In modern industrial manufacturing, the demand for high-precision surface finishing, such as polishing and grinding, has grown significantly. Traditional manual polishing is labor-intensive, inefficient, and inconsistent, leading to quality issues. Robotic systems offer a solution, but their performance heavily depends on the end effector, which must provide precise force control and adaptability. Existing end effector designs, including mechanical, pneumatic, electric, and other types, often face challenges like insufficient force stability, complex design, computational load, force tracking lag, and overshoot. To address these limitations, I propose a novel hybrid pneumatic-electric end effector for robotic polishing, integrating a voice coil motor for force control and a pneumatic motor for rotational motion. This design aims to enhance force control accuracy, reduce weight, improve response speed, and incorporate damping features. Through mathematical modeling and fuzzy PID control, combined with Adams and MATLAB/Simulink co-simulation, I validate the end effector’s ability to maintain constant force during polishing operations. This approach not only improves productivity but also reduces costs, offering a valuable reference for industrial applications.
The end effector is a critical component in robotic polishing systems, as it directly interacts with the workpiece. Its design must balance force control precision, responsiveness, lightweight construction, and vibration damping. In this work, I focus on developing a hybrid end effector that leverages the strengths of both pneumatic and electric systems. The pneumatic motor handles rotational motion for polishing, while the voice coil motor manages linear displacement for force adjustment. This separation of functions allows for optimized performance. The end effector’s structure is symmetrically arranged to minimize uneven forces and enhance stability. Key requirements include a force control accuracy within ±1 N, overshoot below 8%, mass around 3 kg, and height approximately 250 mm. Materials like steel (yield strength ≥235 MPa) and aluminum alloy (yield strength ≥80 MPa) are selected for strength and weight reduction. For coarse polishing, forces range from 80 N to 100 N, while fine polishing requires 10 N to 30 N. The end effector’s architecture includes a rotary mechanism, an execution mechanism, and a polishing mechanism, as illustrated in the following visualization.
The end effector’s design incorporates several key components. The rotary mechanism consists of a pneumatic motor, bracket, and coupling, mounted on an L-shaped plate connected laterally to a six-degree-of-freedom industrial robot. This lateral connection reduces the distance between the end effector and the workpiece, improving accessibility. The execution mechanism features a voice coil motor with its stator fixed to the L-shaped plate and its mover attached to a moving platform. A force sensor is positioned between the moving platform and the polishing tool to measure contact force. The polishing mechanism uses a collet chuck to hold various tools, enhancing versatility. To decouple linear and rotational motions, a ball spline is employed, allowing simultaneous translation and rotation. Tension springs are symmetrically arranged to provide support, guidance, and vibration damping without interfering with the voice coil motor’s movement. Angular contact bearings are placed at both ends to reduce tilting moments. This hybrid end effector leverages the lightweight nature of pneumatic motors and the precise control of voice coil motors, addressing common issues in existing designs.
Component selection is crucial for meeting performance targets. For the voice coil motor, parameters such as peak thrust, continuous thrust, total stroke, and speed are considered. Based on force requirements and dynamic response, I selected a model TMEC-2073-010-000. Its key parameters are summarized in Table 1. The transfer function relating output force to voltage is derived to facilitate control design.
| Parameter | Value |
|---|---|
| Peak Thrust (N) | 273 |
| Continuous Thrust (N) | 110 |
| Total Stroke (mm) | 25 |
| Force Constant (N/A) | 41.2 |
| Resistance (Ω) | 5.5 |
| Inductance (mH) | 4.5 |
| Mover Mass (g) | 285 |
| Stator Mass (g) | 1380 |
The transfer function for the voice coil motor, \( G_1(s) \), is given by:
$$ G_1(s) = \frac{41.2}{0.005s + 6} $$
where \( s \) is the complex frequency variable in Laplace transform. This model represents the dynamic relationship between input voltage and output force, essential for control system design.
