Research Papers

Kinematics for an Actuated Flexible n-Manifold

[+] Author and Article Information
Oded Medina

Department of Mechanical Engineering,
Ariel University,
Ariel 4076113, Israel
e-mail: odedmedina@gmail.com

Amir Shapiro

Department of Mechanical Engineering,
Ben-Gurion University,
Be'er Sheva 8410501, Israel
e-mail: ashapiro@bgu.ac.il

Nir Shvalb

Department of Industrial Engineering,
Ariel University,
Ariel 4076113, Israel
e-mail: nirsh@ariel.ac.il

Manuscript received February 8, 2015; final manuscript received July 27, 2015; published online November 24, 2015. Assoc. Editor: Jun Ueda.

J. Mechanisms Robotics 8(2), 021009 (Nov 24, 2015) (8 pages) Paper No: JMR-15-1028; doi: 10.1115/1.4031301 History: Received February 08, 2015; Revised July 27, 2015; Accepted August 08, 2015

Recent years show an increasing interest in flexible robots due to their adaptability merits. This paper introduces a novel set of hyper-redundant flexible robots which we call actuated flexible manifold (AFM). The AFM is a two-dimensional hyper-redundant grid surface embedded in 2 or 3. Theoretically, such a mechanism can be manipulated into any continuous smooth function. We introduce the mathematical framework for the kinematics of an AFM. We prove that for a nonsingular configuration, the number of degrees of freedom (DOF) of an AFM is simply the number of its grid segments. We also show that for a planar rectangular grid, every nonsingular configuration that is also energetically stable is isolated. We show how to calculate the forward and inverse kinematics for such a mechanism. Our analysis is also applicable for three-dimensional hyper-redundant structures as well. Finally, we demonstrate our solution on some actuated flexible grid-shaped surfaces.

Copyright © 2016 by ASME
Your Session has timed out. Please sign back in to continue.


