In modern automated production lines, especially in the wood processing industry, the efficient and reliable handling of heavy, large-format panels like doors is a critical challenge. Traditional methods relying on manual labor or simple mechanical aids are inefficient and costly. The core component enabling automated material transfer is the robot’s end effector. Conventional designs, such as scoop-type or vacuum-based end effectors, often fall short for heavy-duty applications due to limitations in load capacity, reliability, or the need for auxiliary manual operations. Therefore, the development of a robust, high-speed end effector capable of handling substantial payloads with minimal impact on the workpiece is paramount for achieving full production line automation.
This article presents the design and in-depth mechanical analysis of a novel clamping-style end effector. Our design focuses on achieving rapid pre-positioning and powerful, stable gripping for heavy wooden panels. The core innovation lies in the synergistic combination of a dual-lead screw mechanism for fast positioning and a self-locking wedge mechanism for generating immense clamping force. We will detail the structural design, establish comprehensive kinematic and static force models, and perform dynamic simulations to optimize key parameters. The primary goal is to create an end effector that is structurally simple, transmits force smoothly, handles heavy loads, and minimizes impact on the workpiece, thereby fulfilling the demands of high-efficiency, heavy-load palletizing systems.
1. Structural Design and Operational Principle of the End Effector
The designed end effector is primarily composed of two integrated subsystems: the Fast Positioning Mechanism and the Heavy-Duty Clamping Mechanism. The overall three-dimensional model is depicted below, illustrating the arrangement of key components.
1.1 Fast Positioning Mechanism: This subsystem is responsible for the initial, rapid approach and pre-clamping of the wooden panel. It consists of a dual-output DC servo motor, two trapezoidal lead screws with opposite hand threads, flange-mounted screw nuts, linear guide rails, support plates, and lateral clamping plates. The servo motor is fixed to a central support plate. Its two output shafts are connected via couplings to the two trapezoidal screws. The flange nuts engaged with these screws are mounted on the lateral plates, which are themselves mounted on linear guide rails. When the servo motor is energized, the screws rotate. Due to the opposite thread directions, the two lateral plates move symmetrically towards each other (or apart), allowing for quick adjustment to the panel’s width. Rubber pads equipped with pressure sensors are attached to these plates. The motor stops once a predetermined pre-clamping force is detected. The trapezoidal thread profile provides a self-locking feature, ensuring the position is maintained without continuous motor power.
1.2 Heavy-Duty Clamping Mechanism: This subsystem generates the final, high-magnitude clamping force required to securely hold the heavy panel. It comprises a double-acting pneumatic cylinder, two opposing wedge blocks, wedge push plates, and specialized rubber pads. The pneumatic cylinder is fixed to one of the lateral plates. The wedge blocks are attached to the cylinder’s rods. The wedge push plates, which house the final gripping rubber pads, are seated in trapezoidal guide slots on the lateral plates. After the fast positioning mechanism secures the panel, the pneumatic cylinder actuates, driving the two wedge blocks outward. The inclined surfaces of the wedges press against the wedge push plates, forcing them to clamp down on the panel. The wedge mechanism provides significant force amplification, enabling a relatively small pneumatic force to generate a very large clamping force at the end effector’s contact points.
The operational sequence is as follows: The palletizing robot maneuvers the end effector into position above the target panel. The fast positioning mechanism actuates, quickly moving the lateral plates to gently pre-clamp the panel. Subsequently, the heavy-duty clamping mechanism engages, with the wedges amplifying the pneumatic force to apply the full, secure clamping force. This two-stage process ensures both speed and a powerful, stable grip suitable for heavy loads.
2. Theoretical Mechanical Analysis of the End Effector
To quantify the performance and establish design criteria, a theoretical analysis of the forces and kinematics within the end effector is essential.
2.1 Analysis of the Fast Positioning Mechanism
The fast positioning mechanism converts the rotary motion of the servo motor into linear motion via the trapezoidal screw pairs. The kinematic relationship for the time required to grip a panel of width $D_2$, starting from an initial opening $D_1$, is given by:
$$
t = \frac{D_1 – D_2}{2 n p}
$$
where $n$ is the motor speed (rpm), and $p$ is the lead of the screw (mm/rev). The factor of 2 accounts for the two screws moving symmetrically.
