The global citrus industry is a vital agricultural sector, yet it faces significant challenges in labor-intensive harvesting. Manual picking is strenuous and inefficient, driving the need for robotic automation. A critical component of any harvesting robot is the end effector—the device that physically interacts with and detaches the fruit. Citrus fruits present a unique challenge for end effector design due to their tough, woody stems (peduncles), which cannot be easily broken by twisting or pulling without risking damage to the fruit. This necessitates a cutting mechanism, often leading to bulky, complex designs where gripping and cutting actions are separate. This paper addresses these challenges by presenting the design, optimization, and testing of a novel occlusal end effector for citrus harvesting. The core innovation is a spherical, biting motion that integrates gripping and shearing into a single, compact action, reducing operational disturbance in cluttered orchard environments.
1. Introduction and State of the Art
Robotic fruit harvesting has seen extensive research, with various end effector designs proposed for different fruit types. For fruits like apples, tomatoes, and pears, which possess an abscission layer, end effectors often rely on simple grasping, twisting, or pulling actions to achieve detachment. These designs prioritize gentle handling and low energy consumption. However, for citrus fruits, the absence of a reliable abscission layer and the presence of a lignified stem require a different approach. A successful citrus end effector must reliably sever the peduncle while securely capturing the fruit to prevent it from falling and getting bruised by branches.
Existing research into citrus end effectors can be broadly categorized. Some designs forego cutting entirely, relying on high gripping forces and rotation, but this often leads to poor success rates or fruit damage. Other, more prevalent designs incorporate a dedicated cutting mechanism—such as scissors, blades, or saws—separate from the gripper. While effective, this separation increases the end effector’s size, weight, and complexity, making it more likely to collide with and disturb surrounding foliage during operation. Recent advancements have explored integrated solutions. For instance, bio-inspired designs mimicking a snake’s bite have been proposed, using a pneumatic actuator to drive a biting shear action. Another design features a fork-type cutter with laser guidance for stem length control but suffers from a small fruit-positioning tolerance, demanding extremely high precision from the vision and robotic arm systems.
This paper builds upon these concepts, focusing on a shearing-based solution. The key insight is that a dual-blade scissor-like action is most effective for cutting woody stems, and the parameters of this cut—especially blade gap—are crucial for success. We introduce an end effector that performs a spherical closure, akin to a mouth closing, where the inner surfaces of two hemispherical shells act both to envelope the fruit and to drive two opposing blades in a precise shearing motion against the stem. This fusion of functions results in a compact, low-disturbance design. The development process involved: 1) a comprehensive analysis of citrus physical and stem-shearing mechanical properties to inform design parameters, 2) the geometric and kinematic design of the occlusal mechanism, 3) a parameter optimization to maximize fruit-positioning tolerance while controlling the critical blade gap, 4) structural analysis via finite element simulation, and 5) field validation of a prototype. The end effector demonstrated a high success rate in severing citrus stems, meeting the practical requirements for automated harvesting.
2. Analysis of Citrus Physical Characteristics
The design of an effective harvesting end effector is fundamentally grounded in the physical properties of the target fruit. For citrus, this entails understanding both its geometric dimensions and the mechanical behavior of its stem during shearing.
2.1 Geometric Properties of Citrus Fruit
To determine the necessary internal dimensions of the end effector’s capturing cavity, the geometric size of mature ‘Red Beauty’ citrus fruits was measured. A sample of 100 fruits was randomly selected from an orchard, and their major (equatorial) and minor (polar) diameters were recorded using calipers. The statistical summary is presented in Table 1.
| Parameter | Major Diameter (mm) | Minor Diameter (mm) |
|---|---|---|
| Maximum | 81.9 | 79.1 |
| Minimum | 60.1 | 54.8 |
| Average | 70.4 | 64.9 |
The data shows that citrus fruits are generally oblate spheroids, with the major diameter typically larger than the minor diameter. However, the difference is usually within 10 mm. For the purpose of designing the containment shell of the end effector, the fruit can be effectively modeled as a sphere with a diameter range of 60.1 mm to 81.9 mm. To provide a safe margin for fruit entry and accommodation, the internal diameter of the capturing shell was designed to be 100 mm.
