A Mathematical Modeling Method Elucidating the Integrated Gripping Performance of Ant Mandibles and Bio-inspired Grippers

Abstract

The ability to grip unhatched eggs is a skill exploited by the ants Harpegnathos venator, as they care their brood in tunneled nests, which is of extreme difficulty to keep the eggs intact while gripping. In this paper we propose a mathematical modeling method to elucidate the mechanism of such a gripping behavior in the ant mandibles. The new method can be subdivided into following steps. As a preliminary, the concavity geometry and mandible kinematics are examined experimentally. Second, coordinate transformation is used to predict the real-time spatial topology of the concavity. Third, we come up with a new method to quantify the workspace required to grip and the contact area between the concavity and ant egg. Our model indicates that the biaxial rotation fashion with specialized concavities can reduce workspace by 40% and increase contact area by 53% on average compared with the uniaxial rotation pattern, which augments success rate of gentle gripping. This methodology may have applications in evaluating mechanical performance in both natural and artificial grippers.

This is a preview of subscription content, log in to check access.

References

  1. [1]

    Negrello F, Mghames S, Grioli G, Garabini M, Catalano M G. A compact soft articulated parallel wrist for grasping in narrow spaces. IEEE Robotics and Automation Letters, 2019, 4, 3161–3168.

    Article  Google Scholar 

  2. [2]

    Galloway K C, Becker K P, Phillips B, Kirby J, Licht S, Tchernov D, Wood R J, Gruber D F. Soft robotic grippers for biological sampling on deep reefs. Soft Robotics, 2016, 3, 23–33.

    Article  Google Scholar 

  3. [3]

    Blanes C, Mellado M, Ortiz C, Valera A. Technologies for robot grippers in pick and place operations for fresh fruits and vegetables. Spanish Journal of Agricultural Research, 2011, 9, 1130–1141.

    Article  Google Scholar 

  4. [4]

    Sinatra N R, Teeple C B, Vogt D M, Parker K K, Gruber D F, Wood R J. Ultragentle manipulation of delicate structures using a soft robotic gripper. Science Robotics, 2019, 4, eaax5425.

    Article  Google Scholar 

  5. [5]

    Manns M, Morales J, Frohn P. Additive manufacturing of silicon based PneuNets as soft robotic actuators. 51 st CIRP Conference on Manufacturing Systems (CIRP CMS), Stockholm, Sweden, 2018, 72, 328–333.

    Google Scholar 

  6. [6]

    Tai K, El-Sayed A-R, Shahriari M, Biglarbegian M, Mahmud S. State of the art robotic grippers and applications. Robotics, 2016, 5, UNSP 11.

    Article  Google Scholar 

  7. [7]

    Monkman G J, Hesse S, Steinmann R, Schunk H. Robot Grippers, John Wiley & Sons, New Jersey, USA, 2007, 212–218.

    Google Scholar 

  8. [8]

    Yang Y, Chen Y H, Li Y T, Chen M Z Q, Wei Y. Bioinspired robotic fingers based on pneumatic actuator and 3D printing of smart material. Soft Robotics, 2017, 4, 147–162.

    Article  Google Scholar 

  9. [9]

    Deng H, Zhong G L, Li X F, Nie W. Slippage and deformation preventive control of bionic prosthetic hands. IEEE-ASME Transactions on Mechatronics, 2017, 22, 888–897.

    Article  Google Scholar 

  10. [10]

    Zhang Y, Deng H, Zhong G L. Humanoid design of mechanical fingers using a motion coupling and shape-adaptive linkage mechanism. Journal of Bionic Engineering, 2018, 15, 94–105.

    Article  Google Scholar 

  11. [11]

    Paul J. Mandible movements in ants. 21st International Congress of the European-Society-of-Comparative-Physiology-and-Biochemistry, Liege, Belgium, 2001, 131, 7–20.

    Google Scholar 

  12. [12]

    Zhang W, Li M H, Zheng G B, Guan Z J, Wu J N, Wu Z G. Multifunctional mandibles of ants: Variation in gripping behavior facilitated by specific microstructures and kinematics. Journal of insect physiology, 2019, 120, 103993.

    Article  Google Scholar 

  13. [13]

    Popov V L, Filippov A E, Gorb S N. Biological microstructures with high adhesion and friction. Numerical approach. Physics-Uspekhi, 2016, 59, 829–845.

    Article  Google Scholar 

  14. [14]

    Niederegger S, Gorb S, Jiao Y K. Contact behaviour of tenent setae in attachment pads of the blowfly Calliphora vicina (Diptera, Calliphoridae). Journal of Comparative Physiology A, 2002, 187, 961–970.

    Article  Google Scholar 

  15. [15]

    Gravish N, Wilkinson M, Autumn K. Frictional and elastic energy in gecko adhesive detachment. Journal of the Royal Society Interface, 2008, 5, 339–348.

    Article  Google Scholar 

  16. [16]

    Peeters C, Hoelldobler B, Moffett M, Ali T M M. “Wall-papering” and elaborate nest architecture in the ponerine ant Harpegnathos saltator. Insectes Sociaux, 1994, 41, 211–218.

    Article  Google Scholar 

  17. [17]

    Meudec M, Lenoir A. Social responses to variation in food supply and nest suitability in ants (Tapinoma erraticum). Animal Behaviour, 1982, 30, 284–292.

    Article  Google Scholar 

  18. [18]

    Furneaux P J, Mackay A L. Crystalline protein in the chorion of insect egg shells. Journal of Ultrastructure Research, 1972, 38, 343–359.

    Article  Google Scholar 

  19. [19]

    Michels J, Gorb S N. Detailed three-dimensional visualization of resilin in the exoskeleton of arthropods using confocal laser scanning microscopy. Journal of Microscopy, 2012, 245, 1–16.

