实现期望轨迹的平面铰链四杆机构优化综合

Optimal Synthesis of Planar Hinge Four Bar Mechanism with Desired Trajectory

通过对标准位置基础铰链四杆机构和一般位置带展杆铰链四杆机构的连杆转角傅里叶级数展开式的深入研究,发现归一化后的连杆曲线谐波特征参数与连杆展杆的长度l_0和展角α无关,只与基础杆长l_1、l_2、l_3、l_4有关。故以期望轨迹与连杆上E点轨迹的谐波特征参数中幅值相差最小为优化目标,只需优化设计出l_1、l_2、l_3、l_4这4个参数,进而计算求得其他6个参数。所有的计算过程都由Matlab程序自动完成。该方法能快速准确地完成实现任意期望轨迹的四杆机构尺度设计,且不受离散点个数和初值设定的限制,与传统的优化设计直接法和电子图谱间接法相比,降低了优化的维数,提高了运算效率,且轨迹的重合度极高,为平面连杆机构的轨迹综合提供了比较理想的设计方法。

This paper studies the Fourier series expansion of the connecting rod angle of standard position base hing four bar mechanism and general position extension hing four bar linkage mechanism. It is found that the harmonic characteristic parameters normalized of connecting rod curve have nothing to do with the length l0 and the angle α of extension of the connecting rod,but relate to the length of foundation rod,l1、l2、l3 and l4. Therefore,optimization target is the minimum amplitude difference between the desired trajectory and the E point trajectory of the connecting rod. It is only necessary to optimal design the four parameters of l1、l2、l3 and l4,and the other 6 parameters are calculated further. All calculations are performed automatically by the Matlab program. This method can rapidly and accurately realize the four bar scale design of any desired trajectory,and it is not limited by the number of discrete points and initial values,which reduces the dimension of optimization and improves the efficiency of calculation compared with the traditional optimization design of the direct method and the electron atlas indirect method. And the coincidence degree of track is extremely high. It provides an ideal design method for the trajectory synthesis of planar linkage mechanism.