基于面对称Bricard单元的弹性空间过约束机构运动分岔与输出特性分析

doi:10.3901/JME.2025.21.048

摘要/Abstract

摘要： 空间过约束机构具有驱动输入少、刚度高、折展比大等独特优势，在航空航天、机器人领域具有广泛的应用前景。近年来，结合弹性/柔性结构发掘空间过约束机构的力学特性成为研究热点。鉴于此，基于矩形面对称Bricard单元，提出一种含分布式弹性元件的对称双锥台型空间过约束机构(简称对称双锥台Bricard弹性机构)，并探讨其准静态力学输出行为。以矩形面对称Bricard机构为骨架单元，在铰点之间放置弹性元件，完成对称双锥台Bricard弹性机构的结构设计，并结合单元分岔特性和组装形式对其分岔构型进行了详细分析。建立了对称双锥台Bricard弹性机构的准静态力学输出模型，结合分岔构型分析了整体力学输出特性。研究结果表明，所设计的对称双锥台Bricard弹性机构具有灵活的参数调节能力和丰富的非线性刚度输出特性，改变分岔路径可以实现正刚度、负刚度、准零刚度、零力值、分段力值等输出特性切换。当各弹性元件刚度相等时，对称双锥台Bricard弹性机构具有线性负刚度特性，并联正刚度元件后能实现全运动行程上的恒零刚度输出，极大扩展了零刚度范围，在超低频隔振、人机交互等领域展现出巨大的性能优势。

关键词: 面对称Bricard机构, 机构分岔, 准静态模型, 参数分析, 非线性刚度, 恒零刚度

Abstract: Spatial over-constrained mechanisms offer unique advantages, including reduced driving inputs, high stiffness, and a large aspect ratio, making them promising for applications in aerospace and robotics. Recently, incorporating elastic/flexible elements to investigate the mechanical properties of these mechanisms has emerged as a significant research area. In view of this, based on the rectangular plane-symmetric Bricard unit, a symmetric double frustum spatial over-constrained mechanism with distributed elastic elements (referred to as the symmetric double frustum Bricard elastic mechanism) is proposed, and its quasi-static mechanical behavior is examined. The proposed symmetric double frustum Bricard elastic mechanism consists of two rectangular plane-symmetric Bricard units serving as the supporting skeleton, with elastic elements placed between hinge points. The different configurations are analyzed by combining motion bifurcation characteristics and unit assembly form. A quasi-static mechanical model of the symmetric double frustum Bricard elastic mechanism was established, and the equivalent output of different configurations is then obtained. The results suggest that the elastic Bricard mechanism exhibits flexible parameter adjustment capabilities and rich nonlinear stiffness characteristics, and changing the bifurcation path can achieve switching of output characteristics such as positive stiffness, negative stiffness, quasi-zero stiffness, zero force, and piecewise force. When the stiffness of the introduced elastic elements is equal, the symmetric double frustum Bricard elastic mechanism demonstrates linear negative stiffness. By connecting a positive stiffness element as a corrector, the symmetric double frustum Bricard elastic mechanism achieves constant-zero-stiffness output across its entire motion range, significantly broadening the zero-stiffness range. This design indicates huge performance advantages in ultra-low frequency vibration isolation and human-computer interaction.

Key words: plane-symmetric Bricard mechanism, motion bifurcation, quasi-static model, parameter analysis, nonlinear stiffness, constant-zero stiffness

中图分类号:

TH112

刘世伟, 李龙, 吕胜男, 丁希仑. 基于面对称Bricard单元的弹性空间过约束机构运动分岔与输出特性分析[J]. 机械工程学报, 2025, 61(21): 48-59.

LIU Shiwei, LI Long, Lü Shengnan, DING Xilun. Motion Bifurcation and Output Characteristics of Spatial Over-constrained Mechanisms with Elastic Elements Based on Rectangular Plane-symmetric Bricard Units[J]. Journal of Mechanical Engineering, 2025, 61(21): 48-59.

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