In modern agriculture, the automation of harvesting processes is crucial for improving efficiency, reducing labor costs, and minimizing crop damage. Cluster tomatoes, also known as truss tomatoes, have gained popularity due to their appealing appearance and extended shelf life. However, harvesting these tomatoes manually is labor-intensive and prone to damage. Robotic systems offer a promising solution, with the end effector being a critical component that directly interacts with the crop. In this study, we focus on designing and analyzing an end effector specifically for harvesting cluster tomatoes. Our goal is to develop a device that can securely clamp the parent branch of the tomato cluster and perform a clean cut, enabling efficient and damage-free harvesting.
The end effector is the part of a robotic system that handles the physical interaction with objects. For agricultural robots, the design of the end effector must account for the delicate nature of produce, variability in size and shape, and environmental conditions. Previous research has explored various end effector designs for fruits like apples, citrus, and solitary tomatoes, often using suction cups, grippers, or cutting mechanisms. However, for cluster tomatoes, which are harvested by severing the parent branch that holds multiple fruits, there is a need for specialized clamping and cutting tools. Our work addresses this gap by proposing a novel end effector that combines a dual-V clamping mechanism with a rotary cutting system. This design aims to provide stable gripping and precise separation, ensuring the integrity of the tomato cluster during harvesting.
The overall structure of our end effector consists of three main modules: the clamping module, the cutting module, and the drive system. The clamping module features two fingers with V-shaped tips that move along guide rails. When actuated by a servo motor, these fingers close symmetrically to grip the parent branch of the tomato cluster. The V-shaped design ensures a firm hold by creating multiple contact points along the branch. Above the clamping fingers, the cutting module includes three rotary blades arranged at 120-degree angles and driven by a separate motor. This setup allows for adjustable blade height and efficient cutting once the branch is clamped. The drive system integrates the servo motor for clamping and the cutting motor, both mounted on a frame that can be attached to a robotic arm. During operation, the robotic arm positions the end effector near the tomato cluster. The clamping fingers close to secure the parent branch, followed by the activation of the cutting blades to sever the branch. The robotic arm then transports the harvested cluster to a collection bin, where the fingers release it. This process mimics manual harvesting but with enhanced precision and speed.
To ensure the reliability of the clamping action, we conducted a theoretical analysis based on screw theory. This framework is widely used in robotics to evaluate force closure, which determines whether a grip can resist arbitrary external forces and moments. In our case, the parent branch of the tomato cluster is approximated as a cylinder, and the clamping fingers exert forces at four contact points due to the dual-V design. Each contact point is modeled as a frictional point contact, allowing us to represent the grip using wrenches (force and torque combinations). Let the coordinate system be defined with the Z-axis along the branch’s longitudinal direction and the XOY plane as its cross-section. The position and orientation of the i-th contact point relative to the branch coordinate system are given by $(P_{ci}, R_{ci})$. The contact wrench at the i-th point is expressed as:
$$ \mathbf{F}_i = (\mathbf{f}_i, \mathbf{m}_i) $$
where $\mathbf{f}_i$ is the force vector and $\mathbf{m}_i$ is the moment vector. For line contacts, the wrench basis $\mathbf{B}_{ci}$ in the contact coordinate system is:
$$ \mathbf{B}_{ci} = \begin{bmatrix} 1 & 0 & 0 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 & 0 & 0 \\ 0 & 0 & 1 & 0 & 0 & 0 \end{bmatrix}^T $$
The contact force in the contact coordinates is $\mathbf{F}_{ci} = \mathbf{B}_{ci} \mathbf{f}_{ci}$, where $\mathbf{f}_{ci}$ is the force intensity vector. The friction cone constraints are given by:
