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浙江大学学报(工学版)
J4  2011, Vol. 45 Issue (12): 2159-2168    DOI: 10.3785/j.issn.1008-973X.2011.12.014
    
Kinematic analysis of planar pin-bar linkages
by arc-length method
ZU Yi-zhen, DENG Hua
Space Structures Research Centre, Zhejiang University, Hangzhou 310058, China
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Abstract  

The arc-length method was applied for the kinematic analysis of planar pin-bar linkages, so the kinematic path and state stability of those systems could be solved in a unified way. Based on the finite element method(FEM), the basic kinematic equation of pinbar linkages was established with the control parameters defined as the elongations of driving bars. An arc-length numerical strategy was put forward to solve the kinematic path of pin-bar linkages. The variance of minimal eigenvalue of tangent stiffness matrix was employed to determine the stability of equilibrium configuration on the kinematic trajectory. The method for pinpointing the singular point in the kinematic path was presented, and the criterion for determining the bifurcation of those singular points was also discussed. In order to trace the bifurcation paths, the basic kinematic equation was further reconstructed by introducing an additional constraint equation. An illustrative example of reticulated cylindrical shell with ‘mechanismmethod’ erection, which has been modelled as a pinbar linkage, was analyzed by the method put forward to investigate the state characteristics during lifting under different segment divisions and slings layouts. The result shows that this arclength computational strategy is valid for the simulation of lifting process and determination of critical state of planar pinbar linkages.

Published: 01 December 2011
CLC:  TU 323  
  TU 311.2  
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Cite this article:

ZU Yi-zhen, DENG Hua. Kinematic analysis of planar pin-bar linkages
by arc-length method. J4, 2011, 45(12): 2159-2168.

URL:

https://www.zjujournals.com/eng/10.3785/j.issn.1008-973X.2011.12.014     OR     https://www.zjujournals.com/eng/Y2011/V45/I12/2159


基于弧长法的平面连杆机构运动分析

将弧长法应用于平面连杆机构的运动解析,使得体系运动路径和形态稳定性跟踪可统一求解.基于有限元法,建立以驱动杆件伸长量为控制变量的连杆机构运动分析基本方程.提出弧长法求解体系运动路径的基本策略,并通过监测体系切线刚度矩阵最小特征值的变化来跟踪运动形态的稳定性.阐述了精确定位运动路径中奇异点的计算方法以及判别奇异点是否为运动分岔点的准则.进一步通过增加约束条件并修改控制方程,实现分岔路径的跟踪.将一采用“机构法”施工的柱面网壳简化为平面连杆机构,根据基于弧长法的机构运动分析方法分析了不同分段、不同吊索布置情况下机构的提升形态特点.计算结果表明：该弧长法计算策略能够有效实现平面连杆机构的施工路径模拟和临界状态的判别.

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