2.2 Shearing Mechanical Properties of Citrus Stems
Since the proposed end effector employs a dual-blade scissor-like shearing action to sever the stem, a detailed understanding of the stem’s shearing mechanics is paramount. The force required to cut the stem under various conditions dictates the necessary actuator force and informs critical design parameters like blade sharpness and gap.
First, the diameter distribution of citrus stems was investigated. Measurements from 100 stems revealed a normal distribution ranging from 2 mm to 4 mm, with the majority falling between 2.5 mm and 3.5 mm. This defines the operational range for the shearing mechanism of the end effector.
Shearing tests were conducted using a microcomputer-controlled electronic universal material testing machine. Custom shear blades (30° edge angle, Cr12MoV steel) were mounted on the machine’s fixtures. Fresh citrus stems, harvested within 24 hours, were used for all tests. The force-displacement curve during shearing typically shows a force that increases to a distinct peak (the peak shear force) and then drops sharply upon stem failure. This peak shear force is the critical metric for designing the end effector’s cutting capability.
The factors influencing the peak shear force were categorized into controllable and uncontrollable variables from a harvesting robot’s perspective.
- Uncontrollable Factors: Stem diameter (2-4 mm), stem oblique angle γ (the angle between the stem axis and the normal to the shear plane, 0-75°), and number of leaves obstructing the cut (0-3 pieces).
- Controllable Factors: Shear speed (20-200 mm/min) and blade gap (0.5-2.0 mm).
A series of experiments were designed where one factor was varied while others were held at default values (stem diameter: 3.0 mm, shear speed: 100 mm/min, oblique angle: 0°, leaves: 0, blade gap: 0.5 mm). For each test condition, 10 repetitions were performed, and the average peak shear force was calculated. Response surface models were fitted to the data using a second-order polynomial (Poly22) model based on the least squares method.
1. Effect of Stem Diameter and Shear Speed: The fitted response surface for peak shear force (z, in N) as a function of stem diameter (x, in mm) and shear speed (y, in mm/min) is shown in Figure 5a of the original work. The governing equation is:
$$z = 19.71 – 12.36x – 0.01981y + 5.215x^2 – 0.01934xy + 0.0001924y^2 \quad (R^2 = 0.9922)$$
The analysis confirms that stem diameter is the primary factor, with shear force increasing significantly with diameter. Shear speed has a minor, inverse effect.
2. Effect of Stem Diameter and Oblique Angle: The response for stem diameter (x) and oblique angle (y1, in degrees) is given by:
$$z = 11.98 – 6.782x – 0.2101y_1 + 3.441x^2 – 0.04275xy_1 + 0.003421y_1^2 \quad (R^2 = 0.9895)$$
The oblique angle becomes a significant factor beyond 30°, substantially increasing the required shear force at higher angles. This informs the ideal approach angle for the robotic arm.
3. Effect of Stem Diameter and Leaf Obstruction: The model for leaves blocked (y2) is:
$$z = 6.476 – 3.47x + 0.2907y_2 + 3.119x^2 + 0.06311xy_2 + 0.03125y_2^2 \quad (R^2 = 0.9981)$$
A few leaves in the shear path have a negligible effect on the peak force, simplifying the end effector’s operational requirements.
