The development of efficient and non-destructive end-effectors represents a crucial technological hurdle for the widespread adoption and industrialization of fruit harvesting robots. While rigid grippers offer high precision and force, their inherent lack of compliance and adaptability often leads to bruising and damage of delicate produce. To overcome these limitations, this paper presents the design, simulation, and experimental validation of a novel three-fingered flexible end effector inspired by the Fin Ray Effect (FRE). Utilizing finite element analysis (FEA), five distinct internal structural configurations for the flexible fingers were evaluated to determine the optimal design balancing contact force and structural deformation. A prototype was fabricated based on the optimal model, and comprehensive experiments were conducted. Results demonstrate that the developed flexible end effector can reliably grasp loads up to 1.6 kg, achieving a grip-to-weight ratio of 3.44, and offers universal, protective handling for fruits with diameters up to 13 cm.
1. Introduction and Design Principles
The global fruit industry faces significant challenges during the harvesting season, characterized by labor-intensive processes, high costs, and workforce shortages. Robotic harvesting has emerged as a promising solution. The end effector, being the component in direct contact with the fruit, is paramount to the system’s success. Its design must ensure secure grasping while preventing damage to the often tender and variably shaped produce.
Traditional rigid end effectors, though powerful, suffer from poor adaptability and often cause surface damage. Alternatives like pneumatic soft grippers or jamming-based systems may lack sufficient grasping force for robust fruit detachment. This work focuses on a flexible end effector design based on the passive adaptation of the FRE. The core design principles for the harvesting end effector are: (1) non-destructive gripping of delicate fruits; (2) high shape adaptability to accommodate natural variations; (3) strong enveloping capability for stable holds; and (4) structural simplicity, reliability, and cost-effectiveness.
The proposed end effector comprises two main assemblies: the flexible finger modules and the fixed drive mechanism. The finger’s geometry is a triangular structure featuring two inclined fin rays connected by a series of internal ribs. Upon contact with an object, the structure bends concavely around it, enabling conformal grasping. The key innovation lies in the optimization of the internal rib configuration to enhance the layer jamming effect and overall performance.
To systematically study the influence of rib architecture, five distinct finger designs were conceived, varying rib shape, distribution angle, and density:
- Parallel Sparse Ribs
- Parallel Thickened Ribs
- Parallel Dense Ribs
- Inclined Sparse Ribs
- Inclined Dense Ribs
The finger length is designed to be 100 mm to adequately envelop medium-sized fruits (e.g., apples, oranges) with diameters up to 130 mm, ensuring a fingertip coverage exceeding 75% of the fruit’s circumference during a three-fingered grasp.
The fixed drive assembly was carefully engineered to maximize the operational workspace and avoid interference. It consists of finger mounts, a support base (with fixed and moving plates connected by linkages), and a leadscrew motor. Crucially, the motor is mounted with the screw oriented downward, preventing any protruding components from entering the fruit grasping zone and causing potential damage.
2. Finite Element Analysis and Structural Optimization
The flexible fingers are fabricated from Thermoplastic Polyurethane (TPU), a material known for its high elasticity, toughness, and durability. Predicting the non-linear deformation of such hyperelastic structures under load requires sophisticated simulation. A finite element analysis (FEA) was conducted using ANSYS Workbench to evaluate the structural response of the five finger designs.
The TPU material was modeled with a density ($\rho$) of 1200 kg/m³, a Young’s Modulus ($E$) of 11.7 MPa, and a Poisson’s ratio ($\nu$) of 0.45. A static structural simulation was set up. The bottom surface of the finger was defined as a fixed support, and concentrated loads of 5 N and 10 N were applied normally to the expected central contact area on one fin ray.
