The rapid evolution of industrial intelligence and the sustained growth in demand for textiles, such as socks, are driving a profound transformation towards smart manufacturing in textile factories. In traditional production models, monotonous and highly repetitive material handling tasks remain heavily reliant on manual labor. However, the persistent rise in labor costs and increasing labor shortages have become critical bottlenecks hindering the industrial upgrading of these factories. The introduction of handling robots presents a viable solution, capable of transporting materials to specified locations with precision and efficiency, thereby significantly boosting productivity and reducing reliance on manual labor.
Nevertheless, conventional robot end effectors are often designed for grasping objects of a single, specific shape and size. These specialized tools typically perform only a dedicated grasping task, struggling to meet the diverse handling demands in a sock factory where objects vary greatly in shape and dimension. Switching between different handling tasks often requires frequent changes of the end effector on traditional robots, which not only increases equipment costs but also severely reduces overall production efficiency. While researchers have proposed various solutions to this adaptability problem, significant limitations often remain, making them unsuitable for the complex, real-world requirements of textile production lines.
Therefore, to address the challenges posed by complex product structures, vast dimensional differences, and the inherent lack of adaptability in single-structure robots, we have designed a novel, linkage-driven, multi-functional end-effector for a dual-arm handling robot. The primary goal of this end-effector is to enhance the automation level of material handling in sock factories. Its design is characterized by structural simplicity, integrating both a mechanical hand module and a pallet module. This dual-functionality allows the end effector to perform precise and enveloping grasps on small, complex items like spools and finished socks via the mechanical hand, while also enabling the stable transport of large material boxes through the coordinated use of the pallet module and the dual robot arms. This end effector, with its straightforward structure and ease of control, is engineered to adapt to the cargo handling needs of various complex scenarios, offering a valuable reference for the intelligent upgrading of the textile industry.
Modular Design and Operational Principles of the End-Effector
Our proposed end-effector adopts a core philosophy of modular design, primarily consisting of two distinct units: the Pallet Module and the Mechanical Hand Module. The mechanical hand module itself is composed of fingers, a palm, and a transmission system, while the pallet module is securely mounted onto the upper and lower housings of the palm.
The pallet module is specifically engineered for transporting large material boxes commonly found in sock factories. To enhance its load-bearing capacity, stability, and adaptability to boxes of various specifications, this module utilizes a reinforced I-beam structure. In contrast, the mechanical hand module is responsible for the precise grasping of smaller materials like thread spools and socks. To accommodate objects of different shapes and sizes and to ensure that delicate items like yarn and textiles are not damaged during grasping, the mechanical hand features a cooperative three-finger configuration. Each finger is equipped with a compliant covering and an integrated sensory system. The actuation of the mechanical hand is achieved through a multi-degree-of-freedom, linkage-based transmission scheme. This approach not only guarantees the dexterity of the end effector but also ensures its operational stability in complex working environments. This modular architecture allows the end effector to be rapidly configured for different task requirements, significantly boosting the flexibility and automation level of the factory’s handling processes.
Finger Mechanism and Grasping Modes
A single finger of the mechanical hand module possesses three phalanges: the proximal, medial, and distal phalanges. This multi-jointed design grants the finger an adaptive capability, allowing it to conform to the shape of a target object during grasping, thereby ensuring both reliability and efficiency. The specific link lengths defining the finger’s geometry are summarized in the table below.
| Link Description | Symbol | Length (mm) |
|---|---|---|
| Proximal Phalanx | $l_{AC}$ | 45.0 |
| Medial Phalanx | $l_{CE}$ | 30.0 |
| Distal Phalanx | $l_{EG}$ | 30.0 |
| Drive Link | $l_{AH}$ | 11.5 |
| Connecting Link 1 | $l_{DH}$ | 40.0 |
| Connecting Link 2 | $l_{BF}$ | 29.0 |
The finger operates in two fundamental grasping modes: enveloping grasp and fingertip grasp. The underlying principle for both involves a coordinated underactuated mechanism:
- Enveloping Grasp: The servo motor rotates the drive link $AH$. Under the constraint of an elastic element (e.g., a torsion spring), the proximal phalanx link $ACB$ rotates until it makes contact with the object, where a mechanical stop is engaged. Subsequently, the driving force overcomes the damping force of the elastic element between link $ACB$ and drive link $AH$, releasing one degree of freedom. The drive link $AH$ then drives the medial phalanx link $DCE$ to continue moving until it fully contacts the object, completing the enveloping grasp for that finger.
