Piezoelectrically actuated compliant mechanisms are key techniques in designing micro/nano manipulators, precision positioning stages/grippers and many other mechanical instruments. By considering the coupling relationship among piezoelectric actuator, compliant mechanisms and their external loads, a new modeling methodology in Laplace domain is proposed to capture the coupling dynamic characteristics of such a complex system. The coupled dynamic model of piezo-actuated compliant mechanisms subjected to mass-spring-damper loads with an accessorial force is analytically derived in the form of transfer function based on the concept of two-port dynamic stiffness model and control theory. The coupled dynamic model is further transformed into a generalized control block diagram in a unified form. As an application case, the static and dynamic performances of a typical flexure-based precision manipulator actuated by amplified piezoelectric stacks are analyzed with the presented model. It is demonstrated, both numerically and experimentally, that the proposed approach is accurate and straightforward for solving the coupled dynamic modeling issue in piezo-actuated compliant mechanisms subjected to external loads, and would be general enough for a wide class of applications involving multi-domain dynamic problems.

压电致动的柔顺机构是设计微型/纳米机械手，精密定位台/夹具和许多其他机械仪器的关键技术。通过考虑压电致动器，柔顺机构及其外部载荷之间的耦合关系，提出了一种在拉普拉斯域中的新建模方法，以捕获这种复杂系统的耦合动力学特性。基于两端口动态刚度模型和控制理论的概念，以传递函数的形式分析导出了压电驱动的柔顺机构在附加弹簧力的作用下的耦合动力学模型。耦合的动态模型被进一步转换成统一形式的通用控制框图。作为一个应用案例 利用所提出的模型分析了典型的基于挠曲的，由放大的压电堆驱动的精密机械手的静态和动态性能。在数值和实验上都表明，所提出的方法对于解决压电加载的顺应机构在承受外部载荷时的耦合动力学建模问题是准确而直接的，并且对于涉及多域的广泛应用是足够通用的动态问题。