Research Papers

Modular Advantage and Kinematic Decoupling in Gravity Compensated Robotic Systems

[+] Author and Article Information
Nick Eckenstein

e-mail: neck@seas.upenn.edu

Mark Yim

e-mail: yim@grasp.upenn.edu
Department of Mechanical Engineering,
University of Pennsylvania,
Philadelphia, PA 19104

Contributed by the Mechanisms and Robotics Committee of ASME for publication in the JOURNAL OF MECHANISMS AND ROBOTICS. Manuscript received July 7, 2011; final manuscript received July 30, 2013; published online October 4, 2013. Assoc. Editor: Vijay Kumar.

J. Mechanisms Robotics 5(4), 041013 (Oct 04, 2013) (10 pages) Paper No: JMR-11-1076; doi: 10.1115/1.4025218 History: Received July 07, 2011; Revised July 30, 2013

Two new designs for gravity compensated modular robotic systems are presented and analyzed. The gravity compensation relies on using zero-free-length springs approximated by a cable and pulley system. Simple yet powerful parallel four-bar modules enable the low-profile self-contained modules with sequential gravity compensation using the spring method for motion in a vertical plane. A second module that is formed as a parallel six-bar mechanism adds a horizontal motion to the previous system that also yields a complete decoupling of position and orientation of the distal end of a serial chain. Additionally, we introduce the concept of vanishing effort where as the number of modules that comprise an articulated serial chain increases, the actuation authority required at any joint reduces. Essentially, this results in a method for distributing actuation along the length of an articulated chain. Prototypes were designed and constructed validating the analysis and accomplishing the functions of a general serial-type manipulator arm.

