The mechanization of agricultural harvesting, particularly for delicate fruits like navel oranges, presents significant challenges. The end effector, as the direct interface between the robotic system and the crop, is paramount to the success and efficiency of the entire operation. Its design must reconcile the often-conflicting requirements of secure grasping, precise cutting, adaptability to natural variation, and operational speed. Traditional end-effector designs frequently separate the gripping and cutting functions, leading to bulky mechanisms with complex control requirements. This complexity hinders efficiency and adaptability in dense orchard environments. This article details the design, analysis, and experimental validation of a novel, compact end effector for robotic navel orange harvesting. The core innovation lies in the integration of a shearing mechanism directly into a multi-finger underactuated gripper, creating a single, streamlined device capable of enveloping, clamping, and severing the fruit stem in one continuous, swift motion. This “swallowing” type harvesting method, where the fruit is released through the center of the end effector, is a key feature designed to minimize cycle time for continuous picking.
The proposed end effector is fundamentally an underactuated system, meaning it achieves multiple degrees of freedom and complex motion sequences from a single primary actuator. This principle significantly simplifies the control system, reduces weight, and enhances reliability. The overall architecture is a two-layer, three-finger mechanical hand. One layer consists of enveloping fingers which also serve as the carrier for the cutting mechanism. The other layer comprises simpler clamping fingers whose sole function is to secure the fruit firmly against the shearing forces. The shearing action is accomplished by three synchronized blade mechanisms, each based on a slider-crank (rocker-slider) configuration, mounted on the tips of the enveloping fingers. A single electric linear actuator provides the driving force, which is transmitted through a network of linkages to orchestrate the sequential operation of first the clamping, then the shearing. The use of lightweight, high-strength aluminum alloy for critical components ensures structural integrity while maintaining a low mass.
Mechanical Design and Analysis of the Underactuated End Effector
The design of the end effector is driven by the physiological characteristics of navel oranges and the constraints of orchard operation. The three-finger configuration is chosen for its stability and natural grasping geometry. The two distinct finger layers allow for dedicated functions: secure holding and precise cutting.
Structural Configuration of the Underactuated Gripper
The gripper mechanism features three identical units arranged symmetrically at 120-degree intervals. Each unit consists of one clamping finger and one two-phalanx enveloping finger. The clamping finger is a single rigid link, actuated indirectly. Its primary role is to apply a stabilizing force on the fruit body, ensuring it does not rotate or slip during the cutting action. The force for clamping is supplied by a torsion spring located at the finger’s pivot joint. This spring is compressed as the finger is opened by the initial motion of a shared driving linkage. When the linkage reverses to close the fingers, the spring’s stored energy provides the clamping force, making the clamping action passive and adaptive to fruit size.
The enveloping finger has two phalanges: a fixed proximal phalanx for structural stability and a movable distal phalanx. This distal phalanx is specifically designed to carry the shearing mechanism. To ensure the three cutting blades converge properly on the fruit stem, the rotational range of the distal phalanx is mechanically limited. A linkage system, connected to the same central driving slider as the clamping fingers, controls its motion. A torsion spring at its joint ensures the shearing mechanism remains retracted until the enveloping motion is complete, thereby enforcing the correct operational sequence. The kinematic relationship for the linkage driving the enveloping finger can be derived from a four-bar mechanism model. The angular velocities of the links are related by:
$$\dot{\alpha}_1 = \frac{h_1}{h_1 + l_1} \dot{\theta}_1 + \frac{h_2}{h_2 + l_4} \dot{\theta}_2$$
where \(\alpha_1\) is the angular displacement of the driving link, \(\theta_1\) and \(\theta_2\) are the angular displacements of the finger’s proximal and distal phalanges, \(l_1\) and \(l_4\) are link lengths, and \(h_1\), \(h_2\) are instantaneous lever arms determined by the geometry.
