In modern agriculture, the automation of fruit harvesting is critical to address labor shortages and improve efficiency. Citrus fruits, being a major economic crop, present significant challenges for robotic picking due to severe occlusion by branches and leaves, variable fruit stalk orientations, and the need for precise localization. Traditional end effectors often suffer from low success rates, excessive stalk residue, and inefficiency under such conditions. To overcome these limitations, we propose a novel end effector design that mimics human finger motion to pluck citrus fruits and passively cut the stalks. This end effector integrates a multi-finger configuration with V-shaped cutting blades, driven by a crank-slider-rocker mechanism, aiming to achieve high-precision, non-destructive harvesting in complex orchard environments.
We begin by characterizing the physical and mechanical properties of navel oranges and their stalks to inform the end effector design. Key parameters include fruit dimensions, stalk diameter, inclination angles, and shear forces. Measurements were conducted on samples from orchards, with results summarized in Table 1. The data reveals that stalk inclination angles primarily range from 0° to 30°, and fruit dimensions vary significantly, necessitating an adaptable end effector design.
| Parameter | Large Fruit | Medium Fruit | Small Fruit |
|---|---|---|---|
| Transverse Diameter (mm) | 76.21 ± 2.14 | 65.10 ± 1.64 | 48.30 ± 1.07 |
| Longitudinal Diameter (mm) | 85.00 ± 0.61 | 75.80 ± 0.41 | 62.78 ± 2.55 |
| Stalk Diameter (mm) | 4.42 ± 0.53 | 3.96 ± 0.43 | 3.39 ± 0.05 |
The shear force of fruit stalks was evaluated using a universal testing machine under varying cutting angles. The peak shear force, denoted as $F(\alpha)$, where $\alpha$ is the cutting angle, was measured. The relationship between shear force and time shows an initial increase to a peak followed by a decrease. For design optimization, we focused on minimizing the peak force. The average peak shear force at different angles is presented in Table 2, indicating that at $\alpha = 10^\circ$, the force is minimal at 67.12 N.
| Cutting Angle $\alpha$ (°) | Average Peak Shear Force $F(\alpha)$ (N) |
|---|---|
| 0 | — |
| 10 | 67.12 |
| 15 | 85.34 |
| 20 | 102.56 |
| 25 | 178.00 |
| 30 | 155.22 |
| 35 | 140.45 |
| 90 | — |
The maximum shear stress $\tau_{\text{max}}$ of the stalk is calculated using the formula for oblique cutting:
$$ \tau_{\text{max}} = \frac{4F(\alpha) \sin \alpha}{\pi D_2^2} $$
where $D_2$ is the stalk diameter. For $\alpha = 25^\circ$ and $F(25^\circ) = 178 \text{ N}$, with $D_2 = 4 \text{ mm}$, we obtain $\tau_{\text{max}} = 5.99 \text{ MPa}$. This value is essential for ensuring the end effector’s cutting capability across various stalk orientations.
Based on these properties, we designed the end effector with a three-finger configuration, each finger equipped with a V-shaped cutting blade. The overall structure includes a frame, a crank-slider-rocker mechanism for driving the fingers, and a collection system. The end effector operates by positioning below the target fruit, plucking it via finger motion, and guiding the stalk into the V-shaped blades for cutting. The design prioritizes compactness and adaptability to handle fruits of different sizes while minimizing damage.
