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Mechanical computing

Abstract

Mechanical mechanisms have been used to process information for millennia, with famous examples ranging from the Antikythera mechanism of the Ancient Greeks to the analytical machines of Charles Babbage. More recently, electronic forms of computation and information processing have overtaken these mechanical forms, owing to better potential for miniaturization and integration. However, several unconventional computing approaches have recently been introduced, which blend ideas of information processing, materials science and robotics. This has raised the possibility of new mechanical computing systems that augment traditional electronic computing by interacting with and adapting to their environment. Here we discuss the use of mechanical mechanisms, and associated nonlinearities, as a means of processing information, with a view towards a framework in which adaptable materials and structures act as a distributed information processing network, even enabling information processing to be viewed as a material property, alongside traditional material properties such as strength and stiffness. We focus on approaches to abstract digital logic in mechanical systems, discuss how these systems differ from traditional electronic computing, and highlight the challenges and opportunities that they present.

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Fig. 1: Three-level hierarchy of a computational system.
Fig. 2: Non-volatile and volatile mechanical bit abstractions as building blocks for mechanical computing.
Fig. 3: Networking mechanical computing units for digital logic.
Fig. 4: Environmental interactions.

References

  1. 1.

    Freeth, T. et al. Decoding the ancient Greek astronomical calculator known as the Antikythera mechanism. Nature 444, 587–591 (2006).

    ADS  CAS  PubMed  Article  PubMed Central  Google Scholar 

  2. 2.

    Bromley, A. G. Charles Babbage’s analytical engine, 1838. Ann. Hist. Comput. 20, 29–45 (1998).

    MathSciNet  MATH  Article  Google Scholar 

  3. 3.

    Bush, V. The differential analyzer. A new machine for solving differential equations. J. Franklin Inst. 212, 447–488 (1931).

    MATH  Article  Google Scholar 

  4. 4.

    Roy, K., Jaiswal, A. & Panda, P. Towards spike-based machine intelligence with neuromorphic computing. Nature 575, 607–617 (2019).

    ADS  CAS  PubMed  Article  PubMed Central  Google Scholar 

  5. 5.

    Adleman, L. M. Molecular computation of solutions to combinatorial problems. Science 266, 1021–1024 (1994).

    ADS  CAS  PubMed  Article  PubMed Central  Google Scholar 

  6. 6.

    McEvoy, M. A. & Correll, N. Materials that couple sensing, actuation, computation, and communication. Science 347, 1261689 (2015).

    CAS  PubMed  Article  PubMed Central  Google Scholar 

  7. 7.

    Hauser, H., Ijspeert, A. J., Füchslin, R. M., Pfeifer, R. & Maass, W. Towards a theoretical foundation for morphological computation with compliant bodies. Biol. Cybern. 105, 355–370 (2011).

    MathSciNet  PubMed  MATH  Article  PubMed Central  Google Scholar 

  8. 8.

    Müller, V. C. & Hoffmann, M. What is morphological computation? On how the body contributes to cognition and control. Artif. Life 23, 1–24 (2017).

    PubMed  Article  PubMed Central  Google Scholar 

  9. 9.

    Laschi, C. & Mazzolai, B. Lessons from animals and plants: the symbiosis of morphological computation and soft robotics. IEEE Robot. Autom. Mag. 23, 107–114 (2016).

    Article  Google Scholar 

  10. 10.

    Caulfield, H. J. & Dolev, S. Why future supercomputing requires optics. Nat. Photon. 4, 261–263 (2010).

    CAS  Article  Google Scholar 

  11. 11.

    Miller, D. A. Are optical transistors the logical next step? Nat. Photon. 4, 3–5 (2010).

    ADS  CAS  Article  Google Scholar 

  12. 12.

    Ospelkaus, C. et al. Microwave quantum logic gates for trapped ions. Nature 476, 181–184 (2011).

    ADS  CAS  PubMed  Article  PubMed Central  Google Scholar 

  13. 13.

    Lekitsch, B. et al. Blueprint for a microwave trapped ion quantum computer. Sci. Adv. 3, e1601540 (2017).

    ADS  PubMed  PubMed Central  Article  CAS  Google Scholar 

  14. 14.

    Katsikis, G., Cybulski, J. S. & Prakash, M. Synchronous universal droplet logic and control. Nat. Phys. 11, 588–596 (2015).

