0
Research Papers

Simultaneous Topological and Dimensional Synthesis of Planar Morphing Mechanisms

[+] Author and Article Information
Lawrence W. Funke

Department of Aerospace and
Mechanical Engineering,
University of Notre Dame,
Notre Dame, IN 46556
e-mail: lfunke@nd.edu

James P. Schmiedeler

Fellow ASME
Department of Aerospace and
Mechanical Engineering,
University of Notre Dame,
Notre Dame, IN 46556
e-mail: schmiedeler.4@nd.edu

1Corresponding author.

Manuscript received October 13, 2016; final manuscript received January 13, 2017; published online March 9, 2017. Assoc. Editor: Venkat Krovi.

J. Mechanisms Robotics 9(2), 021009 (Mar 09, 2017) (9 pages) Paper No: JMR-16-1306; doi: 10.1115/1.4035878 History: Received October 13, 2016; Revised January 13, 2017

This paper presents a general method to perform simultaneous topological and dimensional synthesis for planar rigid-body morphing mechanisms. The synthesis is framed as a multi-objective optimization problem for which the first objective is to minimize the error in matching the desired shapes. The second objective is typically to minimize the actuating force/moment required to move the mechanism, but different applications may require a different choice. All the possible topologies are enumerated for morphing mechanism designs with a specified number of degrees of freedom (DOF), and infeasible topologies are removed from the search space. A multi-objective genetic algorithm (GA) is then used to simultaneously handle the discrete nature of the topological optimization and the continuous nature of the dimensional optimization. In this way, candidate solutions from any of the feasible topologies enumerated can be evaluated and compared. Ultimately, the method yields a sizable population of viable solutions, often of different topologies, so that the designer can manage engineering tradeoffs in selecting the best mechanism. Three examples illustrate the strengths of this method. The first examines the advantages gained by considering and optimizing across all the topologies simultaneously. The second and third demonstrate the method's versatility by incorporating prismatic joints into the morphing chain to allow for morphing between shapes that have significant changes in both shape and arc length.

FIGURES IN THIS ARTICLE
<>
Copyright © 2017 by ASME
Topics: Chain , Design , Topology , Errors
Your Session has timed out. Please sign back in to continue.

