0
Research Papers

Tuning of a Rigid-Body Dynamics Model of a Flapping Wing Structure With Compliant Joints

[+] Author and Article Information
Joseph Calogero

Mem. ASME
Department of Mechanical and
Nuclear Engineering,
The Pennsylvania State University,
University Park, PA 16802
e-mail: jcalogero7@gmail.com

Mary Frecker

Fellow ASME
Department of Mechanical and
Nuclear Engineering,
The Pennsylvania State University,
University Park, PA 16802
e-mail: mxf36@psu.edu

Zohaib Hasnain

Mem. ASME
Department of Aerospace Engineering,
The University of Maryland,
Hampton, VA 23666
e-mail: zohaibhasnain@gmail.com

James E. Hubbard, Jr.

Fellow ASME
Department of Aerospace Engineering,
The University of Maryland,
Hampton, VA 23666
e-mail: hubbard@nianet.org

Manuscript received June 30, 2017; final manuscript received October 10, 2017; published online December 20, 2017. Assoc. Editor: Larry L Howell.

J. Mechanisms Robotics 10(1), 011007 (Dec 20, 2017) (11 pages) Paper No: JMR-17-1195; doi: 10.1115/1.4038441 History: Received June 30, 2017; Revised October 10, 2017

A method for validating rigid-body models of compliant mechanisms under dynamic loading conditions using motion tracking cameras and genetic algorithms is presented. The compliant mechanisms are modeled using rigid-body mechanics as compliant joints (CJ): spherical joints with distributed mass and three-axis torsional spring dampers. This allows compliant mechanisms to be modeled using computationally efficient rigid-body dynamics methods, thereby allowing a model to determine the desired stiffness and location characteristics of compliant mechanisms spatially distributed into a structure. An experiment was performed to validate a previously developed numerical dynamics model with the goal of tuning unknown model parameters to match the flapping kinematics of the leading edge spar of an ornithopter with contact-aided compliant mechanisms (CCMs), compliant mechanisms that feature self-contact to produce nonlinear stiffness, inserted. A system of computer motion tracking cameras was used to record the kinematics of reflective tape and markers placed along the leading edge spar with and without CCMs inserted. A genetic algorithm was used to minimize the error between the model and experimental marker kinematics. The model was able to match the kinematics of all markers along the spars with a root-mean-square error (RMSE) of less than 2% of the half wingspan over the flapping cycle. Additionally, the model was able to capture the deflection amplitude and harmonics of the CCMs with a RMSE of less than 2 deg over the flapping cycle.

FIGURES IN THIS ARTICLE
<>
Copyright © 2018 by ASME
Your Session has timed out. Please sign back in to continue.

