Abstract
In this paper, we establish a dynamic model of a six-degrees-of-freedom (6-DOF) compliant positioning platform based on bridge-type amplifiers. Based on the elastic beam theory and energy relationship, we derived the bridge-type amplifier’s dynamic model using the Lagrange equation. Then, we established a dynamic model of the compliant platform based on the equivalent mass and equivalent stiffness of the bridge-type amplifier, and the analysis formula of the natural frequency was derived. Finally, the analytical models of natural frequencies of the bridge-type amplifier and the compliant platforms were verified using the finite element analysis (FEA) method. Through modal experiments, the damping ratio and natural frequency were identified. Step response experiments in the X/Y direction and Z direction were performed. The phenomenon that the experimental results appeared to match the theoretical calculations indicates that the dynamic model was accurate.
Highlights
The compliant positioning platform driven by a piezoelectric actuator (PZA) is widely used in aerospace technology, Microelectronics Mechanical Systems (MEMS), biomedical engineering, optical engineering, and other modern precision engineering fields [1,2], taking advantage of the advantages of a PZA, such as the ultra-high displacement resolution, high-frequency response, and large output force [3,4], as well as the characteristics of a flexible hinge, such as high precision, fast response, and compact structure [5,6]
The 6-DOF micro/nano-positioning compliant platform of this study is based on bridge-type amplifiers, as shown in Figure 1, consisting of a top platform, a middle platform, and a bottom platform
We inserted the PZA into the bridge-type amplifier and applied a preload force on both ends of the PZA through two screws to ensure a stable connection between tMhiecrtowmaoc.hiTnhese20f2ix0,in11g, 1h0o24les of the compliant platform were fixed to a fixed base mounted on the o1p4toicfa1l7 table to reduce ground vibration
Summary
The compliant positioning platform driven by a piezoelectric actuator (PZA) is widely used in aerospace technology, Microelectronics Mechanical Systems (MEMS), biomedical engineering, optical engineering, and other modern precision engineering fields [1,2], taking advantage of the advantages of a PZA, such as the ultra-high displacement resolution, high-frequency response, and large output force [3,4], as well as the characteristics of a flexible hinge, such as high precision, fast response, and compact structure [5,6]. Jiang et al [13] developed an XY 2-DOF compliant positioning platform with stiffness modeling and performance analysis of input and output decoupling characteristics. A parallel 2-DOF flexible platform was developed [15] for XY nano-positioning based on a multi-stage amplification mechanism consisting of a bridge-type amplifier, rhombic amplifier, and Scott–Russell amplifier. A precision 3-DOF vertical positioning platform was developed [16], driven by three PZTs, displacement-amplified by a bridge-type amplifier, and guided by three rotationally symmetric hinges. Xu et al [22] established a dynamic model of the bridge-type amplifier based on the Euler–Bernoulli beam theory and Lagrange equations. Ling et al [24,25,26] deduced a dynamic stiffness matrix of the flexible beam based on D’alembert’s principle to analyze all the kine-matic, static and dynamic performances of compliant mechanisms. The correctness of the theory was verified by finite element analysis (FEA) and experiments
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