Research Papers

Qualitative Mobility Analysis of Wire Flexure Systems Using Load Flow Visualization

[+] Author and Article Information
Sreeshankar Satheeshbabu

Department of Industrial and Enterprise
Systems Engineering,
University of Illinois Urbana-Champaign,
Urbana, IL 61853
e-mail: sthshbb2@illinois.edu

Girish Krishnan

Assistant Professor
Department of Industrial
and Enterprise Systems Engineering,
University of Illinois Urbana-Champaign,
Urbana, IL 61853
e-mail: gkrishna@illinois.edu

1Corresponding author.

Manuscript received January 1, 2016; final manuscript received May 23, 2016; published online September 8, 2016. Assoc. Editor: Larry L Howell.

J. Mechanisms Robotics 8(6), 061012 (Sep 08, 2016) (11 pages) Paper No: JMR-16-1001; doi: 10.1115/1.4033859 History: Received January 01, 2016; Revised May 23, 2016

Mobility analysis is an important step in the conceptual design of flexure systems. It involves identifying directions with relatively compliant motion (freedoms) and directions with relatively restricted motion (constraints). This paper proposes a deterministic framework for mobility analysis of wire flexure systems based on characterizing a kinetostatic vector field known as “load flow” through the geometry. A hypothesis is proposed to identify constraints and freedoms based on the relationship between load flow and the flexure geometry. This hypothesis is mathematically restated to formulate a matrix-based reduction technique that determines flexure mobility computationally. Several examples with varying complexity are illustrated to validate the efficacy of this technique. This technique is particularly useful in analyzing complex hybrid interconnected flexure topologies, which may be nonintuitive or involved with traditional methods. This is illustrated through the computational mobility analysis of a bio-inspired fiber reinforced elastomer pressurized with fluids. The proposed framework combines both visual insight and analytical rigor, and will complement existing analysis and synthesis techniques.

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Fig. 2

Definition of load flow using the concept of transferred load (a) force applied at i producing a deformation uj at point j. (b) The transferred force fjtr is an applied force at j that produces the same displacement uj at j.

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Fig. 3

(a) A parallelogram flexure consisting of two wire flexures in parallel. Load flow for (b) axial displacement, (c) in-plane twist, and (d) transverse displacement (axial displacement and in-plane twist are constraint directions while transverse displacement is a freedom direction.).

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Fig. 1

(a) Parallel flexure, (b) hybrid flexure, and (c) a fiber-reinforced elastomeric cylinder modeled as a spatial wire flexure system

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Fig. 5

Load flow in over constrained parallel flexures. A triangle flexure with (a) its load flow in the constraint direction and (b) in the freedom direction.

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Fig. 4

Load flow for flexure systems for (a) transverse displacement, (b) in-plane rotation, (c) axial displacement, and (d) twist freedom. The point of application of input displacements is represented by a small circle at the center.

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Fig. 6

Load flow for a series flexures in two directions

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Fig. 7

Load flows for a spatial flexure in the constraint (top row) and freedom (bottom) directions. The constraints displayed represent pure x-translation and x-rotation while the freedoms correspond to pure z-translation and a twist along the x-axis.

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Fig. 8

Load flows indicating freedom and constraint directions for a spatial hybrid flexure

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Fig. 15

Analysis of freedom spaces of intermediate rigid bodies

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Fig. 13

Analysis of a wire flexure system equivalent of a sheet flexure in terms of mobility

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Fig. 14

Visualization of freedom and constraint spaces for flexure systems. (a) Pure rotational freedoms, (b) screws as freedom directions, and (c) pure forces as constraints.

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Fig. 9

Explaining the LFC framework for mobility analysis using a cantilever beam. The figure shows the input force and moment required to move the cantilever beam by (a) unit translation in the X direction, (b) unit translation in the Y direction, and (c) unit rotation about the z-axis.

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Fig. 10

Steps involved in the implementation of the framework. The steps enclosed in the dashed box require user interaction, while the rest of the steps are carried out computationally.

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Fig. 11

Case study of (a) five flexure stage and (b) load flow and deformed shape in the freedom direction

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Fig. 12

DOF determination of 3D flexure systems. Blue—rigid members, cyan—flexure limbs, orange—intermediate bodies (see online version for color).

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Fig. 16

Mobility analysis of a FREE: (a) Inspiration of FREEs from soft aquatic wildlife, (b) constituents of FREEs, (c)–(f) different unit displacements applied to the rigid end caps, (g) transverse load flow noticed in the freedom directions, (h) predominantly axial load flow noticed in the constraint direction

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Fig. 17

Determining the freedom space of a FREE



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