The manual harvesting of apples presents significant challenges, including low efficiency, high labor intensity, and inherent safety risks associated with working at height. In recent years, rising labor costs have further exacerbated the economic pressure on orchards. Consequently, there is a pressing need for automated harvesting solutions, such as apple picking robots. The performance and reliability of the robotic end effector—the component that physically interacts with the fruit—are often the critical factors determining the overall success, efficiency, and quality of the harvest. A poorly designed end effector can lead to fruit damage, low detachment success rates, and operational failures. This article details the design process and parametric optimization of a novel, cable-driven three-fingered end effector specifically engineered for automated apple picking. The narrative will proceed from a first-person engineering perspective, outlining the mechanical conception, kinematic analysis, and force-based optimization that culminated in the final design.
The primary design objective was to create a robust, adaptive, and damage-free end effector capable of harvesting apples within a diameter range of 80 to 100 mm. The proposed solution is a cable-actuated, underactuated gripper. Underactuation implies that the number of actuators is fewer than the number of degrees of freedom, which often leads to simpler, lighter, and more compliant mechanisms that can adapt to object geometry. The overall architecture of the end effector can be segmented into three fundamental subsystems: the grasping mechanism, the support and connection structure, and the driving transmission system.
The grasping mechanism is composed of three identical fingers arranged symmetrically at 120-degree intervals around a central axis. Each finger is a two-phalange linkage, comprising a proximal phalanx and a distal phalanx, mimicking a simplified human finger structure. This multi-joint design provides better conformation to the spherical shape of an apple compared to a single rigid claw. To ensure a secure yet non-damaging grip, the inner surface of each phalanx is lined with a soft rubber material. Furthermore, embedded pressure sensors within this padding provide real-time feedback on the contact force, enabling precise control to prevent bruising.
The support and connection structure forms the skeleton of the end effector. It consists of a base disk, a movable lifting disk, a stationary flange disk for robot arm attachment, and several vertical support rods that connect these disks. The support rods act as linear guides for the lifting disk, constraining its motion to a purely vertical translation. The driving transmission system is the actuation heart of the device. It features a stepper motor fixed to the underside of the lifting disk. The motor drives a small drum around which a high-strength traction cable is wound. One end of this cable is anchored to the base disk. The motion is transmitted to the fingers via three thrust links, each connecting the lifting disk to a corresponding finger linkage. Compression springs are mounted on the support rods between the base and lifting disks, providing a restoring force.
The operational principle is elegantly simple. For grasping, the stepper motor rotates in the forward direction, winding the cable onto the drum. This pulls the lifting disk upward against the spring force. The upward motion of the lifting disk pushes the thrust links, which in turn drives the finger linkages, causing all three fingers to close inward synchronously. When the pressure sensors indicate that a preset force threshold has been reached, the motor stops, holding the apple securely. For release, the motor reverses, unwinding the cable. The stored energy in the compressed springs then pushes the lifting disk downward, retracting the thrust links and allowing the fingers to open passively, dropping the apple.
Parametric Analysis and Optimization of the End Effector
The initial conceptual design required rigorous analysis and optimization of several key parameters to ensure reliable performance across the specified fruit size range. The following sections detail this optimization process, focusing on four critical aspects: the radial position of the fingers, the grasping force threshold, the length of the thrust link, and the selection of the drive motor.
1. Optimization of Finger Radial Position
The initial design placed the pivot point of the finger’s base joint at a distance L = 35 mm from the central axis of the end effector. Kinematic simulation revealed a significant issue: when grasping a minimum-diameter apple (80 mm), the contact point on the proximal phalanx was consistently at its very tip, resulting in poor conformity and a unstable grip. The finger was simply too far from the fruit. The goal was to move the finger assembly radially inward to improve contact geometry without compromising the ability to grasp the maximum-diameter apple (100 mm). An incremental optimization was performed.
Let \( L_{new} = L_{initial} – \Delta L \), where \( \Delta L \) is the inward adjustment. The constraint is that the end effector must be able to physically enclose a sphere of diameter \( D_{max} = 100 \) mm. Through geometric simulation, it was determined that the maximum feasible inward adjustment was \( \Delta L = 5 \) mm. Setting \( L_{optimized} = 30 \) mm resulted in significantly improved contact wrapping for both small and large apples, as the finger’s posture allowed the soft pad to engage more of the fruit’s surface area. This enhanced conformity, aided by the compliant finger pad, promised a more stable and distributed grip.