Copyright © 2013 by ASME
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Shen, W.-M., Krivokon, M., Chiu, H., Everist, J., Rubenstein, M., and Venkatesh, J., 2006, “Multimode Locomotion via SuperBot Reconfigurable Robots,” Auton. Rob., 20, pp. 165–177. [CrossRef]
Castano, A., Behar, A., and Will, P., 2002, “The Conro Modules for Reconfigurable Robots,” Mechatronics, IEEE/ASME Transactions, 7(4), pp. 403–409. [CrossRef]
Jorgensen, M., Ostergaard, E., and Lund, H., 2004, “Modular ATRON: Modules for a Self-Reconfigurable Robot,” Proceedings of 2004 IEEE/RSJ International Conference on Intelligent Robots and Systems, IROS 2004, Vol. 2, pp. 2068–2073.
Yim, M., Shen, W.-M., Salemi, B., Rus, D., Moll, M., Lipson, H., Klavins, E., and Chirikjian, G., 2007, “Modular Self-Reconfigurable Robot Systems [Grand Challenges of Robotics],” IEEE Rob. Autom. Mag., 14(1), pp. 43–52. [CrossRef]
Liu, G., Liu, Y., and Goldenberg, A., 2011, “Design, Analysis, and Control of a Spring-Assisted Modular and Reconfigurable Robot,” IEEE/ASME Trans. Mechatron., 16(4), pp. 695–706. [CrossRef]
Wyrobek, K., Berger, E., Van der Loos, H., and Salisbury, J., 2008, “Towards a Personal Robotics Development Platform: Rationale and Design of an Intrinsically Safe Personal Robot,” IEEE International Conference on Robotics and Automation, ICRA 2008, pp. 2165–2170.
Kazerooni, H., 1989, “Statically Balanced Direct Drive Manipulator,” Robotica, 7(02), pp. 143–149. [CrossRef]
Moore, B., Schico, J., and Gosselin, C., 2007, “Determination of the Complete Set of Statically Balanced Planar Four-Bar Mechanisms,” Report No. SFB F013 1, Universite Laval, Quebec, Quebec, QC.
Russo, A., Sinatra, R., and Xi, F., 2005, “Static Balancing of Parallel Robots,” Mech. Mach. Theory, 40(2), pp. 191–202. [CrossRef]
Fattah, A., and Agrawal, S. K., 2006, “On the Design of Reactionless 3-DOF Planar Parallel Mechanisms,” Mech. Mach. Theory, 41(1), pp. 70–82. [CrossRef]
Nathan, R., 1985, “A Constant Force Generation Mechanism,” ASME J. Mech., Transm., Autom. Des., 107(4), pp. 508–512. [CrossRef]
Ulrich, N., and Kumar, V., 1991, “Passive Mechanical Gravity Compensation for Robot Manipulators,” Proceedings of 1991 IEEE International Conference on Robotics and Automation, pp. 1536–1541.
Agrawal, S. K., and Fattah, A., 2004, “Gravity-Balancing of Spatial Robotic Manipulators,” 11th National Conference on Machines and Mechanisms (NaCoMM-2003), Mech. Mach. Theory, 39(12), pp. 1331–1344. [CrossRef]
Wisse, B., van Dorsser, W., Barents, R., and Herder, J., 2007, “Energy-Free Adjustment of Gravity Equilibrators Using the Virtual Spring Concept,” IEEE 10th International Conference on Rehabilitation Robotics, ICORR 2007, pp. 742–750.
van Dorsser, W. D., Barents, R., Wisse, B. M., and Herder, J. L., 2007, “Gravity-Balanced Arm Support With Energy-Free Adjustment,” ASME J. Med. Devices, 1(2), pp. 151–158. [CrossRef]
Barents, R., Schenk, M., van Dorsser, W. D., Wisse, B. M., and Herder, J. L., 2009, “Spring-to-Spring Balancing as Energy-Free Adjustment Method in Gravity Equilibrators,” ASME Conf. Proc., 2009(49040), pp. 689–700 [CrossRef].
van Dorsser, W. D., Barents, R., Wisse, B. M., Schenk, M., and Herder, J. L., 2007, “Energy-Free Adjustment of Gravity Equilibrators Using the Possibility of Adjusting the Spring Stiffness,” IEEE 10th International Conference on Rehabilitation Robotics, ICORR 2007, pp. 1839–1846.
Monsarrat, B., and Gosselin, C., 2003, “Workspace Analysis and Optimal Design of a 3-Leg 6-DOF Parallel Platform Mechanism,” IEEE Trans. Rob. Autom., 19(6), pp. 954–966. [CrossRef]
Gosselin, C. M., 1999, “Static Balancing of Spherical 3-DOF Parallel Mechanisms and Manipulators,” Int. J. Rob. Res., 18(8), pp. 819–829. [CrossRef]
Wang, J., and Gosselin, C. M., 1999, “Static Balancing of Spatial Three-Degree-of-Freedom Parallel Mechanisms,” Mech. Mach. Theory, 34(3), pp. 437–452. [CrossRef]
Lin, P.-Y., Shieh, W.-B., and Chen, D.-Z., 2010, “Design of a Gravity-Balanced General Spatial Serial-Type Manipulator,” ASME J. Mech. Rob., 2(3), p. 031003. [CrossRef]
Lin, P.-Y., 2012, “Design of Statically Balanced Spatial Mechanisms With Spring Suspensions,” ASME J. Mech. Rob., 4(2), p. 021015. [CrossRef]
Gosselin, C. M., 2006, “Adaptive Robotic Mechanical Systems: A Design Paradigm,” ASME J. Mech. Des., 128(1), pp. 192–198. [CrossRef]
Agrawal, S., Banala, S., and Fattah, A., 2006, “A Gravity Balancing Passive Exoskeleton for the Human Leg,” Proceedings of Robotics: Science and Systems.
Fitch, R., and Butler, Z., 2008, “Million Module March: Scalable Locomotion for Large Self-Reconfiguring Robots,” Int. J. Rob. Res., 27(3-4), pp. 331–343. [CrossRef]
