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TECHNICAL PAPERS

Sensor Placement for Angular Velocity Determination

[+] Author and Article Information
Guy M. Genin

Department of Mechanical Engineering, Washington University, St. Louis, MO 63130

Joseph Genin

Department of Mechanical Engineering, New Mexico State University, Las Cruces, NM 88003

J. Dyn. Sys., Meas., Control 128(3), 543-547 (Aug 23, 2005) (5 pages) doi:10.1115/1.2192823 History: Received September 30, 2003; Revised August 23, 2005

Velocity transducer placement to uniquely determine the angular velocity of a rigid body is investigated. The angular velocity of a rigid body can be determined with no fewer than five properly placed velocity transducers, if no other types of sensors are present and no algebraic constraint equation involving the angular velocity vector can be written. Complete characterization of the velocity of a rigid body requires six transducers. Choice of transducer placement and orientation requires care, as suboptimal transducer placement can result in data from which the determination of a unique angular velocity vector is impossible. Conditions for successful transducer placement are established, and two examples of adequate transducer placement are presented: an Earth-penetrating projectile, and a bioengineering device for the measurement of head motion.

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Copyright © 2006 by American Society of Mechanical Engineers
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Figures

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Figure 1

An Earth-penetrator instrumented with two triaxial velocity transducers. This scheme cannot measure the component of the angular velocity vector parallel to the line connecting A and F.

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Figure 2

A rod whose 3-D motion is constrained in such a way that ω∙rF∕A=0

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Figure 3

An Earth-penetrator instrumented with six unidirectional velocity transducers. The placement does not allow unique determiniation of the x component of angular velocity.

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Figure 4

A placement scheme for six uni-directional velocity transducers that allows the unique determination of the angular velocity vector

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Figure 5

(a) Headgear for motion measurement. (b) A placement scheme that allows a unique determination of the angular velocity vector with five unidirectional velocity transducers.

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