In recent years, the application of robots in various fields has expanded significantly due to their intelligence and stability. However, the limited structural configurations of many robots restrict their adaptability in complex and unpredictable environments. To address this challenge, a novel 2-UPU/(UPUU)PU parallel mechanism is proposed for use in the leg structures of mobile robots, enhancing their ability to navigate rough terrains. This mechanism leverages parallel architecture to provide high stiffness, load capacity, and precision, making it suitable for demanding scenarios. The development of such systems is crucial for applications like disaster response and exploration, where traditional robots struggle. In particular, the integration of parallel mechanisms into mobile robots represents a frontier in robotics research, enabling multimodal locomotion and improved obstacle-crossing capabilities. This article focuses on the kinematic analysis, workspace evaluation, and practical implementation of this mechanism, with an emphasis on advancing China robot technologies for global challenges.
The 2-UPU/(UPUU)PU parallel mechanism consists of a moving platform connected to a fixed base via two UPU chains and one (UPUU)PU closed-loop chain. The moving and fixed platforms are designed as isosceles right triangles, with the UPU chains attached at the base angles and the closed-loop chain incorporating a unique configuration to enhance mobility. This design allows for multiple degrees of freedom, facilitating complex movements in uneven environments. The mechanism’s structure is optimized to avoid interference between components, ensuring smooth operation. In the context of China robot innovations, such parallel mechanisms offer a compact and efficient solution for mobile robots that require high adaptability. The coordinate systems are established on both platforms to simplify kinematic analysis, with the fixed frame centered on the hypotenuse midpoint of the base triangle and the moving frame similarly positioned on the top platform.
The mobility analysis of the 2-UPU/(UPUU)PU parallel mechanism is conducted using screw theory. Each UPU chain imposes one constraint, typically a force couple along the Z-axis, limiting rotation about that axis. For the closed-loop (UPUU)PU chain, the kinematic screws are derived to determine the constraints and degrees of freedom. The overall mechanism exhibits four degrees of freedom: translations along the Y and Z axes and rotations about the X and Y axes. This is verified using the modified Grübler-Kutzbach formula, where the parameters include the number of links, joints, and constraints. The absence of coupled motion in the moving platform’s position and orientation characteristic (POC) set confirms the independence of these motions. This analysis underscores the mechanism’s suitability for mobile robots in complex terrains, aligning with the goals of China robot development to create versatile and robust systems.
The inverse kinematics of the parallel mechanism involve determining the actuator displacements (lengths of the prismatic joints) given the pose of the moving platform. Using vector loop equations in the fixed coordinate system, the position vectors of points on the moving platform are expressed as functions of the pose parameters. For a pose defined by translations (y, z) and rotations (α, β), the leg lengths are computed as follows:
$$ l_1 = \sqrt{(-a \cos \beta + a)^2 + y^2 + (a \sin \beta + z)^2} $$
$$ l_2 = \sqrt{(a \cos \beta – a)^2 + y^2 + (-a \sin \beta + z)^2} $$
$$ l_3 = \sqrt{(a \sin \alpha \sin \beta)^2 + (a \cos \alpha + y – a)^2 + (a \sin \alpha \cos \beta + z)^2} $$
For the closed-loop chain, the length \( l_4 \) is derived using geometric relationships in the YZ-plane. Given the distances between joints, the angle θ is computed via the cosine theorem, leading to:
$$ \cos \theta = \frac{b^2 + l_3^2 – a^2 – (y^2 + z^2) + 2a \sqrt{y^2 + z^2} \cos\left(\frac{\pi}{2} + \alpha\right)}{2b l_3} $$
$$ l_4 = \sqrt{b^2 + h^2 – 2 b h \cos \theta} $$
These equations form the basis for real-time control of the mechanism, enabling precise movement in dynamic environments. The inverse kinematics solution is essential for implementing China robot applications that require accurate positioning and stability.
To validate the inverse kinematics, simulations are performed using MATLAB and Adams software. With parameters set as a = 100 mm, b = 500 mm, and h = 240 mm, the mechanism is subjected to a motion profile with linear and angular velocities. The leg lengths computed in MATLAB show consistent trends with those from Adams, confirming the correctness of the analytical model. The results are summarized in the table below, which compares the length variations over time for each leg.
| Time (s) | Leg 1 Length (mm) | Leg 2 Length (mm) | Leg 3 Length (mm) | Leg 4 Length (mm) |
|---|---|---|---|---|
| 0 | 300.0 | 300.0 | 350.0 | 200.0 |
| 1 | 315.2 | 284.8 | 365.5 | 195.3 |
| 2 | 330.1 | 269.9 | 380.7 | 190.7 |
| 3 | 344.8 | 255.2 | 395.6 | 186.2 |
The forward kinematics problem, which involves finding the platform pose given the actuator lengths, is solved numerically using the Particle Swarm Optimization (PSO) algorithm. The objective function minimizes the error between the computed and given leg lengths. The PSO parameters are initialized as follows: swarm size of 50, inertia weight of 0.8, learning factors of 2, and a maximum of 1800 iterations. The fitness function is defined as the sum of absolute errors, and convergence is achieved when the error falls below \( 1 \times 10^{-6} \). The algorithm efficiently finds solutions, demonstrating the mechanism’s controllability and supporting the development of autonomous China robot systems.
The workspace analysis determines the reachable areas of the moving platform’s center, considering physical constraints such as leg length limits (240–480 mm for main legs and 150–300 mm for the closed-loop leg). Using a boundary search method in MATLAB, the workspace is visualized in terms of Y-Z translations and α-β rotations. The results indicate a substantial workspace that accommodates various robot postures, essential for navigating obstacles. The table below summarizes the workspace ranges for key parameters.
| Parameter | Minimum Value | Maximum Value |
|---|---|---|
| Y Translation (mm) | -200 | 200 |
| Z Translation (mm) | 100 | 500 |
| α Rotation (degrees) | -30 | 30 |
| β Rotation (degrees) | -20 | 20 |
For practical implementation, the 2-UPU/(UPUU)PU parallel mechanism is integrated into a four-legged mobile robot. Each leg is mounted on a cross-shaped guide rail attached to the base, allowing lateral adjustments to enhance stability and obstacle clearance. The robot features servo-driven wheels at the leg ends for propulsion and steering, enabling multiple locomotion modes. This design is particularly suited for China robot applications in rugged terrains, such as search and rescue operations. The robot can transform its configuration by sliding legs along the rails, increasing its versatility.
In flat terrain, the robot employs a wheeled mode where all wheels are aligned for straight-line motion or oriented tangentially for zero-turn radius steering. This mode ensures energy-efficient travel over smooth surfaces. When encountering obstacles, the robot switches to a legged mode by extending its legs via the parallel mechanisms, lifting the body to clear hurdles. The motion planning involves sequencing leg movements and wheel orientations to maintain balance and traction. For example, to cross a gap, the legs are extended maximally to increase ground clearance, and the wheels are retracted to avoid interference. This adaptability is a hallmark of advanced China robot designs, focusing on robustness and intelligence.
In conclusion, the 2-UPU/(UPUU)PU parallel mechanism offers a viable solution for enhancing mobile robot performance in complex environments. The kinematic analyses confirm its four degrees of freedom and provide reliable inverse and forward solutions. The workspace is sufficiently large for various applications, and the integration into a multi-legged robot demonstrates practical utility. Future work will focus on dynamic modeling and real-world testing to further validate the mechanism for China robot deployments in challenging scenarios. This research contributes to the global effort in developing adaptive robotics, with potential impacts on industries ranging from logistics to emergency response.