基于几何代数的冗余驱动过约束并联机构解析静刚度分析与设计方法研究

Redundantly actuated over-constrained parallel mechanisms have promising potential in applications that require huge load capacity, high rigidity and accuracy. Elastic deformations of links, joints and actuators as well as internal force resulted by redundant actuation must be carefully considered in the kinematic design stage. However, performance evaluation and dimension synthesis are usually finished in the level of rigid mechanics or elastic mechanics separately. There has been a lack of frame-independent analytical elasto-static stiffness index with clear physical meaning and rigid-flexible coupled dimension synthesis method. Particularly, few has studied the influence of internal forces on the overall kinematic performance of the mechanism. Hence, it is important to establish the mapping rules between internal force and elasto-static stiffness and provide scientific and reasonable performance index and design method. . In the framework of geometric algebra, this project studies analytical static analysis method of redundantly actuated over-constrained parallel mechanisms as well as mapping rules between internal forces and static stiffness. An analytical static stiffness performance index will be established and corresponding optimization method will be proposed. A prototype will be built for verifying. The achievement of this project will provide a new theoretical foundation and method for performance evaluation and dimensional synthesis, which is helpful for independent innovation of manufacturing equipment based on parallel or hybrid mechanisms.

冗余驱动过约束并联机构在大负载、高刚度和高精度任务中应用前景广阔。在运动学设计时必须同时考虑几何尺寸、杆件/关节/驱动器的弹性变形及冗余驱动产生的内力对机构性能的影响。但目前往往只是单纯从刚体力学层面或弹性静力学层面进行性能评估和尺度综合，缺乏具有物理意义清楚、与坐标系/尺度无关的解析静刚度指标和刚柔耦合尺度综合方法，特别是系统内力对机构整体运动学性能的影响少有人关注。因此，如何建立冗余驱动过约束并联机构内力与静刚度之间的映射规律，提出科学合理的性能评价指标和优化设计方法，是当前机构学亟需回答的重要问题。本项申请在几何代数框架下，重点研究冗余驱动过约束并联机构解析静力分析方法、内力与静刚度映射规律、建立解析静刚度指标，给出对应的刚柔耦合尺度优化方法，并以实验样机验证。研究成果将为冗余驱动过约束并联机构性能评价和尺度综合提供新的理论依据和方法支持，推动我国并/混联构型加工装备的自主创新。

冗余驱动过约束并联机构在大负载、高刚度和高精度任务中应用前景广阔。在运动学设计时必须同时考虑几何尺寸、杆件/关节/驱动器的弹性变形及冗余驱动产生的内力对机构性能的影响。但目前往往只是单纯从刚体力学层面或弹性静力学层面进行性能评估和尺度综合，缺乏具有物理意义清楚、与坐标系/尺度无关的解析静刚度指标和刚柔耦合尺度综合方法，特别是系统内力对机构整体运动学性能的影响少有人关注。因此，如何建立冗余驱动过约束并联机构内力与静刚度之间的映射规律，提出科学合理的性能评价指标和优化设计方法，是当前机构学亟需回答的重要问题。本项申请提出了基于应变能和几何代数的考虑杆件和关节柔度的静弹性刚度模型，建立了修订的矩阵位移法梁单元刚度矩阵，并在此基础上得到了铰链刚度矩阵在自身铰空间的解析表达式，提出了考虑刚度矩阵非对角线元素耦合作用的综合刚度性能指标，解耦了线刚度和角刚度，具有明确的物理量纲和物理意义，提出了刚柔耦合尺度优化设计方法，并通过实验样机进行了验证。研究成果获浙江省自然科学二等奖1项，在本领域国内外主流期刊上发表论文共12篇，申请发明专利4项，授权实用新型专利3项，登记软件著作权3项。研究成果为冗余驱动过约束并联机构性能评价和尺度综合提供了新的理论依据和方法支持。