The primary load during positioning is the friction resistance $F_Q$ from the linear guides. With $G_1$ as the weight of the lateral plate assembly and $G_2$ as the weight of the wooden panel, and $\mu_g$ as the guide’s friction coefficient, the friction force is:
$$
F_Q = \mu_g (G_1 + G_2)
$$
A force analysis of the screw-nut pair is crucial for sizing the motor. The torque $T_1$ required to drive the screw against the friction force $F_Q$ is derived from the inclined plane model of the screw thread:
$$
T_1 = F_Q \frac{d_2}{2} \frac{\cos(\lambda) \sin(\lambda + \rho)}{\cos(\rho)}
$$
Here, $d_2$ is the pitch diameter of the screw, $\lambda$ is the lead angle, and $\rho$ is the friction angle ($\tan \rho = \mu_s$, where $\mu_s$ is the coefficient of friction between the screw and nut).
The transmission efficiency $\eta$ of the screw is a key performance metric:
$$
\eta = \frac{\tan \lambda}{\tan(\lambda + \rho)}
$$
This equation shows efficiency depends on $\lambda$ and $\rho$. Efficiency increases with $\lambda$ but is constrained by practical manufacturing limits and the need for self-locking when the mechanism is under load from the clamping force $F_{clamp}$. The self-locking condition, which prevents back-driving, is:
$$
\lambda \le \rho
$$
When this condition is met, the fast positioning mechanism will hold its position regardless of the clamping force applied by the subsequent wedge mechanism, provided the screw strength is sufficient.
2.2 Analysis of the Heavy-Duty Clamping Mechanism
The wedge mechanism is the force-amplifying heart of the end effector. To prevent slippage, the total clamping force $2F_{clamp}$ (from two sides) must overcome the panel’s weight $G$. With $\mu_r$ as the coefficient of friction between the rubber pad and the wood, the requirement is:
$$
2F_{clamp} \ge \frac{G}{\mu_r} \quad \text{or} \quad F_{clamp} \ge \frac{G}{2\mu_r}
$$
A detailed static force analysis of the wedge and push plate assembly yields the force relationships. The following table defines the key parameters used in the analysis.
| Symbol | Description |
|---|---|
| $F_{drive}$ | Pneumatic cylinder driving force |
| $F_{clamp}$ | Clamping force output per wedge push plate |
| $\theta$ | Wedge angle (inclination angle) |
| $\phi_1, \phi_2, \phi_3$ | Friction angles at different contact interfaces |
| $l$ | Length of wedge push plate in contact with guide |
| $b$ | Cantilever length of wedge push plate |
| $d$ | Width of the guide slot |
From force equilibrium on the wedge block, the relationship between the cylinder force $F_{drive}$ and the force $R_{21}$ exerted by the wedge on the push plate can be found. A more comprehensive analysis considering the equilibrium of the wedge push plate (including moments) leads to the final expression for the clamping force $F_{clamp}$ as a function of $F_{drive}$:
$$
F_{clamp} = F_{drive} \cdot \frac{\cos \phi_1}{\cos(\theta+\phi_1+\phi_2) \tan \phi_3 – \sin(\theta+\phi_1+\phi_2) + \sin(\theta+\phi_1+\phi_2)\left(1 – 2b/l – (d/l)\tan \phi_3 \right)}
$$
The force amplification ratio, or mechanical advantage $i$, of the clamping mechanism is therefore:
$$
i = \frac{F_{clamp}}{F_{drive}} = \frac{\cos \phi_1}{\cos(\theta+\phi_1+\phi_2) \tan \phi_3 – \sin(\theta+\phi_1+\phi_2) + \sin(\theta+\phi_1+\phi_2)\left(1 – 2b/l – (d/l)\tan \phi_3 \right)}
$$
For an initial simplified estimation, neglecting friction in the guide ($\phi_3 \approx 0$) and at the wedge-push plate interface ($\phi_1, \phi_2 \approx 0$), the ideal relationship simplifies to:
$$
F_{drive} \approx F_{clamp} \cdot \tan \theta
$$
This clearly shows the force amplification effect: a smaller wedge angle $\theta$ results in a larger clamping force $F_{clamp}$ for a given cylinder force $F_{drive}$.
3. Dynamic Simulation and Parameter Optimization of the End Effector
To validate the design and optimize the key parameter—the wedge angle $\theta$—a dynamic simulation was performed using ADAMS software. A model of the heavy-duty clamping mechanism was created for three different wedge angles: 45°, 30°, and 15°. The simulation aimed to analyze the transient response, impact on the workpiece, and final steady-state force.