    CAS  Article  Google Scholar 

  15. 15.

    Weaver, J. A., Melin, J., Stark, D., Quake, S. R. & Horowitz, M. A. Static control logic for microfluidic devices using pressure-gain valves. Nat. Phys. 6, 218–223 (2010).

    CAS  Article  Google Scholar 

  16. 16.

    Mosadegh, B., Bersano-Begey, T., Park, J. Y., Burns, M. A. & Takayama, S. Next-generation integrated microfluidic circuits. Lab Chip 11, 2813–2818 (2011).

    CAS  PubMed  Article  PubMed Central  Google Scholar 

  17. 17.

    Woodhouse, F. G. & Dunkel, J. Active matter logic for autonomous microfluidics. Nat. Commun. 8, 15169 (2017).

    ADS  PubMed  PubMed Central  Article  Google Scholar 

  18. 18.

    Preston, D. J. et al. Digital logic for soft devices. Proc. Natl Acad. Sci. USA 116, 7750–7759 (2019).

    ADS  CAS  PubMed  PubMed Central  Article  Google Scholar 

  19. 19.

    Volkov, A. G., Adesina, T., Markin, V. S. & Jovanov, E. Kinetics and mechanism of Dionaea muscipula trap closing. Plant Physiol. 146, 323–324 (2008).

    Article  CAS  Google Scholar 

  20. 20.

    Yang, R., Lenaghan, S. C., Zhang, M. & Xia, L. A mathematical model on the closing and opening mechanism for venus flytrap. Plant Signal. Behav. 5, 968–978 (2010).

    PubMed  PubMed Central  Article  Google Scholar 

  21. 21.

    Jiang, Y., Korpas, L. M. & Raney, J. R. Bifurcation-based embodied logic and autonomous actuation. Nat. Commun. 10, 128 (2019). Demonstrates environmentally responsive mechanical logic by using bistable beam mechanisms and stimuli-responsive materials.

    ADS  PubMed  PubMed Central  Article  CAS  Google Scholar 

  22. 22.

    Horsman, C., Stepney, S., Wagner, R. C. & Kendon, V. When does a physical system compute? Proc. Royal Soc. Lond. A 470, 20140182 (2014). Provides a framework for unconventional computing, distinguishing abstract computation from physical embodiment.

    ADS  MATH  Google Scholar 

  23. 23.

    Feynman, R. P. Feynman Lectures on Computation (CRC Press, 2018).

  24. 24.

    MacLennan, B. J. Natural computation and non-Turing models of computation. Theor. Comput. Sci. 317, 115–145 (2004).

    MathSciNet  MATH  Article  Google Scholar 

  25. 25.

    Silva, A. et al. Performing mathematical operations with metamaterials. Science 343, 160–163 (2014).

    ADS  MathSciNet  CAS  PubMed  MATH  Article  PubMed Central  Google Scholar 

  26. 26.

    Mohammadi Estakhri, N., Edwards, B. & Engheta, N. Inverse-designed metastructures that solve equations. Science 363, 1333–1338 (2019).

    ADS  MathSciNet  CAS  PubMed  MATH  Article  PubMed Central  Google Scholar 

  27. 27.

    Zangeneh-Nejad, F. & Fleury, R. Topological analog signal processing. Nat. Commun. 10, 2058 (2019).

    ADS  PubMed  PubMed Central  Article  CAS  Google Scholar 

  28. 28.

    Howell, L. L. Compliant Mechanisms (John Wiley & Sons, 2001).

  29. 29.

    Qiu, J., Lang, J. H. & Slocum, A. H. A curved-beam bistable mechanism. J. Microelectromech. Syst. 13, 137–146 (2004).

    Article  Google Scholar 

  30. 30.

    Oh, Y. S. & Kota, S. Synthesis of multistable equilibrium compliant mechanisms using combinations of bistable mechanisms. J. Mech. Des. 131, 021002 (2009).

    Article  Google Scholar 

  31. 31.

    Cazottes, P., Fernandes, A., Pouget, J. & Hafez, M. Bistable buckled beam: modeling of actuating force and experimental validations. J. Mech. Des. 131, 101001 (2009).

    Article  Google Scholar 

  32. 32.

    Camescasse, B., Fernandes, A. & Pouget, J. Bistable buckled beam: elastica modeling and analysis of static actuation. Int. J. Solids Struct. 50, 2881–2893 (2013).