$$ \mathbf{F}_{ci} \in FC_{ci} = \{\mathbf{w} \in \mathbb{R}^6 : \sqrt{f_x^2 + f_y^2} \leq \mu f_z, f_z \geq 0\} $$
where $\mu$ is the coefficient of friction. Transforming the contact wrenches to the branch coordinate system using the adjoint transformation:
$$ \mathbf{G}_i = \begin{bmatrix} \mathbf{R}_{ci} & \mathbf{0} \\ \mathbf{P}_{ci} \times \mathbf{R}_{ci} & \mathbf{R}_{ci} \end{bmatrix} \mathbf{B}_{ci} $$
where $\mathbf{P}_{ci}$ is the cross-product matrix of the position vector. The total wrench exerted on the branch by n contacts is:
$$ \mathbf{F}_0 = \sum_{i=1}^n \mathbf{G}_i \mathbf{f}_{ci} = \mathbf{G} \mathbf{f}_c $$
with $\mathbf{G} = [\mathbf{G}_1 \cdots \mathbf{G}_n]$ and $\mathbf{f}_c = [\mathbf{f}_{c1}^T \cdots \mathbf{f}_{cn}^T]^T$. For force closure, given any external wrench $\mathbf{F}_e$ acting on the branch, there must exist a vector $\mathbf{f}_c$ within the friction cones such that:
$$ \mathbf{G} \mathbf{f}_c = -\mathbf{F}_e $$
In our design, the four contact points are symmetrically arranged around the branch. Assuming a branch radius r, the positions in the XOY plane are:
$$ \mathbf{P}_{c1} = \left(-\frac{\sqrt{2}}{2}r, \frac{\sqrt{2}}{2}r, 0\right), \quad \mathbf{P}_{c2} = \left(\frac{\sqrt{2}}{2}r, \frac{\sqrt{2}}{2}r, 0\right) $$
$$ \mathbf{P}_{c3} = \left(\frac{\sqrt{2}}{2}r, -\frac{\sqrt{2}}{2}r, 0\right), \quad \mathbf{P}_{c4} = \left(-\frac{\sqrt{2}}{2}r, -\frac{\sqrt{2}}{2}r, 0\right) $$
The orientation matrices $\mathbf{R}_{ci}$ align the contact normals with the branch surface. For instance, for contact point 1:
$$ \mathbf{R}_{c1} = \begin{bmatrix} -\frac{\sqrt{2}}{2} & -\frac{\sqrt{2}}{2} & 0 \\ \frac{\sqrt{2}}{2} & -\frac{\sqrt{2}}{2} & 0 \\ 0 & 0 & -1 \end{bmatrix} $$
Similar matrices are derived for other points. Substituting into the wrench basis transformation, we obtain the grasp matrix $\mathbf{G}$. For a typical external wrench, such as a gravitational force along the negative Z-axis $\mathbf{F}_e = [0, 0, -10, 0, 0, 0]^T$ N (assuming a cluster mass of 1 kg), we can solve for $\mathbf{f}_c$. The solution confirms that feasible contact forces exist within the friction cones, ensuring force closure. This analysis validates that our dual-V clamping design can stably grip the tomato branch under operational conditions.
Beyond force closure, we also developed a stable clamping model to determine the required gripping force. The clamping fingers exert a preload force F on each side, which translates into normal forces at the four contact areas. Due to symmetry, the normal forces are equal: $F_{11} = F_{12} = F_{21} = F_{22}$. The relationship between the preload force and the normal force at each V-shaped face is:
$$ F_{11} = F \sin\left(\frac{\alpha}{2}\right) $$
where $\alpha = 90^\circ$ is the angle between the V faces. For static equilibrium, the sum of frictional forces must balance the weight of the cluster G:
$$ 4 \mu F_{11} = G $$
Substituting $\mu = 0.6$ (typical for rubber-coated fingers on plant material) and $G = 10$ N (for a 1 kg cluster), we solve for the normal force:
$$ F_{11} = \frac{G}{4\mu} = \frac{10}{4 \times 0.6} \approx 4.17 \, \text{N} $$
Then, the required preload force per finger is:
$$ F = \frac{F_{11}}{\sin(45^\circ)} = \frac{4.17}{0.7071} \approx 5.90 \, \text{N} $$
However, to account for dynamic effects and safety margins, we derived a more conservative value. Considering moments and potential slippage, we calculated that a clamping force of $F \geq 8.24 \, \text{N}$ is sufficient to prevent dropping the cluster. This force is achievable with standard servo motors, ensuring practicality in field applications.
To evaluate the performance of our end effector, we constructed a physical prototype and conducted load-bearing experiments. The prototype used a servo motor (torque 20 N·cm) for clamping and a DC motor for cutting. The fingers were made of aluminum with rubber padding to increase friction. We tested branches with diameters ranging from 3 mm to 8 mm, representing typical sizes of tomato cluster parent branches. The experiments included static and dynamic load tests to simulate real harvesting conditions, where vibrations and movements may occur.
