类Exechon并联机构模块可重构概念设计与运动学分析

Conceptual Reconfigurable Design and Kinematic Analysis of the Exechon-Like Parallel Kinematic Machine

可重构与模块化设计是实现并联机构多功能、提升装备加工柔性的关键技术.受商用Exechon并联机构模块优异性能的设计启发,在其变异机构Exe-Variant的基础上,应用机构变异思想提出两种类Exechon并联机构模块——Exe-Ⅰ和Exe-Ⅱ.基于可锁定关节、模块化支链以及可重构并联机构的设计思路,依次开展Exechon、Exe-Variant、Exe-Ⅰ和Exe-Ⅱ等4种类Exechon并联机构的模块化、可重构概念设计.针对以上并联机构模块进行运动学分析:运用螺旋理论分析类Exechon并联机构的系统螺旋系,构建类Exechon并联机构的系统全雅克比矩阵,依次分析机构自由度和奇异性;通过矢量闭环方程推导其逆运动学模型和动平台连带运动;以"分层切片"的工作空间搜索方法预估其工作空间.运动学对比分析表明:对类Exechon并联机构模块开展的可重构设计,保留了并联机构的自由度类型和结构奇异性特征,并显著改善了部分类Exechon并联机构的逆运动学连带运动的复杂程度以及动平台可达工作空间的分布.最后,借助3D打印技术制作了Exe-Ⅰ并联机构模块的原理样机,运动学精度实验结果与理论分析结果吻合较好,数据的绝对误差在±0.4 mm以内,并且其相对误差不大于实验值的3.2%,验证了运动学分析的正确性.本文提出的可重构与模块化概念设计,可为类Exechon并联机构模块的高效可重构设计及其工程应用提供关键技术支撑.

Reconfigurable and modular designs can be a key technology to realize the versatility as well as improve the flexibility of parallel kinematic machines(PKMs). Inspired by the design of the high-performance Exechon PKM, two novel Exechon-like PKMs-Exe-Ⅰ and Exe-Ⅱ are proposed on the basis of the Exe-Variant PKM. Four types of reconfigurable Exechon-like PKM modules-Exechon, Exe-Variant, Exe-Ⅰ, and Exe-Ⅱ were conceptually designed by following the design flows of lockable joints, modular limbs, and reconfigurable PKMs. With regard to the kinematic analysis of Exechon-like PKMs, the degrees of freedom(DoF)and singularities were analyzed with the screw theory, wherein the screw systems of the Exechon-like PKMs were formulated and overfull Jacobian matrices of the PKMs were derived. Loop-closure equations were formulated to develop the inverse kinematic model and parasitic motions of the moving platform. The reachable workspaces of the proposed PKMs were predicted by a "sliced partition" algorithm. A comparative analysis of the kinematics shows that the reconfigurable design of the Exechon-like PKMs can keep the DoF of the PKMs and their architectural singularities unchanged. The analysis also shows that the reconfigurable design can significantly improve the complexity of the parasitic motions of inverse kinematics and the distributions of the moving platform's reachable workspaces for several Exechon-like PKMs. Finally, using the 3D printing technology, a laboratory prototype of Exe-Ⅰ PKM was built to conduct the kinematic experiment. The experimental values agree well with the theoretical values. The absolute error is less than ±0.4 mm and the relative error is within 3.2%, which verifies the effectiveness of the proposed kinematic analysis module. The conceptual designs of reconfigurable and modular PKMs in this study can prove to be key techniques to realize efficient recon-figurable designs and engineering applications of Exechon-like PKMs.