Enhanced mathematical modeling of the displacement amplification ratio for piezoelectric compliant mechanisms

Abstract

Piezo-actuated, flexure hinge-based compliant mechanisms have been frequently used in precision engineering in the last few decades. There have been a considerable number of publications on modeling the displacement amplification behavior of rhombus-type and bridgetype compliant mechanisms. However, due to an unclear geometric approximation and mechanical assumption between these two flexures, it is very difficult to obtain an exact description of the kinematic performance using previous analytical models, especially when the designed angle of the compliant mechanisms is small. Therefore, enhanced theoretical models of the displacement amplification ratio for rhombus-type and bridge-type compliant mechanisms are proposed to improve the prediction accuracy based on the distinct force analysis between these two flexures. The energy conservation law and the elastic beam theory are employed for modeling with consideration of the translational and rotational stiffness. Theoretical and finite elemental results show that the prediction errors of the displacement amplification ratio will be enlarged if the bridge-type flexure is simplified as a rhombic structure to perform mechanical modeling. More importantly, the proposed models exhibit better performance than the previous models, which is further verified by experiments.

Kinetostatic and Dynamic Modeling of Flexure-Based Compliant Mechanisms: A Survey

“…Constrained reactions should be also calculated in advance as the function of external loads by virtue of boundary conditions. Then, the deflection formula and the principle of energy conservation or the principle of virtual work [178] in mechanics of materials can be employed to formulate the kinetostatics of compliant mechanisms [80] M i ðxÞ ¼ EI Á y 00 i (5) where y i is the deflection of the ith flexible beam. The prime denotes the derivative with respect to spatial coordinate x.…”

“…As to the modeling of compliant mechanisms with small deformation, Castigliano's second theorem was utilized to model the kinetostatics of bridge-type flexure amplifiers in 2003 [76], while elastic beam theory was employed for the kinetostatics of this type of amplifier in 2006 [77]. These two methods are now widely used to design compliant mechanisms with small deflections [78][79][80][81]. However, inner-force analysis is required in these two methods, resulting in great complexity in serial-parallel compliant mechanisms.…”

Verifying the Performance Characteristics of the (micro) Robotic Devices

“…In the literature, there are few approaches on how to calculate the amplification ratio R amp (ratio between output displacement o Y and input displacement i X ). There are: the ideal model (geometric model) [9,10], the elastic beam method (depends on the flexure elements Rhombus type -elastic arms and bridge type -flexure hinges) [11], matrix methods, Castigliano's second theorem [4] and method based on analysis of results from simulation software. In the following are described equations for calculation of the amplification ratio, force analysis, and stress calculation, with the assumption that one (output) side of the linear-linear motion transformation device is fixed to the frame.…”

“…Unfortunately, (2.1) offer only basic and very rough results of the amplification radio, and could be useful for very small displacements (in range of nanometers). The equation based on elastic beam method for the Rhombus type of mechanical amplifier [11] is expressed as…”

Design and Performance Analysis of a TLET‐Type Flexure Hinge

“…LEM's functions are similar those of CMs which transfer force, motion, and energy [1][2][3][4][5][6]. CMs can be manufactured by the 3D printing technique, wire discharged machining process, or CNC machine from a solid [7,8]. Unlike CMs, LEM is fabricated from a sheet material with plastic or metal lamina material [9].…”