The smooth curvature model: An efficient representation of Euler-Bernoulli flexures as robot joints

IEEE Transactions on Robotics

Volumn 28, Issue 4, 2012, Pages 761-772

  Odhner, Lael U ^a   Dollar, Aaron M ^a  

^a YALE UNIVERSITY   (United States)

Author keywords

Beam bending; flexible; flexures; joints; robot

Indexed keywords

BEAM BENDING; BUCKLING LOADS; COMPUTATIONALLY EFFICIENT; CONTINUUM MODEL; EULER-BERNOULLI; FINITE ELEMENT; FLEXIBLE; FLEXURE HINGE; FLEXURE JOINTS; FLEXURES; HOMOGENEOUS TRANSFORMATIONS; JACOBIANS; JOINT KINEMATICS; JOINT MODELS; LARGE DEFORMATIONS; LOW-DIMENSIONAL MODELS; LOW-ORDER POLYNOMIALS; NUMERICAL INTEGRATIONS; RIGID LINKS; ROBOT JOINT; THREE PARAMETERS; TRADITIONAL JOINTS;

BUCKLING; CONTINUUM MECHANICS; HINGES; JOINTS (STRUCTURAL COMPONENTS); ROBOTS;

BENDING (DEFORMATION);

EID: 84865021125     PISSN: 15523098     EISSN: None     Source Type: Journal    
DOI: 10.1109/TRO.2012.2193232     Document Type: Conference Paper

References (31)

