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Frontiers of Mechanical Engineering

Front Mech Eng    2013, Vol. 8 Issue (2) : 160-168
Nonlinear dynamics and analysis of a four-bar linkage with clearance
Yuanguang TANG1, Zongyu CHANG1(), Xiaogang DONG1, Yafei HU2, Zhenjiang YU1
1. College of Engineering, Ocean University of China, Qingdao 266100, China; 2. Institute for Research in Construction, National Research Council, Regina, SK S4S 7J7, Canada
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In this paper, nonlinear dynamic behavior of a four-bar linkage considering clearance is studied. The dynamic model of the linkage with a clearance between coupler and rocker is developed firstly. Then the dynamic equations of this mechanism are solved by a numerical method. According to the calculated response, compliance, force and trajectory of pin in joint bearing are obtained. Effects of clearance magnitude and the relationship between a mechanism with clearance and without clearance are studied. By using Poincare Map, it is proved that strange attractors or chaos exist in the dynamic response. In addition, phenomena of chaos, periodic response and subharmonic response also can be found in the special condition. Bifurcation diagram is used to suggest that bifurcation and fractal phenomena exist in the dynamic response of this mechanism.

Keywords four-bar linkage      chaos      bifurcation      strange attractors      dynamics     
Corresponding Author(s): CHANG Zongyu,   
Issue Date: 05 June 2013
 Cite this article:   
Yuanguang TANG,Zongyu CHANG,Xiaogang DONG, et al. Nonlinear dynamics and analysis of a four-bar linkage with clearance[J]. Front Mech Eng, 2013, 8(2): 160-168.
Fig.1  Scheme of four-bar linkage with clearance
Fig.2  Model of radical clearance model
li (m)mi (kg)Ii (kg·m2)lsi (m)
ground link0.2
Tab.1  Parameters of linkage
Fig.3  Response when clearance is 0.1 mm: (a) displacement magnitude versus crank angle; (b) trajectory of the pin center in the journal bearing; (c) contact force vector in the journal bearing
Fig.4  Response when clearance is 0.5 mm: (a) displacement magnitude versus crank angle; (b) trajectory of the pin center in the journal bearing; (c) contact force vector in the journal bearing
Fig.5  Response of the linkage without clearance: (a) Displacement magnitude between the journal center and the pin center versus time; (b) Trajectory of the pin center in the journal bearing; (c) Contact force vector in the journal bearing
Fig.6  Poincare map for angular velocity of 320 r/min and clearance of 0.15 mm (200 points)
Fig.7  Poincare map for angular velocity of 320 r/min and clearance of 0.15 mm (2000 points)
Fig.8  Poincare map for angular velocity of 320 r/min and clearance of 0.5 mm
Fig.9  Poincare map for angular velocity of 320 r/min and clearance of 0.101 mm
Fig.10  Poincare map for angular velocity of 320 r/min and clearance of 0.1 mm
Fig.11  Bifurcation diagram with varying clearance
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