The mechanized harvesting of safflower stigma presents significant challenges, primarily characterized by high breakage rates and low clean harvesting efficiency. This work addresses these issues through the design and optimization of a novel end effector mechanism. The proposed design employs a V-shaped opposite cutting principle to achieve precise and gentle separation of the stigmas from the flower head. The core of this end effector is a pair of V-shaped blades driven by a rotary cam mechanism, enabling a synchronized, inward cutting motion.
The performance of the harvesting end effector is fundamentally governed by its kinematic and structural parameters. The cutting process involves a complex interaction between the blade geometry and the biomechanical properties of the safflower stigma and its connective tissue (the “neck”). To minimize damage, a sliding-cut action is utilized. The condition for initiating this slide is derived from a force balance analysis at the contact point between the stigma cluster and the blades. Considering the stigma as an elastic material, the analysis focuses on the point where it begins to slide towards the cutting center. The forces include normal contact forces from the blades ($$F_{N1}$$, $$F_{N2}$$) and frictional forces along the blade edges ($$F_{f1}$$, $$F_{f2}$$). Assuming symmetrical blades with equal rake angles ($$\beta$$), the equilibrium condition for impending slide is given by:
$$
\begin{aligned}
F_{f1} + F_{f2} \cos(2\beta) &= F_{N2} \sin(2\beta) \\
F_{N1} &= F_{f2} \sin(2\beta) + F_{N2} \cos(2\beta)
\end{aligned}
$$
where the frictional forces are related to the normal forces by the friction coefficient: $$F_f = \mu F_N = \tan(\gamma) F_N$$, with $$\gamma$$ being the friction angle. Solving these equations yields the minimum rake angle required for sliding to occur:
$$
\beta \geq \gamma
$$
Experimental measurement determined the friction angle $$\gamma$$ between the stigma and the blade material to be approximately 23°. Therefore, the blade rake angle must be greater than or equal to 23° to ensure effective sliding cut and prevent the stigma from being pushed aside.
Another critical parameter is the blade clearance angle or wedge angle ($$\alpha$$). A smaller wedge angle reduces cutting resistance but compromises blade strength. The total cutting force ($$F_D$$) for one blade during the final stage of cutting (when the material thickness being compressed is half the original) was derived considering material compression, friction on the blade face, and the force at the blade edge:
$$
F_D = \delta l \sigma + \frac{1}{2} mg \tan \gamma + \frac{lE}{8k} \left[ \tan \alpha + \tan \gamma (\sin^2 \alpha + \mu \cos^2 \alpha) \right]
$$
where $$\delta$$ is the blade edge thickness, $$l$$ is the effective cutting length, $$\sigma$$ is the ultimate stress of the stigma material, $$m$$ is the mass of the cut stigma, $$g$$ is gravity, $$E$$ is the elastic modulus, $$k$$ is a strain transfer coefficient, and $$\mu$$ is Poisson’s ratio. This equation shows that the cutting force increases with the wedge angle $$\alpha$$, particularly for angles greater than 30°. Thus, the wedge angle should be kept below 30° to minimize cutting force and potential stigma damage.
The kinematic design of the cam-driven end effector is crucial for smooth operation. The blades are attached to sliders that follow a heart-shaped cam groove. The relationship between the cam rotation angle ($$\phi$$) and the blade displacement ($$y$$), velocity ($$v$$), and acceleration ($$a$$) are given by:
$$
\begin{aligned}
y &= l \tan\left(\frac{\pi}{6} – \phi\right) \\
v &= \frac{l \omega}{\cos^2\left(\frac{\pi}{6} – \phi\right)} \\
a &= \frac{2l \omega^2 \sin\left(\frac{\pi}{6} – \phi\right)}{\cos^3\left(\frac{\pi}{6} – \phi\right)}
\end{aligned}
$$
where $$l$$ is the fixed distance from the cam center to the slider guide, and $$\omega$$ is the angular velocity of the cam. To avoid sharp acceleration changes that could cause impact and damage, the motor speed profile is divided into five segments: variable acceleration, constant acceleration, constant velocity, constant deceleration, and variable deceleration. The constant velocity phase, where acceleration is minimal, is designed to coincide with the actual cutting stroke to ensure a stable and smooth cutting action.
