During actual motion, there are inevitably clearances between the motion pairs of the mechanism, and the clearances will have a large impact on stability of the mechanism. Previous studies mainly focused on the dynamic response of simple mechanisms with single clearance and less on chaos. Even if chaos is studied, it mainly focused on the chaos of mechanisms and less on the chaos of clearance joints; however, it is well known that the analysis of chaotic characteristics of clearance is the key to fault diagnosis of kinematic pairs. In order to give a computational methodology for dynamic analysis of planar multi-link mechanism considering multi-clearances and master the dynamic response of planar multi-link mechanism, the dynamic response and chaos of a planar six-bar mechanism are researched. A multiple clearances dynamic model of planar six-bar mechanism is built by Lagrange multiplier method, and the dynamic model is solved by Runge–Kutta method. The influence of different clearance positions, clearance numbers and clearance sizes on dynamic response of mechanism is analyzed. The nonlinear characteristic analysis of six-bar mechanism is conducted, and chaotic phenomena of the clearance joint are explained by Poincaré maps and phase diagrams. The bifurcation diagram at clearance of the revolute joint changes with different clearance values, friction coefficients and driving speeds is given. Those above results provide an important theoretical basis for the study of influence of multi-clearance on dynamic responses and chaotic phenomena of planar multi-link mechanism.

中文翻译：

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考虑旋转间隙的平面多连杆机构的动态响应和混沌

在实际运动过程中，机构的运动副之间不可避免地存在间隙，该间隙将对机构的稳定性产生很大的影响。以前的研究主要集中在具有单一间隙的简单机构的动态响应上，而对混沌的响应则较少。即使研究了混沌，也主要集中在机构的混沌上，而较少关注间隙关节的混沌。然而，众所周知，间隙的混沌特性分析是运动学对故障诊断的关键。为了给出一种考虑多间隙的平面多连杆机构动力学分析的计算方法，并掌握平面多连杆机构的动力响应，研究了平面六连杆机构的动力响应和混沌现象。用拉格朗日乘数法建立了平面六连杆机构的多间隙动力学模型，并用龙格-库塔方法求解了动力学模型。分析了不同间隙位置，间隙数量和间隙尺寸对机构动态响应的影响。进行了六连杆机构的非线性特性分析，并通过庞加莱图和相图解释了间隙接头的混沌现象。给出了旋转关节间隙处的分叉图，其随间隙值，摩擦系数和驱动速度的变化而变化。以上结果为研究多间隙对平面多连杆机构动力响应和混沌现象的影响提供了重要的理论基础。通过Runge-Kutta方法求解动力学模型。分析了不同间隙位置，间隙数量和间隙尺寸对机构动态响应的影响。进行了六连杆机构的非线性特性分析，并通过庞加莱图和相图解释了间隙接头的混沌现象。给出了旋转关节间隙处的分叉图，其随间隙值，摩擦系数和驱动速度的变化而变化。上述结果为研究多间隙对平面多连杆机构动力响应和混沌现象的影响提供了重要的理论基础。通过Runge-Kutta方法求解动力学模型。分析了不同间隙位置，间隙数量和间隙尺寸对机构动态响应的影响。进行了六连杆机构的非线性特性分析，并通过庞加莱图和相图解释了间隙接头的混沌现象。给出了旋转关节间隙处的分叉图，其随间隙值，摩擦系数和驱动速度的变化而变化。以上结果为研究多间隙对平面多连杆机构动力响应和混沌现象的影响提供了重要的理论基础。进行了六连杆机构的非线性特性分析，并通过庞加莱图和相图解释了间隙接头的混沌现象。给出了旋转关节间隙处的分叉图，其随间隙值，摩擦系数和驱动速度的变化而变化。上述结果为研究多间隙对平面多连杆机构动力响应和混沌现象的影响提供了重要的理论基础。进行了六连杆机构的非线性特性分析，并通过庞加莱图和相图解释了间隙接头的混沌现象。给出了旋转关节间隙处的分叉图，其随间隙值，摩擦系数和驱动速度的变化而变化。上述结果为研究多间隙对平面多连杆机构动力响应和混沌现象的影响提供了重要的理论基础。