The mesh convergence was critically assessed. Different element sizes (resolutions 2 through 6) were tested for the Parallel Thickened Rib design under 10 N load. The total deformation stabilized with finer meshing, as shown in Table 1. A high-resolution mesh (Resolution 6) was selected for all subsequent comparative analyses to ensure result accuracy.
| Mesh Resolution | Nodes | Elements | Total Deformation under 10N (mm) |
|---|---|---|---|
| 2 | 17,673 | 8,693 | 17.247 |
| 3 | 22,343 | 11,380 | 17.785 |
| 4 | 30,641 | 16,227 | 18.273 |
| 5 | 35,042 | 18,788 | 18.694 |
| 6 | 49,124 | 27,227 | 19.307 |
The simulation outcomes for all five designs under 5 N and 10 N loads are summarized in Table 2. The key performance metrics were total deformation and directional deformation along the loading axis.
| Finger Design | Total Deformation @5N (mm) | Total Deformation @10N (mm) | Directional Deformation @5N (mm) | Directional Deformation @10N (mm) |
|---|---|---|---|---|
| Parallel Sparse | 16.004 | Failure | 15.328 | Failure |
| Parallel Thickened | 10.017 | 19.307 | 15.269 | 22.771 |
| Parallel Dense | 10.243 | 17.439 | 9.911 | 16.598 |
| Inclined Sparse | 13.710 | Failure | 13.144 | Failure |
| Inclined Dense | 10.533 | 18.068 | 11.172 | 17.339 |
Analysis: The sparse rib designs (both parallel and inclined) exhibited the largest deformation under 5 N, indicating high flexibility. However, they experienced structural failure (simulated excessive distortion/tearing) under the 10 N load, signifying insufficient rigidity for reliable grasping. The dense rib designs did not fail and provided moderate deformation, but their adaptability was somewhat constrained by the pronounced layer jamming effect. The Parallel Thickened Rib design emerged as the optimal compromise. It withstood the 10 N load without failure while offering superior directional deformation (conformability) compared to the dense designs. This structure effectively balances compliance for gentle contact with the necessary structural integrity for secure holding, making it the chosen design for the prototype end effector.
The contact mechanics can be conceptually related to the deformation. The average contact pressure $P_{avg}$ on the fruit is related to the total contact force $F$ and the enveloped surface area $A_{contact}$:
$$ P_{avg} \approx \frac{F}{A_{contact}} $$
A larger, more conformal contact area $A_{contact}$, achieved through greater directional deformation, reduces the average pressure on the fruit skin for a given grasping force, thereby minimizing damage risk.
3. Fabrication and Prototype Assembly
The optimized finger design was fabricated using Fused Deposition Modeling (FDM) with TPU filament. A key challenge was printing the intricate internal rib structure without stringing or poor surface finish. This was solved by modeling the finger as a solid triangular prism with an internal cavity in the CAD software. The internal rib pattern was then defined not by geometry, but by the infill parameters (gyroid pattern at high density) within the slicing software (Cura). This method ensured smooth external surfaces and eliminated unnecessary nozzle travel moves, resulting in high-quality, repeatable prints for all five design variants.
The complete end effector prototype was assembled with the 3D-printed TPU fingers, resin finger mounts, a machined stainless-steel support base, and a leadscrew motor. The total weight of the end effector was 464.7 g. A separate control box housing an Arduino microcontroller, motor driver, and power supply was built, featuring simple buttons for open, close, and stop commands.
4. Experimental Validation and Results
A series of experiments were conducted to validate the simulation findings and evaluate the real-world performance of the flexible end effector.
4.1 Finger Load-Displacement Validation
The Parallel Thickened finger was clamped at its base, and a digital force gauge was used to apply a 10 N load at the simulated contact point. The measured displacement was approximately 19.1 mm. This closely matched the FEA result (19.307 mm) obtained with the high-resolution mesh (Resolution 6), validating the accuracy of the simulation methodology.