In static load tests, weights were hung from the clamped branch until slippage or failure occurred. In dynamic load tests, the weight was swung to a 60° angle from vertical in both X and Y directions, creating a 120° pendulum motion with a period of 5 seconds, to simulate disturbances during robot motion. The maximum load before failure was recorded for each branch diameter. The results are summarized in the table below, which shows how the load-bearing capacity varies with diameter and test type.
| Branch Diameter (mm) | Static Load (kg) | Dynamic Load in X-direction (kg) | Dynamic Load in Y-direction (kg) | Minimum Dynamic Load (kg) |
|---|---|---|---|---|
| 3 | 2.385 | 1.200 | 1.015 | 1.015 |
| 4 | 2.450 | 1.350 | 1.100 | 1.100 |
| 5 | 2.520 | 1.500 | 1.250 | 1.250 |
| 6 | 2.600 | 1.650 | 1.400 | 1.400 |
| 7 | >2.600* | 1.800 | 1.550 | 1.550 |
| 8 | >2.600* | 2.000 | 1.700 | 1.700 |
*For diameters 7 mm and 8 mm, static load testing was stopped at 2.600 kg due to elastic deformation of the finger material, but no slippage occurred.
The data indicate that load-bearing capacity increases with branch diameter, as expected due to larger contact areas. Dynamic loads are lower than static loads, reflecting the impact of disturbances. The minimum dynamic load observed was 1.015 kg for a 3 mm branch, which exceeds the typical mass of a tomato cluster (around 0.52 kg for such branches). This confirms that our end effector can reliably handle cluster tomatoes during harvesting. Additionally, we noted that performance was slightly better in the X-direction than the Y-direction, likely due to the alignment of the V-shaped faces with the clamping mechanism. These results validate the design and provide guidelines for operational parameters, such as clamping force adjustment based on branch size.
The cutting module was also tested separately to ensure clean severance of the branch. Using three rotary blades at 3000 RPM, we achieved cuts with minimal fraying or damage to the branch. The cutting time was under 2 seconds, which is acceptable for harvesting cycles. Integration with the clamping module showed smooth operation, with no interference between the blades and the fingers. Overall, the end effector demonstrated robustness and efficiency in laboratory conditions.
In conclusion, our study presents a comprehensive design and analysis of an end effector for harvesting cluster tomatoes. The dual-V clamping mechanism provides force closure and stable gripping, as verified by screw theory. The calculated clamping force of 8.24 N ensures secure holding of the tomato cluster. Experimental results from load-bearing tests show that the end effector can withstand dynamic loads up to 1.015 kg for the smallest branches, far exceeding typical cluster weights. This performance makes it suitable for real-world applications. Future work could focus on optimizing the material selection to reduce weight, integrating sensors for adaptive control, and testing in greenhouse environments. The end effector represents a significant step toward automated harvesting of cluster tomatoes, offering potential benefits in productivity and crop quality.
From a broader perspective, the development of specialized end effectors like this one highlights the importance of tailored solutions in agricultural robotics. As farming faces challenges such as labor shortages and the need for sustainable practices, robotic systems with intelligent end effectors will play a key role. Our design contributes to this field by addressing the unique requirements of cluster tomato harvesting. By combining mechanical design with theoretical analysis and experimental validation, we have created a reliable tool that can be adapted for similar crops. We believe that continued innovation in end effector technology will drive the adoption of robotics in agriculture, leading to more efficient and resilient food systems.
To further elaborate on the theoretical aspects, let us delve deeper into the screw theory analysis. The concept of wrenches and twists is fundamental in robotics for describing forces and motions. A wrench $\mathbf{W} = (\mathbf{f}, \mathbf{m})$ represents a combination of force $\mathbf{f}$ and moment $\mathbf{m}$, while a twist $\mathbf{T} = (\mathbf{v}, \boldsymbol{\omega})$ represents linear velocity $\mathbf{v}$ and angular velocity $\boldsymbol{\omega}$. In grasping, force closure ensures that the contact wrenches can balance any external wrench. Mathematically, this is equivalent to the grasp matrix $\mathbf{G}$ having full row rank and the friction cones spanning the wrench space. For our four-contact point model, we can compute the rank of $\mathbf{G}$ to verify force closure. Using the positions and orientations defined earlier, the grasp matrix is:
$$ \mathbf{G} = \begin{bmatrix}
-\frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2} & 0 & \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2} & 0 & \frac{\sqrt{2}}{2} & -\frac{\sqrt{2}}{2} & 0 & -\frac{\sqrt{2}}{2} & -\frac{\sqrt{2}}{2} & 0 \\
-\frac{\sqrt{2}}{2} & -\frac{\sqrt{2}}{2} & 0 & \frac{\sqrt{2}}{2} & -\frac{\sqrt{2}}{2} & 0 & -\frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2} & 0 & \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2} & 0 \\
0 & 0 & -1 & 0 & 0 & -1 & 0 & 0 & -1 & 0 & 0 & -1 \\
0 & 0 & -\frac{\sqrt{2}}{2}r & 0 & 0 & \frac{\sqrt{2}}{2}r & 0 & 0 & \frac{\sqrt{2}}{2}r & 0 & 0 & -\frac{\sqrt{2}}{2}r \\
0 & 0 & -\frac{\sqrt{2}}{2}r & 0 & 0 & -\frac{\sqrt{2}}{2}r & 0 & 0 & \frac{\sqrt{2}}{2}r & 0 & 0 & \frac{\sqrt{2}}{2}r \\
\frac{\sqrt{2}}{2}r & -\frac{\sqrt{2}}{2}r & 0 & -\frac{\sqrt{2}}{2}r & -\frac{\sqrt{2}}{2}r & 0 & \frac{\sqrt{2}}{2}r & \frac{\sqrt{2}}{2}r & 0 & -\frac{\sqrt{2}}{2}r & \frac{\sqrt{2}}{2}r & 0
\end{bmatrix} $$
This matrix has rank 6, confirming that the grasp can resist arbitrary wrenches in all directions. Additionally, we analyzed the quality of force closure using metrics like the smallest singular value of $\mathbf{G}$, which relates to the force efficiency. A larger value indicates better force transmission from the actuators to the object. For our design, the smallest singular value was computed numerically for typical branch radii, showing adequate performance for diameters between 3 mm and 8 mm.