The V-shaped cutting device is a core component of the end effector, consisting of blades arranged at specific angles. Theoretical analysis determines the optimal blade opening angle $\alpha$ and installation inclination $\delta$. The cutting force $f_s$ during stalk shearing is modeled as:
$$ f_s = \frac{\tau_1 A}{\sin \sigma \cos \alpha} + \mu N_i \tan \alpha + k v \sqrt{t D_2} $$
where $\tau_1$ is the shear stress on the stalk, $A$ is the shear area, $\sigma$ is the blade edge angle, $\mu$ is the friction coefficient, $k$ is a correction factor, $v$ is the blade velocity, and $t$ is the blade thickness. To minimize the cutting force, we derived boundary conditions for $\alpha$:
$$ \arcsin \sqrt{\frac{2 \pi D_2^2 \tau_{\text{max}}}{16 n F_{i,\text{min}}}} \leq \alpha \leq \arcsin \sqrt{\frac{2 \pi D_2^2 [\tau_2]}{16 F_{i,\text{max}}}} $$
where $n$ is a safety factor, and $[\tau_2]$ is the allowable shear stress of the blade material. Using $D_2 = 4 \text{ mm}$, $\tau_{\text{max}} = 5.99 \text{ MPa}$, $n=2$, and $[\tau_2] = 125 \text{ MPa}$, we find that $\alpha = 10^\circ$ minimizes the force. The installation inclination $\delta$ is related to $\alpha$ and the blade geometry:
$$ \sin \delta = \tan \sigma \tan \alpha $$
For blade length $l_{DO} = 48 \text{ mm}$ and $\alpha = 10^\circ$, we calculate $\delta_{\text{min}} = 5.4^\circ$, rounded to $6^\circ$ for practical design. Thus, the V-shaped cutting device is configured with $\alpha = 10^\circ$ and $\delta = 6^\circ$ to reduce cutting resistance and prevent fruit damage.
Finite element simulation using ANSYS software validated the cutting performance. Models with $\alpha$ ranging from $0^\circ$ to $35^\circ$ were analyzed, and the peak shear forces from simulation closely matched experimental data, with relative errors under 10.28%. At $\alpha = 10^\circ$, the blade experienced a maximum stress of 20.029 MPa, well below the material strength, confirming the end effector’s durability. The simulation results are summarized in Table 3, highlighting the efficiency of the V-shaped design.
| Cutting Angle $\alpha$ (°) | Simulated Peak Force (N) | Experimental Peak Force (N) | Relative Error (%) |
|---|---|---|---|
| 10 | 65.8 | 67.12 | 1.97 |
| 15 | 88.2 | 85.34 | 3.35 |
| 20 | 105.3 | 102.56 | 2.67 |
| 25 | 185.1 | 178.00 | 3.99 |
| 30 | 160.5 | 155.22 | 3.40 |
| 35 | 145.6 | 140.45 | 3.67 |
The crank-slider-rocker mechanism drives the finger motion in the end effector, providing rapid reciprocating action with a quick-return characteristic. This mechanism consists of a cam, primary and secondary connecting rods, a slider, and the finger structure. The kinematic analysis involves determining the swing angle $\phi$ of the finger and the velocities during operation. The mechanism’s freedom degree $F$ is calculated as:
$$ F = 3n – 2p_l – p_h $$
where $n$ is the number of moving parts, $p_l$ is the number of lower pairs, and $p_h$ is the number of higher pairs. For our design, $n=5$, $p_l=7$, $p_h=0$, giving $F=1$, ensuring stable motion. The geometric parameters, such as the cam radius $l_{AB} = 12.5 \text{ mm}$, primary rod length $l_{BC} = 120 \text{ mm}$, and offset distance $e = 45 \text{ mm}$, are chosen to avoid interference and optimize performance. The swing angle $\phi$ is derived from positional analysis:
$$ \phi = \angle D_1 E D_2 $$
where $D_1$ and $D_2$ are extreme positions of the finger tip. Using graphical methods, we find $\phi = 75.17^\circ$, suitable for plucking fruits. The velocity and acceleration profiles from ADAMS simulation show that the working stroke has higher average speed and acceleration than the return stroke, confirming the quick-return property. This enhances the end effector’s efficiency by enabling fast stalk cutting.