4. Effect of Stem Diameter and Blade Gap: This is the most critical controllable factor. The response surface is defined by:
$$z = -5.504 + 1.593x + 10.75y_3 + 2.901x^2 – 4.19xy_3 + 2.661y_3^2 \quad (R^2 = 0.9737)$$
where y3 is the blade gap in mm. Furthermore, the success rate of shearing was recorded for different gaps, as shown in Table 2.
| Blade Gap (mm) | Shear Success Rate for Stem Diameter (mm) | ||||
|---|---|---|---|---|---|
| 2.0 | 2.3 | 3.0 | 3.6 | 4.0 | |
| 0.5 | 100% | 100% | 100% | 100% | 100% |
| 1.0 | 80% | 100% | 100% | 100% | 100% |
| 1.5 | 0% | 50% | 100% | 100% | 100% |
| 2.0 | 0% | 0% | 70% | 100% | 100% |
The results are decisive: a large blade gap severely impairs the ability to shear thinner stems. For reliable operation across the typical stem diameter range, the end effector must be designed to maintain a blade gap of 1 mm or less throughout the cutting action. This finding became a central constraint in the optimization of the mechanism.
3. Design of the Occlusal Citrus Harvesting End Effector
3.1 Conceptual and Preliminary Design
The core design philosophy was to unify the gripping and shearing functions into a single, coherent motion driven by one actuator, thereby minimizing size and complexity. Inspiration was drawn from a biological biting or swallowing action. The mechanism is based on a spherical four-bar linkage variant. Two hemispherical shells—an inner shell and an outer shell—are mounted on coaxial hinge shafts fixed to a central frame, allowing them to rotate like jaws. The outer shell has a slot along its equator. A connecting link is attached to the inner shell, passes through this slot, and connects to one end of a curved driving link. Another curved link is connected to the outer shell. The opposite ends of both curved links are joined to the rod of a linear electric actuator.
Blades are mounted on lugs located opposite the hinge points on each shell. In the open state, the shells are rotated downward, creating a large spherical opening. During operation, the robotic arm positions the open end effector around the fruit. Upon activation, the electric retractor pulls the curved links, causing both spherical shells to rotate upward and close in a biting motion. As they close, they envelop the fruit, and the blades converge to shear the stem captured between them. The fruit is then securely held within the spherical cavity, protected from branch impacts. To release the fruit, the actuator extends, opening the shells.
3.2 Geometric Modeling and Parameter Optimization
The kinematic geometry of the end effector was modeled to establish the relationship between design parameters and performance. Key parameters include the lengths of the shell links ($l_{CF}$, $l_{CH}$), the blade arms ($l_{FG}$, $l_{HI}$), and the fixed angles of the blade mounts relative to the shell links ($θ_5$, $θ_6$). The initial design provided a baseline, but an optimization routine was necessary to enhance performance.
Optimization Model: Two primary objectives guided the optimization of the end effector:
- Maximize Fruit-Positioning Tolerance: This is the ability of the end effector to successfully acquire the fruit despite errors in robotic arm positioning or visual recognition. It is directly related to the distance between the blade tips ($G$ and $I$) in the fully open state. A larger opening accommodates greater positional error.
- Control Blade Gap During Closure: As established by the mechanical tests, maintaining a blade gap ≤1 mm during shearing is critical for success. The design must ensure this gap is minimized and controlled throughout the biting arc.
Therefore, an optimization model was formulated with the following components:
- Design Variables: $X = (l_{CF}, l_{CH}, l_{FG}, l_{HI}, θ_5, θ_6)$.
- Objective Function: Maximize the initial distance between blade tips $l_{GI}$.
$$F(X) = \max \sqrt{(x_G – x_I)^2 + (y_G – y_I)^2}$$ - Main Constraints:
- Blade Gap Control: Ensure the distance from the rotation center $C$ to each blade tip is nearly equal during shearing, implying a parallel shear. This was enforced as: $0 \text{ mm} \leq l_{CG} – l_{CI} \leq 1 \text{ mm}$, where $l_{CG}$ and $l_{CI}$ are calculated from the geometry.
- Shear Completion: Ensure the blade tips cross the vertical centerline by 2-3 mm at the end of the stroke for complete severance: $2 \text{ mm} \leq x_{G’} \leq 3 \text{ mm}$ and $-3 \text{ mm} \leq x_{I’} \leq -2 \text{ mm}$.
