A rigid-flexible hybrid drive active parallel mechanism for wave compensation was proposed in order to reduce the damage caused by wind and waves in the transport of container goods at sea. The mathematical model of positional inverse solution was established based on the matrix rotation principle and the geometric closure method of the dynamic platform of rigid-flexible hybrid parallel mechanism. The mathematical model of the positional forward solution was constructed by using spatial geometry. The second order effect matrix of acceleration and velocity Jacobian was established by using the derivation rule to obtain the positional inverse solution. The system stiffness matrix was derived on the basis that the rope is a flexible variable body, and the factors affecting the system stiffness and the principle of increasing the system stiffness were explored. In addition, the kinematics and system stiffness values were verified by numerical simulation, and the input and output data errors of the inverse and positive solutions were not more than 2.25% of the actual errors. Results showed that the theoretical simulation curve and the prototype simulation curve coincided, and the error was not more than 7.4%, which verified the correctness of the kinematics model. The influence of stiffness factors on the stiffness of system was found according to the stiffness matrix. Finally, the parallel mechanism of the rope-driven rigid-flexible hybrid wave compensation was experimentally verified, and the compensation effect of the mechanism was more than 90%. Results provide theoretical support for the motion and the mechanism design of rigid-flexible hybrid active parallel mechanism for wave compensation.
Yuan CHEN,Deng-hui GUO,Li-xia TIAN. Design and modeling of wire-driven rigid-flexible parallel mechanism for wave compensation. Journal of ZheJiang University (Engineering Science), 2021, 55(5): 810-822.
Tab.1Comparison between calculated with given rope lengths
Fig.5Rope variation vector and unit vector under small displacement
参数
数值
固定平台的直径×厚度/mm
100×20
动平台的直径×厚度/mm
50×10
支链长度×导程/mm
70×600
支链刚度系数/(N·m?1)
200
绳索截面面积/mm2
0.83
绳索弹性模量/GPa
70.5
Tab.2Parameters of rigid-flexible hybrid parallel mechanism
Fig.6Change in length of rope
Fig.7Change in rope velocity when angle α and angle β change with time according to predetermined trajectory
Fig.8Change in rope acceleration when angle α and angle β change with time according to predetermined trajectory
Fig.9Change in system stiffness when dynamic platform rotates around X axis
Fig.10Changes in system stiffness when height changes in Z direction
Fig.11Effect of rope preload on overall stiffness of system
Fig.12Experimental prototype of wire-driven rigid-flexible parallel mechanism for wave compensation
Fig.13PID control block of control system
Fig.14Compensation motion of end effector position and attitude
Fig.15Motion curve of end effector of supply ship and compensation mechanism
Fig.16Change curve of rope tension during swing in X direction
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