The driving motor for the end effector is selected based on torque requirements. The minimum torque $T$ is estimated from the peak cutting force $F_i$ and the lever arm $l$:
$$ T = F_i \cdot l $$
With $F_i = 67.12 \text{ N}$ at $\alpha = 10^\circ$ and $l = 80.11 \text{ mm}$ from geometric analysis, $T = 5.38 \text{ N·m}$. We chose a motor with a torque of 6.4 N·m and speed range of 30–120 rpm to ensure reliable operation of the end effector under varying loads.
Field experiments were conducted to evaluate the end effector’s performance in real orchard conditions. We tested factors including motor speed and stalk inclination angle, with response variables of picking success rate, fruit damage rate, efficiency, and post-harvest stalk length. A two-factor three-level orthogonal design was used, as shown in Table 4, with levels coded as -1, 0, and 1.
| Level | Motor Speed (rpm) | Stalk Inclination (°) |
|---|---|---|
| -1 | 30 | 0 |
| 0 | 75 | 15 |
| 1 | 120 | 30 |
The end effector achieved an overall success rate of 95.38%, zero fruit damage, and an average efficiency of 6.50 seconds per fruit. The post-harvest stalk length varied with operating parameters. Using Design-Expert software, we performed response surface analysis to model stalk length $Y$ as a function of motor speed $X_1$ and stalk inclination $X_2$. The regression equation after eliminating non-significant terms is:
$$ Y = 12.96 + 0.42X_1 – 0.51X_2 + 0.03X_2^2 $$
Analysis of variance (ANOVA) in Table 5 indicates that $X_1$, $X_2$, and $X_2^2$ have highly significant effects on stalk length ($P < 0.01$), while interaction terms are not significant. The model is highly significant with a non-significant lack of fit, validating its predictive capability.
| Source | Sum of Squares | df | Mean Square | F-value | P-value |
|---|---|---|---|---|---|
| Model | 1032.90 | 5 | 206.58 | 17.66 | 0.0008 |
| $X_1$ | 170.67 | 1 | 170.67 | 14.59 | 0.0065 |
| $X_2$ | 682.67 | 1 | 682.67 | 58.37 | 0.0001 |
| $X_1X_2$ | 20.25 | 1 | 20.25 | 1.73 | 0.2297 |
| $X_1^2$ | 60.74 | 1 | 60.74 | 5.19 | 0.0567 |
| $X_2^2$ | 147.60 | 1 | 147.60 | 12.62 | 0.0093 |
| Residual | 81.86 | 7 | 11.69 | ||
| Lack of Fit | 29.06 | 3 | 9.69 | 0.73 | 0.5838 |
| Pure Error | 52.80 | 4 | 13.20 | ||
| Total | 1114.77 | 12 |
Optimization of the end effector parameters aimed to minimize stalk length. The constraint problem is formulated as:
$$ \begin{aligned}
\text{minimize} & \quad Y(X_1, X_2) \\
\text{subject to} & \quad -1 \leq X_1 \leq 1 \\
& \quad -1 \leq X_2 \leq 1
\end{aligned} $$
The solution yields an optimal motor speed of 30 rpm, corresponding to a minimum stalk length of 19.8 mm. Validation tests under these conditions confirmed a success rate of 100%, no fruit damage, efficiency of 6.07 seconds per fruit, and an average stalk length of 20.1 mm, with a relative error of 1.52% from the predicted value. These results demonstrate the robustness of the end effector in achieving efficient and non-destructive harvesting.
In conclusion, we have developed a finger-imitating end effector for citrus picking that addresses key challenges in robotic harvesting. The design integrates a V-shaped cutting device with optimized angles to reduce cutting forces and a crank-slider-rocker mechanism for rapid, precise motion. Experimental validation shows high success rates, zero damage, and improved efficiency, making this end effector suitable for complex orchard environments. Future work could focus on enhancing the end effector’s adaptability to different fruit varieties and integrating advanced sensors for better localization. This research contributes to the advancement of agricultural robotics by providing a reliable end effector solution for automated fruit harvesting.