球面5R并联机构的动力学建模及动载分配优化

在动载条件下,为实现并联机构驱动器低能耗、平稳地运行,针对一种球面5R并联机构,对其进行动载分配优化。首先利用矢量法得到了机构的运动学正反解,考虑重力、外力和各构件惯性力的作用,采用拉格朗日方法和虚功原理建立了球面5R并联机构的动力学模型,并对机构的数值算例进行了动力学仿真验证,结果表明:理论值与仿真值的最大误差为1.3%,验证了动力学模型的正确性。然后,基于动力学模型,考虑驱动器输出功率和力矩因素,定义了机构的多目标优化函数,采用B样条插值法规划轨迹,并用归一化加权求和法优化求解该机构的最优轨迹。最后,通过数值算例,验证了优化方法的可行性,且优化结果表明:功率峰值降幅为分别为11.77%、48.75%,力矩峰值降幅分别为0%、51.17%,速度峰值降幅分别为20.97%、8.1%。说明该优化方法可以有效降低驱动器输出峰值,使得并联机构驱动器运行平稳,且该优化方法也适用于其他并联机构。

Dynamic modeling and dynamic load distribution optimization of a spherical 5R parallel mechanism

In order to realize low energy consumption and smooth operation of the parallel mechanism driver, the dynamic load distribution of a spherical 5R parallel mechanism was optimized. First, the positive and negative solutions of the kinematic equation were deduced by the vector method. Then, considering gravity, the external force, and the inertial force of each component, the dynamic model of the spherical 5R parallel mechanism was established using the Lagrange method and the virtual work principle. A dynamic numerical simulation of the mechanism of this process was carried out. The results indicate that the maximum error of the theoretical value and simulation value is 1.3%, which verifies the correctness of the dynamic model. Subsequently, the multi-objective optimization function of the mechanism was established considering additional objectives, based on the dynamic model. In this regard, the power, torque, and the B spline interpolation method were used to plan the trajectory of the moving platform. The optimal trajectory of the actuator was determined using the normalized weighted-sum approach. Finally, the feasibility of the optimization method was verified using a numerical example. The results indicate that the peak amplitude of the power is 11.77% and 48.75%, the peak moment is 0% and 51.17%, and the peak velocity is 20.97% and 8.1%. Based on these results, the peak output value of the actuator can be effectively reduced using the optimization method, so that the output of the parallel mechanism driver is more stable. This optimization method of dynamic load distribution is also practical for use in other parallel mechanisms.