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TECHNICAL PAPERS

Dynamic Analysis of Rectilinear Motion of a Self-Propelling Disk With Unbalance Masses

[+] Author and Article Information
T. Das, R. Mukherjee

Department of Mechanical Engineering, Michigan State University, 2555 Engineering Building, East Lansing, MI 48824-1226

J. Appl. Mech 68(1), 58-66 (Apr 16, 2000) (9 pages) doi:10.1115/1.1344903 History: Received June 24, 1999; Revised April 16, 2000
Copyright © 2001 by ASME
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References

Brown,  H. B., and Xu,  Y., 1997, “A Single-Wheel Gyroscopically Stabilized Robot,” IEEE Robotics and Automation Magazine, 4, No. 3, pp. 39–44.
Koshiyama,  A., and Yamafuji,  K., 1993, “Design and Control of All-Direction Steering Type Mobile Robot,” Int. J. Robot. Res., 12, No. 5, pp. 411–419.
Halme, A., Schonberg, T., and Wang, Y., 1996, “Motion Control of a Spherical Mobile Robot,” Proc. AMC’96-MIE.
Bicchi, A., Balluchi, A., Prattichizzo, D., and Gorelli, A., 1997, “Introducing the Sphericle: An Experimental Testbed for Research and Teaching in Nonholonomy,” Proc. IEEE Int. Conference on Robotics and Automation, pp. 2620–2625.
Mukherjee, R., and Minor, M., 1999, “A Simple Motion Planner for a Spherical Mobile Robot,” IEEE/ASME Int. Conference on Advanced Intelligent Mechatronics, Atlanta, GA.
Ehlers,  G. W., Yavin,  Y., and Frangos,  C., 1996, “On the Motion of a Disk Rolling on a Horizontal Plane: Path Controllability and Feedback Control,” Comput. Methods Appl. Mech. Eng., 137, pp. 345–356.
Yavin,  Y., 1997, “Inclination Control of the Motion of a Rolling Disk by Using a Rotor,” Comput. Methods Appl. Mech. Eng., 146, pp. 253–263.
Yavin,  Y., 1999, “Stabilization and Motion Control of the Motion of a Rolling Disk by Using Two Rotors Fixed Along Its Axis,” Comput. Methods Appl. Mech. Eng., 169, pp. 107–122.
Getz, N., 1995, “Internal Equilibrium Control of a Bicycle,” 34th IEEE Conference on Decision and Control, New Orleans, LA.
Rui, C., and McClamroch, N. H., 1995, “Stabilization and Asymptotic Path Tracking of a Rolling Disk,” 34th IEEE Conference on Decision and Control, New Orleans, LA.
Kirk, D. E., 1970, Optimal Control Theory: An Introduction, Prentic-Hall, Englewood Cliffs, NJ.
Greenwood, D. T., 1988, Principles of Dynamics, Prentice-Hall, Englewood Cliffs, NJ.

Figures

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The disk with reciprocating masses
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Different phases in the leading half of the disk
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A particular configuration of the reciprocating masses
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Shaded region indicates feasible parameter values for the solution in Section 3.2
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Comparison of the approximate and optimal solutions for a disk of unity radius
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Shaded region indicates feasible parameter values for the solution in Section 4.2
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A geometric interpretation of the motion of the center of mass
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Variation of trajectory parameters during a sinusoidal variation of acceleration
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Normalized trajectories of the unbalance masses at two specific instants of time

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