- Fingertip Grasp: The servo motor rotates the drive link $AH$. Prior to object contact, the finger essentially has one degree of freedom due to the elastic constraint. The motion continues until the fingertip contacts the object and forms a mechanical stop, achieving a precise fingertip pinch grasp.
This compact underactuated design maintains sufficient grasping force while enabling stable and adaptive grasping, significantly enhancing the end effector’s ability to handle materials of varying shapes and sizes.
Comprehensive Kinematic Modeling of the End-Effector Finger
Kinematic analysis is fundamental for understanding and controlling the motion of the end effector. It comprises forward kinematics (determining the fingertip position given joint angles) and inverse kinematics (determining the required joint angles to achieve a desired fingertip position). We employ the Denavit-Hartenberg (D-H) parameter method to construct a complete kinematic model for a single finger of the mechanical hand module, which is representative as all fingers are identical.
Forward Kinematics Analysis
We establish the D-H coordinate frames for a single finger. The transformation from frame $i-1$ to frame $i$ is described by the homogeneous transformation matrix $^{i-1}_{i}T$:
$$
^{i-1}_{i}T = \begin{bmatrix}
\cos\theta_i & -\sin\theta_i & 0 & a_{i-1}\\
\sin\theta_i \cos\alpha_{i-1} & \cos\theta_i \cos\alpha_{i-1} & -\sin\alpha_{i-1} & -d_i \sin\alpha_{i-1}\\
\sin\theta_i \sin\alpha_{i-1} & \cos\theta_i \sin\alpha_{i-1} & \cos\alpha_{i-1} & d_i \cos\alpha_{i-1}\\
0 & 0 & 0 & 1
\end{bmatrix}
$$
For our planar finger mechanism, the parameters simplify. The D-H parameters are listed below:
| Link i | $\alpha_{i-1}$ (deg) | $a_{i-1}$ (mm) | $\theta_i$ (deg) | $d_i$ (mm) |
|---|---|---|---|---|
| 1 | 0 | 0 | $\theta_1$ | 0 |
| 2 | 0 | $l_{AC}$ | $\theta_2$ | 0 |
| 3 | 0 | $l_{CE}$ | $\theta_3$ | 0 |
The overall transformation from the base frame (0) to the fingertip frame (3) is obtained by successive multiplication:
$$ ^{0}_{3}T = ^{0}_{1}T \cdot ^{1}_{2}T \cdot ^{2}_{3}T $$
Accounting for the offset of the fingertip point $G$ from the third frame origin, the position of the fingertip $G$ in the base frame is given by $^{0}_{3}T \cdot T(l_{EG}, 0, 0)$, yielding:
$$
^{0}_{3}T = \begin{bmatrix}
\cos\theta_{123} & -\sin\theta_{123} & 0 & l_{AC}\cos\theta_1 + l_{CE}\cos\theta_{12}\\
\sin\theta_{123} & \cos\theta_{123} & 0 & l_{AC}\sin\theta_1 + l_{CE}\sin\theta_{12}\\
0 & 0 & 1 & 0\\
0 & 0 & 0 & 1
\end{bmatrix}
$$
$$
\text{Fingertip Position: } \begin{cases}
x_G = l_{AC}\cos\theta_1 + l_{CE}\cos\theta_{12} + l_{EG}\cos\theta_{123} \\
y_G = l_{AC}\sin\theta_1 + l_{CE}\sin\theta_{12} + l_{EG}\sin\theta_{123} \\
z_G = 0
\end{cases}
$$
Where $\theta_{12} = \theta_1 + \theta_2$ and $\theta_{123} = \theta_1 + \theta_2 + \theta_3$.
