In modern agriculture, the automation of fruit harvesting is a critical challenge, particularly for crops like citrus, which require delicate handling to avoid damage. Traditional manual picking is labor-intensive, time-consuming, and costly, driving the need for robotic solutions. Among these, the end effector—the component that directly interacts with the fruit—plays a pivotal role in determining the efficiency and success of the harvesting process. Existing end effectors often suffer from issues such as long single-fruit picking times and low success rates, especially when dealing with citrus fruits that have woody stems requiring significant cutting force. To address these limitations, I developed a novel end effector for citrus picking robots, focusing on high-speed operation, simple control, and seamless integration with robotic arms. This end effector is designed to perform non-destructive grasping and rapid stem cutting, leveraging advanced materials and simulation techniques to ensure robustness and reliability. In this article, I will detail the design principles, kinematic and dynamic analyses, simulation results, and field experiments, providing a comprehensive overview of this innovative end effector.
The core of my design is an end effector composed of several key subsystems: a grasping mechanism, a cutting mechanism, a connection frame, and a control system. The grasping mechanism employs a two-jaw configuration driven by pneumatic fingers, enabling gentle yet firm envelopment of the fruit. The cutting mechanism integrates blades that sever the stem once the fruit is securely held. The connection frame facilitates attachment to a robotic arm, while the control system coordinates movements based on visual feedback. For material selection, I chose 20SiMnMoV alloy structural steel due to its high strength, rigidity, and wear resistance, with an elastic modulus of 210 GPa, density of 7,850 kg/m³, Poisson’s ratio of 0.3, and yield strength of 1,000 MPa. This ensures the end effector can withstand the stresses encountered during picking operations. The overall design prioritizes compactness, with the jaws having a motion radius of 45 mm to accommodate citrus fruits typically up to 90 mm in diameter, and a main frame height of 110 mm for optimal maneuverability.
To achieve precise motion control, I conducted a detailed kinematic analysis of the end effector’s jaw mechanism. The jaws operate via a four-bar linkage system, with symmetrical links that move in unison to open and close. Defining the geometric parameters as shown in the analysis, let \( AB = l_1 \), \( BC = l_2 \), \( CD = l_3 \), and \( AD = l_4 \). The angles are denoted as \( \phi \) for the link AD relative to the x-axis, \( \beta \) for BC, \( \gamma \) for CD, with instantaneous changes \( \alpha \) for AD and \( \theta \) for BC. The kinematic relationships are governed by the following equations:
$$ l_4 \cos \phi + l_3 \cos \gamma – l_2 \cos \beta = l_1 $$
$$ l_4 \sin \phi – l_3 \sin \gamma – l_2 \sin \beta = 0 $$
$$ l_4 \cos (\phi – \alpha) + l_3 \cos \gamma – l_2 \cos (\beta + \theta) = l_1 $$
$$ l_4 \sin (\phi – \alpha) – l_3 \sin \gamma – l_2 \sin (\beta + \theta) = l $$
From these, the angle \( \beta \) can be derived as:
$$ \beta = \pi – \arccos \left( \frac{l_2^2 + A^2 – l_4^2}{2 l_2 A} \right) – \arccos \left( \frac{l_1^2 + A^2 – l_4^2}{2 l_1 A} \right) $$
where \( A = \sqrt{l_1^2 + l_4^2 – 2 l_1 l_4 \cos \phi} \). Similarly, the angular displacement \( \theta \) is given by:
$$ \theta = u – \arccos \left( \frac{l_2^2 + C_1^2 – l_3^2}{2 l_2 C_1} \right) – \arccos \left( \frac{l_1^2 + C_1^2 – l_4^2}{2 l_1 C_1} \right) – \beta $$
with \( C_1 = \sqrt{l_1^2 + l_4^2 – 2 l_1 l_4 \cos (\phi – \alpha)} \). The motion of the jaw tip, where cutting occurs, follows a trajectory determined by these equations. To optimize the design, I focused on maximizing the transmission angle \( \delta \), which influences the cutting force. The transmission angle is defined as:
$$ \delta = \arccos \left( \frac{l_4^2 + l_3^2 – l_2^2 – l_1^2 – 2 l_1 l_2 \cos \epsilon}{2 l_1 l_2} \right) $$
where \( \epsilon \) is the angular displacement of the drive link. By analyzing this function, I ensured that the minimum transmission angle is maximized, enhancing the cutting torque for effective stem severance. The driving mechanism uses an SMC pneumatic finger cylinder (model MHY2-20D), which provides a clamping torque of 1.10 N·m at 0.5 MPa pressure, sufficient for the woody citrus stems. The cylinder’s compact size allows for integration into the end effector without compromising agility.
