Previously, the contact states between the bearing and journal of a spatial revolute joint (SRJ) with both axial and radial clearances were solved in the global coordinate system (GCS), which is complex and requires iterations. In this paper, a local-coordinate representation for the SRJs with clearance is combined with a vector-form particle-element method, i.e. finite particle method (FPM), to provide a more practical means for evaluation of the dynamic effects due to clearance. Firstly, the fundamentals of the FPM for analysis of spatial mechanisms are briefed. Then, a local-coordinate representation based on the revolution axis of the bearing is proposed. Specifically, the geometry of the journal and bearing is explicitly expressed using the coordinate transformation. The axial and radial contact states are evaluated by substituting the parametric equations and transforming them to quadratic and quartic equations, respectively, which can be analytically solved without iterations. The contact forces are evaluated in the local-coordinate representation and then transformed into the GCS representation. Two numerical examples, i.e. a spatial slider-crank mechanism and a spatial double pendulum, are provided to demonstrate the feasibility of the proposed method, by which the effects of joint-joint interaction and joint-flexible component interaction are fully discussed.

中文翻译：

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基于矢量粒子元法的空间旋转间隙节的局部坐标表示

以前，具有轴向和径向间隙的空间旋转接头 (SRJ) 的轴承和轴颈之间的接触状态是在全局坐标系 (GCS) 中解决的，这很复杂并且需要迭代。本文将具有间隙的SRJs的局部坐标表示与矢量形式的粒子元方法，即有限粒子法（FPM）相结合，为评估间隙引起的动力效应提供了一种更实用的方法。首先，简要介绍了用于分析空间机制的 FPM 的基本原理。然后，提出了一种基于轴承旋转轴的局部坐标表示。具体来说，轴颈和轴承的几何形状使用坐标变换明确表示。通过代入参数方程并将它们分别转换为二次和四次方程来评估轴向和径向接触状态，无需迭代即可解析求解。接触力在局部坐标表示中进行评估，然后转换为 GCS 表示。两个数值例子，即一个空间滑块-曲柄机构和一个空间双摆，证明了该方法的可行性，通过它充分讨论了关节-关节相互作用和关节-柔性部件相互作用的影响。接触力在局部坐标表示中进行评估，然后转换为 GCS 表示。两个数值例子，即一个空间滑块-曲柄机构和一个空间双摆，证明了该方法的可行性，通过它充分讨论了关节-关节相互作用和关节-柔性部件相互作用的影响。接触力在局部坐标表示中进行评估，然后转换为 GCS 表示。两个数值例子，即一个空间滑块-曲柄机构和一个空间双摆，证明了该方法的可行性，通过它充分讨论了关节-关节相互作用和关节-柔性部件相互作用的影响。