The physical and mechanical properties of the safflower variety used (“Yumin No-Thorn”) were measured to inform the design, as summarized in the table below:
| Parameter | Range | Average Value |
|---|---|---|
| Fruit Ball Diameter (mm) | 28.62 – 36.35 | 32.37 |
| Neck Diameter (mm) | 5.26 – 9.62 | 7.64 |
| Stigma Spread Width (mm) | 40.63 – 52.25 | 46.87 |
| Fruit Ball Height (mm) | 24.07 – 30.76 | 26.52 |
To validate the design and identify the optimal operating parameters, a three-factor, five-level Box-Behnken Response Surface Methodology (RSM) experiment was conducted. The factors were the stepper motor speed (which determines cutting speed), the blade rake angle ($$\beta$$), and the blade wedge angle ($$\alpha$$). The response variables were the stigma breakage rate ($$y_1$$) and the stigma clean harvesting rate ($$y_2$$), defined as:
$$
y_1 = \frac{m_1}{m_2} \times 100\% , \quad y_2 = \frac{m_2}{m} \times 100\%
$$
where $$m_1$$ is the mass of broken stigmas, $$m_2$$ is the total mass of harvested stigmas from a single flower head, and $$m$$ is the total mass of all stigmas on that flower head. The experimental design with coded factor levels is shown below:
| Code | Motor Speed, x1 (rpm) | Rake Angle, x2 (°) | Wedge Angle, x3 (°) |
|---|---|---|---|
| -2 | 14.0 | 25.0 | 10.0 |
| -1 | 17.5 | 30.0 | 15.0 |
| 0 | 21.0 | 35.0 | 20.0 |
| 1 | 24.5 | 40.0 | 25.0 |
| 2 | 28.0 | 45.0 | 30.0 |
A total of 23 experimental runs were performed. The results were analyzed using ANOVA to develop second-order polynomial regression models for the two responses. For the stigma breakage rate ($$y_1$$), the significant model terms (p < 0.01) were the quadratic terms of all three factors ($$x1^2$$, $$x2^2$$, $$x3^2$$) and the interaction between rake and wedge angles ($$x2x3$$). For the clean harvesting rate ($$y_2$$), the significant terms were the linear effect of motor speed ($$x1$$) and the quadratic effect of the wedge angle ($$x3^2$$). The lack-of-fit tests for both models were not significant, indicating good model adequacy. The final regression models in terms of coded factors are:
$$
\begin{aligned}
y_1 &= 3.52 + 0.29x_1 – 0.22x_2 + 0.20x_3 + 0.14x_1x_2 + 0.076x_1x_3 + 0.46x_2x_3 + 0.33x_1^2 + 0.58x_2^2 + 0.71x_3^2 \\
y_2 &= 94.26 + 0.65x_1 – 0.52x_2 – 0.25x_3 – 0.14x_1x_2 – 0.21x_1x_3 – 0.24x_2x_3 – 0.15x_1^2 – 0.25x_2^2 – 0.51x_3^2
\end{aligned}
$$
The analysis of variance (ANOVA) for the developed models is summarized in the following table:
| Source | Stigma Breakage Rate (y1) | Clean Harvesting Rate (y2) | ||
|---|---|---|---|---|
| F-value | p-value | F-value | p-value | |
| Model | 29.78 | < 0.0001 | 12.66 | < 0.0001 |
| x1 – Motor Speed | 13.23 | 0.0030 | 35.40 | < 0.0001 |
| x2 – Rake Angle | 8.02 | 0.0141 | 23.06 | 0.0003 |
| x3 – Wedge Angle | 6.10 | 0.0282 | 4.93 | 0.0448 |
| x1x2 | 1.65 | 0.2219 | 0.78 | 0.3925 |
| x1x3 | 0.46 | 0.5081 | 1.93 | 0.1886 |
| x2x3 | 16.95 | 0.0012 | 2.40 | 0.1452 |
| x1² | 30.98 | < 0.0001 | 3.50 | 0.0841 |
| x2² | 94.22 | < 0.0001 | 8.89 | 0.0106 |
| x3² | 141.67 | < 0.0001 | 39.65 | < 0.0001 |
| Lack of Fit | 2.87 | 0.0896 | 0.91 | 0.5205 |
The response surface analysis revealed clear trends. The stigma breakage rate exhibited a convex response to each factor, with a distinct minimum point. Specifically, the breakage rate decreased and then increased with increasing motor speed, rake angle, and wedge angle. The clean harvesting rate increased with motor speed and showed a concave response to the wedge angle, peaking at an intermediate value. A multi-objective optimization was performed with the goals of minimizing $$y_1$$ and maximizing $$y_2$$. The numerical optimization function in the software identified the following optimal parameter set: Motor Speed = 22.5 rpm, Blade Rake Angle = 34.2°, Blade Wedge Angle = 19.1°. At this point, the predicted responses were a stigma breakage rate of 3.74% and a clean harvesting rate of 94.63%.
Field validation tests were conducted using a prototype end effector integrated with a delta parallel robot for positioning. The tests were performed under the optimal parameters identified. The results from five repeated trials showed an average stigma breakage rate of 3.97% and an average clean harvesting rate of 94.28%. These values show close agreement with the model predictions, with relative errors of 5.8% and 0.37% for breakage rate and clean harvesting rate, respectively. This confirms the reliability of the optimization model and the effectiveness of the designed end effector mechanism.
In conclusion, the V-shaped opposite cutting end effector presented in this work provides an effective solution for the mechanized harvesting of safflower stigmas. The mechanical design, based on a cam-driven synchronized cutting action and a V-shaped blade geometry that promotes sliding cut, successfully addresses the key challenges of high breakage and low harvest efficiency. Through rigorous theoretical analysis of the cutting mechanics and a structured experimental optimization process, the critical parameters of the end effector were identified. The optimal configuration achieves a high clean harvesting rate while maintaining a very low stigma breakage rate, demonstrating the practical viability of this end effector design for integration into automated safflower harvesting systems.