Shvalb, N. , Moshe, B. B. , and Medina, O. , 2013, “ A Real-Time Motion Planning Algorithm for a Hyper-Redundant Set of Mechanisms,” Robotica, 31(8), pp. 1327–1335. [CrossRef]
Shapiro, A. , Greenfield, A. , and Choset, H. , 2007, “ Frictional Compliance Model Development and Experiments for Snake Robot Climbing,” IEEE International Conference on Robotics and Automation, Rome, Italy, pp. 574–579.
Ota, T. , Degani, A. , Zubiate, B. , Wolf, A. , Choset, H. , Schwartzman, D. , and Zenati, M. A. , 2006, “ Epicardial Atrial Ablation Using a Novel Articulated Robotic Medical Probe Via a Percutaneous Subxiphoid Approach,” Innovations, 1(6), pp. 335–340. [PubMed]
Yamada, H. , Takaoka, S. , and Hirose, S. , 2013, “ A Snake-Like Robot for Real-World Inspection Applications (The Design and Control of a Practical Active Cord Mechanism),” Adv. Rob., 27(1), pp. 47–60. [CrossRef]
Chirikjian, G. S. , 1997, “ Inverse Kinematics of Binary Manipulators Using a Continuum Model,” J. Intell. Rob. Syst., 19(1), pp. 5–22. [CrossRef]
Hamerly, G. , and Elkan, C. , 2002, “ Alternatives to the k-Means Algorithm That Find Better Clusterings,” 11th International Conference on Information and Knowledge Management, ACM, pp. 600–607.
Kim, S. , Laschi, C. , and Trimmer, B. , 2013, “ Soft Robotics: A Bioinspired Evolution in Robotics,” Trends Biotechnol., 31(5), pp. 287–294. [CrossRef] [PubMed]
Onal, C. D. , Chen, X. , Whitesides, G. M. , and Rus, D. , 2011, “ Soft Mobile Robots With On-Board Chemical Pressure Generation,” 15th International Symposium on Robotics Research (ISRR), Flagstaff, AZ, Aug. 28–Sept. 1.
Shepherd, R. , Ilievski, F. , Choi, W. , Morin, S. , Stokes, A. , Mazzeo, A. , Chen, X. , Wang, M. , and Whitesides, G. , 2011, “ Multigait Soft Robot,” Proc. Natl. Acad. Sci., 108(51), pp. 20400–20403. [CrossRef]
Kim, S. , Hawkes, E. , Choy, K. , Joldaz, M. , Foleyz, J. , and Wood, R. , 2009, “ Micro Artificial Muscle Fiber Using NiTi Spring for Soft Robotics,” IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS 2009), St. Louis, MO, Oct. 10–15, pp. 2228–2234.
Laschi, C. , Cianchetti, M. , Mazzolai, B. , Margheri, L. , Follador, M. , and Dario, P. , 2012, “ Soft Robot Arm Inspired by the Octopus,” Adv. Rob., 26(7), pp. 709–727. [CrossRef]
Calisti, M. , Giorelli, M. , Levy, G. , Mazzolai, B. , Hochner, B. , Laschi, C. , and Dario, P. , 2011, “ An Octopus-Bioinspired Solution to Movement and Manipulation for Soft Robots,” Bioinspiration Biomimetics, 6(3), p. 036002. [CrossRef] [PubMed]
Zheng, T. , Branson, D. T. , Guglielmino, E. , Kang, R. , Cerda, G. A. M. , Cianchetti, M. , Follador, M. , Godage, I . S. , and Caldwell, D. G. , 2013, “ Model Validation of an Octopus Inspired Continuum Robotic Arm for Use in Underwater Environments,” ASME J. Mech. Rob., 5(2), p. 021004. [CrossRef]
Trimmer, B. , 2014, “ A Journal of Soft Robotics: Why Now?,” Soft Rob., 1(1), pp. 1–4. [CrossRef]
Walker, I. , Dawson, D. , Flash, T. , Grasso, F. , Hanlon, R. , Hochner, B. , Kier, W. , Pagano, C. , Rahn, C. , and Zhang, Q. , 2005, “ Continuum Robot Arms Inspired by Cephalopods,” Proc. SPIE, 5804, pp. 303–314.
Trivedi, D. , Rahn, C. D. , Kier, W. M. , and Walker, I. D. , 2008, “ Soft Robotics: Biological Inspiration, State of the Art, and Future Research,” Appl. Bionics Biomech., 5(3), pp. 99–117. [CrossRef]
Reddy, J. N. , 2007, Theory and Analysis of Elastic Plates and Shells, CRC Press, Boca Raton, FL.
Ali, S. , Boyer, F. , and Porez, M. , 2011, “ Terrestrial Locomotion Modeling Bio-Inspired by Elongated Animals,” Procedia Comput. Sci., 7, pp. 317–319. [CrossRef]
Leyendecker, S. , and Kanso, E. , 2009, “ Locomotion of a Submerged Cosserat Beam,” ASME Paper No. DETC2009-87198.
Spillmann, J. , and Teschner, M. , 2009, “ Cosserat Nets,” IEEE Trans. Visualization Comput. Graph., 15(2), pp. 325–338. [CrossRef]
Popov, E. , 2001, “ Geometrical Modeling of Tent Fabric Structures With the Stretched Grid Method,” 11th International Conference on Computer Graphics and Vision (GRAPHICON2001), UNN, Nizhny Novgorod, Russia, Sept. 10–17, pp. 138–143.
Blanc, D. , and Shvalb, N. , 2012, “ Generic Singular Configurations of Linkages,” Topol. Appl., 159(3), pp. 877–890. [CrossRef]
Kelley, J. L. , and Stone, M. , 1955, General Topology, Vol. 233, van Nostrand, Princeton, NJ.
Merlet, J.-P. , 2012, Parallel Robots, Springer Science & Business Media, New York.
Warner, S. , 1990, Modern Algebra, Dover Publications, New York.
Blanc, D. , and Shvalb, N. , 2011, “ Actuations of Linkages and Their Singularities,” Ariel University. Ariel, Israel, epub.
Murray, R. M. , Li, Z. , Sastry, S. S. , and Sastry, S. S. , 1994, A Mathematical Introduction to Robotic Manipulation, CRC Press, Boca Raton, FL.


Grahic Jump Location
Fig. 1

An 8×8×2 AFM grid in its initial configuration

Grahic Jump Location
Fig. 2

Crawling on the constraints. (A) Crawling on a cylindrical constraint defined by a single segment length by projecting the desired direction v on n's null space, k, where n=∇f. Motion proceeds in the general direction of v′. (B) represents a configuration in which two segments lengths are to be met.

Grahic Jump Location
Fig. 3

A portion of the AFM grid which constitutes a double four-bar mechanism

Grahic Jump Location
Fig. 4

Relaxation procedure: reducing edge 7–8 in a planar AFM with no relaxation (a) and with relaxation (b), and (c) simultaneously reducing two edges in a three-dimensional AFM

Grahic Jump Location
Fig. 5

Relaxation procedure: (a) the upper and lower grids are taken to be identical, sampling the desire function, and keeping the upper and the lower grids at a given distance and (b) the relaxed mechanism with its (encircled) angles slightly changed

Grahic Jump Location
Fig. 6

An 8 × 8 grid and its configuration change due to three external forces

Grahic Jump Location
Fig. 7

Design III of an AFM. The SMA actuator is initially curved and aligns when actuated. Such a design enhances the ability of the segment's ends to change their mutual distance.

Grahic Jump Location
Fig. 8

Mechanical experimentations with design III compared with the simulation results. The root mean square given in link length units (of nodes positions in both the simulation and the real experimentation) was found to be 0.24.

Grahic Jump Location
Fig. 9

Design II of an AFM. A 24DOF manifold attains three configurations.

Grahic Jump Location
Fig. 10

The SMA beam model with 7DOF actuating two corner actuators

Grahic Jump Location
Fig. 11

The 12DOF manifold using linear servo motors



Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In