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Research Papers

Linear Estimation of the Rigid-Body Acceleration Field From Point-Acceleration Measurements

[+] Author and Article Information
Philippe Cardou

Department of Mechanical Engineering, Laval University, Adrien-Pouliot Building, Room No. 1504, Quebec City, QC, G1V 0A6, Canadapcardou@gmc.ulaval.ca

Jorge Angeles

Department of Mechanical Engineering, Centre for Intelligent Machines, McGill University, Macdonald Engineering Building, Room No. 461, 817 Sherbrooke Street West, Montreal, QC, H3A 2K6, Canada

CPM(a ) is defined as (a×x)/x, for any a, xR3.

Given a subspace U of Rn, the space U of all vectors orthogonal to U is called the orthogonal complement (44) of U.

J. Dyn. Sys., Meas., Control 131(4), 041013 (May 21, 2009) (10 pages) doi:10.1115/1.3117209 History: Received May 25, 2008; Revised January 05, 2009; Published May 21, 2009

Among other applications, accelerometer arrays have been used extensively in crashworthiness to measure the acceleration field of the head of a dummy subjected to impact. As it turns out, most accelerometer arrays proposed in the literature were analyzed on a case-by-case basis, often not knowing what components of the rigid-body acceleration field the sensor allows to estimate. We introduce a general model of accelerometer behavior, which encompasses the features of all acclerometer arrays proposed in the literature, with the purpose of determining their scope and limitations. The model proposed leads to a classification of accelerometer arrays into three types: point-determined; tangentially determined; and radially determined. The conditions that define each type are established, then applied to the three types drawn from the literature. The model proposed lends itself to a symbolic manipulation, which can be readily automated, with the purpose of providing an evaluation tool for any acceleration array, which should be invaluable at the development stage, especially when a rich set of variants is proposed.

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Copyright © 2009 by American Society of Mechanical Engineers
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Figures

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Figure 1

The acceleration field of a rigid body moving in space

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Figure 2

A rigid body equipped with n accelerometers moving in space

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Figure 3

Geometry of the 3–2–2–2 accelerometer array (4)

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Figure 4

Geometry of a six-accelerometer array (44)

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Figure 5

Geometry of a 12-accelerometer array (45)

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