This paper establishes a kinematics model for a six degree-of-freedom (DOF) manipulator, and verifies its correctness through simulation and experiment. First, the model was set up through the D-H method. Then, the homogenous matrix transform was introduced to perform forward kinematics analysis and calculate the attitude of the end effector. Then, the manipulator position and trajectory were simulated on Robotics Toolbox for MATLAB and RoboDK. Finally, the simulated trajectory was verified through an experiment on stacking operation in the lab environment. The results show that the established kinematics model of the manipulator is correct, laying a solid theoretical basis for offline programming and calibration of manipulators.
Paper board with bending stiffness is usually used as the substrates on cigarette package printing industry. The vibration of these paper boards in high speed affects the printing precision. The dynamic characteristics and stability of moving paper board with finite interior elastic point supports and elastic edges restrained are investigated. First, the energy function of the system is established by using the extended Hamilton's principle; second, the dimensionless equations of motion for the moving paper board are obtained using the element-free Galerkin method. The equations of motion and the eigenvalue equations of the system are established. The relationship between the first three complex frequencies of the system and the moving speed is then obtained by the numerical calculation. The effects of the elastic point supports, the elastically restrained edges, and the dimensionless speed of the motion on the dynamic stability of the paper board are analyzed. The critical speed when the paper board is in a stable state under different conditions is obtained. The results improve the dynamic stability of the paper board in printing process and provide the theoretical basis for the optimization of printing equipment.
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