4.2 Grasping Force and Load Capacity Test
The prototype’s maximum grasping force was measured by having it grip a fruit connected to a tensile force gauge. The end effector consistently achieved an average pull force of 16 N before slippage. This translates to a safe grasping capacity for fruits weighing up to 1.6 kg. The grip-to-weight ratio, a key performance indicator, is calculated as:
$$ Grip\text{-}to\text{-}Weight\ Ratio = \frac{Max\ Grasped\ Weight}{End\text{-}Effector\ Weight} = \frac{1.6\ kg}{0.465\ kg} \approx 3.44 $$
This demonstrates that the flexible end effector can handle loads significantly heavier than its own mass, confirming its practical strength for fruit harvesting tasks.
4.3 Universal Fruit Grasping Test
The adaptability and non-destructive capability were tested on a variety of fruits with different shapes and sizes: cherry tomatoes, strawberries, mandarins, oranges, tomatoes, pears, and apples. For each fruit type, five samples were used. A successful grasp was defined as one where the fruit was held securely for 30 seconds and released with no visible surface damage.
The enveloping performance was quantified using a simplified coverage ratio. The approximate fruit surface area $S_{fruit}$ is estimated from its major diameter $D$. The effective contact area provided by the three fingers $S_{contact}$ is related to their deformed geometry. The coverage ratio $C_r$ is:
$$ C_r = \frac{S_{contact}}{S_{fruit}} \approx k \cdot \frac{A_{finger}}{ \pi (D/2)^2 } $$
where $A_{finger}$ is the effective area of one finger in contact and $k$ is a factor accounting for three-finger coordination. The experimental results are summarized in Table 3.
| Fruit Type | Avg. Max Diameter (mm) | Estimated Avg. Coverage Ratio, $C_r$ | Success Rate |
|---|---|---|---|
| Cherry Tomato | 28.7 | ~78% | 100% |
| Strawberry | 47.4 | ~66% | 100% |
| Mandarin | 51.1 | ~60% | 100% |
| Orange | 85.9 | ~34% | 100% |
| Tomato | 92.7 | ~33% | 100% |
| Pear | 100.3 | ~23% | 100% |
| Apple | 103.4 | ~23% | 100% |
The flexible end effector achieved a 100% success rate across all fruit types. Smaller fruits achieved high coverage ratios (>60%), leading to extremely stable and gentle grasps. For larger fruits, the coverage ratio was lower but still sufficient for secure holding, as evidenced by the successful tests and the independent force capacity measurement. The passive adaptation of the FRE structure allowed every finger to conform to the local fruit contour, distributing pressure evenly and preventing point-load damage.
4.4 Comparative Analysis
Informal comparisons were made against two common three-fingered alternatives: a pneumatic soft gripper and a rigid robotic gripper. The pneumatic gripper, while very soft, often failed to achieve a stable grip on heavier, smooth-skinned fruits like apples, and its measured pull-off force was lower (~7 N). The rigid gripper, although strong, frequently caused visible indentation or bruising on the fruit skin during grasping due to its lack of compliance. The presented FRE-based flexible end effector demonstrated a superior combination of sufficient force (16 N), excellent adaptability, and non-destructive contact, highlighting its specific advantages for agricultural harvesting applications.
5. Conclusion
This research successfully designed, optimized, and validated a novel flexible end effector for fruit harvesting robots. By leveraging the biomimetic Fin Ray Effect and conducting systematic finite element analysis, an optimal internal rib structure (Parallel Thickened) was identified that optimally balances flexibility and structural strength. The fabricated prototype demonstrated exceptional performance: a high load capacity of 1.6 kg (grip-to-weight ratio of 3.44) and a 100% success rate in non-destructively grasping a wide variety of fruits up to 13 cm in diameter. The end effector passively conforms to irregular shapes, ensuring stable, low-pressure contact that is critical for handling delicate produce. This work provides a practical and effective solution to a key challenge in agricultural robotics, paving the way for more reliable and commercially viable automated harvesting systems. Future work will focus on integrating this end effector with advanced machine vision and control algorithms for fully autonomous operation in orchard environments.