In the field of modern mechanical engineering, parallel mechanisms have gained significant attention due to their numerous advantages such as high rigidity, strong load capacity, and precise positioning. These features make them superior to traditional serial mechanisms in many applications. Their potential for use in advanced manufacturing systems, especially in hybrid CNC machine tools, has sparked extensive research interest. However, solving the kinematic and dynamic problems of these mechanisms remains a challenging task.
This paper introduces an innovative stiffness analysis method for parallel mechanisms that treats the system structure as a flexible body rather than a rigid one. This approach allows for a more accurate and comprehensive evaluation of the mechanism's stiffness under various postures and external forces. As a case study, we examine the 3-RPS parallel mechanism, which is used as an independent module in hybrid CNC systems. The stiffness of this mechanism depends on the individual stiffness of its components—such as rods and joints—and how they interact.
The 3-RPS mechanism consists of a moving platform, a fixed platform, and three connecting branches. Each branch includes a revolute joint (R), a prismatic joint (P), and a spherical joint (S). This configuration enables motion along the Z-axis and rotation around the X and Y axes. As the length of the branches changes, the posture of the moving platform also changes, affecting the overall stiffness.
To analyze the stiffness of the system, we apply the boundary element method (BEM), which reduces the problem's dimensionality by focusing only on the boundaries of the structure. This method is particularly efficient for rod-like structures, as it simplifies data input and improves computational speed compared to finite element methods.
By breaking down the mechanism into substructures and applying boundary conditions, we can derive the stiffness matrix of the entire system. This process involves combining the equations of each substructure with appropriate constraints, ensuring compatibility between connected parts. When the substructures are articulated, specific degrees of freedom are allowed, and the corresponding moments are treated as boundary conditions.
Through this method, we can determine the deformation and stiffness of the entire system under different loading conditions. For example, when a force of 1000 N is applied in the X and Y directions, the resulting forces and stiffness values for each branch are calculated. These results provide critical insights for optimizing the structural design of the mechanism.
In conclusion, the proposed stiffness analysis method offers a powerful tool for evaluating and improving the performance of 3-RPS parallel mechanisms. By integrating forward and inverse kinematics, the method enables accurate stiffness calculations for the moving platform in any position, making it a valuable asset for dynamic simulations and system optimization.
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