Regarding the clamping force calculation, we extended the model to include moments induced by the weight of the cluster. Assuming the cluster is a point mass hanging at a distance L from the grip point, the equilibrium equations become:
$$ \sum F_z = 0: \quad 4 \mu F_{11} – G = 0 $$
$$ \sum M_x = 0: \quad 2 F_{11} r \cos(45^\circ) – G L = 0 $$
Solving these, we obtain a revised clamping force that accounts for the moment arm. For L = 50 mm (typical for tomato clusters), the required force increases slightly, but still within the range of our servo motor. This detailed analysis ensures that the end effector can handle realistic harvesting scenarios where the cluster may swing or be offset from the grip point.
In terms of design optimization, we considered factors such as finger geometry, material selection, and actuation method. The V-angle of 90° was chosen based on a trade-off between grip stability and stress concentration. Smaller angles increase normal forces but may damage the branch, while larger angles reduce grip. Finite element analysis (FEA) was performed on the finger design to ensure structural integrity under maximum loads. The results showed that aluminum fingers with a thickness of 5 mm can withstand stresses up to 50 MPa, well below the yield strength of aluminum (around 200 MPa). For the cutting module, blade sharpness and speed were optimized to minimize cutting force and energy consumption. Experiments with different blade materials (stainless steel vs. carbon steel) indicated that stainless steel provided better durability and corrosion resistance, important for humid greenhouse environments.
The control system for the end effector is another critical aspect. We implemented a simple open-loop control for the clamping and cutting actions, but future versions could include closed-loop feedback using force sensors or vision systems. For instance, a force sensor on the fingers could adjust the clamping force based on branch diameter, preventing damage to delicate branches. Similarly, a camera could guide the robotic arm to position the end effector accurately. Integration with a robotic platform would involve communication protocols and synchronization with arm movements.
To contextualize our work, we compare it with existing end effectors for agricultural harvesting. Many designs focus on solitary fruits, using suction or enveloping grippers. For example, suction-based end effectors are common for tomatoes but may not work well for clusters due to the irregular shape and multiple fruits. Enveloping grippers, such as those used for apples, often require complex mechanisms and may crush delicate stems. Our design addresses these limitations by targeting the parent branch, which is more uniform and robust. This approach allows for simpler mechanics and reliable performance. Additionally, the inclusion of a cutting module within the end effector streamlines the harvesting process, reducing the need for separate tools.
Potential limitations of our end effector include dependency on branch accessibility and susceptibility to environmental factors like moisture or dirt on the branches. Field testing in greenhouses will be necessary to evaluate these issues. Moreover, the end effector may need adjustments for different tomato varieties or crop training systems (e.g., vertical vs. horizontal growth). However, the modular design allows for easy modifications, such as changing finger sizes or blade configurations.
In summary, this study demonstrates the feasibility of a specialized end effector for cluster tomato harvesting. Through theoretical modeling, prototype development, and experimental validation, we have shown that the design meets the requirements for stable gripping and efficient cutting. The end effector contributes to the advancement of agricultural robotics by providing a practical solution for a challenging harvesting task. As robotics technology continues to evolve, we anticipate further improvements in end effector adaptability, intelligence, and integration with autonomous systems, ultimately transforming how crops are harvested and managed.