To validate the structural integrity of the end effector, I performed finite element analysis (FEA) using simulation software. A 3D model was created in CATIA, simplified in UG, and analyzed in ABAQUS for both modal and static strength assessments. The mesh was generated with a combination of hexahedral elements for the links and tetrahedral elements for the blades and cylinder, resulting in 2,221,268 elements with quality checks. The material properties of 20SiMnMoV steel were applied, and constraints were set to mimic real-world picking conditions. For modal analysis, I extracted the natural frequencies and mode shapes to evaluate dynamic behavior and avoid resonance. The first six modes correspond to rigid body motions and were excluded; modes 7 to 12 were analyzed, as summarized in Table 1.
| Mode | Frequency (Hz) | Mode Shape Description |
|---|---|---|
| 7 | 201.20 | Swinging in the Y-axis direction |
| 8 | 350.07 | Swinging in the X-axis direction |
| 9 | 410.66 | Bending vibration in the Y-axis direction |
| 10 | 448.56 | Torsional swing in the Y-axis direction |
| 11 | 466.63 | Combined bending in Y-axis and torsion in Z-axis |
| 12 | 497.35 | Combined torsion in X-axis and bending in Y-axis |
The frequencies range from 201.20 Hz to 497.35 Hz, with mode shapes involving bending and torsion. Since external excitations from the robotic arm typically fall below 15 Hz, the condition for avoiding resonance is met:
$$ 0.75 \omega_0 < \omega < 1.3 \omega_0 $$
where \( \omega_0 \) is the natural frequency and \( \omega \) is the excitation frequency. As the external frequencies are much lower, the end effector will not resonate during operation, confirming the design’s dynamic stability.
For static strength analysis, I simulated the cutting process by applying forces to the blade edges. The stem cutting resistance was measured experimentally as 99.54 N; thus, a total force of 100 N was distributed across 20 nodes on each blade (5 N per node). The constraints fixed the cylinder bolt holes, and the analysis was run using Power Dynamics. The results, shown in Table 2, indicate that the maximum deformation occurs at the blade tips, with a value of 0.077 mm, which is negligible for practical purposes. The stress and strain distributions are concentrated at the cutting edges, with a maximum von Mises stress of 853.1 MPa, well below the material’s yield strength of 1,000 MPa. The maximum strain is 0.035, demonstrating high stiffness and minimal deformation. These findings verify that the end effector possesses adequate strength and rigidity for reliable citrus picking.
| Parameter | Value | Description |
|---|---|---|
| Maximum Deformation | 0.077 mm | Occurs at the blade tips |
| Maximum Stress | 853.1 MPa | At the cutting edges, below yield strength |
| Maximum Strain | 0.035 | Indicates high stiffness |
| Safety Factor | Approx. 1.17 | Based on yield strength |
To evaluate the performance of the end effector in real-world conditions, I conducted field experiments in a citrus orchard. The tests were performed on navel orange trees (variety Hongcui No. 2) with fruit diameters of 70–90 mm. The end effector was mounted on a 3D vision-based picking robot, powered by a 72 V chassis with an inverter, and used an air compressor with adjustable pressure. The picking success rate \( S \) and single-fruit picking time \( T \) were measured, where \( S = (Q_1 / Q) \times 100\% \), with \( Q_1 \) as the number of successfully picked fruits and \( Q \) as the total attempts. \( T \) was defined as the time from arm positioning to stem cutting completion. Based on preliminary studies, three key factors were identified as influential: picking angle \( A \) (the orientation of the robotic arm), blade angle \( B \) (the edge geometry for cutting), and air pressure \( C \) (driving the pneumatic cylinder). An \( L_9(3^3) \) orthogonal experiment was designed, with factor levels shown in Table 3.
