Abstract
In miniature robotics applications, compliant mechanisms are widely used because of their scalability. In addition, compliant mechanism architecture is compatible with the manufacturing methods used to fabricate small scale robots, such as “foldable robotics”, where the size and the materials used allow much larger deflections. In this paper, the kinematics of compliant mechanisms used in miniature foldable robots are investigated with the assumption of nonlinear large deflections that occur at the flexure joints. The solution of the large beam deflection is acquired using elliptic integrals and is verified with finite element analysis and experiments on a simple small foldable leg linkage. The large deflection model takes joint strain energies into account and yields accurate estimations for load capacity of the mechanism as well as the necessary input torque for actuation of the leg. Therefore, the model presented can be used to estimate the load capacity of a miniature robot, as well as to select appropriate actuators. The work is also extended to estimate the compliant leg kinematics and rigid body dynamics of a foldable robot. The robot’s large deflection simulation results are compared with experiments and a simplified rigid-link pin-joint kinematic model. Our results demonstrate the modeling accuracy of the two approaches and can be used by foldable robotics community when deciding on the strategy to choose for modeling their robots.
Article PDF
Similar content being viewed by others
Explore related subjects
Discover the latest articles, news and stories from top researchers in related subjects.Avoid common mistakes on your manuscript.
References
Shimada, E., Thompson, J., Yan, J., Wood, R., Fearing, R.: Prototyping millirobots using dextrous microassembly and folding. Proc ASME IMECE/DSCD. 69(2), 933–940 (2000)
Wood, R.J., Avadhanula, S., Sahai, R., Steltz, E., Fearing, R.S.: Microrobot design using fiber reinforced composites. J. Mech. Des. 130(5), 052304 (2008)
Whitney, J.P., Sreetharan, P.S., Ma, K.Y., Wood, R.J.: Pop-up book mems. J. Micromech. Microeng. 21(11), 115021 (2011)
Onal CD, Wood RJ, Rus D (2011) Towards printable robotics: origami-inspired planar fabrication of three-dimensional mechanisms. In: robotics and automation (ICRA), 2011 IEEE international conference on, IEEE, pp 4608–4613
Felton, S., Tolley, M., Demaine, E., Rus, D., Wood, R.: A method for building self-folding machines. Science. 345(6197), 644–646 (2014)
Karakadioglu C, Askari M, Ozcan O (2017) Design and operation of MinIAQ: an untethered foldable miniature quadruped with individually actuated legs. In: IEEE international conference on advanced intelligent mechatronics (AIM’17), pp 247–252
Mehta AM, Rus D (2014) An end-to-end system for designing mechanical structures for print-and-fold robots. In: 2014 IEEE international conference on robotics and automation (ICRA), IEEE, pp 1460–1465
Howell LL (2001) Compliant Mechanisms. John Wiley & Sons
Faal, S.G., Chen, F., Tao, W., Agheli, M., Tasdighikalat, S., Onal, C.D.: Hierarchical kinematic design of foldable hexapedal locomotion platforms. Journal of Mechanisms and Robotics. 8(1), 011005 (2016)
Karydis K, Poulakakis I, Tanner HG (2012) A switching kinematic model for an octapedal robot. In: 2012 IEEE/RSJ international conference on intelligent robots and systems, IEEE, pp 507–512
Ozcan O, Baisch AT, Ithier D, Wood RJ (2014) Powertrain selection for a biologically-inspired miniature quadruped robot. In: robotics and automation (ICRA), 2014 IEEE international conference on, IEEE, pp 2398–2405
Soltero DE, Julian BJ, Onal CD, Rus D (2013) A lightweight modular 12-dof print-and-fold hexapod. In: 2013 IEEE/RSJ international conference on intelligent robots and systems, IEEE, pp 1465–1471
Finio, B.M., Wood, R.J.: Distributed power and control actuation in the thoracic mechanics of a robotic insect. Bioinspiration & biomimetics. 5(4), 045006 (2010)
Hoover AM, Fearing RS (2009) Analysis of off-axis performance of compliant mechanisms with applications to mobile millirobot design. In: 2009 IEEE/RSJ international conference on intelligent robots and systems, IEEE, pp 2770–2776
Askari M, Ozcan O (2019) Dynamic modeling and gait analysis for miniature robots in the absence of foot placement control. In: IEEE international conference on robotics and automation (ICRA’19), pp 9754–9760
Hoffman, K.L., Wood, R.J.: Myriapod-like ambulation of a segmented microrobot. Auton. Robot. 31(1), 103 (2011)
Saranli, U., Buehler, M., Koditschek, D.E.: Rhex: a simple and highly mobile hexapod robot. The International Journal of Robotics Research. 20(7), 616–631 (2001)
Shigley JE (2011) Shigley’s Mechanical Engineering Design. Tata McGraw-Hill Education