1. A. M. Dollar and R. D. Howe, "The highly adaptive SDM hand: Design and performance evaluation," Int. J. Robot. Res., vol. 29, pp. 585-597, 2010.
2. F. Lotti, P. Tiezzi, G. Vassura, L. Biagiotti, G. Palli, and C. Melchiorri, "Development of UB hand 3: Early results," in Proc. IEEE Int. Conf. Robot. Autom., 2005, pp. 4499-4504.
3. J. G. Cham, S. A. Bailey, J. E. Clark, R. J. Full, and M. R. Cutkosky, "Fast and robust: Hexapedal robots via shape deposition manufacturing," Int. J. Robot. Res., vol. 21, no. 10-11, pp. 869-882, 2002.
4. R. J. Wood, S. Avadhanula, R. Sahai, E. Steltz, and R. S. Fearing, "Microrobot design using fiber reinforced composites," ASME J. Mech. Design, vol. 130, no. 5, p. 052304, May 2008.
5. A. M. Dollar and R. D. Howe, "Towards grasping in unstructured environments: Grasper compliance and configuration optimization," Adv. Robot., vol. 19, no. 5, pp. 523-543, 2005. (Pubitemid 40893191)
6. R. Digiantonio and G. Lawrence, "Two-shot molding of thermoplastic elastomers," in Proc. SPE Annu. Technol. Conf., 1992, pp. 851-853.
7. R. Merz, F. Prinz, K. Ramaswami, M. Terk, and L. Weiss, "Shape deposition manufacturing," in Proc. Solid Freeform Fabricat. Symp., 1994, vol. 5, pp. 1-8.
8. A. Midha, T. Norton, and L. Howell, "On the nomenclature, classification, and abstractions ofcompliant mechanisms," Trans. ASME, vol. 116, no. 1, pp. 270-280, 1994.
9. H. J. Su, "A pseudorigid-body 3R model for determining large deflection of cantilever beams subject to tip loads," J. Mechan. Robot., vol. 1, no. 2, p. 021008, 2009.
10. B. Horn, "The curve of least energy," ACM Trans. Math. Softw., vol. 9, no. 4, pp. 441-460, 1983.
11. A. Macchelli, C. Melchiorri, and S. Stramgioli, "Port-based modeling and simulation of mechanical systems with rigid and flexible links," IEEE Trans. Robot., vol. 25, no. 5, pp. 1016-1029, Oct. 2009.
12. E. Bayo, "A finite-element approach to control the end-point motion of a single-link flexible robot," J. Robot. Syst., vol. 4, no. 1, pp. 63-75, 1986.
13. M. Hannan and I. Walker, "Kinematics and the implementation of an elephant's trunk manipulator and other continuum style robots," J. Robot. Syst., vol. 20, no. 2, pp. 45-63, 2003.
14. B. A. Jones and I. D. Walker, "Kinematics for multisection continuum robots," IEEE Trans. Robot., vol. 22, no. 1, pp. 43-55, Feb. 2006. (Pubitemid 43245255)
15. S. Timoshenko and D. Young, Advanced Dynamics. New York: McGraw-Hill, 1948, pp. 205-207.
16. A. DeLuca and B. Siciliano, "Closed-form dynamic model of planar multilink lightweight robots," IEEE Trans. Syst., Man, Cybern., vol. 21, no. 4, pp. 826-839, Jul./Aug. 1991. (Pubitemid 23616565)
17. L. U. Odhner and A. M. Dollar, "The smooth curvature flexure model: An accurate, low-dimensional approach for robot analysis," in Proc. Robot.: Sci. Syst. VI, 2010, pp. 137-144.
18. L. U. Odhner and A. M. Dollar, "Fast, accurate models for predicting the compliance of elastic flexure-jointed robots," presented at the ASME Int. Design Eng. Tech. Conf. Comput., In. Eng. Conf., Montreal, QC, Canada, 2010.
19. J. Denavit and R. S. Hartenberg, "A kinematic notation for lower-pair mechanisms based on matrices," ASME J. Appl. Mech, vol. 23, pp. 215-221, 1955.
20. R. Murray, Z. Li, and S. Sastry, A Mathematical Introduction to Robotic Manipulation. Boca Raton, FL: CRC, 1994, pp. 39-45.
21. L. L. Howell, Compliant Mechanisms. Hoboken, NJ: Wiley-Interscience, 2001.
22. G. Chirikjian and J. Burdick, "A modal approach to hyper-redundant manipulator kinematics," IEEE Trans. Robot. Autom., vol. 10, no. 3, pp. 343-354, Jun. 1994.
23. B. Asker, "The spline curve, a smooth interpolating function used in numerical design of ship-lines," BIT Numerical Math., vol. 2, no. 2, pp. 76-82, 1962.
24. R. L. Levien, "From spiral to spline: Optimal techniques in interactive curve design," Ph.D. dissertation, Dept. Elec. Eng. Comp. Sci., Univ. California, Berkeley, 2009.
25. W. Press, S. Teukolsky, W. Vetterling, and B. Flannery, Numerical Recipes in C, 2nd ed. Cambridge, U.K.: Cambridge Univ. Press, 1992, pp. 190-192.
26. R. Levien, "The elastica:Amathematical history," Univ. California, Berkeley, Tech. Rep. No. UCB/EECS-2008-103, 2008.
27. H. Hanafusa and H. Asada, "Stable prehension by a robot hand with elastic fingers," in Proc. 7th Int. Symp. Ind. Robots, 1977, pp. 361-368.
28. M. R. Cutkosky and I. Kao, "Computing and controlling compliance of a robotic hand," IEEE Trans. Robot. Autom., vol. 5, no. 2, pp. 151-165, Apr. 1989.
29. R. W. Brockett and A. Stokes, "On the synthesis of compliant mechanisms," in Proc. IEEE Int. Conf. Robot. Autom., 1991, pp. 2168-2173. (Pubitemid 21716997)
30. J. K. Salisbury, "Active stiffness control of a manipulator in Cartesian coordinates," in Proc. 19th IEEE Conf. Decision Control Including Symp. Adaptive Processes, 1980, Dec. 1980, vol. 19, pp. 95-100. (Pubitemid 11475605)
31. S. Crandall, C. Dahl, and T. Lardner, An Introduction to the Mechanics of Solids, 2nd ed. New York: McGraw-Hill, 1999, p. 587.