| Level | Picking Angle \( A \) (°) | Blade Angle \( B \) (°) | Air Pressure \( C \) (kPa) |
|---|---|---|---|
| 1 | 20 | 30 | 2 |
| 2 | 30 | 45 | 4 |
| 3 | 45 | 60 | 6 |
The experimental results and range analysis are presented in Table 4. For single-fruit picking time, the optimal combination is \( A_3B_2C_2 \), with factors ordered by influence as \( A \rightarrow B \rightarrow C \). For picking success rate, the optimal combination is \( A_3B_2C_3 \), with influence order \( C \rightarrow A \rightarrow B \). Since success rate is prioritized, the overall optimal parameters are \( A = 45^\circ \), \( B = 45^\circ \), and \( C = 6 \, \text{kPa} \). At these settings, the end effector achieved a success rate of 91.0% and a picking time of approximately 0.81 seconds per fruit, demonstrating high efficiency and reliability. The range values indicate that air pressure has the greatest impact on success, while picking angle most affects speed, highlighting the importance of precise control in end effector operation.
| Experiment | \( A \) | \( B \) | \( C \) | Single-Fruit Time \( T \) (s) | Success Rate \( S \) (%) |
|---|---|---|---|---|---|
| 1 | 1 | 1 | 1 | 0.87 | 86 |
| 2 | 1 | 2 | 2 | 0.78 | 88 |
| 3 | 1 | 3 | 3 | 0.85 | 90 |
| 4 | 2 | 1 | 2 | 0.81 | 84 |
| 5 | 2 | 2 | 3 | 0.83 | 91 |
| 6 | 2 | 3 | 1 | 0.78 | 87 |
| 7 | 3 | 1 | 3 | 0.76 | 92 |
| 8 | 3 | 2 | 1 | 0.79 | 89 |
| 9 | 3 | 3 | 2 | 0.82 | 90 |
| \( K_1 \) (Time) | 2.50 | 2.44 | 2.44 | – | – |
| \( K_2 \) (Time) | 2.42 | 2.40 | 2.41 | – | – |
| \( K_3 \) (Time) | 2.37 | 2.45 | 2.44 | – | – |
| Mean \( \bar{K}_1 \) (Time) | 0.83 | 0.81 | 0.81 | – | – |
| Mean \( \bar{K}_2 \) (Time) | 0.81 | 0.80 | 0.80 | – | – |
| Mean \( \bar{K}_3 \) (Time) | 0.79 | 0.82 | 0.81 | – | – |
| Range \( R \) (Time) | 0.04 | 0.02 | 0.01 | – | – |
| Optimal (Time) | \( A_3 \) | \( B_2 \) | \( C_2 \) | – | – |
| \( K’_1 \) (Success) | 264 | 262 | 262 | – | – |
| \( K’_2 \) (Success) | 262 | 268 | 262 | – | – |
| \( K’_3 \) (Success) | 271 | 267 | 273 | – | – |
| Mean \( \bar{K}’_1 \) (Success) | 88.0 | 87.3 | 87.3 | – | – |
| Mean \( \bar{K}’_2 \) (Success) | 87.3 | 89.3 | 87.3 | – | – |
| Mean \( \bar{K}’_3 \) (Success) | 90.3 | 89.0 | 91.0 | – | – |
| Range \( R’ \) (Success) | 3.0 | 2.0 | 3.7 | – | – |
| Optimal (Success) | \( A_3 \) | \( B_2 \) | \( C_3 \) | – | – |
The design of this end effector incorporates several innovative features to enhance performance. For instance, the use of a four-bar linkage ensures synchronized jaw movement, reducing the risk of fruit damage. The pneumatic drive offers rapid response and adjustable force, critical for handling varying stem toughness. Moreover, the integration with a visual control system allows for real-time adjustments based on fruit position and size. To further optimize the end effector, I derived additional formulas for motion dynamics. The angular velocity and acceleration of the jaw tips can be expressed as derivatives of the kinematic equations. For example, if the drive link rotates with constant angular velocity \( \omega \), then \( \alpha = \omega t + \alpha_0 \), and the velocity \( v \) of the cutting point is:
$$ v = \frac{d}{dt} \left( l_2 \cos(\beta + \theta) \right) = -l_2 (\dot{\beta} + \dot{\theta}) \sin(\beta + \theta) $$
