复杂大挠度分布柔度式柔顺机构的椭圆积分精确建模及设计方法

A distributed-compliance compliant mechanism is a device that transfers or converts motion, force and energy through the deflections of its flexible segments. Distributed-compliance compliant mechanisms exhibit many advantages such as large workspace and superior reliability compared to lumped-compliance compliant mechanisms. However, because the motion of a distributed-compliance compliant mechanism is always accompanied by complex large deflections of its compliant members, it is very difficult to achieve accurate modeling of compliant mechanism. Based on the comprehensive elliptic integral solution to the nonlinear deformation of large-deflection beams, the problems of inflection points, bifurcate paths, skip of paths and multiple solutions during the motion of distributed-compliance compliant mechanisms are deeply discussed. The comprehensive solution is capable of expediently and efficiently solving the kinetostatic analysis of complex distributed-compliance compliant mechanisms. The accurate models and solutions for compliant mechanisms are researched from the two aspects of load-displacement and strain-energy. Dimensional designs of compliant mechanisms are further discussed. According to the typical compliant mechanisms, the principled sample machine and the testing system for compliant mechanisms are built so that the theoretical methods are verified. Based on the above results, the common software modules are researched. We hope to develop the comprehensive solution into a general tool for accurately modeling and designing planar distributed-compliance compliant mechanisms.

分布柔度式柔顺机构是一类利用材料的弹性变形传递或转换运动、力和能量的机构，相对于集中柔度式柔顺机构而言，具有运动空间大及可靠性高等优点。由于分布柔度式柔顺机构常常伴随着复杂的大挠度非线性变形过程，使得机构的精确建模变得异常困难。本项目将基于申请人在前期工作中推导的大挠度梁非线性变形的完备椭圆积分解，深入探讨分布柔度式柔顺机构运动过程中的拐点的出现与消失、路径分叉、路径跳转以及多解问题，使完备椭圆积分解能更方便、高效地应用于复杂分布柔度式柔顺机构大挠度变形的运动静力学特性求解；从载荷位移和应变能两个方面开展柔顺机构精确建模与求解，进一步对柔顺机构进行尺寸综合设计；针对典型柔顺机构，制作原理样机，建立柔顺机构测试系统，对理论方法进行验证。基于上述理论成果，开发通用软件模块，并将完备椭圆积分解发展成为分布柔度式平面柔顺机构精确建模与设计的通用工具。

本项目针对分布柔度式柔顺机构大挠度梁非线性变形问题，通过分析机构运动过程中载荷-位移关系，得到求解大挠度梁非线性变形的载荷-位移完备椭圆积分模型。载荷-位移模型可以可用来求解柔性构件变形过程中包含任意拐点数的变形以及各种末端载荷情况的细长梁，可以求解分布柔度式柔顺机构多解问题。通过深入分析分布柔度式柔顺机构运动过程中的拐点的出现与消失、路径分叉、路径跳转以及多解问题，从基本应力应变关系出，分析得到柔性杆件应变能完备椭圆积分模型。基于最小作用量原理，利用机构应变能模型作为分布柔度式柔顺机构多解判断标准。.结合粒子群优化算法以及平面大变形梁的链式梁约束模型，为完备椭圆积分模型作为初值选择，解决柔顺机构初值敏感问题，使得载荷-位移完备椭圆积分模型以及应变能完备椭圆积分模型可以有效地发展为柔顺机构的分析及设计方法，对于分布柔度式柔顺机构的精确分析具有重要的理论研究与实际应用价值。.为完备椭圆积分模型的实用性，选择典型分布柔度式柔顺机构进行分析与尺度综合设计。以圆弧导向柔顺机构为例，分析机构多解问题，以及应变能模型在多解问题中的判别依据。通过对交叉铰链及LITF铰链进行大转角分析，展现了这类铰链在大转角情况下刚度非线性显著增强的特性，预测了簧片存在拐点的变形情况,并对柔顺铰链的运动范围、载荷承载能力等进行分析。将所设计柔性构件应用于无针注射触动装置、三维石膏打印推动装置等实际产品设计相结合，用理论模型验证了其可行性。在此基础上，搭建分布柔度式柔顺机构测试平台，用实验验证完备椭圆积分模型求解及分析的正确性。.本基金所给出的完备椭圆积分模型，在柔顺机构建模问题上效率和准确性都表现出优异的性能，能更方便、高效地应用于复杂分布柔度式柔顺机构大挠度变形的运动静力学特性求解。