Kinematic accuracy analysis of flexible mechanisms with uncertain link lengths and joint clearances

A general method of kinematic accuracy analysis is presented for the flexible planar mechanisms with stochastic parameters such as uncertain link lengths and joint clearances. The impact-pair model is employed to describe the separation and impact phenomena between the two components in the clearance joint. The dynamic equations of the flexible mechanism with stochastic parameters are established by finite element method and solved by the Newmark method. The Monte Carlo method is introduced to analyse the kinematic accuracy of the flexible mechanisms. A numerical example shows the effects of link flexibility and joint clearances on the kinematic accuracy of the planar mechanism with stochastic parameters using the proposed approach.

[1]  Ferdinand Freudenstein,et al.  Dynamic Analysis of Mechanical Systems With Clearances—Part 1: Formation of Dynamic Model , 1971 .

[2]  B. Kang,et al.  Stochastic approach to kinematic reliability of open-loop mechanism with dimensional tolerance , 2010 .

[3]  Roberto Caracciolo,et al.  Experimental validation of a model-based robust controller for multi-body mechanisms with flexible links , 2008 .

[4]  Inna Sharf,et al.  Literature survey of contact dynamics modelling , 2002 .

[5]  S. Dubowsky,et al.  Design and Analysis of Multilink Flexible Mechanisms With Multiple Clearance Connections , 1977 .

[6]  G. N. Sandor,et al.  A General Method for Kineto-Elastodynamic Analysis and Synthesis of Mechanisms , 1972 .

[7]  Meng Xian-ju.  Analytical model of accuracy probability for linkages with clearances , 2004 .

[8]  G. G. Lowen,et al.  Survey of investigations into the dynamic behavior of mechanisms containing links with distributed mass and elasticity , 1972 .

[9]  M. Ganapathi,et al.  On the nonlinear axisymmetric dynamic buckling behavior of clamped functionally graded spherical caps , 2007 .

[10]  Hamilton Horth Mabie,et al.  Mechanisms and Dynamics of Machinery , 1963 .

[11]  S. J. Lee,et al.  The Determination of the Probabilistic Properties of Velocities and Accelerations in Kinematic Chains With Uncertainty , 1991 .

[12]  David Allen Turcic,et al.  Dynamic Analysis of Elastic Mechanism Systems. Part I: Applications , 1984 .

[13]  Tian Huang,et al.  Dynamics and elasto-dynamics optimization of a 2-DOF planar parallel pick-and-place robot with flexible links , 2009 .

[14]  Carlo Innocenti,et al.  Kinematic Clearance Sensitivity Analysis of Spatial Structures With Revolute Joints ( , 2002, DAC 2002.

[15]  R. C. Winfrey,et al.  Elastic Link Mechanism Dynamics , 1971 .

[16]  D. Marghitu,et al.  Dynamic analysis of a planar rigid-link mechanism with rotating slider joint and clearance , 2003 .

[17]  Wang Guo-qing.  Application of Nonlinear Contact Model in Chaos Analysis of a Mechanism with Clearance Joints , 2005 .

[18]  Jen-San Chen,et al.  Effects of Crank Length on the Dynamics Behavior of a Flexible Connecting Rod , 2001 .

[19]  Yan Shaoze.  Monte Carlo simulation of motion errors for four-bar linkages with clearances , 2007 .

[20]  Chen Hongbin.  Dynamic performance of deployable structures with flexible members and clearance connections , 2003 .

[21]  Adrian Sandu,et al.  Modeling Multibody Systems with Uncertainties. Part I: Theoretical and Computational Aspects , 2006 .

[22]  K. H. Hunt,et al.  Coefficient of Restitution Interpreted as Damping in Vibroimpact , 1975 .

[23]  Sun Zhi-li,et al.  Simulation on Motion Reliability of Crank-Slider Mechanism , 2006 .

[24]  Jorge Ambrósio,et al.  On the contact detection for contact-impact analysis in multibody systems , 2010 .

[25]  Shaoze Yan,et al.  Elasto-Plastic Analysis of Clearance Connections Subjected to Impact Loads , 2004 .

[26]  S. Dubowsky,et al.  An Analytical and Experimental Study of the Prediction of Impacts in Planar Mechanical Systems With Clearances , 1984 .

[27]  Ming-June Tsai,et al.  Accuracy analysis of a multi-loop linkage with joint clearances , 2008 .

[28]  Ahmet S. Yigit,et al.  SPRING-DASHPOT MODELS FOR THE DYNAMICS OF A RADIALLY ROTATING BEAM WITH IMPACT , 1990 .

[29]  Zexiang Li,et al.  A general approach for accuracy analysis of parallel manipulators with joint clearance , 2005, 2005 IEEE/RSJ International Conference on Intelligent Robots and Systems.

[30]  Ming-June Tsai,et al.  Kinematic sensitivity analysis of linkage with joint clearance based on transmission quality , 2004 .

[31]  David Allen Turcic,et al.  Dynamic Analysis of Elastic Mechanism Systems, Part I: Generalized Equations of Motion , 1983 .

[32]  Selçuk Erkaya,et al.  Investigation on effect of joint clearance on dynamics of four-bar mechanism , 2009 .

[33]  Yan-Hui Wang,et al.  Dynamic modeling of flexible multibody systems with parameter uncertainty , 2008 .