Park, M., Chitta, S., Teichman, A., and Yim, M., 2008, “Automatic Configuration Recognition Methods in Modular Robots,” Int. J. Rob. Res., 27(3-4), pp. 403–421. [CrossRef]
Soper, R., Mook, D., and Reinholz, C., 1997, “Vibration of Nearly Perfect Spring Equilibrators,” Proceedings of ASME DETC, Paper No. DAC-3768.
Herder, J. L., 2001, “Energy-Free Systems: Theory, Conception, and Design of Statically Balanced Spring Mechanisms,” Ph.D. thesis, TU Delft, Delft University of Technology, The Netherlands.
Sastra, J., Chitta, S., and Yim, M., 2009, “Dynamic Rolling for a Modular Loop Robot,” Int. J. Rob. Res., 28(6), pp. 758–773. [CrossRef]
White, P., 2011, “Miniaturization Methods for Modular Robotics: External Actuation and Dielectric Elastomer Actuation,” Ph.D. thesis, University of Pennsylvania, Philadelphia, PA.
Christensen, D., Campbell, J., and Stoy, K., 2010, “Anatomy-Based Organization of Morphology and Control in Self-Reconfigurable Modular Robots,” Neural Comput. Appl., 19, pp. 787–805. [CrossRef]
Castano, A., and Will, P., 2002. A Polymorphic Robot Team, A K Peters/CRC Press, Boca Raton, FL, pp. 139–160.
Kutzer, M. D. M., Moses, M. S., Brown, C. Y., Scheidt, D. H., Chirikjian, G. S., and Armand, M., 2010, “Design of a New Independently-Mobile Reconfigurable Modular Robot,” 2010 IEEE International Conference on Robotics and Automation (ICRA), pp. 2758–2764.
Zykov, V., Chan, A., and Lipson, H., 2007, “Molecubes: An Open-Source Modular Robotics Kit,” IROS-2007 Self-Reconfigurable Robotics Workshop.
Murata, S., Yoshida, E., Kamimura, A., Kurokawa, H., Tomita, K., and Kokaji, S., 2002, “M-TRAN: Self-Reconfigurable Modular Robotic System,” IEEE/ASME Trans. Mechatron., 7(4), pp. 431–441. [CrossRef]
Kurokawa, H., Kamimura, A., Yoshida, E., Tomita, K., Murata, S., and Kokaji, S., 2002, “Self-Reconfigurable Modular Robot (M-TRAN) and Its Motion Design,” 7th International Conference on Control, Automation, Robotics and Vision, ICARCV 2002, Vol. 1, pp. 51–56.
Yim, M., Homans, S., and Roufas, K., 2001, “Climbing With Snake-Like Robots,” IFAC Workshop on Mobile Robot Technology, pp. 21–22.
Yim, M., Duff, D., and Roufas, K., 2000, “PolyBot: A Modular Reconfigurable Robot,” Proceedings of IEEE International Conference on Robotics and Automation, ICRA’00, Vol. 1, pp. 514–520.
Yim, M., Roufas, K., Duff, D., Zhang, Y., Eldershaw, C., and Homans, S., 2003, “Modular Reconfigurable Robots in Space Applications,” Auton. Rob., 14, pp. 225–237. [CrossRef]
Salemi, B., Moll, M., and Shen, W., 2007, “SUPERBOT: A Deployable, Multi-Functional, and Modular Self-Reconfigurable Robotic System,” IEEE/RSJ International Conference on Intelligent Robots and Systems, IEEE, pp. 3636–3641.


Grahic Jump Location
Fig. 1

A basic gravity compensation mechanism for a rotational joint. The mass of the arm is simplified to a point mass.

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Fig. 2

Full gravity compensated four-bar system, showing joints and labels. Points marked with “X” correspond to P0, P1, P2, etc.

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Fig. 3

Typical configuration of larger extended system, with simplified joint representation

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Fig. 4

Traditional arm, with same (functional) joint sequence as in four-bar system.

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Fig. 5

3D model of six-link parallel manipulator Inset: Universal joint oriented as necessary

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Fig. 6

Comparison of systems, simple and decomposed four-bar mechanisms and single-bar

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Fig. 7

Comparison of Kinematic Profiles

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Fig. 8

Demonstration of Inertia Calculation Principles Arcs represent curvature of path taken by the point touching the frame. All points on arms not attached to the base rotate about some point L away.

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Fig. 9

System Hanging Passively

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Fig. 10

Comparison of error for spring-pulley systems

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Fig. 11

Systems compared in Table 3 are a gravity compensated arm (top), uncompensated CKBot modules with extended links (middle), and a CKBot chain without extended links (bottom). Each circle represents a joint or CkBot.

Grahic Jump Location
Fig. 12

Second Prototype extended, hanging passively




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