Dexterous magnetic manipulation of ferromagnetic objects is well established, with three to six degrees of freedom possible depending on object geometry1. There are objects for which non-contact dexterous manipulation is desirable that do not contain an appreciable amount of ferromagnetic material but do contain electrically conductive material. Time-varying magnetic fields generate eddy currents in conductive materials2,3,4, with resulting forces and torques due to the interaction of the eddy currents with the magnetic field. This phenomenon has previously been used to induce drag to reduce the motion of objects as they pass through a static field5,6,7,8, or to apply force on an object in a single direction using a dynamic field9,10,11, but has not been used to perform the type of dexterous manipulation of conductive objects that has been demonstrated with ferromagnetic objects. Here we show that manipulation, with six degrees of freedom, of conductive objects is possible by using multiple rotating magnetic dipole fields. Using dimensional analysis12, combined with multiphysics numerical simulations and experimental verification, we characterize the forces and torques generated on a conductive sphere in a rotating magnetic dipole field. With the resulting model, we perform dexterous manipulation in simulations and physical experiments.
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All data generated and scripts for analyses during this study are included in the published article and can be found using the following link: https://osf.io/uk3rx/.
Abbott, J. J., Diller, E. & Petruska, A. J. Magnetic methods in robotics. Annu. Rev. Control Robot. Auton. Syst. 3, 57–90 (2020).
Hertz, H. Miscellaneous Papers Chapter 2 [transl. Jones, D. E. & Schott, G. A.] (Macmillan, 1896).
Griffiths, D. J. Introduction to Electrodynamics 4th edition (Cambridge Univ. Press, 2017).
Nagel, J. R. Induced eddy currents in simple conductive geometries: mathematical formalism describes the excitation of electrical eddy currents in a time-varying magnetic field. IEEE Antennas Propag. Mag. 3, 81–88 (2018).
Youngquist, R. C., Nurge, M. A., Starr, S. O., Leve, F. A. & Peck, M. A. A slowly rotating hollow sphere in a magnetic field: first steps to de-spin a space object. Am. J. Phys. 84, 181–191 (2016).
Nurge, M. A., Youngquist, R. C. & Starr, S. O. A thick-walled sphere rotating in a uniform magnetic field: the next step to de-spin a space object. Am. J. Phys. 85, 596–610 (2017).
Nurge, M. A., Youngquist, R. C. & Starr, S. O. Drag and lift forces between a rotating conductive sphere and a cylinderical magnet. Am. J. Phys. 86, 443–452 (2018).
Sharma, K. K. et al. Space debris reduction using eddy currents. In 2018 Atmospheric Flight Mechanics Conf., 3161 (American Institute of Aeronautics and Astronautics, 2018).
Reinhardt, B. Z. & Peck, M. A. New electromagnetic actuator for on-orbit inspection. J. Spacecraft Rockets 53, 241–248 (2016).
Liu, X., Lu, Y., Zhou, Y. & Yin, Y. Prospects of using a permanent mangetic end effector to despin and detumble an uncooperative target. Adv. Space Res. 61, 2147–2158 (2018).
Smith, Y. R., Nagel, J. R. & Rajamani, R. K. Eddy current seperation for recovery of non-ferrous metallic particles: a comprehensive review. Miner. Eng. 133, 149–159 (2019).
Buckingham, E. On physically similar systems; illustrations of the use of dimensional equations. Phys. Rev. 4, 345 (1914).
Shan, M., Guo, J. & Gill, E. Review and comparison of active space debris capturing and removal methods. Prog. Aerosp. Sci. 80, 18–32 (2016).
Mark, C. P. & Kamath, S. Review of active space debris removal methods. Space Policy 47, 194–206 (2019).
Kessler, D. J., Johnson, N. L., Liou J. C. & Matney, M. The Kessler syndrome: implications to future space operations. Adv. Astronaut. Sci. 137, AAS 10-016 (2010).
Opiela, J. N. A study of the material density distribution of space debris. Adv. Space Res. 43, 1058–1064 (2009).
Pelrine, R. et al. Diamagnetically levitated robots: an approach to massively parallel robotic systems with unusual motion properties. IEEE Int. Conf. Robotics and Automation, 739–744 (2012).
