PARAMETRIC STUDY OF A SINGLE FLEXIBLE LINK BASED ON TIMOSHENKO AND EULER-BERNOULLI BEAM THEORIES

In this research the sensitivity analysis (SA) of the geometric parameters such as: length, thickness and width of a single link flexible manipulator on maximum deflection (MD) of the end effector and vibration energy (VE) of that point are conducted. The motion equation of the system is developed based on Gibbs-Appel (G-A) formulation. Also for modeling the elastic property of the system the assumption of assumed modes method (AMM) is applied. In this study, two theories are used to obtain the end-point MD and VE of the end effector. Firstly, the assumption of Timoshenko beam theory (TBT) has been applied to consider the effects of shear and rotational inertia. After that, EulerBernoulli beam theory (EBBT) is used. Then Sobol’s sensitivity analysis method is applied to determine how VE and end-point MD is influenced by those geometric parameters. At the end of the research, results of two mentioned theories are compared.

[1]  Santosha K. Dwivedy,et al.  Shape Optimization of Flexible Robotic Manipulators , 2006 .

[2]  William Becker,et al.  A comparison of two sampling methods for global sensitivity analysis , 2012, Comput. Phys. Commun..

[3]  Constantinos C. Pantelides,et al.  Monte Carlo evaluation of derivative-based global sensitivity measures , 2009, Reliab. Eng. Syst. Saf..

[4]  I. Sobol,et al.  About the use of rank transformation in sensitivity analysis of model output , 1995 .

[5]  Astrid Jourdan,et al.  Global sensitivity analysis using complex linear models , 2011, Statistics and Computing.

[6]  Saltelli Andrea,et al.  Global Sensitivity Analysis: The Primer , 2008 .

[7]  M. Korayem,et al.  The effect of off-end tip distance on the nanomanipulation based on rectangular and V-shape cantilevered AFMs , 2010 .

[8]  Vera Novak,et al.  Sensitivity Analysis and Model Assessment: Mathematical Models for Arterial Blood Flow and Blood Pressure , 2008, Cardiovascular engineering.

[9]  Steven Dubowsky,et al.  Probabilistic modeling and analysis of high-speed rough-terrain mobile robots , 2004, IEEE International Conference on Robotics and Automation, 2004. Proceedings. ICRA '04. 2004.

[10]  Moharam Habibnejad Korayem,et al.  Dynamic load-carrying capacity of mobile-base flexible joint manipulators , 2005 .

[11]  George Z. Gertner,et al.  A general first-order global sensitivity analysis method , 2008, Reliab. Eng. Syst. Saf..

[12]  Peter Eberhard,et al.  Control and Parameter Optimization of Flexible Robots* , 2000 .

[13]  Stefano Tarantola,et al.  SAMO 2001: methodological advances and innovative applications of sensitivity analysis , 2003, Reliability Engineering & System Safety.

[14]  Gianni Bellocchi,et al.  Comparison of sensitivity analysis techniques: A case study with the rice model WARM , 2010 .

[15]  Moharam Habibnejad Korayem,et al.  Sensitivity analysis of nanoparticles pushing critical conditions in 2-D controlled nanomanipulation based on AFM , 2009 .

[16]  A. Saltelli,et al.  A quantitative model-independent method for global sensitivity analysis of model output , 1999 .

[17]  Ilya M. Sobol,et al.  Sensitivity Estimates for Nonlinear Mathematical Models , 1993 .