- Interference Prevention: Prevent the lower blade from colliding with the upper blade assembly: $l_{GI} \leq l_{CF} \sinθ_5$.
- Practical Bounds: Set reasonable limits on link lengths and angles based on the overall end effector size and desired motion.
The optimization was solved using MATLAB’s `fmincon` solver. After 25 iterations, the optimal design variables were found:
$$X_{opt} = (80.00, 79.99, 31.84, 31.83, 68.00, 67.98)$$
The optimized initial blade tip distance $F(X_{opt})$ was 103.17 mm, a 15.4% increase from the preliminary design’s 89.43 mm. The fruit-positioning tolerance η, calculated as the percentage increase of the entry size over the fruit diameter, improved substantially:
$$\eta = \frac{L_g – D_h}{D_h} \times 100\%$$
where $L_g$ is the maximum entry dimension and $D_h$ is the fruit diameter. The tolerance range improved from 9.2%-48.8% to 26.0%-71.7%. This significant enhancement makes the end effector much more robust to positioning inaccuracies.
3.3 Static Force Analysis
A static analysis was conducted at the moment of shearing to determine the required actuator force. Using the principle of virtual work and kinematic relations (instant centers), the relationship between the actuator force $F_A$ and the shear force $F_S$ (approximately equal for each blade, $F_G \approx F_I$) applied to the stem was derived. The analysis, neglecting friction and inertial forces, yielded a relation of the form:
$$F_S \approx \frac{F_A \cdot l_{BC} \cdot l_{A’J^*}}{2 \cdot l_{CF} \cdot l_{B’J^*} \cdot \sinθ_5}$$
where $l_{A’J^*}/l_{B’J^*}$ is a ratio related to the instant center of the driving link, which increases during the stroke. This implies the mechanical advantage, and thus the available cutting force, increases as the end effector closes—a beneficial characteristic for overcoming the peak shear force. Based on this analysis and the measured peak shear forces (up to ~50 N for a 4 mm stem), a linear electric actuator with a 500 N maximum thrust force and a 30 mm/s speed was selected to provide a substantial safety margin.
4. Structural Analysis via Finite Element Simulation
To validate the structural integrity of the design and to investigate the effects of component flexibility—particularly important as the spherical shells were to be 3D printed from a resin material—a finite element analysis (FEA) was performed using ANSYS Workbench.
Model Setup: A transient structural simulation was set up to model the shearing moment. Materials were assigned: Cr12MoV steel for the blades, isotropic properties for the stem (modeled as a cylinder), and Yellow-Green Resin for the 3D-printed shells (Young’s Modulus: 2.70 GPa, Poisson’s ratio: 0.42). The stem was bound to the blades using a bonded contact. Appropriate joints (revolute, fixed) were applied to simulate the mechanism’s constraints, and a displacement was applied to the actuator connection point to drive the closing motion.
Simulation Results and Insights:
- Deformation and Blade Gap: The simulation confirmed that deformation of the resin shells occurs under load. The blade tips exhibited displacements primarily in the Y-axis (closing direction) of 0.78-1.25 mm for the upper blade and 0.31-0.78 mm for the lower blade. Crucially, the displacements did not cause significant misalignment that would widen the effective shearing gap. The largest deformation (approx. 4.4-5.8 mm) occurred at the hinge areas of the shells. To compensate for this elastic deflection and ensure full closure for shearing, the stroke of the electric actuator was increased by 5 mm beyond the kinematic calculation.
- Stress Validation: The stress cloud plots for the shells showed a maximum von Mises stress in the range of 30.5-45.8 MPa. Comparing this to the material’s tensile strength (49-58 MPa) and flexural strength (69-76 MPa) confirmed that the shells have a sufficient safety factor for the operational loads, validating the strength of the end effector’s structure.
