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

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.

Rate-Dependent Hysteresis Modeling and Compensation of Piezo-Driven Flexure-Based Mechanism

Updating parameters according to the driving rate of input, the rate-dependent Prandtl-Ishlinskii （PI） model is widely used in hysteresis modeling and compensation. In order to improve the modeling accuracy, two PI models identified at low and high driving rates separately are incorporated through a combination law. For the piezo- driven flexure-based mechanism, the very low damping ratio makes it easy to excite the structural vibration. As a re- suit, the measured hysteresis loop is greatly distorted and the modeling accuracy of the identified P1 model is signifi- cantly affected. In this paper, a novel time-efficient parameter identification method which utilizes the superimposed sinusoidal signals as the control input is proposed. This method effectively avoids the excitation of the structural vibra- tion. In addition, as the driving rate of the superimposed sinusoidal signals covers a wide range, all the coefficients required for modeling the rate-dependence can be identified through only one set of experimental data. Hysteresis modeling and trajectory tracking experiments were performed on a 2-DOF piezo-driven flexure-based mechanism. The experimental results show that the combined hysteresis model maintains the modeling accuracy over the entire work- ing range of the flexure-based mechanism. The mechanism＇s hysteresis is significantly suppressed by the use of the inverse PI model as the feedforward controller; and better result is achieved when a feedback loop is also incorporated. The tracking performance of the flexure-based mechanism is greatly improved.