to nonlinear at higher loads (10 N). The FREM model effectively characterized this behavior, validating the use of quasi-static equilibrium equations for the system under the tested conditions.

Significance and Claims
The paper claims that the proposed framework successfully bridges the gap between high-fidelity simulation and real-time control requirements for soft robotics. By utilizing the Finite Rigid Elements Method, the authors provide a computationally efficient analytical model that maintains sufficient accuracy (3% error) for the development of force controllers, avoiding the computational overhead of full FEM simulations during control loops.

The research demonstrates that combining parametric FEM optimization with FREM theoretical modeling creates a robust foundation for designing bio-inspired soft grippers. The authors assert that this approach enables the precise force control necessary for handling delicate agricultural products, offering a reliable alternative to black-box data-driven methods that require extensive retraining and lack interpretability. The validated model serves as a practical tool for deriving optimal designs and implementing intelligent control strategies in dynamic soft robotic applications.