    Article  Google Scholar 

  33. 33.

    Wu, C. C., Lin, M. J. & Chen, R. The derivation of a bistable criterion for double V-beam mechanisms. J. Micromech. Microeng. 23, 115005 (2013).

    ADS  Article  Google Scholar 

  34. 34.

    Ion, A., Wall, L., Kovacs, R. & Baudisch, P. Digital mechanical metamaterials. In Proc. 2017 CHI Conference on Human Factors in Computing Systems 977–988 (ACM, 2017). Demonstrates the use of 3D-printed modular bistable elements to perform digital logic, including ‘combination lock’ mechanisms.

  35. 35.

    Song, Y. et al. Additively manufacturable micro-mechanical logic gates. Nat. Commun. 10, 882 (2019). Realizes a full set of digital mechanical logic gates via 3D printing of bistable flexural beams.

    ADS  PubMed  PubMed Central  Article  Google Scholar 

  36. 36.

    Hälg, B. On a micro-electro-mechanical nonvolatile memory cell. IEEE Trans. Electron Dev. 37, 2230–2236 (1990). Provides an early example of the use of constrained beams to represent binary information.

    ADS  Article  Google Scholar 

  37. 37.

    Raney, J. R. et al. Stable propagation of mechanical signals in soft media using stored elastic energy. Proc. Natl Acad. Sci. USA 113, 9722–9727 (2016). Demonstrates mechanical diodes and logic gates based on the propagation of stable, nonlinear transition waves in architected soft systems of coupled bistable beams.

    ADS  CAS  PubMed  PubMed Central  Article  Google Scholar 

  38. 38.

    Yasuda, H., Tachi, T., Lee, M. & Yang, J. Origami-based tunable truss structures for non-volatile mechanical memory operation. Nat. Commun. 8, 962 (2017). Demonstrates volumetric origami cells with tuneable stability and stiffness that store bit information in a bistable potential-energy landscape.

    ADS  PubMed  PubMed Central  Article  CAS  Google Scholar 

  39. 39.

    Hanna, B. H., Lund, J. M., Lang, R. J., Magleby, S. P. & Howell, L. L. Waterbomb base: a symmetric single-vertex bistable origami mechanism. Smart Mater. Struct. 23, 094009 (2014).

    ADS  Article  Google Scholar 

  40. 40.

    Silverberg, J. L. et al. Origami structures with a critical transition to bistability arising from hidden degrees of freedom. Nat. Mater. 14, 389–393 (2015).

    ADS  CAS  PubMed  Article  PubMed Central  Google Scholar 

  41. 41.

    Saito, K., Tsukahara, A. & Okabe, Y. New deployable structures based on an elastic origami model. J. Mech. Des. 137, 021402 (2015).

    Article  Google Scholar 

  42. 42.

    Jianguo, C., Xiaowei, D., Ya, Z., Jian, F. & Yongming, T. Bistable behavior of the cylindrical origami structure with Kresling pattern. J. Mech. Des. 137, 061406 (2015).

    Article  Google Scholar 

  43. 43.

    Waitukaitis, S., Menaut, R., Chen, B. G. & van Hecke, M. Origami multistability: from single vertices to metasheets. Phys. Rev. Lett. 114, 055503 (2015).

    ADS  PubMed  Article  CAS  PubMed Central  Google Scholar 

  44. 44.

    Yasuda, H. & Yang, J. Reentrant origami-based metamaterials with negative Poisson’s ratio and bistability. Phys. Rev. Lett. 114, 185502 (2015).

    ADS  CAS  PubMed  Article  PubMed Central  Google Scholar 

  45. 45.

    Ishida, S., Uchida, H., Shimosaka, H. & Hagiwara, I. Design and numerical analysis of vibration isolators with quasi-zero-stiffness characteristics using bistable foldable structures. J. Vib. Acoust. 139, 031015 (2017).

    Article  Google Scholar 

  46. 46.

    Fang, H., Li, S., Ji, H. & Wang, K. W. Dynamics of a bistable Miura-origami structure. Phys. Rev. E 95, 052211 (2017).

    ADS  MathSciNet  PubMed  Article  PubMed Central  Google Scholar 

  47. 47.