References

Yoon, H.-S. , and Washington, G. , 2010, “ An Optimal Method of Shape Control for Deformable Structures With an Application to a Mechanically Reconfigurable Reflector Antenna,” Smart Mater. Struct., 19(10), p. 105004.
Lu, K. , and Kota, S. , 2003, “ Design of Compliant Mechanisms for Morphing Structural Shapes,” J. Intell. Mater. Syst. Struct., 14(6), pp. 379–391. [CrossRef]
Daynes, S. , and Weaver, P. M. , 2011, “ A Shape Adaptive Airfoil for a Wind Turbine Blade,” Proc. SPIE, 7979, p. 79790H.
Maheri, A. , Noroozi, S. , and Vinney, J. , 2007, “ Application of Combined Analytical/FEA Coupled Aero-Structure Simulation in Design of Wind Turbine Adaptive Blades,” Renewable Energy, 32(12), pp. 2011–2018. [CrossRef]
Zhao, K. , Schmiedeler, J. P. , and Murray, A. P. , 2012, “ Design of Planar, Shape-Changing Rigid-Body Mechanisms for Morphing Aircraft Wings,” ASME J. Mech. Rob., 4(4), p. 041007.
Wiggins, L. D. , Stubbs, M. D. , Johnston, C. O. , Robertshaw, H. H. , Reinholtz, C. F. , and Inman, D. J. , 2004, “ A Design and Analysis of a Morphing Hyper-Elliptic Cambered Span (HECS) Wing,” AIAA Paper No. 2004-1885.
Kota, S. , Hetrick, J. , Osborn, R. , Paul, D. , Pendleton, E. , Flick, P. , and Tilmann, C. , 2003, “ Design and Application of Compliant Mechanisms for Morphing Aircraft Structures,” Proc. SPIE, 5054, pp. 24–33.
Neal, D. A. , Good, M. G. , Johnston, C. O. , Robertshaw, H. H. , Mason, W. H. , and Inman, D. J. , 2004, “ Design and Wind-Tunnel Analysis of a Fully Adaptive Aircraft Configuration,” AIAA Paper No. 2004-1727.
Trease, B. , and Kota, S. , 2009, “ Design of Adaptive and Controllable Compliant Systems With Embedded Actuators and Sensors,” ASME J. Mech. Des., 131(11), p. 111001.
Vos, R. , Gurdal, Z. , and Abdalla, M. , 2010, “ Mechanism for Warp-Controlled Twist of a Morphing Wing,” J. Aircr., 47(2), pp. 450–457. [CrossRef]
Frank, G. J. , Joo, J. J. , Sanders, B. , Garner, D. M. , and Murray, A. P. , 2008, “ Mechanization of a High Aspect Ratio Wing for Aerodynamic Control,” J. Intell. Mater. Syst. Struct., 19(9), pp. 1101–1112. [CrossRef]
Calkins, F. T. , and Mabe, J. H. , 2010, “ Shape Memory Alloy Based Morphing Aerostructures,” ASME J. Mech. Des., 132(11), p. 111012.
Inoyama, D. , Sanders, B. P. , and Joo, J. J. , 2008, “ Topology Optimization Approach for the Determination of the Multiple-Configuration Morphing Wing Structure,” J. Aircr., 45(6), pp. 1853–1863. [CrossRef]
Muhammad, A. , Nguyen, Q. V. , Park, H. C. , Hwang, D. Y. , Byun, D. , and Goo, N. S. , 2010, “ Improvement of Artificial Foldable Wing Models by Mimicking the Unfolding/Folding Mechanism of a Beetle Hind Wing,” J. Bionic Eng., 7(2), pp. 134–141. [CrossRef]
Daynes, S. , Weaver, P. M. , and Trevarthen, J. A. , 2011, “ A Morphing Composite Air Inlet With Multiple Stable Shapes,” J. Intell. Mater. Syst. Struct., 22(9), pp. 961–973. [CrossRef]
Miles, R. , Howard, P. , Limbach, C. , Zaidi, S. , Lucato, S. , Cox, B. , Marshall, D. , Espinosa, A. M. , and Driemeyer, D. , 2011, “ A Shape-Morphing Ceramic Composite for Variable Geometry Scramjet Inlets,” J. Am. Ceram. Soc., 94(s1), pp. s35–s41. [CrossRef]
Dürr, J. K. , Honke, R. , Alberti, M. V. , and Sippel, R. , 2003, “ Development and Manufacture of an Adaptive Lightweight Mirror for Space Application,” Smart Mater. Struct., 12(6), pp. 1005–1016. [CrossRef]
Rodrigues, G. , Bastaits, R. , Roose, S. , Stockman, Y. , Gebhardt, S. , Schoenecker, A. , Villon, P. , and Preumont, A. , 2009, “ Modular Bimorph Mirrors for Adaptive Optics,” Opt. Eng., 48(3), p. 034001.
Funke, L. W. , Schmiedeler, J. P. , and Zhao, K. , 2015, “ Design of Planar Multi-Degree-of-Freedom Morphing Mechanisms,” ASME J. Mech. Rob., 7(1), p. 011007.
Funke, L. , and Schmiedeler, J. P. , 2015, “ Design of Multi-Degree-of-Freedom Planar Morphing Mechanisms With Single-Degree-of-Freedom Sub-Chains,” ASME Paper No. DETC2015-47277.
Giaier, K. S. , Myszka, D. H. , Kramer, W. P. , and Murray, A. P. , 2014, “ Variable Geometry Dies for Polymer Extrusion,” ASME Paper No. IMECE2014-38409.
Lu, K.-J. , and Kota, S. , 2006, “ Topology and Dimensional Synthesis of Compliant Mechanisms Using Discrete Optimization,” ASME J. Mech. Des., 128(5), pp. 1080–1091. [CrossRef]
Kim, S. I. , and Kim, Y. Y. , 2014, “ Topology Optimization of Planar Linkage Mechanisms,” Int. J. Numer. Methods Eng., 98(4), pp. 265–286. [CrossRef]
Yoon, G. H. , and Heo, J. C. , 2012, “ Constraint Force Design Method for Topology Optimization of Planar Rigid-Body Mechanisms,” Comput. Aided Des., 44(12), pp. 1277–1296. [CrossRef]
Heo, J. C. , and Yoon, G. H. , 2013, “ Size and Configuration Syntheses of Rigid-Link Mechanisms With Multiple Rotary Actuators Using the Constraint Force Design Method,” Mech. Mach. Theory, 64, pp. 18–38. [CrossRef]
Zhao, K. , and Schmiedeler, J. P. , 2015, “ Using Rigid-Body Mechanism Topologies to Design Shape-Changing Compliant Mechanisms,” ASME J. Mech. Rob., 8(1), p. 011014.
Sedlaczek, K. , and Eberhard, P. , 2009, “ Topology Optimization of Large Motion Rigid Body Mechanisms With Nonlinear Kinematics,” ASME J. Comput. Nonlinear Dyn., 4(2), p. 021011.
Pucheta, M. A. , and Cardona, A. , 2013, “ Topological and Dimensional Synthesis of Planar Linkages for Multiple Kinematic Tasks,” Multibody Syst. Dyn., 29(2), pp. 189–211. [CrossRef]
Murray, A. P. , Schmiedeler, J. P. , and Korte, B. M. , 2008, “ Kinematic Synthesis of Planar, Shape-Changing Rigid-Body Mechanisms,” ASME J. Mech. Des., 130(3), p. 032302.
Persinger, J. A. , Schmiedeler, J. P. , and Murray, A. P. , 2009, “ Synthesis of Planar Rigid-Body Mechanisms Approximating Shape Changes Defined by Closed Curves,” ASME J. Mech. Des., 131(7), p. 071006.
Zhao, K. , Schmiedeler, J. P. , and Murray, A. P. , 2011, “ Kinematic Synthesis of Planar, Shape-Changing Rigid-Body Mechanisms With Prismatic Joints,” ASME Paper No. DETC2011-48503.
Shamsudin, S. A. , Murray, A. P. , Myszka, D. H. , and Schmiedeler, J. P. , 2013, “ Kinematic Synthesis of Planar, Shape-Changing, Rigid Body Mechanisms for Design Profiles With Significant Differences in Arc Length,” Mech. Mach. Theory, 70, pp. 425–440. [CrossRef]
Li, B. , Murray, A. P. , and Myszka, D. H. , 2015, “ Designing Variable-Geometry Extrusion Dies That Utilize Planar Shape-Changing Rigid-Body Mechanisms,” ASME Paper No. DETC2015-46670.