Static Force Analysis of the Gripping Mechanism
Analyzing the static forces is crucial for sizing actuators and springs. The principle of virtual work is applied to the underactuated finger system. The input torque vector \(\mathbf{T}\) from the actuator and the torsion spring, and the external force vector \(\mathbf{F}\) from contact limits and cutting reactions, are related through Jacobian matrices derived from the geometry:
$$\mathbf{F} = \mathbf{J}_v^{-T} \mathbf{J}_{\omega}^{-T} \mathbf{T}$$
The specific expressions for the contact force \(F_1\) at the mechanical limit and the force \(F_2\) related to cutting reaction are:
$$F_1 = \frac{h_1 T_1}{d_1 (h_1 + l_1)} – \frac{h_2 (d_2 + l_2 \cos \theta_2) T_1}{d_1 d_2 (h_2 + l_4)} – \frac{(d_2 + l_2 \cos \theta_2) T_2}{d_1 d_2}$$
$$F_2 = \frac{h_2 T_1}{d_2 (h_2 + l_4)} + \frac{T_2}{d_2}$$
where \(T_1\) is the actuator torque, \(T_2 = -(k_2 \theta_2 + \tau_2)\) is the torsional spring torque (with stiffness \(k_2\) and preload \(\tau_2\)), and \(d_1, d_2, l_2\) are geometric dimensions.
For the clamping finger, the force \(F_3\) exerted on the fruit is a function of the fruit’s radius \(r\) and the torsion spring parameters:
$$F_3 = \frac{T_3}{l_5} = \frac{(k_1 \theta_4 + \tau_1)}{l_5}$$
where \(k_1\) is the clamping spring stiffness, \(\theta_4\) is its angular deflection, \(\tau_1\) is its initial torque, and \(l_5\) is the moment arm. To prevent fruit drop, the sum of the vertical components of the three clamping forces must exceed the fruit’s weight \(mg\):
$$\sum_{i=1}^{3} F_{3,i} \cos \beta_3 \geq mg$$
Analysis of navel orange weight versus radius (\(G = mg \approx 0.1535r – 2.9198\)) and the maximum permissible gripping force to avoid bruising (approx. 25.57 N) allows for the optimal selection of the clamping spring stiffness. A stiffness \(k_1 = 15 \text{ N·mm/deg}\) was chosen, ensuring stable grip across a range of fruit sizes without damage.
Design and Mechanics of the Integrated Shearing Mechanism
The shearing mechanism is a critical subsystem of this integrated end effector. It consists of three independent blade assemblies, each mounted on the distal phalanx of an enveloping finger. Each assembly is a slider-crank mechanism where the “crank” is a rocker link holding the blade, and the “slider” is driven by the underactuated linkage. When the enveloping fingers complete their stroke and are held by their mechanical limits, further motion of the main driver is transferred to these sliders, causing the three blades to converge radially and cut the stem.
The force analysis for cutting determines the required actuator torque. Assuming the stem is centered and cut simultaneously by three blades at 120° intervals, the required driving torque \(M\) for one blade mechanism is related to the cutting force \(F_{K}\) by the geometry of the rocker-slider:
$$M = F_{K} \frac{l_{OA} \sin(\delta_1 + \delta_2)}{\cos \delta_2}$$
where \(l_{OA}\) is the rocker length, and \(\delta_1\), \(\delta_2\) are angular orientations of the links. Empirical tests determined that a maximum force of \(F_K = 72.5 \text{ N}\) is needed to cut stems up to 4 mm in diameter. With designed parameters \(l_{OA}=22\text{ mm}, \delta_1=24^\circ, \delta_2=5^\circ\), the minimum required torque is calculated as \(M \approx 775.75 \text{ N·mm}\). This informed the selection of a 12V electric linear actuator with a 400 N thrust capacity and 20 mm/s speed.
Motion Error Tolerance and Structural Verification
For the three-blade cutting system to function without interference, the positional alignment of the blades is critical. Deformation under load at the finger joints could misalign the blades, causing jamming or failed cuts. Therefore, the allowable motion error range must be defined and verified.
Determination of Allowable Error Range
The analysis focuses on the potential rotational error \(\delta\) at the distal phalanx pivot due to structural deformation. Based on the geometry of two adjacent blades and an optimal blade gap \(e_1 = 1.5 \text{ mm}\) for efficient cutting, the condition to avoid interference is derived from the projected coordinates of key points on the blade mechanism. The mathematical condition is expressed as:
$$(L_1 – L_2)\tan \delta + e_1 = z_F – z_E$$
where \(L_1, L_2, z_F, z_E\) are geometric functions of the finger length \(l_{DE}\), blade length \(l_{EF}\), finger mounting radius \(R\), and the error angle \(\delta\). Solving this equation with the designed dimensions yields the safe operational range for the error angle: \(-1.1^\circ < \delta < 2.0^\circ\) (negative indicates inward deflection).
