This paper presents a new method for the realization of a planar compliant behavior with an elastic mechanism. The mechanisms considered are parallel with symmetric geometry. We show that any planar stiffness matrix can be realized using a parallel mechanism with four line springs connected symmetrically. Among the four springs, two are identical parallel springs equidistant from the stiffness center, and the other two identical springs intersect at the stiffness center. A synthesis procedure based on geometry is presented and mechanism compactness is discussed.
Issue Section:
Research Papers
References
1.
Huang
, S.
, and Schimmels
, J. M.
1998, “The Bounds and Realization of Spatial Stiffnesses Achieved With Simple Springs Connected in Parallel
,” IEEE Trans. Rob. Automat.
14
(3
), pp. 466
–475
.2.
Huang
, S.
, and Schimmels
, J. M.
, 1998, “Achieving an Arbitrary Spatial Stiffness With Springs Connected in Parallel
,” ASME J. Mech. Des.
, 120
(4
), pp. 520
–526
.3.
Ball
, R. S.
1900, A Treatise on the Theory of Screws
, Cambridge University Press
, London
.4.
Dimentberg
, F. M.
, 1965, “The Screw Calculus and its Applications in Mechanics
,” Foreign Technology Division, Wright-Patterson Air Force Base, Dayton, OH. Document No. FTD-HT-23-1632-67.5.
Griffis
, M.
, and Duffy
, J.
, 1991, “Kinestatic Control: A Novel Theory for Simultaneously Regulating Force and Displacement
,” ASME J. Mech. Des.
, 113
(4
), pp. 508
–515
.6.
Patterson
, T.
, and Lipkin
, H.
, 1993, “Structure of Robot Compliance
,” ASME J. Mech. Des.
115
(3
), pp. 576
–580
.7.
Loncaric
, J.
, 1985, “Geometrical Analysis of Compliant Mechanisms in Robotics
,” Ph.D. thesis, Harvard University, Cambridge, MA.8.
Loncaric
, J.
, 1987, “Normal Forms of Stiffness and Compliance Matrices
,” IEEE J. Rob. Autom.
3
(6
), pp. 567
–572
.9.
Griffis
, M.
, and Duffy
, J.
, 1993, “Global Stiffness Modeling of a Class of Simple Compliant Couplings
,” Mech. Mach. Theory
, 28
(2
), pp. 207
–224
.10.
Ciblak
, N.
, and Lipkin
, H.
, 1994, “Asymmetric Cartesian Stiffness for the Modelling of Compliant Robotic Systems
,” The ASME 23rd Biennial Mechanisms Conference
, Design Engineering Division DE-Vol. 72.11.
Howard
, W. S.
,Zefran
, M.
, and Kumar
, V.
, 1998, “On the 6×6 Stiffness Matrix for Three Dimensional Motions
,” Mech. Mach. Theory
, 33
(4
), pp. 389
–408
.12.
Chen
, S.
, and Kao
, I.
, 2000, “Conservative Congruence Transformation for Joint and Cartesian Stiffness Matrices of Robotic Hands and Fingers
,” Int. J. Rob. Res.
, 19
(9
), pp. 835
–847
.13.
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
(1
), pp. 99
–103
.14.
Roberts
, R. G.
, 1999, “Minimal Realization of a Spatial Stiffness Matrix With Simple Springs Connected in Parallel
,” IEEE Trans. Rob. Autom.
, 15
(5
), pp. 953
–958
.15.
Ciblak
, N.
, and Lipkin
, H.
, 1999, “Synthesis of Cartesian Stiffness for Robotic Applications
,” Proceedings of the IEEE International Conference on Robotics and Automation
.16.
Huang
, S.
, and Schimmels
, J. M.
, 2000, “The Eigenscrew Decomposition of Spatial Stiffness Matrices
,” IEEE Trans. Rob. Autom.
16
(2
), pp. 146
–156
.17.
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
(3
), pp. 353
–358
.18.
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
(5
), pp. 603
–608
.19.
Huang
, S.
, and Schimmels
, J. M.
, 2001, “Minimal Realizations of Spatial Stiffnesses With Parallel or Serial Mechanisms Having Concurrent Axes
,” J. Rob. Syst.
, 18
(3
), pp. 135
–246
.20.
Huang
, S.
, and Schimmels
, J. M.
, 2002, “Realization of Those Elastic Behaviors That Have Compliant Axes in Compact Elastic Mechanisms
,” J. Rob. Syst.
19
(3
), pp. 143
–154
.21.
Choi
, K.
,Jiang
, S.
, and Li
, Z.
, 2002, “Spatial Stiffness Realization With Parallel Springs Using Geometric Parameters
,” IEEE Trans. Rob. Autom.
, 18
(3
), pp. 264
–284
.22.
Hong
, M. B.
, and Choi
, Y. J.
, 2009, “Screw System Approach to Physical Realization of Stiffness Matrix With Arbitrary Rank
,” ASME J. Mech. Rob.
, 1
(2
), p. 021007
.23.
Su
, H.-J.
, Dorozhkin
, D. V.
, and Vance
, J. M.
, 2009, “A Screw Theory Approach for the Conceptual Design of Flexible Joints for Compliant Mechanisms
,” ASME J. Mech. Rob.
, 1
(4
), p. 041009
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