Inverse Kinematics Solution
Given a desired fingertip position $(x_G, y_G)$, we need to solve for the joint angles $(\theta_1, \theta_2, \theta_3)$. We employ a geometric approach. Let:
$$
k_1 = x_G – l_{EG}\cos\theta_{123}, \quad k_2 = y_G – l_{EG}\sin\theta_{123}
$$
From the forward kinematics, we have $k_1 = l_{AC}\cos\theta_1 + l_{CE}\cos\theta_{12}$ and $k_2 = l_{AC}\sin\theta_1 + l_{CE}\sin\theta_{12}$. Squaring and adding these equations eliminates $\theta_1$:
$$ k_1^2 + k_2^2 = l_{AC}^2 + l_{CE}^2 + 2l_{AC}l_{CE}\cos\theta_2 $$
Thus, we can solve for $\theta_2$:
$$ \theta_2 = \pm \arccos\left( \frac{k_1^2 + k_2^2 – l_{AC}^2 – l_{CE}^2}{2 l_{AC} l_{CE}} \right) $$
The $\pm$ sign corresponds to elbow-up and elbow-down configurations. Subsequently, $\theta_1$ can be found using the two-argument arctangent function and the law of cosines/sines:
$$ \theta_1 = \text{atan2}(k_2, k_1) \mp \arccos\left( \frac{k_1^2 + k_2^2 + l_{AC}^2 – l_{CE}^2}{2 l_{AC} \sqrt{k_1^2 + k_2^2}} \right) $$
Finally, $\theta_3$ is determined from the overall orientation constraint $\theta_{123} = \text{atan2}(y_G – l_{AC}\sin\theta_1 – l_{CE}\sin\theta_{12}, \quad x_G – l_{AC}\cos\theta_1 – l_{CE}\cos\theta_{12})$ and the relation $\theta_3 = \theta_{123} – \theta_1 – \theta_2$.
Workspace Analysis
The workspace of a finger defines the set of all points in space that its fingertip can reach. It is a critical metric for assessing the dexterity and task adaptability of the end effector. Using the Robotics Toolbox in MATLAB, we constructed a simulation model of the single finger. The Monte Carlo method was employed by randomly sampling joint angles within their physical limits ($\theta_1: [0, 90^\circ]$, $\theta_2: [0, 110^\circ]$, $\theta_3: [0, 90^\circ]$) and computing the corresponding fingertip positions via the forward kinematics equations. The resulting point cloud, representing the finger’s reachable workspace, is plotted. Analysis of the workspace projection reveals a continuous, crescent-shaped region without internal voids. This continuity is essential for ensuring smooth and uninterrupted motion trajectories during task execution, which directly contributes to the operational precision and reliability of the mechanical hand module within the overall end effector system.
| Workspace Characteristic | Description | Implication for End-Effector |
|---|---|---|
| Shape | Crescent / Semilunar | Well-suited for enveloping cylindrical objects like spools. |
| Continuity | No internal holes or gaps. | Enables smooth paths for fingertip during grasping maneuvers. |
| Area Coverage | Approx. $12,500 \, \text{mm}^2$ in XY-plane. | Adequate range for handling typical sock factory small items. |
Static Force and Grasping Stability Analysis
Beyond kinematics, evaluating the force transmission and grasp stability is crucial for the practical application of the end effector. For an underactuated finger, the relationship between the input torque $\tau$ at the motor and the contact forces $F_i$ at the phalanges can be derived using the principle of virtual work or the Jacobian transpose.
