Now the six-axis force sensor (6-AFS) is used widely,
and as the core components, mechanical properties of its elastic bodies are
significant. With the increase of dynamic loads, studies on dynamic
characteristics of the 6-AFS become more and more important. In this paper, the
study focuses on the free vibration problem of a novel 6-AFS. The research
approach is to decompose the sensor into several separate elastic bodies (four
lamellas and upper and lower membranes) and research these elastic bodies
respectively. The free vibration of the lamella is studied based on
Rayleigh-Ritz method and the separation of variables. The analytical solutions
of free vibration of the membranes are deduced according to the nature of
Bessel functions. Both the analytical results are simulated with MATLAB.
Compared the simulated diagrams with actual situations, they are very close.
The mode shapes obtained play a major role in solving the forced vibration of the
Cite this paper
D. Xu and Z. Wang, "Free Vibration Analysis of Elastic Bodies for Six-Axis Force Sensor," Journal of Sensor Technology, Vol. 3 No. 1, 2013, pp. 13-20. doi: 10.4236/jst.2013.31003.
 J. K. Paik, B. H. Shin, Y. B. Bang and Y. B. Shim, “Development of an Anthropomorphic Robotic Arm and Hand for Interactive Humanoids,” Journal of Bionic Engineering, Vol. 9, No. 2, 2012, pp. 133-142.
 G. De Maria, C. Natale and S. Pirozzi, “Force/Tactile Sensor for Robotic Applications,” Sensors and Actuators A: Physical, Vol. 175, 2012, pp. 60-72.
 T. Yoshikawa and T. Miyazaki, “A Six-Axis Force Sensor with Three-Dimensional Cross-Shape Structure,” IEEE International Conference on Robotics and Automation, Scottsdale, 14-19 May 1989, pp. 249-255.
 Q. K. Liang, D. Zhang, Q. J. Song, Y. J. Ge, H. B. Cao and Y. Ge, “Design and Fabrication of a Six-Dimensional Wrist Force/Torque Sensor Based on E-Type Membranes Compared to Cross Beams,” Measurement, Vol. 43, No. 10, 2010, pp. 1702-1719.
 A. G. Song, J. Wu, G. Qin and W. Y. Huang, “A Novel Self-Decoupled Four Degree-Of-Freedom Wrist Force/ Torque Sensor,” Measurement, Vol. 40, No. 9-10, 2007, pp. 883-891. doi:10.1016/j.measurement.2006.11.018
 Y. Haddab, Q. Chen, P. Lutz, “Improvement of Strain Gauges Micro-Forces Measurement Using Kalman Optimal Filtering,” Mechatronics, Vol. 19, No. 4, 2009, pp. 457-462. Hdoi:10.1016/j.mechatronics.2008.11.012
 D. Z. Xu, Z. C. Wu and Y. J. Ge, “The Solution to and the Analysis with Cross-Coupling Matrix of Six-Axis Wrist Force Sensor for Robot,” Chinese Journal of Scientific Instrument, Vol. 26, No. 1, 2005, pp. 75-80.
 Y. F. Xing and L. Bo, “Characteristic Equations and Closed-Form Solutions for Free Vibrations of Rectangular Mindlin Plates,” Acta Mechanica Solida Sinica, Vol. 22, No. 2, 2009, pp. 125-136.
 A. W. Leissa, “Vibration of Plates,” Office of Technology Utilization, Washington, 1969.
 S. Ilanko, “Comments on the Historical Bases of the Rayleigh and Ritz Methods,” Journal of Sound and Vibration, Vol. 319, No. 1-2, 2009, pp. 731-733.
 L. Dozio, “On the Use of the Trigonometric Ritz Method for General Vibration Analysis of Rectangular Kirchhoff Plates,” Thin-Walled Structure, Vol. 49. No. 1, 2011, pp. 129-144. Hdoi:10.1016/j.tws.2010.08.014
 X. H. Si, W. X. Lu and F. L. Chu, “Modal Analysis of Circular Plates with Radial Side Cracks and in Contact with Water on One Side Based on the Rayleigh-Ritz Method, ” Journal of Sound and Vibration, Vol. 331, No. 1, 2012, pp. 231-251. Hdoi:10.1016/j.jsv.2011.08.026
 J. N. Reddy, “An Introduction to the Finite Element Method,” 2nd Edition, McGraw-Hill, New York, 1993.
 I. Ramu and S. C. Mohanty, “Study on Free Vibration Analysis of Rectangular Plate Structures Using Finite Element Method,” Procedia Engineering, Vol. 38, No. 1, 2012, pp. 2758-2766. Hdoi:10.1016/j.proeng.2012.06.323
 G. Akhras and W. Li, “Stability and Free Vibration Analysis of Thick Piezoelectric Composite Plates Using Spline Finite Strip Method,” International Journal of Mechanical Sciences, Vol. 53, No. 8, 2011, pp. 575-584.
 C. Shu, W. X. Wu, H. Ding and C. M. Wang, “Free Vibration Analysis of Plates Using Least-Square-Based Finite Difference Method,” Computer Methods in Applied Mechanics and Engineering, Vol. 196, No. 7, 2007, pp. 1330-1343. Hdoi:10.1016/j.cma.2006.09.008
 P. Zhu and K. M. Liew, “Free Vibration Analysis of Moderately Thick Functionally Graded Plates by Local Kriging Meshless Method,” Composite Structures, Vol. 93, No. 11, 2011, pp. 2925-2944.
 S. A. Eftekhari and A. A. Jafari, “A Mixed Method for Free and Forced Vibration of Rectangular Plates,” Applied Mathematical Modeling, Vol. 36, No. 6, 2012, pp. 2814-2831. Hdoi:10.1016/j.apm.2011.09.050
 S. Timoshenko and S. Woinowsky-Krieger, “Theory of Plates and Shells,” 2nd Edition, McGraw-Hill, Inc., New York, 1959.
 R. K. Jain, “Vibrations of Circular Plates of Variable Thickness under an Inplane Force,” Journal of Sound and Vibration, Vol. 23, No. 4, 1972, pp. 407-414.