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Research Papers

Design of Planar, Shape-Changing Rigid-Body Mechanisms for Morphing Aircraft Wings

[+] Author and Article Information
Kai Zhao1

James P. Schmiedeler

Department of Aerospace and Mechanical Engineering,  University of Notre Dame, Notre Dame, IN 46556schmiedeler.4@nd.edu

Andrew P. Murray

Department of Mechanical and Aerospace Engineering,  University of Dayton, Dayton, OH 45469murray@udayton.edu

1

Corresponding author.

J. Mechanisms Robotics 4(4), 041007 (Sep 17, 2012) (10 pages) doi:10.1115/1.4007449 History: Received August 11, 2011; Revised June 08, 2012; Published September 17, 2012; Online September 17, 2012

This paper presents a procedure to synthesize planar rigid-body mechanisms, containing both prismatic and revolute joints, capable of approximating a shape change defined by a set of morphing curves in different positions. The existing mechanization process is extended specifically to enable the design of morphing aircraft wings. A portion of the closed-curve morphing chain that has minimal displacement is identified as the structural ground after the segmentation process. Because of the revolute joints placed at the endpoints of the ground section, the moving links of the fixed-end morphing chain need to be repositioned relative to each of the desired wing shapes so as to minimize the error in approximating them. With the introduction of prismatic joints, a building-block approach is employed to mechanize the fixed-end morphing chain. The blocks are located in an assembly position to generate a single degree-of-freedom (DOF) mechanism. Because of the additional constraints associated with prismatic joints compared to revolute joints, the size of the solution space is reduced, so random searches of the design space to find solution mechanisms are ineffective. A multi-objective genetic algorithm is employed instead to find a group of viable designs that tradeoff minimizing matching error with maximizing mechanical advantage. The procedure is demonstrated with a synthesis example of a 1-DOF mechanism approximating eight closed-curve wing profiles.

Copyright © 2012 by American Society of Mechanical Engineers
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Figures

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Figure 1

(a) A set of eight airfoil shapes in different positions. The maximum airfoil camber labeled by position 1 and the minimum airfoil camber labeled by position 8 are in solid lines. Dashed lines are intermediate positions. (b) Generated morphing chain with six segments to approximate eight different wing shapes. (c) Solution single-DOF mechanism synthesized from the chain.

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Figure 2

Flowchart for the rigid-body shape-changing synthesis approach for morphing aircraft wings

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Figure 3

(a) Three target profiles. (b) Two of the target profiles are shifted to minimize the distance relative to the third. (c) A mean profile (solid line). (d) The mean profile shifted to minimize the distance relative to each of the target profiles. [19]

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Figure 4

Definition of the design variables and elements of the objective function for the optimization procedure to align the moving segments of the fixed-end morphing chain (shown as solid lines) with position i of the desired wing shape (shown as dashed lines)

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Figure 5

Basic building blocks: (a) RRR block and (b) PRR block

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Figure 6

Assembly of building blocks to yield a 1-DOF mechanism that approximates (a) an open-curve design profile and (b) a closed-curve design profile

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Figure 7

The challenge of locating two building blocks after the least squares approach to minimize the error in approximating the design profiles in n different positions has been implemented

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Figure 8

Definition of design variables and parameters used in the numerical optimization method to solve the challenge of locating building blocks created by the least squares approach

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Figure 9

Horizontal and vertical loads applied on the wing profile during morphing

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Figure 10

Plot of the largest movement D of all points in the morphing chain. Points that moved less 0.07 ft were considered as candidates for the ground section.

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Figure 11

Repositioning of the fixed-end morphing chain to be in the eight positions closest to the eight wing shapes

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Figure 12

Simplified point loads (lb) applied on each segment of the fixed-end morphing chain

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Figure 13

Record of the Pareto front for the adaptive wing design example

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Figure 14

Single-DOF mechanism approximating eight wing profiles. (a) and (j) are in the positions near the input limit. (b)–(i) show the closest position of the solution mechanism to each profile.

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Figure 15

Solid model of the solution mechanism approximating eight wing profiles

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