| Summary: | 碩士 === 國立中正大學 === 機械工程學系暨研究所 === 102 === The study is devoted in the effects of the link flexibility and joint clearance on the loading deflection and vibration of a parallel robot. For the loading deflection, links are considered as two-node beam elements and the structure matrix is adopted to establish the stiffness matrix of links. The nodal deflection would be derived based on the stiffness matrix. However, some of the nodal deflections are dependent accordance with the constrain by the joints and the rigid body. Therefore, the effects of the joint clearance are formulated using an explicit mathematical model which is the function of the applied force and clearance amount, and the constrain equations of nodal deflections on the rigid link are formulated based on the geometry. The equivalent stiffness and the loading deflection of the moved platform are derived based on the links stiffness and constrain equations of joints and links. In addition, we can find that the equivalent stiffness of the moved platform is not constant in the workspace of the parallel robot, and it is dependent on the posture of the robot. Finally, we program the loading deflection analysis by MATLAB, and the correction is confirmed by comparing the analysis results with those simulated via ABAQUS.
For the vibration analysis, we derive the potential and dynamic energy based on the analysis model component of beam elements. The Lagrange function is applied to find the mass and stiffness matrix of the parallel robot. However, the nodal vibration are constrained by the structure of the parallel robot. We apply the transform matrix and constrain equations to decouple the independent and dependent terms, and we establish the dynamic equation of the delta robot. Therefore, the nature frequencies and vibration modes are defined by solved the eigenvalues and eigenvectors. We also confirmed the correction by comparing the result with those analysis applying ABAQUS. In addition, the nature frequencies are dependent with the position in the workspace, and the difference is also shown in results. Finally, the analysis program is programmed with Graphical User Interface (GUI) to provide convenience to users.
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