2. Determination of Harvesting Method and Force Threshold
Selecting an appropriate detachment method is crucial. While cutting the stem is possible, it typically requires a higher force (18-30 N). A more efficient method for ripe apples is twisting, which leverages the natural abscission layer that forms between the fruit stem (pedicel) and the branch. The torsional force required to break this abscission layer is typically between 2-5 N.
To prevent damage, the grasping force must remain below the apple’s bio-yield point—the stress at which permanent tissue damage begins. Based on empirical data from compression tests, the bio-yield force for a typical apple, considering the contact area of the finger pad, is approximately \( F_{yield} \approx 7 \) N. Therefore, this value was set as the upper limit for the normal contact force \( F_N \) applied by each finger.
We must verify that the resulting frictional force is sufficient to transmit the required torsional detachment force. The coefficient of static friction \( \mu \) between the rubber finger pad and the apple skin is approximately 0.4. The total maximum frictional force \( F_{friction-total} \) provided by three fingers is:
$$ F_{friction-total} = 3 \times \mu \times F_N = 3 \times 0.4 \times 7 = 8.4 \text{ N} $$
Since \( 8.4 \text{ N} > 5 \text{ N} \), the frictional force at the bio-yield threshold is more than adequate to apply the necessary twisting torque for stem detachment. Thus, a force threshold of \( F_{threshold} = 7 \) N per finger was adopted.
3. Kinematic and Static Analysis for Thrust Link Length Optimization
The thrust link is a critical component translating vertical motion into finger closure. Its length \( L_{TL} \) affects both the mechanical advantage (force amplification) and the overall size of the end effector. A longer link provides a larger lever arm, reducing the required actuation force but increasing the device’s footprint. A shorter link increases compactness but demands higher force from the actuator. We analyze the two extreme cases: grasping a \( D_1=100 \) mm apple and a \( D_2=80 \) mm apple.
First, a static force analysis is performed on a single finger in the fully grasped configuration. The known parameters are the finger contact forces \( F_1 = F_2 = 7 \) N (on distal and proximal phalanges, respectively) and their points of application. Their resultant \( F_3 \) and its moment arm \( L_1 \) about the finger’s base pivot can be determined from the geometry. Equilibrium requires that this moment is balanced by the moment generated by the thrust link force \( F_{TL} \):
$$ F_3 \cdot L_1 = F_{TL} \cdot L_2 $$
where \( L_2 \) is the moment arm of \( F_{TL} \).
The relationship between \( L_2 \), the thrust link length \( L_{TL} \), and the link angle \( \beta \) is derived from the geometry of the four-bar linkage formed by the finger and the link:
$$ L_2 = 38 \cos(\theta + \beta) = 38\cos\theta\cos\beta – 38\sin\theta\sin\beta $$
$$ L_{TL} \sin\beta = L_3 $$
Here, \( \theta \) is the angle of the driving link attached to the finger, and \( L_3 \) is a fixed horizontal distance obtained from the grasp geometry. For a given apple diameter, \( \theta \) and \( L_3 \) are constants determined by the final finger posture.
Combining these equations with the moment equilibrium formula allows us to express the required thrust link force \( F_{TL} \) as a function of its length \( L_{TL} \). The table below summarizes the constants for the two extreme cases:
| Apple Diameter (mm) | \( F_3 \) (N) | \( L_1 \) (mm) | \( \theta \) (deg) | \( L_3 \) (mm) |
|---|---|---|---|---|
| 100 | 16.5 | 57.9 | 7.5 | 14.7 |
| 80 | 12.5 | 49.8 | 22.9 | 12.0 |
Solving the system yields the following functional relationships:
For D=100 mm: $$ F_{TL} = \frac{955.4 \cdot L_{TL}}{37.7 \sqrt{L_{TL}^2 – 216.1} – 72.9} $$
For D=80 mm: $$ F_{TL} = \frac{622.5 \cdot L_{TL}}{35 \sqrt{L_{TL}^2 – 144} – 178.8} $$
Plotting these functions reveals that for \( L_{TL} < 20 \) mm, the required force decreases sharply with increasing length. For \( L_{TL} > 20 \) mm, the force reduction becomes more gradual. A length of \( L_{TL} = 40 \) mm was selected as an optimal compromise, providing a substantial mechanical advantage (\( F_{TL} \approx 28.8 \) N for 100mm, \( F_{TL} \approx 21.5 \) N for 80mm) while maintaining a compact form factor for the end effector.