    Kamrava, S., Mousanezhad, D., Ebrahimi, H., Ghosh, R. & Vaziri, A. Origami-based cellular metamaterial with auxetic, bistable, and self-locking properties. Sci. Rep. 7, 46046 (2017).

    ADS  CAS  PubMed  PubMed Central  Article  Google Scholar 

  48. 48.

    Faber, J. A., Arrieta, A. F. & Studart, A. R. Bioinspired spring origami. Science 359, 1386–1391 (2018).

    ADS  CAS  PubMed  Article  PubMed Central  Google Scholar 

  49. 49.

    Filipov, E. T. & Redoutey, M. Mechanical characteristics of the bistable origami hypar. Extreme Mech. Lett. 25, 16–26 (2018).

    Article  Google Scholar 

  50. 50.

    Sengupta, S. & Li, S. Harnessing the anisotropic multistability of stackedorigami mechanical metamaterials for effective modulus programming. J. Intell. Mater. Syst. Struct. 29, 2933–2945 (2018).

    Article  Google Scholar 

  51. 51.

    Liu, K., Tachi, T. & Paulino, G. H. Invariant and smooth limit of discrete geometry folded from bistable origami leading to multistable metasurfaces. Nat. Commun. 10, 4238 (2019).

    ADS  PubMed  PubMed Central  Article  CAS  Google Scholar 

  52. 52.

    Bhovad, P., Kaufmann, J. & Li, S. Peristaltic locomotion without digital controllers: exploiting multi-stability in origami to coordinate robotic motion. Extreme Mech. Lett. 32, 100552 (2019).

    Article  Google Scholar 

  53. 53.

    Yang, N., Zhang, M., Zhu, R. & Niu, X. D. Modular metamaterials composed of foldable obelisk-like units with reprogrammable mechanical behaviors based on multistability. Sci. Rep. 9, 18812 (2019).

    ADS  CAS  PubMed  PubMed Central  Article  Google Scholar 

  54. 54.

    Wang, L.-C. et al. Active reconfigurable tristable square-twist origami. Adv. Funct. Mater. 30, 1909087 (2020).

    CAS  Article  Google Scholar 

  55. 55.

    Treml, B., Gillman, A., Buskohl, P. & Vaia, R. Origami mechanologic. Proc. Natl Acad. Sci. USA 115, 6916–6921 (2018). Presents an environmentally responsive origami platform using the waterbomb fold pattern as a mechanical storage device that writes, erases and rewrites itself in response to a time-varying environmental signal.

    ADS  CAS  PubMed  PubMed Central  Article  Google Scholar 

  56. 56.

    Glusker, M., Hogan, D. M. & Vass, P. The ternary calculating machine of Thomas Fowler. IEEE Ann. Hist. Comput. 27, 4–22 (2005).

    MathSciNet  Article  Google Scholar 

  57. 57.

    Hayes, B. Computing science: third base. Am. Sci. 89, 490–494 (2001).

    Article  Google Scholar 

  58. 58.

    Yasuda, H., Korpas, L. M. & Raney, J. R. Transition waves and formation of domain walls in multistable mechanical metamaterials. Phys. Rev. Appl. 13, 054067 (2020).

    ADS  CAS  Article  Google Scholar 

  59. 59.

    Mahboob, I. & Yamaguchi, H. Bit storage and bit flip operations in an electromechanical oscillator. Nat. Nanotechnol. 3, 275–279 (2008). Demonstrates a volatile mechanical memory device in which binary information is abstracted in the phase offset of the beam oscillation.

    CAS  PubMed  Article  PubMed Central  Google Scholar 

  60. 60.

    Badzey, R. L., Zolfagharkhani, G., Gaidarzhy, A. & Mohanty, P. A controllable nanomechanical memory element. Appl. Phys. Lett. 85, 3587 (2004).

    ADS  CAS  Article  Google Scholar 

  61. 61.

    Noh, H., Shim, S. B., Jung, M., Khim, Z. G. & Kim, J. A mechanical memory with a dc modulation of nonlinear resonance. Appl. Phys. Lett. 97, 033116 (2010).

    ADS  Article  CAS  Google Scholar 

  62. 62.

    Mahboob, I., Flurin, E., Nishiguchi, K., Fujiwara, A. & Yamaguchi, H. Interconnect-free parallel logic circuits in a single mechanical resonator. Nat. Commun. 2, 198 (2011).

    ADS  CAS  PubMed  Article  PubMed Central  Google Scholar 

  63. 63.