The Jacobian matrix $J$ relates joint velocities $\dot{\theta} = [\dot{\theta}_1, \dot{\theta}_2, \dot{\theta}_3]^T$ to the fingertip velocity $[v_x, v_y]^T$ in the base frame. For a planar 3R manipulator, it is given by:
$$
J = \begin{bmatrix}
-l_{AC}s_1 – l_{CE}s_{12} – l_{EG}s_{123} & -l_{CE}s_{12} – l_{EG}s_{123} & -l_{EG}s_{123} \\
l_{AC}c_1 + l_{CE}c_{12} + l_{EG}c_{123} & l_{CE}c_{12} + l_{EG}c_{123} & l_{EG}c_{123}
\end{bmatrix}
$$
Where $s_1=\sin\theta_1$, $c_{12}=\cos\theta_{12}$, etc. According to the static force relationship, the joint torques $\tau = [\tau_1, \tau_2, \tau_3]^T$ required to produce a force $F = [F_x, F_y]^T$ at the fingertip is:
$$ \tau = J^T F $$
In our underactuated design, only one actuator torque $\tau_{in}$ is directly applied. The distribution of this torque to the virtual joint torques depends on the linkage transmission ratios and the state of the elastic elements. A simplified model for the contact force $F_{contact}$ during an enveloping grasp, assuming force closure on an object, can be estimated by considering the mechanical advantage of the linkage at a specific configuration. For a given configuration defined by angles $(\theta_1, \theta_2, \theta_3)$, an effective transmission ratio $\eta$ can be computed geometrically, leading to:
$$ F_{contact} \approx \frac{\eta \cdot \tau_{in}}{r_{object}} $$
where $r_{object}$ is the effective radius of the grasped object. This analysis ensures that the designed end effector can generate sufficient grasping force for secure manipulation of textile items without causing damage, a key requirement for its practical utility.
Control Strategy and Sensory Integration for the End-Effector
The functionality of a sophisticated end effector is fully realized only with an appropriate control strategy and sensory feedback. Our design incorporates a hierarchical control approach:
- Low-Level Joint Control: Each finger’s servo motor is controlled via a PID loop to accurately track the desired joint trajectory or position derived from the inverse kinematics or a predefined grasping sequence.
- Grasping Mode Selection: The control system selects between Fingertip and Enveloping grasp modes based on object recognition input from a vision system (e.g., identifying a spool vs. a flat sock).
- Compliance and Force Limiting: The inherent compliance from the elastic elements in the finger linkage is supplemented by torque sensing at the motor or tactile sensors on the finger pads. This allows for force-controlled grasping, preventing excessive force on delicate items like yarn or finished socks.
- Dual-Arm Coordination for Pallet Module: When using the pallet module, the control system coordinates the motion of both robot arms to ensure synchronized lifting and stable transport of the material box. This involves calculating and enforcing relative pose constraints between the two end effector platforms.
The proposed sensory suite for the end effector includes:
– Tactile/Pressure Sensors: Embedded in the finger pads to detect contact and measure grip force.
– Proximity Sensors: To detect the presence of an object before contact.
– Inertial Measurement Unit (IMU): Potentially integrated on the pallet module to monitor the orientation and stability of the carried load.
| Control Mode | Primary Sensor Input | Actuator Output | Target Application |
|---|---|---|---|
| Position Control | Motor Encoder | Precise joint angle | Pre-grasp positioning. |
| Force/Impedance Control | Tactile Sensor / Current Sensing | Limited motor torque | Grasping delicate textiles. |
| Dual-Arm Coordinated Control | Arm Joint Encoders, IMU | Synchronized arm trajectories | Stable material box transport. |
Simulation and Experimental Validation of End-Effector Performance
To validate the multi-functionality and practical applicability of our end effector design, we conducted a series of simulation experiments using ADAMS dynamic simulation software, targeting the three primary handling tasks.
1. Enveloping Grasp of Yarn Spools
A 3D model of the end effector and a cylindrical yarn spool was imported into ADAMS. Contact forces, joints, and a motion driver for the finger actuator were defined. The simulation captured the sequential contact of the proximal and medial phalanges, culminating in a stable enveloping grasp. The results confirmed that the underactuated mechanism successfully conformed to the spool’s shape without slippage, verifying the end effector’s capability for secure and damage-free handling of raw materials.
