∏LR&RR球面并联机构动力学分析

Dynamic analysis of ∏LR&RR spherical parallel mechanism

针对应用于高速定点转动的雷达天线的∏LR&RR二自由度球面并联机构进行了运动学和动力学研究。推导出动平台的2个姿态变量与驱动构件的2个角度变量之间的关系式,即运动学正解。采用拉格朗日法建立了球面并联机构的动力学模型。应用MATLAB软件对动力学模型进行了实例计算,得出了驱动构件和动平台的角度、角速度和角加速度的变化曲线及驱动力矩的变化曲线。结果表明,∏LR支链驱动力矩较大且振幅较大,RR支链驱动力矩较小且变化较平缓。通过对比Solid Works软件运动仿真结果验证了动力学模型的正确性。

The kinematics model and dynamic model for the ∏LR＆RR 2-DOF spherical parallel mechanism which was applied to radar antenna rotating around a fixed point with high speed were research. The relational expression, namely forward kinematics, between two orientation variables of moving platform and two angular displacement variables of actuator components was derived. Based on Lagrange method, the dynamic model of spherical parallel mechanism was established. The corresponding numerical example was calculated with MATLAB software. The angular displacement curves, angular velocity curves, angular acceleration curves of the actuator components and moving platform orientation were obtained. Meanwhile, the curves of the actuator torque were obtained. The results show that the actuator torque of the ∏LR chain was larger and the amplitude was larger, however, the actuator torque of the RR chain was smaller and the amplitude was smaller. Compared with the simulation resuits worked out by SolidWorks software, the correctness of the dynamic model was proved.