    Ahmed, S. et al. A compact adder and reprogrammable logic gate using micro-electromechanical resonators with partial electrodes. IEEE Trans. Circuits Syst. II 66, 2057–2061 (2019).

    Article  Google Scholar 

  64. 64.

    Serra-Garcia, M. Turing-complete mechanical processor via automated nonlinear system design. Phys. Rev. E 100, 042202 (2019).

    ADS  CAS  PubMed  Article  PubMed Central  Google Scholar 

  65. 65.

    Venstra, W. J., Westra, H. J. R. & Van Der Zant, H. S. J. Mechanical stiffening, bistability, and bit operations in a microcantilever. Appl. Phys. Lett. 97, 193107 (2010). Utilizes nonlinear dynamics in microcantilevers to demonstrate bit operations in volatile dynamic systems through modulation of the driving frequency.

    ADS  Article  CAS  Google Scholar 

  66. 66.

    Zhang, S., Yin, L. & Fang, N. Focusing ultrasound with an acoustic metamaterial network. Phys. Rev. Lett. 102, 194301 (2009).

    ADS  PubMed  Article  CAS  PubMed Central  Google Scholar 

  67. 67.

    Nesterenko, V. F. Dynamics of Heterogeneous Materials (Springer-Verlag, 2001).

  68. 68.

    Liang, B., Guo, X. S., Tu, J., Zhang, D. & Cheng, J. C. An acoustic rectifier. Nat. Mater. 9, 989–992 (2010).

    ADS  CAS  PubMed  Article  PubMed Central  Google Scholar 

  69. 69.

    Li, N. et al. Colloquium: Phononics: Manipulating heat flow with electronic analogs and beyond. Rev. Mod. Phys. 84, 1045–1066 (2012).

    ADS  Article  Google Scholar 

  70. 70.

    Maldovan, M. Sound and heat revolutions in phononics. Nature 503, 209–217 (2013).

    ADS  CAS  PubMed  Article  PubMed Central  Google Scholar 

  71. 71.

    Kim, E. & Yang, J. Wave propagation in single column woodpile phononic crystals: formation of tunable band gaps. J. Mech. Phys. Solids 71, 33–45 (2014).

    ADS  MATH  Article  Google Scholar 

  72. 72.

    Fleury, R., Sounas, D. L., Sieck, C. F., Haberman, M. R. & Alù, A. Sound isolation and giant linear nonreciprocity in a compact acoustic circulator. Science 343, 516–519 (2014).

    ADS  CAS  PubMed  Article  PubMed Central  Google Scholar 

  73. 73.

    Zheng, B. & Xu, J. Mechanical logic switches based on DNA-inspired acoustic metamaterials with ultrabroad low-frequency band gaps. J. Phys. D 50, 465601 (2017).

    Article  CAS  Google Scholar 

  74. 74.

    Bilal, O. R., Foehr, A. & Daraio, C. Bistable metamaterial for switching and cascading elastic vibrations. Proc. Natl Acad. Sci. USA 114, 4603–4606 (2017). Uses geometric nonlinearities to switch and amplify elastic vibrations via magnetic coupling, allowing logic and simple calculations.

    ADS  CAS  PubMed  PubMed Central  Article  Google Scholar 

  75. 75.

    Li, F., Anzel, P., Yang, J., Kevrekidis, P. G. & Daraio, C. Granular acoustic switches and logic elements. Nat. Commun. 5, 5311 (2014). Provides an example of a mechanical metamaterial that allows logic operations via nonlinear dynamics in a granular chain.

    ADS  CAS  PubMed  Article  PubMed Central  Google Scholar 

  76. 76.

    Li, X. F. et al. Tunable unidirectional sound propagation through a sonic-crystal-based acoustic diode. Phys. Rev. Lett. 106, 084301 (2011).

    ADS  PubMed  Article  CAS  PubMed Central  Google Scholar 

  77. 77.

    Babaee, S., Viard, N., Wang, P., Fang, N. X. & Bertoldi, K. Harnessing deformation to switch on and off the propagation of sound. Adv. Mater. 28, 1631–1635 (2016).

    CAS  PubMed  Article  PubMed Central  Google Scholar 

  78. 78.

    Merkle, R. C. Two types of mechanical reversible logic. Nanotechnology 4, 114–131 (1993).

