面向多维振动试验系统的并联机构基础研究

According to the problems of vibration test system nowadays, parallel mechanism would be researched on the axpects of mechanism synthesis, kinematics, dynamics and prototype. The 6-DOF parallel mechanism which satisfied the requirements of vibration tests can be synthesized and optimized, based on a typical 6-DOF parallel mechanism 6-UPS. The kinematics problems, including the inverse kinematics and the forward kinematics problems, would be studied by both analytical method and numerical method, and the emphasis is the forward kinematics problem. Jacobian matrix can be established by the vector closed principle and screw theory, from which the mapping relationships of speed and force, the distribution of the singular trajectory can be studied. Nowadays, the algorithm of solving the workspace is based on the inverse kinematics analysis. To make up its deficiency, singularity-free workspace based on forward kinematics would be studied on the basis of kinematics analysis and singularity analysis. By absorbing the advantage of natural orthogonal complement method and variational principle, recursive modeling approach with the computational efficiency of O (n) for dynamics of multi-body system with closed-loops would be established, as well as high efficiency integration algorithm with good numerical stability. A multidimensional vibration test system based on parallel mechanism would be developed, and the algorithm of multibody system dynamics with closed-loops would be verified by the test system. Considering complexity of multi-dimensional vibration and merits of parallel mechanism, this project will improve the reliability of vibration test and have important academic theory significance and engineering application value.

针对目前振动试验系统存在的问题，围绕机构综合、运动学、动力学以及原型样机等工作展开研究。基于典型的6自由度并联机构6-UPS综合出所需要的并联机构并进行优化设计。通过解析和数值两个方面对机构的运动学正反解问题进行研究，着重研究机构的运动学正解。根据矢量封闭原理以及螺旋理论建立机构的雅可比矩阵，研究其速度、力的映射关系以及奇异轨迹的分布状况。在运动学及奇异性研究基础上，研究基于运动学正解的无奇异工作空间求解算法，以弥补目前工作空间求解依赖于运动学反解的不足。采用空间算子代数并吸收自然正交补方法、变分原理的优点，研究建立计算效率为O（n）的闭环多体动力学递推建模方法以及高效率且具有良好数值稳定性的积分算法。研制一套基于并联机构的多维振动试验系统，同时对闭环多体系统动力学进行验证。本项目综合考虑了多维振动的复杂性和并联机构的优点，对提高振动试验的可靠性具有重要的学术理论意义和工程应用价值。

针对目前振动试验系统难以实现空间多维振动模拟的问题，项目提出利用并联机构可以实现复杂空间运动的优势开展面向多维振动的并联机构基础研究来解决此问题。基于典型的6自由度并联机构6-UPS综合出所需要的并联机构并进行优化设计。采用解析的方法研究了6-UPS机构的运动学正解问题，并将其表达为一元十四次的代数方程，结果表明该机构的运动学正解具有28组解。同时研究了带附加传感器的6-UPS机构的运动学正解问题，该问题可以表达为二元一次方程组，具有唯一解。获取了奇异轨迹表达式，该表达形式具有258项，形式简洁，有望在实时控制中获得应用。在运动学及奇异性研究基础上，研究基于运动学正解的无奇异工作空间求解算法，以弥补目前工作空间求解依赖于运动学反解的不足。研究了基于哈密顿正则方程的链式多体系统递推建模方法。搭建了一套基于并联机构的多维振动试验系统，并开展了初步试验。本项目对提高振动试验的可靠性具有重要的学术理论意义和工程应用价值。