Finite Element Analysis for Validation
To ensure real-world deformations remain within this safe range, a Finite Element Analysis (FEA) was conducted on the critical distal phalanx and joint assembly under the maximum calculated load during cutting. The maximum stress was found to be approximately 30 MPa, well within the yield strength of aluminum alloy. More importantly, the maximum deformation at the joint was found to be about 0.0005 mm, leading to a blade tip displacement of only 0.085 mm. This displacement corresponds to an angular error far smaller than the \(\pm1.1^\circ\) limit. Therefore, the structural design is validated, confirming that blade interference will not occur under operational loads.
Kinematic Simulation and Experimental Validation
Prior to physical prototyping, a comprehensive kinematic simulation was performed using Adams software to verify the motion sequence and check for component interference throughout the harvesting cycle.
Simulation Results
The simulation model incorporated all moving parts of the end effector. A 20 mm/s velocity was applied to the main driving slider for a 4-second cycle, representing one pick-and-return sequence. The results clearly show the sequential operation:
- Phase 1 (0-1.35 s): The enveloping and clamping fingers close synchronously, guided by their respective torsion springs and linkages, to grasp the fruit. The shearing mechanism remains stationary.
- Phase 2 (1.35 s onward): The enveloping fingers reach their mechanical limit. Continued actuator motion then drives the slider-crank mechanisms, extending the three blades by 25.5 mm to complete the stem cut.
- Phase 3 (Return): The sequence reverses; blades retract first, followed by the fingers opening. The simulation confirmed smooth, non-interfering motion throughout, validating the kinematic design.
Prototype Testing and Performance Evaluation
A physical prototype was manufactured using 3D printing and machined aluminum parts. Rigorous tests were conducted to evaluate the end effector’s performance in two key areas: cutting success rate and clamping reliability.
Cutting Success Tests: Two test scenarios were designed. First, stems of varying diameters (2.5 mm to 4.0 mm) were presented in a centered position. Second, stems of fixed diameter were presented at different off-center angles (0° to 30°) to simulate imperfect positioning by the vision/robotic arm system. The results are summarized below:
| Test Scenario | Parameter | Success Rate |
|---|---|---|
| Variable Stem Diameter (Centered) | 2.5 mm | 100% |
| 3.0 mm | 100% | |
| 3.5 mm | 100% | |
| 4.0 mm | 98% | |
| Fixed Stem Diameter, Variable Angle | 2.5 mm stem, 0°-20° | 100% |
| 2.5 mm stem, 30° | 98% | |
| 3.5 mm stem, 0°-10° | 100% | |
| 3.5 mm stem, 20°-30° | 95% avg. |
Clamping Stability Test: The clamping fingers successfully held navel oranges of various sizes (70-90 mm diameter) securely during the cutting action without any instances of dropping or slippage, achieving a 100% stability rate in controlled tests.
The overall harvesting success rate, factoring in both cutting and clamping performance under realistic conditions (including off-center stems), was calculated to be 95%. The average time for a complete harvest cycle—from finger initiation to retraction after fruit drop—was measured at 4.3 seconds.
Conclusion
This work presents the successful development of a novel, underactuated, shearing-clamping integrated end effector for robotic navel orange harvesting. The design effectively addresses key challenges in agricultural robotics by combining grasping and cutting into a single, compact, and sequentially controlled mechanism. The use of underactuation simplifies control and improves robustness. Key achievements include:
- The creation of a dual-layer, three-finger end effector where one layer provides adaptive clamping and the other delivers precise, integrated cutting via rocker-slider mechanisms.
- The comprehensive mechanical modeling and FEA that verified structural integrity and ensured the cutting blades would operate without interference under load.
- Kinematic simulation that confirmed the correct, non-colliding sequence of operations from a single actuator input.
- Experimental validation with a physical prototype demonstrating a high overall harvesting success rate of 95% and a fast cycle time of 4.3 seconds per fruit.
This end effector design demonstrates a viable and efficient solution for navel orange harvesting. Its compact and integrated nature also suggests potential applicability for harvesting other similarly sized tree-borne fruits, contributing to the advancement of efficient and automated agricultural systems.