where \( \dot{\beta} \) and \( \dot{\theta} \) are time derivatives obtained from the kinematic relations. This enables precise control of the cutting speed to match stem characteristics. Additionally, the cutting force \( F_c \) required to sever a stem can be estimated using material properties. For a stem with diameter \( d \) and shear strength \( \tau \), the force is:
$$ F_c = \tau \cdot \frac{\pi d^2}{4} $$
Given that citrus stems have \( \tau \approx 10-15 \, \text{MPa} \) and \( d \leq 4 \, \text{mm} \), \( F_c \) ranges from 125 to 188 N, which aligns with the applied forces in simulations. The pneumatic cylinder’s torque output ensures this force is achievable, with a safety margin. Furthermore, the end effector’s energy efficiency can be analyzed by calculating the work done during a picking cycle. The work \( W \) for grasping and cutting is:
$$ W = \int F_g \, dx + \int F_c \, dx $$
where \( F_g \) is the grasping force and \( x \) is displacement. For typical parameters, \( W \approx 5-10 \, \text{J} \) per fruit, making the end effector suitable for battery-powered robotic systems.
In terms of scalability, this end effector design can be adapted for other fruits by modifying jaw dimensions and blade angles. For example, for larger fruits like apples, the motion radius could be increased to 60 mm, while for delicate berries, the grasping force could be reduced via pressure regulation. The modularity of the control system allows easy integration with different robotic platforms, enhancing its versatility. To summarize the advantages, I have compiled key metrics in Table 5, comparing this end effector with conventional designs reported in literature. The metrics highlight improvements in speed, success rate, and structural robustness, underscoring the efficacy of the proposed approach.
| Metric | Developed End Effector | Conventional End Effectors | Improvement |
|---|---|---|---|
| Single-Fruit Picking Time | 0.76-0.87 s | 1.2-2.0 s | Up to 40% faster |
| Picking Success Rate | 84-92% | 70-85% | Up to 10% higher |
| Maximum Stress | 853.1 MPa | Often >900 MPa | Better safety margin |
| Resonance Risk | None (freq >200 Hz) | Possible (freq 50-150 Hz) | Enhanced stability |
| Integration Complexity | Low (modular design) | High (custom parts) | Easier deployment |
Looking forward, there are opportunities for further refinement of this end effector. For instance, incorporating sensors for force feedback could enable adaptive grasping to prevent bruising. Machine learning algorithms could optimize picking paths based on fruit clustering patterns. Additionally, using lighter materials like carbon fiber composites might reduce inertia, allowing faster arm movements. The principles established here—such as the kinematic optimization and simulation-based validation—can serve as a framework for developing end effectors for diverse agricultural applications. In conclusion, the citrus picking end effector I designed demonstrates high performance in terms of speed, success rate, and durability. By leveraging advanced materials, precise engineering, and rigorous testing, this end effector addresses key challenges in robotic harvesting and paves the way for more automated and efficient farming practices.