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TECHNICAL PAPERS

# Numerical Validation of Linear Accelerometer Systems for the Measurement of Head Kinematics

[+] Author and Article Information
Paolo Cappa

Department of Mechanics and Aeronautics,  University of Rome “La Sapienza,” Via Eudossiana, 18-00184 Rome, Italypaolo.cappa@uniroma1.it

Lorenzo Masia, Fabrizio Patanè

Department of Mechanics and Aeronautics,  University of Rome “La Sapienza,” Via Eudossiana, 18-00184 Rome, Italy

J Biomech Eng 127(6), 919-928 (Jul 11, 2005) (10 pages) doi:10.1115/1.2049329 History: Received March 15, 2005; Revised July 11, 2005

## Abstract

The purpose of this study was to analytically exploit the capabilities of head-mounted systems instrumented with linear accelerometers (ACs) for field use in redundant configurations. We simulated different headsets equipped with uni-, bi- or triaxial sensors with a number of axes that lie in the range of 12–24; the ACs were located on a hemispherical surface by adopting a priori criterion while their orientation was randomized. In addition, for a comparative purpose the nine accelerometer scheme (one triaxial AC and three biaxial ACs addressed in the following as “3-2-2-2 configuration”) was also analyzed in the present paper. We simulated and statistically assessed the performances of hemispherical headsets in the test case of a healthy subject walking freely at normal pace over level ground. The numerical results indicated that a well designed instrumented headset can retrieve the angular acceleration and $(a0−g)$ component with rms errors of about 2% and 0.5%, respectively, and angular velocity with a drift error of about 20% in a $6s$ trial. On the contrary, the pose of the headset cannot be evaluated because of the drift induced by the integration process. In general, we can state that headsets with uni-, bi- or triaxial ACs have comparable performances. The main implications of the above-mentioned observations are (a) neither expensive triaxial ACs nor assembling procedure based on the use of orthogonal mounting blocks are needed; (b) redundant arrays of low-cost uni- or biaxial ACs can effectively be used to reach adequate performances in biomechanical studies where head acceleration and velocity are investigated; (c) while estimates of angular acceleration with accelerometers are accurate, estimations of angular velocities, linear velocities and pose are not.

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## Figures

Figure 1

(a) Positioning of the nine-axial AC assembly (“3-2-2-2 configuration”) to the headset in accordance with the scheme proposed by Padgaonkar (13). Chosen criterion of ACs: (b) possible orientations of each typology of ACs; (c) upper view of a helmet equipped with fourteen ACs, with the general rules, see Table 1, adopted for the location of the sensors in each level z=0, R∕2 and R. Even if different types of ACs are depicted over the same headset, each simulated cluster is equipped by the same type of sensor, i.e., only packages of uni-, bi- or triaxial ACs.

Figure 2

Paradigmatic movement investigated in terms of origin displacement p0=(x,y,z) and Euler angles (φ,θ,ψ) as a function of time

Figure 3

Typical output of a simulated trial. The dotted and the solid line represent the errors ε that occurred with 12-axial ACs and 18-axial ACs, respectively. The data are relative to the z component of the errors associated to angular acceleration and velocity.

Figure 4

Overall errors associated to angular acceleration in percentage of the maximum range occurred during the simulated trial as a function of the number of sensitive axes. Results relative to “3-2-2-2 configuration” are indicated with horizontal lines.

Figure 5

Overall errors associated to angular velocity in percentage of the maximum range occurred during the simulated trial as a function of the number of sensitive axes. Results relative to “3-2-2-2 configuration” are indicated with horizontal lines.

Figure 6

Overall errors associated to (a0−g) component in percentage of the maximum range occurred during the simulated trial as a function of the number of sensitive axes. Results relative to “3-2-2-2 configuration” are indicated with horizontal lines.

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