References

Calogero, J. P. J. , Frecker, M. M. I. , Hasnain, Z. , Hubbard , J. E., Jr ., and Hubbard, J. E. , 2016, “ A Dynamic Spar Numerical Model for Passive Shape Change,” Smart Mater. Struct., 25(10), pp. 1–16.
Calogero, J. , Frecker, M. , Hasnain, Z. , and Hubbard, J. E., Jr. , 2015, “A Dynamic Spar Numerical Model for Passive Shape Change,” ASME Paper No. SMASIS2015-8837.
Tummala, Y. , Wissa, A. , Frecker, M. , and Hubbard, J. E., Jr. , 2014, “ Design and Optimization of a Contact-Aided Compliant Mechanism for Passive Bending,” ASME J. Mech. Rob., 6(3), p. 031013. [CrossRef]
Cirone, S. A. , Hayes, G. R. , Babcox, B. L. , Frecker, M. , Adair, J. H. , and Lesieutre, G. A. , 2012, “ Design of Contact-Aided Compliant Cellular Mechanisms With Curved Walls,” J. Intell. Mater. Syst. Struct., 23(16), pp. 1773–1785. [CrossRef]
Mehta, V. , Frecker, M. , and Lesieutre, G. A. , 2012, “ Two-Step Design of Multicontact-Aided Cellular Compliant Mechanisms for Stress Relief,” ASME J. Mech. Des., 134(12), p. 121001. [CrossRef]
Mankame, N. D. , and Ananthasuresh, G. K. K. , 2004, “ Topology Optimization for Synthesis of Contact-Aided Compliant Mechanisms Using Regularized Contact Modeling,” Comput. Struct., 82(15–16), pp. 1267–1290. [CrossRef]
Calogero, J. , Frecker, M. , Wissa, A. A. , and Hubbard, J. E., Jr. , 2014, “Optimization of a Bend-Twist-and-Sweep Compliant Mechanism,” ASME Paper No. SMASIS2014-7518.
Tummala, Y. , Frecker, M. I. , Wissa, A. A. , and Hubbard, J. E., Jr. , 2013, “Design Optimization of a Twist Compliant Mechanism With Nonlinear Stiffness,” ASME Paper No. SMASIS2013-3031.
Tummala, Y. , Frecker, M. I. , Wissa, A. A. , and Hubbard, J. E., Jr. , 2013, “ Design and Optimization of a Bend-and-Sweep Compliant Mechanism,” Smart Mater. Struct., 22(9), p. 094019. [CrossRef]
Wissa, A. A. , Tummala, Y. , Hubbard , J. E., Jr ., and Frecker, M. I. , 2012, “ Passively Morphing Ornithopter Wings Constructed Using a Novel Compliant Spine: Design and Testing,” Smart Mater. Struct., 21(9), p. 094028. [CrossRef]
Mehta, V. , Frecker, M. , and Lesieutre, G. A. , 2009, “ Stress Relief in Contact-Aided Compliant Cellular Mechanisms,” ASME J. Mech. Des., 131(9), p. 091009. [CrossRef]
Saxena, A. , 2013, “ A Contact-Aided Compliant Displacement-Delimited Gripper Manipulator,” ASME J. Mech. Rob., 5(4), p. 041005. [CrossRef]
Reddy, B. V. S. N. , Naik, S. V. , and Saxena, A. , 2012, “ Systematic Synthesis of Large Displacement Contact-Aided Monolithic Compliant Mechanisms,” ASME J. Mech. Des., 134(1), p. 011007. [CrossRef]
Sharma, D. , Deb, K. , and Kishore, N. N. , 2008, “ Towards Generating Diverse Topologies of Path Tracing Compliant Mechanisms Using a Local Search Based Multi-Objective Genetic Algorithm Procedure,” IEEE Congress on Evolutionary Computation ( IEEE World Congress on Computational Intelligence) (CEC), Hong Kong, China, June 1–6, pp. 2004–2011.
Venkiteswaran, V. K. , and Su, H.-J. , 2016, “ Extension Effects in Compliant Joints and Pseudo-Rigid-Body Models,” ASME J. Mech. Des., 138(9), p. 092302. [CrossRef]
Altuzarra, O. , Diez, M. , Corral, J. , and Campa, F. J. , 2017, “ Kinematic Analysis of a Flexible Tensegrity Robot,” New Advances in Mechanisms, Mechanical Transmissions and Robotics, B. Corves , E.-C. Lovasz , M. Hüsing , I. Maniu , and C. Gruescu , eds., Springer International Publishing, Cham, Switzerland, pp. 457–464. [CrossRef]
Hao, G. , and Hand, R. B. , 2016, “ Design and Static Testing of a Compact Distributed-Compliance Gripper Based on Flexure Motion,” Arch. Civil Mech. Eng., 16(4), pp. 708–716. [CrossRef]
Yang, T.-S. , Shih, P.-J. , and Lee, J.-J. , 2016, “ Design of a Spatial Compliant Translational Joint,” Mech. Mach. Theory, 107, pp. 338–350. [CrossRef]
Howell, L. L. , 2001, Compliant Mechanisms, Wiley, New York.
Tummala, Y. , 2013, “ Design and Optimization of Contact-Aided Compliant Mechanisms With Nonlinear Stiffness,” Ph.D. dissertation, The Pennsylvania State University, State College, PA. https://etda.libraries.psu.edu/catalog/19681
Alqasimi, A. , and Lusk, C. , 2014, “Design of a Linear Bi-Stable Compliant Crank-Slider-Mechanism (LBCCSM),” ASME Paper No. DETC2014-34285.
Tantanawat, T. , and Kota, S. , 2007, “ Design of Compliant Mechanisms for Minimizing Input Power in Dynamic Applications,” ASME J. Mech. Des., 129(10), pp. 1064–1075. [CrossRef]
Manzo, J. , and Garcia, E. , 2009, “ Analysis and Optimization of the Active Rigidity Joint,” Smart Mater. Struct., 18(12), p. 125020. [CrossRef]
Vogtmann, D. E. , Gupta, S. K. , and Bergbreiter, S. , 2013, “ Characterization and Modeling of Elastomeric Joints in Miniature Compliant Mechanisms,” ASME J. Mech. Rob., 5(4), p. 041017. [CrossRef]
Wong, K. V. , 2015, “ Research and Development of Drones for Peace—High Power High Energy Supply Required,” ASME J. Energy Resour. Technol., 137(3), p. 034702. [CrossRef]
Friswell, M. I. , 2014, “Morphing Aircraft: An Improbable Dream?,” ASME Paper No. SMASIS2014-7754.
Shyy, W. , Berg, M. , and Ljungqvist, D. , 1999, “ Flapping and Flexible Wings for Biological and Micro Air Vehicles,” Prog. Aerosp. Sci., 35(5), pp. 455–505. [CrossRef]
Tummala, Y. , Wissa, A. , Frecker, M. , and Hubbard, J. E., Jr ., 2010, “Design of a Passively Morphing Ornithopter Wing Using a Novel Compliant Spine,” ASME Paper No. SMASIS2010-3637.
Wissa, A. , Tummala, Y. , Hubbard , J. E., Jr. , Frecker, M. , and Brown, A. , 2011, “Testing of Novel Compliant Spines for Passive Wing Morphing,” ASME Paper No. SMASIS2011-5198.
Tobalske, B. W. , 2000, “ Biomechanics and Physiology of Gait Selection in Flying Birds,” Physiol. Biochem. Zool., 73(6), pp. 736–750. [CrossRef] [PubMed]
Howell, L. L. , and Magleby, S. P. , 2013, Handbook of Compliant Mechanisms, Wiley, Chichester, UK. [CrossRef] [PubMed] [PubMed]
Wissa, A. , and 2014, “Inertial Effects Due to Passive Wing Morphing in Ornithopters,” AIAA Paper No. 2014-1123.
Wissa, A. , Grauer, J. , Guerreiro, N. , Hubbard, J. , Altenbuchner, C. , Tummala, Y. , Frecker, M. , and Roberts, R. , 2015, “ Free Flight Testing and Performance Evaluation of a Passively Morphing Ornithopter,” Int. J. Micro Air Veh., 7(1), pp. 21–40. [CrossRef]
COMSOL, 2017, “ COMSOL Multiphysics® 5.1 Release Overview,” COMSOL, Stockholm, Sweden, accessed Nov. 21, 2017, https://www.comsol.co.in/release/5.1
Vicon, 2017, “Vicon Vantage,” Vicon, Oxford, UK, accessed Mar. 17, 2015, http://vicon.com/products/camera-systems/vantage
Wissa, A. , Calogero, J. , Wereley, N. , Hubbard, J. E. , and Frecker, M. , 2015, “ Analytical Model and Stability Analysis of the Leading Edge Spar of a Passively Morphing Ornithopter Wing,” Bioinspir. Biomim., 10(6), p. 065003. [CrossRef] [PubMed]
Haug, E. J. , 1989, Computer Aided Kinematics and Dynamics of Mechanical Systems, Allyn and Bacon, Boston, MA.
Klein, V. , and Morelli, E. A. , 2006, Aircraft System Identification, American Institute of Aeronautics and Astronautics, Reston, VA.
The MathWorks, 2015, “MATLAB 8.5, Optimization Toolbox,” The MathWorks Inc., Natick, MA.

