Enabling the transfer matrix method to model serial–parallel compliant mechanisms including curved flexure beams

IF 3.4 Q1 ENGINEERING, MECHANICAL
Mingxiang Ling, Lei Yuan, Tingjun Zeng, Xianmin Zhang
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引用次数: 0

Abstract

Compliant mechanisms with curved flexure hinges/beams have potential advantages of small spaces, low stress levels, and flexible design parameters, which have attracted considerable attention in precision engineering, metamaterials, robotics, and so forth. However, serial–parallel configurations with curved flexure hinges/beams often lead to a complicated parametric design. Here, the transfer matrix method is enabled for analysis of both the kinetostatics and dynamics of general serial–parallel compliant mechanisms without deriving laborious formulas or combining other modeling methods. Consequently, serial–parallel compliant mechanisms with curved flexure hinges/beams can be modeled in a straightforward manner based on a single transfer matrix of Timoshenko straight beams using a step-by-step procedure. Theoretical and numerical validations on two customized XY nanopositioners comprised of straight and corrugated flexure units confirm the concise modeling process and high prediction accuracy of the presented approach. In conclusion, the present study provides an enhanced transfer matrix modeling approach to streamline the kinetostatic and dynamic analyses of general serial–parallel compliant mechanisms and beam structures, including curved flexure hinges and irregular-shaped rigid bodies.

Abstract Image

使传递矩阵法能够模拟包括弯曲挠性梁在内的串联-平行顺从机构
具有弯曲挠性铰链/梁的顺应机构具有空间小、应力水平低、设计参数灵活等潜在优势,在精密工程、超材料、机器人等领域引起了广泛关注。然而,曲面挠性铰链/梁的串联-并联配置通常会导致复杂的参数设计。在这里,传递矩阵法可用于分析一般串并联顺从机构的运动学和动力学,而无需推导费力的公式或结合其他建模方法。因此,可以根据蒂莫申科直梁的单一传递矩阵,通过逐步的程序,以简单的方式对具有弯曲挠性铰链/梁的串联-平行顺从机构进行建模。在两个由直形和波纹形挠曲单元组成的定制 XY 纳米定位器上进行的理论和数值验证证实了所介绍方法的简洁建模过程和高预测精度。总之,本研究提供了一种增强型传递矩阵建模方法,可简化一般串联-并联顺应机构和梁结构(包括弯曲挠性铰链和不规则形状刚体)的运动静力学和动力学分析。
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CiteScore
3.50
自引率
0.00%
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