2. Fingertip Grasp of Finished Socks
For simulating sock grasping, a rectangular block was used as a simplified model for the bundled product. The simulation demonstrated the finger’s ability to perform a precise pinch grasp, securing the object firmly at the fingertips. This validated the end effector’s proficiency in handling soft, compressible, and variably shaped finished goods.
3. Pallet-Based Material Box Transport
The simulation focused on the dual-arm coordination. Two instances of the end effector (with active pallet modules) were positioned under a model of a standard material box. A coordinated vertical motion was applied to both arms. The simulation confirmed stable lifting and holding of the box, with no significant tilting or relative sliding, demonstrating the robustness of the pallet module design for bulk transport tasks.
The table below summarizes key performance metrics observed or derived from the simulations:
| Task | Key Performance Indicator (KPI) | Simulation Result | Status |
|---|---|---|---|
| Yarn Spool Grasp | Grasp Stability (No Slip) | Maintained throughout motion | Pass |
| Sock Bundle Grasp | Precision (Fingertip Contact) | Object secured at distal phalanges | Pass |
| Box Transport | Load Stability (Max Tilt Angle) | < 1.5 degrees during lift/move | Pass |
| All Tasks | Structural Integrity (Max Stress) | Below yield strength of material | Pass |
Discussion on Application and Calibration
The successful simulation results underscore the end effector’s potential. For real-world deployment in a sock factory, several practical aspects must be addressed:
- Tool Center Point (TCP) Calibration: Precise calibration of the TCP for both the mechanical hand’s pinch point and the pallet’s engagement points is essential for accurate positioning by the robot arms.
- Quick-Change Mechanism: While the design is integrated, a robust and quick-change interface between the end effector’s base and the robot arm flange would facilitate maintenance or future upgrades.
- Cycle Time Optimization: The speed of the grasping sequence and the dual-arm coordinated motion must be optimized to meet production line cycle time requirements without compromising stability.
- Integration with Factory Systems: The end effector’s control system must communicate seamlessly with higher-level Manufacturing Execution Systems (MES) or Warehouse Management Systems (WMS) to receive handling commands and confirm task completion.
The modularity of this end effector design also opens possibilities for further customization. For instance, the finger pad material can be changed to different polymers or silicones to adjust friction coefficients for specific materials. The pallet module’s dimensions can be easily modified to suit different standard container sizes used in the factory.
Conclusion and Future Perspectives
In response to the diverse material handling demands in modern sock factories, we have presented the design and analysis of a novel, linkage-driven, multi-functional end-effector for dual-arm robots. The modular architecture, combining a specialized pallet module with an adaptive underactuated mechanical hand module, enables a single end effector to perform both large-box transport and precise small-item grasping. Comprehensive kinematic modeling using the D-H method provided the foundation for motion planning and control. Workspace analysis confirmed a continuous and practical range of motion. Simulation experiments in ADAMS successfully validated the end effector’s core functionalities, demonstrating its ability to securely handle yarn spools, finished socks, and material boxes.
Compared to traditional single-purpose end effectors, this design offers superior task adaptability, operational flexibility, and structural rationality, presenting significant practical value and a promising application prospect for automating textile and similar light-industry logistics. The integrated approach reduces the need for tool changers and simplifies the robotic cell layout.
Future work will focus on several enhancements to increase the intelligence and robustness of the end effector system. Firstly, integrating more advanced flexible electronic skins and multi-modal sensory data (tactile, force, proximity) will enable finer perception and adaptive grip adjustment. Secondly, implementing machine learning algorithms for grasp planning based on real-time vision input could allow the end effector to handle an even wider, unforeseen variety of objects. Finally, exploring more sophisticated dual-arm coordination algorithms and dynamic load compensation will further improve the speed and stability of the pallet-based transport operations, pushing the boundaries of autonomous handling in smart manufacturing environments.