弹性变形条件下过约束并联机构的受力分析与动力协调研究

As a special kind of parallel mechanism, the overconstrained parallel mechanism has the characteristics of simple structure, high accuracy and rigidity, which has played an important role in many cases. Since force analysis of the overconstrained parallel mechanism is very complicated, there are very few investigations on the force analysis of the overconstrained parallel mechanism at home and abroad, especially in the condition of system elastic deformation. In this project, force analysis and dynamic coordination of the overconstrained parallel mechanism (including the passive overconstrained parallel mechanism, the redundantly actuated parallel mechanism, and the redundantly actuated parallel mechanism) will be carried out thoroughly and systematically in the condition that system elastic deformation is taken into account. The correlation between overconstraint wrenches of the passive parallel mechanism and system stiffness, and that between actuation wrenches of the redundantly actuated parallel mechanism and system stiffness are investigated, deformation compatibility equations and system stiffness model are established, all joint reactions of the passive overconstrained parallel mechanism are solved, unified dynamic coordination model of the redundantly actuated parallel mechanism among external load, system stiffness matrix and joint actuated forces. Besides, numerical simulation study on a certain amount of typical overconstrained parallel mechanisms, and experimental investigation of the hybrid force/position control based on the self-developed five-DOF 5-UPS/PRPU redundantly actuated parallel machine tool are performed to test the results of theoretical analysis effectively.

过约束并联机构作为一种特殊的并联机构，具有结构简单、精度高和刚度大的优点，在很多场合发挥了重要的作用。由于过约束并联机构力学问题很复杂，国内外对过约束并联机构力学问题进行系统研究的文献还非常少，尤其在弹性变形的条件下。本项目将在考虑系统弹性变形的条件下，对过约束并联机构（包括被动过约束并联机构、冗余驱动并联机构和冗余驱动过约束并联机构）的受力分析和动力协调进行深入、系统地研究：分析被动过约束并联机构的约束力螺旋和冗余驱动并联机构的驱动力螺旋与系统刚度的相关性，建立变形协调方程和系统刚度模型，求解被动过约束并联机构所有关节的约束反力，建立冗余驱动并联机构包含外载荷、系统刚度矩阵以及关节驱动力的统一动力协调模型。本项目还要对一定数量的典型过约束并联机构开展数值仿真研究，并基于本课题组自主研发的5-UPS/PRPU五自由度冗余驱动并联机床开展力/位混合控制实验研究，以有效检验理论分析结果。

主动过约束（冗余驱动）和被动过约束并联机构因其特有的优点在很多场合发挥了重要作用，尤其是在需要高承载能力的场合，而过约束的存在使得这两类过约束并联机构的受力分析属于超静定问题，分析难度大。鉴于目前国内外关于主动过约束和被动过约束并联机构受力分析的研究非常少，本项目在考虑系统弹性变形的条件下，对这两类过约束并联机构的受力问题展开了深入、系统的研究：分析被动过约束并联机构约束力螺旋与系统刚度的相关性，基于并联机构典型支链构型的刚度模型研究建立被动过约束并联机构的系统刚度模型的一般方法，研究建立系统弹性变形之间的协调方程的简便方法，研究建立外载荷与约束力螺旋之间、外载荷与驱动力之间、约束力螺旋与关节约束反力之间解析关系的一般方法；研究分析冗余驱动并联机构的驱动力螺旋（驱动关节所产生的约束力螺旋）与系统刚度的相关性，研究分析冗余驱动并联机构系统的刚度模型，建立系统弹性变形之间的协调方程，研究建立包含外载荷、系统刚度矩阵、关节驱动力的动力协调方程的一般方法，在此基础上进一步研究冗余驱动并联机构的动力协调优化控制；研究分析一定数量的典型被动过约束并联机构和冗余驱动并联机构的力学特性，并采用数值仿真方法检验理论分析结果；改造并升级5-UPS/PRPU五自由度冗余驱动并联机床的软、硬件控制系统，开展力/位混合控制实验研究。通过上述研究，本项目建立了研究主动和被动过约束并联机构力学问题比较完整的具有普适性的一般方法和理论体系；揭示了弹性变形条件下主动过约束力螺旋系和被动过约束力螺旋系影响机构内部载荷分布的机理；建立了在考虑系统弹性变形条件下冗余驱动并联机构的统一动力协调模型。研究成果为过约束并联机构的受力分析提供了重要的理论指导，进而为此类机构的设计及应用研究奠定了坚实的基础，为冗余驱动并联机构驱动力协调分配提供了新的思路，并为考虑系统弹性变形的冗余驱动并联机器人动力学控制提供了理论基础。