Closed-Form Modeling and Analysis of an XY Flexure-Based Nano-Manipulator

Abstract

Flexure-based mechanisms are widely utilized in nano manipulations. The closed-form statics and dynamics modeling is difficult due to the complex topologies, the inevitable compliance of levers, the Hertzian contact interface, etc. This paper presents the closed-form modeling of an XY nano-manipulator consisting of statically indeterminate symmetric (SIS) structures using leaf and circular flexure hinges. Theoretical analysis reveals that the lever’s compliance, the contact stiffness, and the load mass have significant influence on the static and dynamic performances of the system. Experiments are conducted to verify the effectiveness of the established models. If no piezoelectric actuator (PEA) is installed, the influence of the contact stiffness can be eliminated. Experimental results show that the estimation error on the output stiffness and first natural frequency can reach 2% and 1.7%, respectively. If PEAs are installed, the contact stiffness shows up in the models. As no effective method is currently available to measure or estimate the contact stiffness, it is impossible to precisely estimate the performance of the overall system. In this case, the established closed-form models can be utilized to calculate the bounds of the performance. The established closed-form models are widely applicable in the design and optimization of planar flexure-based mechanisms.