5. Prototype Development and Field Harvesting Test
A physical prototype of the optimized occlusal citrus harvesting end effector was fabricated. Key components like the blades and frame were machined from metal, while the complex spherical shells and connecting links were 3D printed from the specified Yellow-Green Resin. The selected 500 N electric linear actuator was integrated to provide the driving force.
Field Test Procedure: The prototype was tested in a citrus orchard in November 2023. The end effector was manually positioned over target ‘Red Beauty’ citrus fruits to evaluate its core shearing and capturing function, isolating the mechanism’s performance from robotic vision and arm control complexities. For each trial, the fruit stem diameter and the resulting cut angle were recorded, along with the success or failure of clean stem severance and fruit capture.
Test Results: A total of 20 picking trials were conducted on fruits with varying stem diameters. The results are summarized in Table 3.
| Trial | Stem Diameter (mm) | Cut Angle (°) | Result | Trial | Stem Diameter (mm) | Cut Angle (°) | Result |
|---|---|---|---|---|---|---|---|
| 1 | 3.1 | 11 | Success | 11 | 3.3 | 10 | Success |
| 2 | 3.1 | 0 | Success | 12 | 3.9 | 15 | Success |
| 3 | 2.8 | 14 | Success | 13 | 2.9 | 22 | Success |
| 4 | 3.6 | 22 | Success | 14 | 2.6 | 0 | Success |
| 5 | 3.2 | 6 | Success | 15 | 2.5 | 6 | Success |
| 6 | 2.6 | 33 | Success | 16 | 3.0 | 17 | Success |
| 7 | 4.0 | 8 | Success | 17 | 3.9 | 30 | Failure |
| 8 | 4.0 | 12 | Success | 18 | 3.2 | 17 | Success |
| 9 | 3.5 | 3 | Success | 19 | 3.0 | 35 | Success |
| 10 | 2.7 | 25 | Success | 20 | 2.3 | 10 | Success |
The field test yielded a 95% success rate (19 out of 20) for cleanly severing stems with diameters ≤ 4 mm. The single failure occurred on a fruit with a 3.9 mm stem at a 30° cut angle, a condition identified by the mechanical tests as demanding a higher shear force. This high success rate validates the design principles, optimization, and the practical functionality of the occlusal end effector. The spherical shell design successfully captured and protected the fruit after shearing in all successful trials.
6. Conclusion
This paper presented the comprehensive development of a novel occlusal end effector for robotic citrus harvesting. The work systematically progressed from fundamental biomechanical studies to optimized design, simulation, and field validation.
The key contributions and findings are:
- Biomechanical Foundation: Detailed shear tests quantified the effects of stem diameter, oblique angle, and—most critically—blade gap on the peak shear force. Establishing that a blade gap under 1 mm is essential for reliable shearing became a cornerstone design constraint.
- Innovative Mechanism Design: The proposed end effector uses a spherical biting motion to integrate fruit gripping and stem shearing into a single, compact action driven by one actuator. This reduces the overall footprint and potential for disturbance in the canopy compared to designs with separate grippers and cutters.
- Parameter Optimization: A formal optimization routine significantly improved the fruit-positioning tolerance from 9.2-48.8% to 26.0-71.7% by maximizing the initial blade opening, while strictly enforcing constraints to maintain a sub-1 mm shearing gap. This greatly enhances the robustness of the end effector to positioning errors from the robotic system.
- Validated Performance: Static and finite element analyses confirmed the structural soundness and informed actuator selection and deflection compensation. The fabrication of a prototype and subsequent field tests demonstrated a 95% success rate in shearing citrus stems under real orchard conditions, proving the practical efficacy of the design.
The occlusal citrus harvesting end effector represents a effective solution to the challenge of automated citrus picking. Its successful performance underscores the importance of a design process grounded in physical properties, guided by systematic optimization, and validated through rigorous testing. Future work will focus on integrating this end effector with a robotic manipulator and machine vision system for fully autonomous harvesting cycles, as well as exploring material and manufacturing improvements for enhanced durability and lower cost.