    ADS  Article  Google Scholar 

  79. 79.

    Howard, M. LEGO Logic Gates and Mechanical Computing https://www.randomwraith.com/logic.html (accessed 19 August 2020).

  80. 80.

    Saharia, K. Lego Logic http://web.archive.org/web/20140206173429/http://keshavsaharia.com/2011/05/29/lego-logic (accessed 19 August 2020).

  81. 81.

    Merkle, R. C. et al. Mechanical computing systems using only links and rotary joints. J. Mech. Robot. 10, 061006 (2018).

    Article  Google Scholar 

  82. 82.

    Berwind, M. F., Kamas, A. & Eberl, C. A hierarchical programmable mechanical metamaterial unit cell showing metastable shape memory. Adv. Eng. Mater. 20, 1800771 (2018).

    Article  Google Scholar 

  83. 83.

    Zhang, T., Cheng, Y., Guo, J. Z., Xu, J. Y. & Liu, X. J. Acoustic logic gates and Boolean operation based on self-collimating acoustic beams. Appl. Phys. Lett. 106, 113503 (2015).

    ADS  Article  CAS  Google Scholar 

  84. 84.

    Wu, Q., Cui, C., Bertrand, T., Shattuck, M. D. & O’Hern, C. S. Active acoustic switches using two-dimensional granular crystals. Phys. Rev. E 99, 062901 (2019).

    ADS  CAS  PubMed  Article  PubMed Central  Google Scholar 

  85. 85.

    Faber, J. A., Udani, J. P., Riley, K. S., Studart, A. R. & Arrieta, A. F. Dome-patterned metamaterial sheets. Adv. Sci. 7, 2001955 (2020).

    CAS  Article  Google Scholar 

  86. 86.

    Shan, S. et al. Multistable architected materials for trapping elastic strain energy. Adv. Mater. 27, 4296–4301 (2015).

    CAS  PubMed  Article  PubMed Central  Google Scholar 

  87. 87.

    Coulais, C., Teomy, E., de Reus, K., Shokef, Y. & van Hecke, M. Combinatorial design of textured mechanical metamaterials. Nature 535, 529–532 (2016).

    ADS  CAS  PubMed  Article  PubMed Central  Google Scholar 

  88. 88.

    Frenzel, T., Kadic, M. & Wegener, M. Three-dimensional mechanical metamaterials with a twist. Science 358, 1072–1074 (2017).

    ADS  CAS  PubMed  Article  PubMed Central  Google Scholar 

  89. 89.

    Kane, C. L. & Lubensky, T. C. Topological boundary modes in isostatic lattices. Nat. Phys. 10, 39–45 (2014).

    CAS  Article  Google Scholar 

  90. 90.

    Süsstrunk, R. & Huber, S. D. Observation of phononic helical edge states in a mechanical topological insulator. Science 349, 47–50 (2015).

    ADS  PubMed  Article  CAS  PubMed Central  Google Scholar 

  91. 91.

    Nash, L. M. et al. Topological mechanics of gyroscopic metamaterials. Proc. Natl Acad. Sci. USA 112, 14495–14500 (2015).

    ADS  CAS  PubMed  PubMed Central  Article  Google Scholar 

  92. 92.

    Paulose, J., Meeussen, A. S. & Vitelli, V. Selective buckling via states of self-stress in topological metamaterials. Proc. Natl Acad. Sci. USA 112, 7639–7644 (2015).

    ADS  CAS  PubMed  PubMed Central  Article  Google Scholar 

  93. 93.

    Chaunsali, R., Chen, C. W. & Yang, J. Experimental demonstration of topological waveguiding in elastic plates with local resonators. New J. Phys. 20, 113036 (2018).

    ADS  CAS  Article  Google Scholar 

  94. 94.

    Liu, B. et al. Topological kinematics of origami metamaterials. Nat. Phys. 14, 811–815 (2018).

    CAS  Article  Google Scholar 

  95. 95.

    Shi, X., Chaunsali, R., Li, F. & Yang, J. Elastic Weyl points and surface arc states in three-dimensional structures. Phys. Rev. Appl. 12, 024058 (2019).

    ADS  CAS  Article  Google Scholar 

  96. 96.

    Bilal, O. R., Süsstrunk, R., Daraio, C. & Huber, S. D. Intrinsically polar elastic metamaterials. Adv. Mater. 29, 1700540 (2017).