Banerjee, A., Bhattacharya, B., Mallik, A.: Large deflection of cantilever beams with geometric non-linearity: analytical and numerical approaches. International Journal of Non-Linear Mechanics. 43(5), 366–376 (2008)
Bisshopp, K., Drucker, D.: Large deflection of cantilever beams. Q. Appl. Math. 3(3), 272–275 (1945)
Holst, G.L., Teichert, G.H., Jensen, B.D.: Modeling and experiments of buckling modes and deflection of fixed-guided beams in compliant mechanisms. J. Mech. Des. 133(5), 051002 (2011)
Howell, L.L., Leonard, J.N.: Optimal loading conditions for non-linear deflections. International journal of non-linear mechanics. 32(3), 505–514 (1997)
Howell, L.L., Midha, A.: Parametric deflection approximations for end-loaded, large-deflection beams in compliant mechanisms. J. Mech. Des. 117(1), 156–165 (1995)
Kimball, C., Tsai, L.W.: Modeling of flexural beams subjected to arbitrary end loads. J. Mech. Des. 124(2), 223–235 (2002)
Mattiasson, K.: Numerical results from large deflection beam and frame problems analysed by means of elliptic integrals. Int. J. Numer. Methods Eng. 17(1), 145–153 (1981)
Saxena, A., Kramer, S.: A simple and accurate method for determining large deflections in compliant mechanisms subjected to end forces and moments. J. Mech. Des. 120(3), 392–400 (1998)
Shoup, T.E., McLarnan, C.W.: On the use of the undulating elastica for the analysis of flexible link mechanisms. Journal of Engineering for Industry. 93(1), 263–267 (1971)
Zhang, A., Chen, G.: A comprehensive elliptic integral solution to the large deflection problems of thin beams in compliant mechanisms. Journal of Mechanisms and Robotics. 5(2), 021006 (2013)
Chen, G., Xiong, B., Huang, X.: Finding the optimal characteristic parameters for 3r pseudo-rigid-body model using an improved particle swarm optimizer. Precis. Eng. 35(3), 505–511 (2011)
Mattson, C.A., Howell, L.L., Magleby, S.P.: Development of commercially viable compliant mechanisms using the pseudo-rigid-body model: case studies of parallel mechanisms. J. Intell. Mater. Syst. Struct. 15(3), 195–202 (2004)
Midha, A., Bapat, S.G., Mavanthoor, A., Chinta, V.: Analysis of a fixed-guided compliant beam with an inflection point using the pseudo-rigid-body model concept. Journal of Mechanisms and Robotics. 7(3), 031007 (2015)
Ramirez IA (2014) Pseudo-Rigid-Body Models for Approximating Spatial Compliant Mechanisms of Rectangular Cross Section. University of South Florida
Su HJ (2008) A load independent pseudo-rigid-body 3r model for determining large deflection of beams in compliant mechanisms. Proceedings of ASME IDETC/CIE (43260) pp 109–121
Su, H.J.: A pseudorigid-body 3r model for determining large deflection of cantilever beams subject to tip loads. Journal of Mechanisms and Robotics. 1(2), 021008 (2009)
Venkiteswaran, V.K., Su, H.J.: A three-spring pseudorigid-body model for soft joints with significant elongation effects. Journal of Mechanisms and Robotics. 8(6), 061001 (2016)
Yu, Y.Q., Feng, Z.L., Xu, Q.P.: A pseudo-rigid-body 2r model of flexural beam in compliant mechanisms. Mech. Mach. Theory. 55, 18–33 (2012)
Yu, Y.Q., Zhu, S.K., Xu, Q.P., Zhou, P.: A novel model of large deflection beams with combined end loads in compliant mechanisms. Precis. Eng. 43, 395–405 (2016)
Chase Jr., R.P., Todd, R.H., Howell, L.L., Magleby, S.P.: A 3-d chain algorithm with pseudo-rigid-body model elements. Mechanics Based Design of Structures and Machines. 39(1), 142–156 (2011)
Hill, T., Midha, A.: A graphical, user-driven newton-raphson technique for use in the analysis and design of compliant mechanisms. J. Mech. Des. 112(1), 123–130 (1990)
Miller, R.: Numerical analysis of a generalized plane elastica. Int. J. Numer. Methods Eng. 15(3), 325–332 (1980)
Tolou, N., Herder, J.: A seminalytical approach to large deflections in compliant beams under point load. Math. Probl. Eng. (2009)
Campanile, L., Hasse, A.: A simple and effective solution of the elastica problem. Proc. Inst. Mech. Eng. C J. Mech. Eng. Sci. 222(12), 2513–2516 (2008)
Frisch-Fay, R.: Applications of approximate expressions for complete elliptic integrals. Int. J. Mech. Sci. 5(3), 231–235 (1963)
Acknowledgements
The authors would like to thank all members of Bilkent Miniature Robotics Laboratory for their invaluable contributions to this work. This project is funded by The Scientific and Technological Research Council of Turkey (TUBITAK) through 3001 program (Grant number: 215 M366).
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflict of Interest
The authors declare that they have no conflict of interest.
Rights and permissions
About this article
Cite this article
Karakadıoğlu, C., Askari, M. & Özcan, O. The Effect of Large Deflections of Joints on Foldable Miniature Robot Dynamics. J Intell Robot Syst 100, 15–28 (2020). https://doi.org/10.1007/s10846-020-01169-1
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10846-020-01169-1