单回路空间两平移并联机构拓扑设计与尺度优化

Topology Design, Dimension Optimization and Workspace Analysis of Spatial Single-loop Two-translation Parallel Mechanisms

摘要:

针对狭小空间内工作机器的需求，根据基于方位特征集的并联机构拓扑设计理论和方法，设计了12个移动副驱动的单回路空间两平移并联机构，并对其进行了自由度计算；对其中8个机构进行运动学建模，分别推导出其一元八次方程（封闭解）和符号式反解，并进行数值算例验证；运用差分进化算法以限定尺度约束下的可达工作空间最大为优化目标，分别对其中8个机构进行尺度优化，并求得其对应的可达工作空间，对比分析后优选出2个具有最大可达工作空间的两平移并联机构；为刚度分析、动力学分析及结构设计奠定了基础。

Abstract:

For the needs of the mechanical components not limited by space when machines working in narrow spaces, according to the topology design theory and method of parallel mechanism (PM) based on position and orientation characteristic (POC) equations, a set of 12 spatial single-loop two-translation PMs, each propelled by two actuated prismatic joints, was designed and the degrees of freedom of each PM were calculated. A comprehensive kinematic modeling effort was undertaken, focusing on eight select PM configurations. Through meticulous analysis and computation, the univariate eighth-degree polynomial equations (i.e., closed-form solution) were derived for each configuration. Symbolic inverse solutions were also derived respectively, Additionally, numerical examples were employed to validate the accuracy and efficacy of these solutions. Leveraging the differential evolution algorithm, an exhaustive effort was made to maximize the working space of the eight PM configurations under consideration. Through iterative refinement and optimization, the maximal operational envelopes of these PMs were meticulously determined, offering insights into their potential operational capabilities within varied working environments. Following a comprehensive comparative analysis of the maximal working spaces achieved by each PM configuration, two configurations boasting the largest working spaces were selected, which served as the foundational basis for subsequent endeavors, including the stiffness analysis, dynamic analysis and structural design of these PMs.