含间隙平面连杆机构运动精度的稳健优化设计

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考虑杆长制造误差和运动副间隙的影响,提出一种平面连杆机构的稳健设计方法。对运动副间隙引起的回转副偏心距及其对平面机构位姿的影响进行分析,用位置矢量方程描述考虑运动副间隙后平面机构的位姿。根据构件两端回转副要素的实际结构,把构件分成两孔型、孔销型、两销型三种类型。把回转副偏心距的大小及其方向视为两个随机变量,建立三种相应的有效杆长计算模型。采用复数矢量法,推导出三种有效杆长计算公式。对所建立的有效杆长计算模型的计算精度进行数值仿真,结果表明其计算精度可满足工程设计要求。基于所建立的有效杆长计算模型,给出再现函数的曲柄滑块机构的稳健优化设计实例,验证了文中方法的有效性和实用性。 A robust design method of planar linkage mechanism is proposed when the length errors of links and the kinematic pair clearances are taken into account.The offset between the socket center and the pin center caused by the clearance in a pin joint is calculated and its effect on the positional posture of a planar linkage mechanism is analyzed.The position vector equation is used to represent the positional posture of a planar linkage mechanism with kinematic pair clearances.According to the pair elements of pin joints at the both ends of links,the links of a mechanism are classified into three types： the link with two sockets,the link with two pins,the link with one socket and one pin.The value and the direction of the offset in a pin joint are viewed as two random variables.Three effective length models corresponding to three link types are proposed and three calculation formulas of effective lengths are derived by using the complex number vector method.The calculation accuracy of the proposed effective length models is validated by simulations and it is showed that the calculation accuracy of the derived formulas is satisfactory to engineering design.Based on the proposed models,an example is given to achieve the robust design optimization of a slider-crank mechanism generating a given function.The example shows that the proposed method is practical and effective.