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TECHNICAL PAPERS

The Duality in Spatial Stiffness and Compliance as Realized in Parallel and Serial Elastic Mechanisms

[+] Author and Article Information
Shuguang Huang, Joseph M. Schimmels

Department of Mechanical and Industrial Engineering, Marquette University, Milwaukee, WI 53201-1881

J. Dyn. Sys., Meas., Control 124(1), 76-84 (Jan 21, 2000) (9 pages) doi:10.1115/1.1434273 History: Received January 21, 2000
Copyright © 2002 by ASME
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References

Ball, R. S., 1990, A Treatise on the Theory of Screws, Cambridge University Press, London.
Dimentberg, F. M., 1995, The Screw Calculus and its Applications in Mechanics. Foreign Technology Division, Wright-Patterson Air Force Base, Ohio. Document No. FTD-HT-23-1632-67.
Griffis,  M., and Duffy,  J., 1991, “Kinestatic Control: A Novel Theory for Simultaneously Regulating Force and Displacement,” ASME J. Mech. Des., 113, No. 4, pp. 508–515.
Patterson,  T., and Lipkin,  H., 1993, “Structure of Robot Compliance,” ASME J. Mech. Des., 115, No. 3, pp. 576–580.
Fasse,  E. D., and Breedveld,  P. C., 1998, “Modeling of Elastically Coupled Bodies: Part I—General Theory and Geometric Potential Function Method,” ASME J. Dyn. Syst., Meas., Control, 120, No. 4, pp. 496–500.
Fasse,  E. D., and Breedveld,  P. C., 1998, “Modeling of Elastically Coupled Bodies: Part II—Exponential and Generalized Coordinate Methods,” ASME J. Dyn. Syst., Meas., Control, 120, No. 4, pp. 501–506.
Chen,  S., and Kao,  I., 2000, “Conservative Congruence Transformation for Joint and Cartesian Stiffness Matrices of Robotic Hands and Fingers,” Int. J. Robot. Res., 19, No. 9, pp. 835–847, Sept.
Griffis,  M., and Duffy,  J., 1993, “Global Stiffness Modeling of a Class of Simple Compliant Couplings,” Mech. Mach. Theory, 28, No. 2, pp. 207–224.
Ciblank, N. and Lipkin, H. 1994, “Asymmetric Cartesian Stiffness for the Modeling of Compliant Robotic Systems,” The ASME 23rd Biennial Mechanisms Conference, Design Engineering Division DE-Vol. 72, New York, NY.
Howard,  W. S., Zefran,  M., and Kumar,  V., 1996, “On the 6×6 Stiffness Matrix for Three Dimensional Motions,” Mech. Mach. Theory, 33, pp. 389–408.
Loncaric, J.,1985, Geometrical Analysis of Compliant Mechanisms in Robotics. PhD thesis, Harvard University, Cambridge, MA.
Huang,  S., and Schimmels,  J. M., 1998, “The Bounds and Realization of Spatial Stiffnesses Achieved with Simple Springs Connected in Parallel,” IEEE Trans. Rob. Autom., 14, No. 3, June, pp. 466–475.
Huang,  S., and Schimmels,  J. M., 2000, “The Bounds and Realization of Spatial Compliances Achieved with Simple Serial Elastic Mechanisms,” IEEE Trans. Rob. Autom., 16, No. 1, Feb., pp. 99–103.
Roberts,  R. G., 1999, “Minimal Realization of a Spatial Stiffness Matrix with Simple Springs Connected in Parallel,” IEEE Trans. Rob. Autom., 15, No. 5, Oct., pp. 953–958.
Ciblak, N. and Lipkin, H.,1999, “Synthesis of Cartesian Stiffness for Robotic Applications,” Proceedings of the IEEE International Conference on Robotics and Automation, pp. 2147–2152, Detroit, MI, May.
Huang,  S., and Schimmels,  J. M., 1990, “Achieving an Arbitrary Spatial Stiffness with Springs Connected in Parallel,” ASME J. Mech. Des., 120, No. 4, Dec., pp. 520–526.
Huang,  S., and Schimmels,  J. M., 2000, “The Eigenscrew Decomposition of Spatial Stiffness Matrices,” IEEE Trans. Rob. Autom., 16, pp. 146–156, Apr.
Huang, S. and Schimmels, J. M., 1999, “The Degree of Translational-Rotational Coupling of a Spatial Stiffness,” Proceedings of the ASME International Mechanical Engineering Congress and Exposition, Nashville, TN, Nov., pp. 787–794.
Huang,  S., and Schimmels,  J. M., 2001, “A Classification of Spatial Stiffness Based on the Degree of Translational-Rotational Coupling,” ASME J. Mech. Des., 123, No. 3, Sept., pp. 353–358.
Roberts,  R. G., 2000, “Minimal Realization of an Arbitrary Spatial Stiffness Matrix with a Parallel Connection of Simple Springs and Complex Springs,” IEEE Trans. Rob. Autom., 16, Oct., pp. 603–608.
Craig, J. J., 1989, Introduction to Robotics: Mechanics and Control, Addison-Wesley NY.
Huang, S., 1998, The Analysis and Synthesis of Spatial Compliance. PhD thesis, Marquette University, Milwaukee, WI.
Patterson,  T., and Lipkin,  H., 1993, “A Classification of Robot Compliance,” ASME J. Mech. Des., 115, No. 3, pp. 581–584.

Figures

Grahic Jump Location
Helical joints loaded with springs. Figure 1(a) illustrates a helical joint loaded with a rotational spring. Figure 1(b) illustrates a helical joint loaded with a translational spring. The pitch of the helical joint is h in length/radian.
Grahic Jump Location
Eigenstructure of an elastic behavior. Figure 2(a) illustrates an interpretation of the spatial elastic behavior with its parallel eigen-mechanism. The body is suspended by 6 screw springs associated with the eigenscrews and eigenstiffnesses of the stiffness matrix. Figure 2(b) illustrates an interpretation of the spatial elastic behavior with the serial eigen-mechanism. The rigid body is suspended by a serial mechanism consisting of 6 elastic helical joints associated with the eigenscrews and eigencompliances of the compliance matrix.

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