Mirica, K. A., Ilievski, F., Ellerbee, A. K., Shevkoplyas, S. S. & Whitesides, G. M. Using magnetic levitation for three dimensional self-assembly. Adv. Mater. 23, 4134–4140 (2011).
Petruska, A. J. & Abbott, J. J. Omnimagnet: an omnidirectional electromagnet for controlled dipole-field generation. IEEE Trans. Magn. 50, 8400410 (2014).
Wright, S. E., Mahoney, A. W., Popek, K. M. & Abbott, J. J. The spherical-actuator-magnet manipulator: a permanent-magnet robotic end-effector. IEEE Trans. Robot. 33, 1013–2924 (2017).
Petruska, A. J. & Abbott, J. J. Optimal permanent-magnet geometries for dipole field approximation. IEEE Trans. Magn. 49, 811–819 (2013).
Lynch, K. M. & Park, F. C. Modern Robotics: Mechanics, Planning, and Control (Cambridge Univ. Press, 2017).
Diller, E., Giltinan, J., Lum, G. Z., Ye, Z. & Sitti, M. Six-degree-of-freedom magnetic actuation for wireless microrobotics. Int. J. Robot. Res. 35, 114–128 (2016).
Kummer, M. P. et al. OctoMag: an electromagnetic system for 5-DOF wireless micromanipulation. IEEE Trans. Robot. 26, 1006–1017 (2010).
Petruska, A. J. & Nelson, B. J. Minimum bounds on the number of electromagnets required for remote magnetic manipulation. IEEE Trans. Robot. 31, 714–722 (2015).
Ryan, P. & Diller, E. Magnetic actuation for full dexterity microrobotic control using rotating permanent magnets. IEEE Trans. Robot. 33, 1398–1409 (2017).
This work was supported by the National Science Foundation under grants 1841845 and 1846341.
J.J.A. has patents and patents pending on electromagnet and permanent-magnet devices designed to generate rotating magnetic dipole fields. The other authors declare no competing interests.
Peer review information Nature thanks Eric Diller and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.
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This document comprises the complete supplementary information associated with the article, organized in eight sections, ordered as the respective topics are introduced in the article: 1. Dimensional analysis. 2. Characterization of force and torque. 3. Model derivation. 4. Experimental verification of force and torque. 5. Comparison of numerical and experimental results. 6. Manipulation numerical simulations. 7 Manipulation experiments. 8. Discussion.
Numerical simulation of dexterous manipulation of a copper sphere in microgravity, with 3-DOF position control along the edges of a cube and uncontrolled orientation, using six dipole-field sources surrounding the sphere. The black line is the path taken, and an orthonormal frame depicts the sphere’s orientation. Highlighting indicates which single dipole-field source is activated at any given instant.
Numerical simulation of dexterous manipulation of a copper sphere in microgravity, with 3-DOF position control along the edges of a cube and 3-DOF constant-orientation control, using six dipole-field sources surrounding the sphere. The black line is the path taken, and an orthonormal frame depicts the sphere’s orientation. Highlighting indicates which single dipole-field source is activated at any given instant.
Dexterous manipulation of a copper sphere floating in a raft on the surface of water, with 2-DOF position control along the edges of a square in the horizontal plane and uncontrolled orientation about the vertical axis, using four electromagnetic dipole-field sources located below the sphere. The yellow line is the path taken, and a red arrow depicts the sphere’s orientation, which is logged over time. Highlighting indicates which single dipole-field source is activated at any given instant, with a blue arrow depicting the axis of rotation of the rotating magnetic dipole.
Dexterous manipulation of a copper sphere floating in a raft on the surface of water, with 2-DOF position control along the edges of a square in the horizontal plane and 1-DOF orientation control about the vertical axis, using four electromagnetic dipole-field sources located below the sphere. The yellow line is the path taken, and a red arrow depicts the sphere’s orientation, which is logged over time. Highlighting indicates which single dipole-field source is activated at any given instant, with a blue arrow depicting the axis of rotation of the rotating magnetic dipole.
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Pham, L.N., Tabor, G.F., Pourkand, A. et al. Dexterous magnetic manipulation of conductive non-magnetic objects. Nature 598, 439–443 (2021). https://doi.org/10.1038/s41586-021-03966-6
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