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Research Papers

Metrics for Evaluation and Design of Large-Displacement Linear-Motion Compliant Mechanisms

[+] Author and Article Information
Allen B. Mackay

 Medical Products Division, W. L. Gore and Associates, Flagstaff, AZ 86001allen.mackay@byu.net

David G. Smith

Compliant Mechanism Research,  Brigham Young University, Provo, UT 84602david.gar.smith@gmail.com

Spencer P. Magleby1

Brian D. Jensen

Larry L. Howell

Department of Mechanical Engineering,  Brigham Young University, Provo, UT 84602lhowell@byu.edu

1

Corresponding author

J. Mech. Des 134(1), 011008 (Jan 04, 2012) (9 pages) doi:10.1115/1.4004191 History: Received August 18, 2009; Revised March 29, 2011; Published January 04, 2012; Online January 04, 2012

This work introduces metrics for large-displacement linear-motion compliant mechanisms (LLCMs) that evaluate the performance tradeoff between displacement and off-axis stiffness. These metrics are nondimensionalized, consisting of relevant characteristics used to describe displacement, off-axis stiffness, actuation force, and size. Displacement is normalized by the footprint of the device, transverse stiffness by a new performance characteristic called virtual axial stiffness, and torsional stiffness by the characteristic torque. These metrics account for the variation of both axial and off-axis stiffness over the range of displacement. The metrics are demonstrated for several microelectromechanical systems (MEMS) that are sensitive to size because of high cost and off-axis stiffness because of function. The use of metrics in design is demonstrated in the design of an LLCM; the resulting design shows increased values for both the travel and transverse-stiffness metrics.

Copyright © 2012 by American Society of Mechanical Engineers
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References

Figures

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Figure 1

Examples of linear-motion mechanisms: (a) rigid-body linear roller bearing; (b) compliant folded-beam mechanism; (c) compliant bistable mechanism

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Figure 2

Key definitions for a typical linear-motion compliant mechanism, including axial and transverse directions and total axial displacement

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Figure 3

The function of transverse stiffness over the range of axial displacement. The solid portion of the graph indicates axial positions within the yield strength of the material.

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Figure 4

The function of torsional stiffness over the range of axial displacement. The solid portion of the graph indicates axial positions within the yield strength of the material.

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Figure 5

The size of 2D linear mechanisms can be described by the bounding box defined by the widest and longest instances. The limiting features of the support structure are indicated by the arrows for these three cases.

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Figure 6

Illustration of the virtual axial stiffness for (a) a bistable mechanism and (b) linear mechanism

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Figure 7

The normalized torsional stiffness can be interpreted as normalized by a characteristic torque as illustrated here with a theoretical mechanism with a force of magnitude Fax , max and couple moment arm of length d

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Figure 8

Three mechanisms used in the case study: (a) folded beam [4]; (b) CT joint [3]; (c) XBob [6]

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Figure 9

Demonstration of the use of the transverse stiffness metric with several sample configurations simulating a variation in in-plane thickness for the three concepts

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Figure 10

Demonstration of the use of the torsional stiffness metric with several sample configurations simulating a variation in in-plane thickness for the three concepts

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Figure 11

Micrographs of (a) a folded-beam suspension large-displacement device, (b) an X-Bob suspension large-displacement device, and (c) a double X-Bob suspension

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Figure 12

Force gauges for measuring axial and transverse force-deflection relationships

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Figure 13

Force-deflection relationships for 4 micro-devices

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Figure 14

Transverse-displacement 3D plot for small X-Bob suspension, similar plots were created for all of the device configurations

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Figure 15

Microscope images of (a) a large X-Bob design and (b) an optimized X-Bob design

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