4. Actuator Selection and System Force Verification
With the thrust link force requirements known, the final step is to select a suitable stepper motor and verify that the entire drive train can generate this force. A NEMA 17 stepper motor (model 42BYGH48P180) with a holding torque of \( T_{hold} = 0.52 \) N·m was initially considered. The force transmission from the motor torque to the thrust link involves the cable-drum system and the equilibrium of the lifting disk.
A force analysis on the lifting disk involves the following:
- Three thrust link reaction forces \( F’_{TL} \) (equal to \( F_{TL} \) from analysis).
- The cable tension \( F_{cable} \).
- The weight \( G \) of the lifting disk, motor, and drum assembly (\( G \approx 5.78 \) N).
- The restoring force from three compression springs \( 3F_{spring} = 3k \Delta h \), where \( k \) is the spring constant and \( \Delta h \) is the disk displacement.
The vertical force equilibrium equation is:
$$ F_{cable} = 3 F’_{TL} \cos\beta + G + 3k \Delta h $$
The motor torque \( T_{motor} \) relates to the cable tension via the drum radius \( R_{drum} = 5 \) mm:
$$ T_{motor} = F_{cable} \cdot R_{drum} $$
The spring constant \( k \) must be chosen so that the springs can reliably return the lifting disk to its home position when the motor reverses. The condition is that the total spring force at maximum compression (\( \Delta h_{max} \approx 4.8 \) mm for 100mm apple) must exceed the weight \( G \):
$$ 3k \Delta h_{max} > G \Rightarrow k > \frac{G}{3 \Delta h_{max}} \approx 0.4 \text{ N/mm} $$
A standard spring with \( k = 0.4 \) N/mm (or 40 N/m) was selected.
Now, the required motor torque can be checked for both extreme cases. Using the operating parameters (\(\beta\), \(\Delta h\)) from the final grasp simulations and the chosen \( k \), the required cable tension and thus motor torque are calculated. The results are compared to the motor’s available torque at the operational speed (e.g., 60 RPM).
| Parameter | Apple D=100 mm | Apple D=80 mm | Units |
|---|---|---|---|
| Req. Thrust Link Force \( F’_{TL} \) | 32.4 | 27.8 | N |
| Link Angle \( \beta \) | 21.5 | 17.5 | deg |
| Disk Displacement \( \Delta h \) | 4.8 | 13.7 | mm |
| Calculated Cable Tension \( F_{cable} \) | ~103 | ~88 | N |
| Required Motor Torque \( T_{req} \) | ~0.515 | ~0.44 | N·m |
| Available Motor Torque @ 60 RPM | 0.51 | 0.51 | N·m |
The analysis confirms that the selected stepper motor, with its torque characteristic, is capable of driving the end effector to achieve the necessary grasping forces for the entire target apple size range. The requirement for the 100 mm apple is marginally higher but within the operational capability of the motor when accounting for system efficiency and the static holding torque.
Conclusion
This detailed design and analysis process has resulted in a fully specified cable-driven end effector for robotic apple harvesting. The key outcomes of the optimization are: an optimized finger radial position of 30 mm from the center; a biologically-informed grasping force threshold of 7 N per finger to prevent damage; a thrust link length of 40 mm balancing force requirement and compactness; and the successful selection of a standard stepper motor capable of providing the necessary actuation force.
The proposed end effector embodies several desirable features for agricultural robotics: underactuation for adaptive grasping, integrated force sensing for damage prevention, a cable-driven mechanism for remote actuation and weight reduction, and a torsional detachment method that mimics efficient manual picking. The systematic approach to optimizing critical parameters—moving from kinematic simulation to static force analysis and dynamic actuator sizing—ensures that the final design is not only conceptually sound but also mechanically feasible. This end effector is designed for integration onto a robotic manipulator, forming a complete apple picking system aimed at improving the efficiency, safety, and cost-effectiveness of modern orchard management.