Abstract

Strength and durability investigations of parallel-mechanism (PM) and robotic systems, used as integral part in modern manufacturing, are necessary at the virtual design stage. Nonetheless, because of the limitations of existing finite element (FE) approaches, flexible-link geometries are often simplified or distorted when converting solid models to FE analysis meshes. This article introduces and demonstrates the use of a new unified geometry/analysis approach for the small-deformation analysis of robotic and parallel mechanism (RPM) systems with flexible links. The approach used in this investigation integrates the geometrically accurate absolute nodal coordinates formulation (ANCF) with the computationally efficient floating frame of reference (FFR) formulation that allows for systematic elimination of high-frequency and insignificant deformation modes. The proposed ANCF/FFR approach allows modeling accurately the stress-free reference configuration geometry, captures the dynamic coupling between the rigid-body and elastic displacements, is based on a unified geometry/analysis mesh that eliminates the need for geometry/analysis model conversion or coordinate transformation, and allows for efficient and accurate solution of the nonlinear dynamic equations that govern the RPM motion. The formulation of the spatial ANCF/FFR equations of motion including the elastic (stress) forces using a general continuum-mechanics approach is presented, and use of the strain split method (SSM) as an FE locking-alleviation technique is discussed. A frequency-convergence analysis of flexible links with tapered geometry is performed and the obtained numerical results are compared with solutions obtained using commercial FE software. The application of the new procedure in the nonlinear dynamics simulations of RPM systems is demonstrated using a spatial parallel mechanism that includes flexible links and prismatic, revolute, and spherical joints.

摘要

并联机构(PM) 和机器人系统的强度和耐久性研究在现代制造中用作不可或缺的一部分，在虚拟设计阶段是必要的。尽管如此，由于现有有限元(FE) 方法的局限性，在将实体模型转换为 FE 分析网格时，柔性连接几何结构通常会被简化或扭曲。本文介绍并演示了使用新的统一几何/分析方法对具有柔性连杆的机器人和并联机构(RPM) 系统进行小变形分析。本研究中使用的方法将几何精确的绝对节点坐标公式(ANCF) 与计算效率高的浮动参考系(FFR) 公式，可以系统地消除高频和微不足道的变形模式。建议的 ANCF/FFR 方法允许对无应力参考配置几何进行准确建模，捕获刚体和弹性位移之间的动态耦合，基于统一的几何/分析网格，无需几何/分析模型转换或坐标变换，并允许有效和准确地解决控制 RPM 运动的非线性动力学方程。提出了使用一般连续介质力学方法的包括弹性（应力）力的空间 ANCF/FFR 运动方程的公式，并使用应变分裂方法(SSM) 作为 FE 锁定缓解技术进行了讨论。对具有锥形几何形状的柔性连杆进行频率收敛分析，并将获得的数值结果与使用商业有限元软件获得的解决方案进行比较。新程序在 RPM 系统非线性动力学模拟中的应用通过使用包括柔性连杆和棱柱、旋转和球形关节的空间并行机制进行了演示。