Motion Bifurcation and Output Characteristics of Spatial Over-constrained Mechanisms with Elastic Elements Based on Rectangular Plane-symmetric Bricard Units

doi:10.3901/JME.2025.21.048

Abstract

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

CLC Number:

TH112

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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