Figures

Grahic Jump Location
Fig. 1

Example 1DOF closed morphing mechanism

Grahic Jump Location
Fig. 2

Example 3DOF fixed-end morphing mechanism

Grahic Jump Location
Fig. 3

Example 2DOF open morphing mechanism

Grahic Jump Location
Fig. 4

Target profile set for the example in Sec. 4

Grahic Jump Location
Fig. 5

Plots showing the percent increase in matching error and maximum required actuating moment for each mechanism in the suitable design region for the example in Sec. 4. The symbols represent different topology permutations. (a) 1DOF solutions for the restricted topology case and (b) 1DOF solutions for the general topology case.

Grahic Jump Location
Fig. 6

Sample solution mechanisms for the example in Sec. 4, shown in configurations closest to the first design profile: (a) topology permutation denoted by squares (□) in Fig. 5(a), (b) topology permutation denoted by circles (o) in Fig. 5(b), (c) topology permutation denoted by left facing triangles (◁) in Fig. 5(b), and (d) topology permutation denoted by x marks (x) in Fig. 5(b)

Grahic Jump Location
Fig. 7

Target profile set for the example in Sec. 5

Grahic Jump Location
Fig. 8

Plots showing the percent increase in matching error and the average maximum required actuating moment for each mechanism in the suitable design region for the example in Sec. 5. Each symbol is a different topology permutation. (a) 1DOF solutions, (b) 2DOF solutions, and (c) 3DOF solutions.

Grahic Jump Location
Fig. 9

3DOF solution mechanism from the topology permutation denoted by circles (o) in Fig. 8(c) for the example in Sec. 5, shown in its configuration closest to the first design profile

Grahic Jump Location
Fig. 10

Target profile set for the example in Sec. 6

Grahic Jump Location
Fig. 11

Plots showing the percent increase in matching error and the average maximum required actuating moment for each mechanism in the suitable design region for the example in Sec. 6. Each symbol is a different topology permutation. (a) 1DOF solutions, (b) 2DOF solutions, and (c) 3DOF solutions.

Grahic Jump Location
Fig. 12

2DOF solution from the topology permutation denoted by squares (□) in Fig. 11(b) for the example in Sec. 6, shown in its configuration closest to the first design profile

Tables

Errata

Discussions

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