For the pneumatic motor, the goal is to achieve a rotational speed of approximately 3000 rpm for effective polishing. Based on power and torque calculations, a suitable model is chosen with parameters listed in Table 2. The pneumatic motor offers advantages in weight and speed control, though it may introduce some lag compared to electric motors.
| Parameter | Value |
|---|---|
| Power (W) | 680 |
| Rated Speed (rpm) | 3000 |
| Rated Torque (N·m) | 3.5 |
| Mass (kg) | 2.7 |
The ball spline is selected to enable motion decoupling. Its design ensures sufficient stiffness and torsional strength to prevent deformation during operation. Parameters for the ball spline are provided in Table 3, confirming it meets mechanical requirements.
| Parameter | Value |
|---|---|
| Length (mm) | 180 |
| Allowable Bending Stress (N/mm²) | 98 |
| Allowable Torsional Stress (N/mm²) | 49 |
| Calculated Bending Stress (N/mm²) | 17.734 |
| Calculated Torsional Stress (N/mm²) | 8.413 |
To achieve precise force control, I develop a mathematical model for the end effector system. The dynamics involve force balance between the voice coil motor, springs, and external contact. The overall system equation is:
$$ m\ddot{x} + c\dot{x} + kx = F_c $$
where \( m \) is the mass of the moving parts, \( c \) is the damping coefficient, \( k \) is the stiffness, \( x \) is the displacement, and \( F_c \) is the contact force between the end effector and workpiece. To track a desired force \( F_r \), I introduce a reference position \( x_r \) and define error terms: \( x_e = x_r – x \) and \( F_e = F_r – F_c \). Substituting these into the dynamics yields:
$$ m\ddot{x}_e + c\dot{x}_e + kx_e = F_e $$
Applying Laplace transform, the transfer function from force error to displacement error is:
$$ G(s) = \frac{1}{ms^2 + cs + k} $$
This transfer function forms the basis for control design. The end effector operates through a force/displacement feedback loop. The force sensor measures the contact force, which is compared to the desired force. The error is fed into a controller that adjusts the voice coil motor’s displacement via current control. The current loop accounts for gravity and friction effects. The gravity-induced current \( i_g \) is:
$$ i_g = \frac{mg}{k_e} $$
where \( g \) is gravitational acceleration and \( k_e \) is the force constant. Friction current \( i_f \) is:
$$ i_f = \frac{\mu v + f_c}{k_e} $$
with \( \mu \) as viscous friction coefficient, \( v \) as velocity, and \( f_c \) as a constant. The total current \( i \) is derived from controller outputs:
$$ i = \frac{G_3[F_r – F_c]G_2 + i_g + i_f}{G_3 + 1} $$
where \( G_2 \) and \( G_3 \) are transfer functions for the force and current controllers, respectively. The actual contact force becomes:
$$ F_c = \frac{G_2 G_3 k_e}{(G_3 + 1) + G_2 G_3 k_e} F_r + \frac{G_3 + 1}{(G_3 + 1) + G_2 G_3 k_e} F_d + \frac{G_3 k_e}{(G_3 + 1) + G_2 G_3 k_e} (i_g + i_f) $$
Here, \( F_d \) represents disturbance forces from springs. This equation shows that the contact force depends on the desired force, disturbances, and system biases. To minimize errors, I employ a fuzzy PID controller, which adapts parameters based on force error and its derivative, offering better performance than conventional PID in handling nonlinearities.
The control strategy for the end effector involves indirect force control through displacement regulation. The fuzzy PID controller adjusts proportional, integral, and derivative gains dynamically. The membership functions for error and error change are defined on domains like Negative Big (NB), Negative Small (NS), Zero (Z), Positive Small (PS), and Positive Big (PB). Rule bases are constructed to modulate gains. For example, if error is PB and error change is NS, then proportional gain is increased slightly. This adaptability reduces overshoot and improves response time. The overall control diagram includes the fuzzy PID block generating current commands for the voice coil motor, which in turn adjusts displacement to maintain constant force.
To validate the end effector design and control approach, I conduct co-simulations using Adams for mechanical dynamics and MATLAB/Simulink for control algorithms. The process begins by modeling the end effector in SolidWorks, exporting it as a Parasolid file, and importing into Adams. Constraints such as fixed joints, revolute joints, and translational joints are applied to replicate real-world motion. Key variables, like displacement and force, are defined for data exchange with MATLAB. In Adams, I set up input signals for displacement control and output signals for force measurement. The Adams-Control plugin links these to MATLAB, where the fuzzy PID controller is implemented in Simulink. The simulation runs interactively, allowing real-time adjustment of PID parameters to achieve force tracking within 5% error.
