In this paper, the 3-RPS parallel mechanism is introduced as a key component in hybrid CNC machine tools. This mechanism is known for its high rigidity, strong load capacity, and precise positioning, which makes it more suitable than traditional serial mechanisms for complex tasks. However, analyzing the kinematics and dynamics of such a system can be quite challenging due to the complexity involved in solving the motion equations and stiffness characteristics.
Unlike conventional methods that treat the structure as rigid, this study proposes a new stiffness analysis approach that considers the system as a flexible body. This allows for a more accurate assessment of how the mechanism deforms under various loads and postures. The analysis focuses on the 3-RPS mechanism, which 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), giving the mechanism three degrees of freedom: translation along the Z-axis and rotation around the X and Y axes.
To perform the stiffness analysis, the boundary element method is employed. This method reduces the problem's dimension by focusing only on the boundaries of each substructure. By discretizing these boundaries and solving the resulting equations, the stiffness matrix of the entire system can be derived. The process involves combining the boundary conditions of individual components, ensuring compatibility between forces and displacements at the joints.
The synthesis of two substructures is illustrated in the figure, where the boundary equations are combined using coordinate transformation matrices. When substructures are rigidly connected, the forces and displacements at the interface must match. For articulated joints, however, some degrees of freedom remain unconstrained, requiring special treatment in the equations to avoid singularities.
After solving the system equations, the static stiffness of the mechanism is determined. This information is crucial for optimizing the design of the system, ensuring that all components work together efficiently under different loading conditions. The results show that the stiffness distribution depends heavily on the structural parameters of each member, such as length, cross-section, and material properties.
Through this analysis, the paper provides a comprehensive framework for evaluating and improving the performance of parallel mechanisms. It highlights the importance of considering flexibility in the system model and demonstrates how the boundary element method can be used effectively for stiffness calculations. This approach not only enhances the accuracy of the analysis but also supports the development of more efficient and robust hybrid machine tools.
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