Figures

Grahic Jump Location
Fig. 5

Camera array setup used for experiment

Grahic Jump Location
Fig. 6

Clamps and platform used in the experiment. The solid spar configuration with reflective tape is shown.

Grahic Jump Location
Fig. 4

Finite element tip angle data for quasi-static simulations of the CCMs with clamped root and pure moment tip load boundary conditions, with bilinear stiffness approximations

Grahic Jump Location
Fig. 3

Fabricated CSA CCMs tested

Grahic Jump Location
Fig. 2

Configurations tested, where 35 and 40 represent the percentage of the distance from the wing root to the wing tip which the CCM's center is located

Grahic Jump Location
Fig. 1

Bend-twist-and-sweep compliant mechanism modeled as a compliant joint (CJ), where yellow is a spherical joint, purple represents three-dimensional (3D) distributed mass, and the spring represents the three-axis torsional spring dampers [1]

Grahic Jump Location
Fig. 7

Experimental tuning procedure

Grahic Jump Location
Fig. 13

CSA-40 comparison of experiment and model for the wing root driving link angle function (top) and CCM bending angle (bottom) with 25% of the experimental data points are shown for visualization purposes

Grahic Jump Location
Fig. 14

CSA-40 position data of CCM root and tip, and wing tip locations of experiment compared to the model. Each marker shows x, y, and z data from the experiment and model with 25% of the experimental data points are shown for visualization purposes.

Grahic Jump Location
Fig. 9

Schematic of solid spar configuration (left) and configurations with a compliant joint inserted (right), where Mi represents the inboard marker, Mo represents the outboard marker, and Mt represents the tip marker

Grahic Jump Location
Fig. 10

Comparison of moving average driving link angle to experimental driving link angles, where each colored line on the left thumbnail represents a different flapping cycle

Grahic Jump Location
Fig. 11

Comparison of the model with a rigid spar assumption to experimental marker position data, where the markers are the experimental data points and the solid line is the model. Each marker plot shows x, y, and z data from the experiment and model with 25% of the data is shown for visualization purposes.

Grahic Jump Location
Fig. 12

Comparison of the model with equivalent structural joints to experimental marker position data, where the markers are the experimental data points and the solid line is the model. Each marker plot shows x, y, and z data from the experiment and model with 25% of the data is shown for visualization purposes.

Grahic Jump Location
Fig. 8

Base ornithopter used by research group with coordinate system and DSNM overlaid [1]

Tables

Errata

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