The simulation tests two scenarios: step force response and sinusoidal force excitation. For both, the desired force is set to 20 N. Results compare fuzzy PID against traditional PID control. In the step force test, traditional PID shows an overshoot of 9.034%, while fuzzy PID reduces it to 0.778%, an improvement of 8.256 percentage points. In the sinusoidal test, traditional PID has an overshoot of 19.125%, and fuzzy PID achieves 1.458%, a reduction of 17.667 percentage points. These outcomes demonstrate that the fuzzy PID controller significantly enhances force stability and responsiveness. The end effector’s performance meets design specifications, with force control accuracy exceeding typical benchmarks. Table 4 summarizes the simulation results, highlighting the advantages of the hybrid end effector under fuzzy PID control.
| Test Condition | Traditional PID Overshoot (%) | Fuzzy PID Overshoot (%) | Improvement (Percentage Points) |
|---|---|---|---|
| Step Force | 9.034 | 0.778 | 8.256 |
| Sinusoidal Force | 19.125 | 1.458 | 17.667 |
The effectiveness of the end effector relies on precise component integration and control tuning. To further analyze performance, I derive additional formulas for system bandwidth and sensitivity. The bandwidth \( B_w \) of the end effector can be estimated from the transfer function \( G(s) \):
$$ B_w = \frac{1}{2\pi} \sqrt{\frac{k}{m}} $$
assuming low damping. For the designed end effector, with \( m = 3 \, \text{kg} \) and \( k \) approximated from spring constants, the bandwidth exceeds 10 Hz, ensuring quick response to force variations. Sensitivity to parameter variations is assessed using the formula:
$$ S = \frac{\Delta F_c / F_c}{\Delta p / p} $$
where \( p \) represents parameters like mass or stiffness. The hybrid design shows low sensitivity due to feedback control, enhancing robustness. Another key aspect is the end effector’s energy efficiency. The pneumatic motor’s power consumption \( P_p \) is given by:
$$ P_p = T \omega $$
where \( T \) is torque and \( \omega \) is angular velocity. For the voice coil motor, power \( P_v \) relates to current \( i \) and resistance \( R \):
$$ P_v = i^2 R $$
Overall, the hybrid end effector optimizes energy use by distributing tasks between pneumatic and electric systems.
In practical applications, the end effector must handle various workpiece materials and surface conditions. I extend the modeling to include contact dynamics between the polishing tool and workpiece. The contact force \( F_c \) can be expressed as:
$$ F_c = K_c (x – x_w) + C_c (\dot{x} – \dot{x}_w) $$
where \( K_c \) and \( C_c \) are contact stiffness and damping, and \( x_w \) is workpiece surface position. This accounts for surface irregularities, making the end effector adaptable to uneven surfaces. The control system continuously adjusts based on force sensor feedback, ensuring consistent polishing quality. The end effector’s design also considers thermal effects, as friction during polishing generates heat. The temperature rise \( \Delta T \) can be approximated by:
$$ \Delta T = \frac{F_c \mu_r v t}{m_t C_p} $$
with \( \mu_r \) as friction coefficient, \( v \) as relative velocity, \( t \) as time, \( m_t \) as tool mass, and \( C_p \) as specific heat. Material selection for components like the force sensor and springs accounts for thermal stability.
To summarize, this hybrid pneumatic-electric end effector offers a comprehensive solution for robotic polishing. The design integrates a voice coil motor for precise force control and a pneumatic motor for efficient rotational motion, achieving high performance in a lightweight package. The fuzzy PID controller outperforms traditional methods in reducing overshoot and improving force tracking. Co-simulation validates the end effector’s capabilities, demonstrating its potential for industrial deployment. Future work could explore adaptive control algorithms, integration with machine vision for path planning, and experimental validation on real robots. This end effector represents a significant step forward in automating polishing processes, contributing to smarter and more flexible manufacturing systems.
Throughout this discussion, the term “end effector” has been emphasized to underscore its central role in robotic systems. The proposed end effector not only addresses current limitations but also opens avenues for further innovation. By leveraging hybrid actuation and advanced control, it sets a new standard for precision and efficiency in surface finishing applications.