基于正交分解的柔顺机构模块化运动静力学综合

Currently, most of the synthesis approaches are designed to obtain precision motion on desired direction, while less attention has been paid to the mechanical properties of a mechanism. By saying mechanical properties, we mean the forces transmitted, the strain energy possessed and the stiffness exhibited by the compliant mechanism during its motion. Thus, this project aims to construct a systematic orthogonal decomposition based kinetostatic synthesis approach for compliant mechanisms through use of building blocks. For this purpose, we use a function to represent the kinetostatic behavior of a compliant mechanisms and decompose the function through combination of orthogonal basis functions in suitable Hilbert spaces. By doing this, we can obtain a feasible way of functional decomposition. Then, building blocks that have the kineostatic behaviors which can be represent by the orthogonal basis function are designed to construct a library of building blocks. Perform the synthesis through use of different type of orthogonal basis functions, after which a size optimization procedure is performed to obtain the final mechanism.

现阶段柔顺机构的综合方法研究主要围绕柔顺机构的运动综合展开，旨在通过构型设计消除几何非线性引起的轴间耦合和寄生运动，在期望的运动方向上获得更高的运动精度。而对柔顺机构展现出的丰富的力学特性关注不够，鲜有系统的综合方法。因此，本次申请将研究兼顾运动和力学特性的柔顺机构综合，即运动静力学综合。申请人拟在模块化综合的基础上引入功能正交分解，通过将机构的综合过程置于Hilbert空间中，依据标准正交基函数实现期望功能的运动静力学分解，并在此基础上构建实现各种基函数（运动静力学曲线）的柔顺机构模块库；结合空间内多种标准正交基函数的叠加实现柔顺机构的综合，之后通过尺度综合完成能够满足设计功能的机构的精细设计。

围绕柔性机构运动静力学特性的可设计性以及综合设计方法不完备这两个核心问题，本项目开展了柔性机构运动静力学分析和设计方法相关研究，从分析方法、模块设计、优化算法和机构设计等各个方面着手，完成了包含几何非线性的运动静力学模型建立方法，构造了以屈曲变形梁为基础的运动静力学特性模块库，设计出基于梯度投影法的高效结构优化算法，并最终形成了具有特殊运动静力学特性的柔性机构设计方法，该方法可以完成兼顾“运动性能”和“力学性能”的柔性机构运动静力学特性设计。在该方法的基础上，本项目还开展了成果的应用研究，基于该方法设计的大行程柔性恒力机构已经应用于大尺寸镜片研磨中，在研磨效果和动态响应等方面展现出了优良的特性。