    Article  CAS  Google Scholar 

  97. 97.

    Sigmund, O. On the design of compliant mechanisms using topology optimization. Mechan. Struct. Mach. 25, 493–524 (1997).

    Article  Google Scholar 

  98. 98.

    Howell, L. L., Midha, A. & Norton, T. Evaluation of equivalent spring stiffness for use in a pseudo-rigid-body model of large-deflection compliant mechanisms. J. Mech. Des. 118, 126–131 (1996).

    Article  Google Scholar 

  99. 99.

    Rocks, J. W. et al. Designing allostery-inspired response in mechanical networks. Proc. Natl Acad. Sci. USA 114, 2520–2525 (2017).

    CAS  PubMed  PubMed Central  Article  Google Scholar 

  100. 100.

    Bielefeldt, B. R., Akleman, E., Reich, G. W., Beran, P. S. & Hartl, D. J. L-system-generated mechanism topology optimization using graph-based interpretation. J. Mech. Robot. 11, 020905 (2019).

    Article  Google Scholar 

  101. 101.

    Wilson, K. E., Henke, E.-F. M., Slipher, G. A. & Anderson, I. A. Rubbery logic gates. Extreme Mech. Lett. 9, 188–194 (2016).

    Article  Google Scholar 

  102. 102.

    Chau, N., Slipher, G. A., O’Brien, B. M., Mrozek, R. A. & Anderson, I. A. A solid-state dielectric elastomer switch for soft logic. Appl. Phys. Lett. 108, 103506 (2016).

    ADS  Article  CAS  Google Scholar 

  103. 103.

    Wissman, J., Dickey, M. D. & Majidi, C. Field-controlled electrical switch with liquid metal. Adv. Sci. 4, 1700169 (2017).

    Article  CAS  Google Scholar 

  104. 104.

    Le Ferrand, H., Studart, A. R. & Arrieta, A. F. Filtered mechanosensing using snapping composites with embedded mechano-electrical transduction. ACS Nano 13, 4752–4760 (2019).

    PubMed  Article  CAS  PubMed Central  Google Scholar 

  105. 105.

    Abdullah, A. M., Braun, P. V. & Hsia, K. J. Programmable shape transformation of elastic spherical domes. Soft Matter 12, 6184–6195 (2016).

    ADS  CAS  PubMed  Article  PubMed Central  Google Scholar 

  106. 106.

    Chen, T., Bilal, O. R., Shea, K. & Daraio, C. Harnessing bistability for directional propulsion of soft, untethered robots. Proc. Natl Acad. Sci. USA 115, 5698–5702 (2018).

    ADS  CAS  PubMed  PubMed Central  Article  Google Scholar 

  107. 107.

    Ambulo, C. P. et al. Four-dimensional printing of liquid crystal elastomers. ACS Appl. Mater. Interfaces 9, 37332–37339 (2017).

    CAS  PubMed  Article  PubMed Central  Google Scholar 

  108. 108.

    Wani, O. M., Zeng, H. & Priimagi, A. A light-driven artificial flytrap. Nat. Commun. 8, 15546 (2017).

    ADS  CAS  PubMed  PubMed Central  Article  Google Scholar 

  109. 109.

    Deirram, N., Zhang, C., Kermaniyan, S. S., Johnston, A. P. R. & Such, G. K. pH-responsive polymer nanoparticles for drug delivery. Macromol. Rapid Commun. 40, e1800917 (2019).

    PubMed  Article  CAS  PubMed Central  Google Scholar 

  110. 110.

    Loukaides, E. G., Smoukov, S. K. & Seffen, K. A. Magnetic actuation and transition shapes of a bistable spherical cap. Int. J. Smart Nano Mater. 5, 270–282 (2014).

    CAS  Article  Google Scholar 

  111. 111.

    Kim, Y., Yuk, H., Zhao, R., Chester, S. A. & Zhao, X. Printing ferromagnetic domains for untethered fast-transforming soft materials. Nature 558, 274–279 (2018).

    ADS  CAS  PubMed  Article  PubMed Central  Google Scholar 

  112. 112.

    Jackson, J. A. et al. Field responsive mechanical metamaterials. Sci. Adv. 4, eaau6419 (2018).

    ADS  CAS  PubMed  PubMed Central  Article  Google Scholar 

  113. 113.