    Article  Google Scholar 

  20. [20]

    Gronenberg W, Brandao C R F, Dietz B H, Just S. Trap-jaws revisited: The mandible mechanism of the ant Acanthognathus. Physiological Entomology, 1998, 23, 227–240.

    Article  Google Scholar 

  21. [21]

    Hashemi A, Kalantari M, Kasser M. Direct Solution of the 7 parameters transformation problem. Applied Mathematics & Information Sciences, 2013, 7, 1375–1382.

    Article  Google Scholar 

  22. [22]

    Yao J L. Rigorous formula for direct calculating parameter in 3D transformation. Bulletin of Surveying and Mapping, 2006, 5, 57–60. (in Chinese)

    Google Scholar 

  23. [23]

    Alexandru P, Visa I, Alexandru C. Modeling the angular capability of the ball joints in a complex mechanism with two degrees of mobility. Applied Mathematical Modelling, 2014, 38, 5456–5470.

    MathSciNet  Article  Google Scholar 

  24. [24]

    Besl P J, McKay H D. A method for registration of 3-D shapes. IEEE Transactions on Pattern Analysis and Machine Intelligence, 1992, 14, 239–256.

    Article  Google Scholar 

  25. [25]

    Varady T, Martin R R, Cox J. Reverse engineering of geometric models — An introduction. Computer Aided Design, 1997, 29, 255–268.

    Article  Google Scholar 

  26. [26]

    Bolle R M, Cooper D B. Bayesian recognition of local 3-D shape by approximating image intensity functions with quadric polynomials. IEEE Transactions on Pattern Analysis and Machine Intelligence, 1984, 6, 418–129.

    Article  Google Scholar 

  27. [27]

    Chen P, Pavlidis T. Image segmentation as an estimation problem. Computer Graphics and Image Processing, 1980, 12, 153–172.

    Article  Google Scholar 

  28. [28]

    Jazar R N. Advanced Dynamics: Rigid Body, Multibody, and Aerospace Applications, John Wiley & Sons, New Jersey, USA, 2011, 357–379.

    Google Scholar 

  29. [29]

    Patek S N, Baio J E, Fisher B L, Suarez A V. Multifunctionality and mechanical origins: Ballistic jaw propulsion in trap-jaw ants. Proceedings of the National Academy of Sciences of the United States of America, 2006, 103, 12787–12792.

    Article  Google Scholar 

  30. [30]

    Larabee F J, Suarez A V. Mandible-powered escape jumps in trap-jaw ants increase survival rates during predator-prey encounters. PLOS ONE, 2015, 10, e0124871.

    Article  Google Scholar 

  31. [31]

    Du N, Fan J T, Wu H J, Chen S, Liu Y. An improved model of heat transfer through penguin feathers and down. Journal of Theoretical Biology, 2007, 248, 727–735.

    MathSciNet  Article  Google Scholar 

  32. [32]

    Giulietti F, Tortora P. Optimal rotation angle about a nonnominal Euler axis. Journal of Guidance Control and Dynamics, 2007, 30, 1561–1563.

    Article  Google Scholar 

  33. [33]

    Aron S, Passera L, Keller L. Queen-worker conflict over sex ratio: A comparison of primary and secondary sex ratios in the Argentine ant, Iridomyrmex humilis. Journal of Evolutionary Biology, 1994, 7, 403–418.

    Article  Google Scholar 

  34. [34]

    Argatov I, Mishuris G. Frictionless elliptical contact of thin viscoelastic layers bonded to rigid substrates. Applied Mathematical Modelling, 2011, 35, 3201–3212.

    MathSciNet  Article  Google Scholar 

  35. [35]

    Blake A. Practical Stress Analysis in Engineering Design, CRC Press, Florida, USA, 1989, 8–10.

    Google Scholar 

  36. [36]

    Vincent J F, Clift S E, Menon C. Biomimetics of campaniform sensilla: Measuring strain from the deformation of holes. Journal of Bionic Engineering, 2007, 4, 63–76.

    Article  Google Scholar 

  37. [37]

    Wang Z K, Zhu M Z, Kawamura S, Hirai S. Comparison of different soft grippers for lunch box packaging. Robotics and Biomimetics, 2017, 4, 10.

    Article  Google Scholar 

Download references

Acknowledgment

We appreciate Dr Huizeng Li from Department of Chemistry, Chinese Academy of Sciences who aided us in capturing the CLSM images on the concavity of the ant mandibles. We thank Miss Jiayi Wu from Sun Yat-Sen University for her contribution to drafting figures in this paper. This work was supported by the research grant of Sun Yat-Sen University for Bairen Plan (Grant No. 76200-18841223), and the National Natural Science Foundation of China (Grant No. 51905556).

Author information

Affiliations

Authors

Corresponding author

Correspondence to Jianing Wu.

Electronic supplementary material

Supplementary material, approximately 14.3 MB.

Supplementary material, approximately 14.3 MB.

Supplementary material, approximately 3.48 MB.

Supplementary material, approximately 3.48 MB.

Supplementary material, approximately 3.15 MB.

Supplementary material, approximately 3.15 MB.

Supplementary material, approximately 2.82 MB.

Supplementary material, approximately 2.82 MB.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Zhang, W., He, Z., Sun, Y. et al. A Mathematical Modeling Method Elucidating the Integrated Gripping Performance of Ant Mandibles and Bio-inspired Grippers. J Bionic Eng (2020). https://doi.org/10.1007/s42235-020-0065-9

Download citation

Keywords

  • ant mandible
  • bio-inspired grippers
  • concavity
  • kinematics
  • workspace
  • contact area