Simulation Setup: The panel mass was set to 110 kg. The required clamping force per side $F_{clamp}$ was calculated using the friction condition with $\mu_r=0.4$: $F_{clamp} \approx 2695 \, \text{N}$. The corresponding ideal driving force $F_{drive}$ was calculated using the simplified formula $F_{drive} = F_{clamp} \cdot \tan \theta$. A flexible spring-damper element (stiffness K=500 N/mm, damping C=300 N·s/mm) was added between the wedge push plate and a fixed reference to model the compliance of the wooden panel. The force in this spring represents the dynamic clamping force.
The table below summarizes the key outcomes extracted from the simulation results for the three wedge angles.
| Wedge Angle $\theta$ | 45° | 30° | 15° |
|---|---|---|---|
| Applied $F_{drive}$ (N) | 2695 | 1556 | 722 |
| Max. Push Plate Accel. (mm/s²) | 95.3 | 36.9 | 13.4 |
| Time to Steady-State (s) | 1.8 | 2.5 | 5.5 |
| Steady-State $F_{clamp}$ (N) | ~2750 | ~2670 | ~2700 |
| Cylinder Stroke (mm) | ~5.6 | ~9.2 | ~21.8 |
| Push Plate Displacement (mm) | ~5.6 | ~5.3 | ~5.4 |
Analysis of Simulation Results:
- Force Amplification: The steady-state clamping forces closely match the target value of ~2695 N for all angles, confirming the basic mechanical advantage principle $F_{drive} \tan \theta \approx F_{clamp}$. The required driving force $F_{drive}$ decreases significantly as $\theta$ decreases.
- Impact on Workpiece: The maximum acceleration of the wedge push plate, which correlates directly with the impact force on the wooden panel, decreases dramatically with the wedge angle. It is reduced by about 2.6 times from 45° to 30°, and by over 7 times from 45° to 15°. A smaller wedge angle greatly reduces the risk of damaging the panel during the clamping process.
- Clamping Speed vs. Stability: There is a clear trade-off between speed and smoothness. While the 45° configuration achieves a steady grip fastest (1.8 s), it does so with a high, potentially damaging acceleration. The 15° configuration is the smoothest but takes the longest to reach full clamping force (5.5 s).
- Actuator Stroke: The necessary stroke of the pneumatic cylinder increases substantially as $\theta$ decreases (from 5.6 mm to 21.8 mm). This is a direct consequence of the kinematic relationship in a wedge mechanism.
Optimization Conclusion: For a high-speed, heavy-load palletizing end effector, the optimal wedge angle must balance several factors: sufficient force amplification, minimal workpiece impact, acceptable clamping cycle time, and practical actuator stroke. Based on the simulation, a wedge angle in the range of **15° to 30°** offers a good compromise. An angle of **approximately 15°** is particularly advantageous when protecting the workpiece is a high priority, as it minimizes impact while still providing enormous force amplification. The longer cycle time can often be mitigated by the robot’s motion planning. This optimized parameter ensures the end effector meets the core requirements of high efficiency, heavy load capacity, and low impact.
4. Conclusion
This work presents the comprehensive design and analysis of a novel heavy-duty end effector for palletizing robots. The two-stage design, featuring a self-locking fast positioning mechanism and a force-amplifying wedge-based clamping mechanism, effectively addresses the limitations of conventional end effectors in heavy-load applications like wooden panel handling. The theoretical models established for both the screw-driven positioning and the wedge clamping provide a solid foundation for sizing components and predicting performance. The dynamic simulation study quantitatively demonstrates the critical influence of the wedge angle on the system’s behavior. It confirms that a smaller angle (around 15°) significantly reduces the impact force on the workpiece—a crucial factor for preventing damage—while still providing the necessary high clamping force and acceptable operational speed.
The proposed end effector offers distinct advantages over scoop-type designs (no need for manual spacer insertion) and vacuum-based systems (simpler, more reliable, and not dependent on surface conditions). Its attributes of structural simplicity, smooth force transmission, high load capacity, low impact, and self-locking reliability make it highly suitable for integration into fully automated, high-efficiency palletizing lines. The methodologies and findings contribute to the advancement of robust end effector design for material handling robotics.