    Jin, Y. et al. Materials tactile logic via innervated soft thermochromic elastomers. Nat. Commun. 10, 4187 (2019).

    ADS  PubMed  PubMed Central  Article  CAS  Google Scholar 

  114. 114.

    Hu, W., Lum, G. Z., Mastrangeli, M. & Sitti, M. Small-scale soft-bodied robot with multimodal locomotion. Nature 554, 81–85 (2018).

    ADS  CAS  PubMed  Article  PubMed Central  Google Scholar 

  115. 115.

    Zhao, H., O’Brien, K., Li, S. & Shepherd, R. F. Optoelectronically innervated soft prosthetic hand via stretchable optical waveguides. Sci. Robot. 1, eaai7529 (2016).

    PubMed  Article  PubMed Central  Google Scholar 

  116. 116.

    Truby, R. L. et al. Soft somatosensitive actuators via embedded 3D printing. Adv. Mater. 30, e1706383 (2018).

    PubMed  Article  CAS  PubMed Central  Google Scholar 

  117. 117.

    Lee, T. H., Bhunia, S. & Mehregany, M. Electromechanical computing at 500 degrees C with silicon carbide. Science 329, 1316–1318 (2010). Demonstrates the capability of electromechanical switches at high temperature.

    ADS  CAS  PubMed  Article  PubMed Central  Google Scholar 

  118. 118.

    Blakey, E. in Advances in Unconventional Computing. Emergence, Complexity and Computation (ed. Adamatzky, A.) 165–182 (Springer, 2017).

  119. 119.

    Roukes, M. L. Mechanical computation, redux? In IEDM Technical Digest. IEEE International Electron Devices Meeting 2004 539–542 (IEEE, 2004).

  120. 120.

    Masmanidis, S. C. et al. Multifunctional nanomechanical systems via tunably coupled piezoelectric actuation. Science 317, 780–783 (2007).

    ADS  CAS  PubMed  Article  PubMed Central  Google Scholar 

  121. 121.

    Pott, B. V. et al. Mechanical computing redux: relays for integrated circuit applications. Proc. IEEE 98, 2076–2094 (2010).

    CAS  Article  Google Scholar 

  122. 122.

    Kam, H., Liu, T. J. K., Stojanović, V., Marković, D. & Alon, E. Design, optimization, and scaling of MEM relays for ultra-low-power digital logic. IEEE Trans. Electron Dev. 58, 236–250 (2011).

    ADS  Article  Google Scholar 

  123. 123.

    Wang, J. & Perez, L. The effectiveness of data augmentation in image classification using deep learning. Preprint at https://arxiv.org/abs/1712.04621 (2017).

  124. 124.

    Houthooft, R. et al. VIME: variational information maximizing exploration. Adv. Neural Inf. Process. Syst. 29, 1109–1117 (2016).

    Google Scholar 

  125. 125.

    Null, L. & Lobur, J. The Essentials of Computer Organization and Architecture (Jones & Bartlett Publishers, 2015).

  126. 126.

    Sauder, J. et al. Automation Rover for Extreme Environments: NASA Innovative Advanced Concepts (NIAC) Phase I Final Report https://www.nasa.gov/sites/default/files/atoms/files/niac_2016_phasei_saunder_aree_tagged.pdf (NASA, 2017).

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Acknowledgements

H.Y. and J.R.R. acknowledge support from Army Research Office award number W911NF-1710147, Air Force Office of Scientific Research award number FA9550-19-1-0285 and DARPA Young Faculty Award W911NF2010278. P.R.B., A.G. and R.A.V. acknowledge support from the Materials and Manufacturing Directorate and the Air Force Office of Scientific Research of the Air Force Research Laboratory. T.D.M. acknowledges support from NSF 1837515 and ARO MURI award W911NF-19-1-0233. S.S. acknowledges support from the SpInspired project, EPSRC grant number EP/R032823/1.

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This file contains the Supplementary Discussion, which briefly outlines how non-binary abstractions can be realized in mechanical systems, and how information storage scales with the base of the abstraction (binary, ternary, etc.) and the number of units. It includes Supplementary Figure 1 and Supplementary References.

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Yasuda, H., Buskohl, P.R., Gillman, A. et al. Mechanical computing. Nature 598, 39–48 (2021). https://doi.org/10.1038/s41586-021-03623-y

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