Measurement of Angular Acceleration of a Rigid Body Using Linear Accelerometers

TLDR

The computation of angular acceleration of a rigid body from measured linear accelerations is a simple procedure based on well‑known kinematic principles, requiring at least six accelerometers in theory, but recent impact‑biomechanics attempts using only six accelerometers failed to capture full 3‑D motion. This paper demonstrates the cause of the inconsistency between theory and practice and specifies the conditions under which the method fails. An alternate method using a special nine‑accelerometer configuration is proposed to overcome these limitations. The stability and superiority of this approach are shown by both hypothetical and experimental data.

Abstract

The computation of angular acceleration of a rigid body from measured linear accelerations is a simple procedure, based on well-known kinematic principles. It can be shown that, in theory, a minimum of six linear accelerometers are required for a complete definition of the kinematics of a rigid body. However, recent attempts in impact biomechanics to determine general three-dimensional motion of body segments were unsuccessful when only six accelerometers were used. This paper demonstrates the cause for this inconsistency between theory and practice and specifies the conditions under which the method fails. In addition, an alternate method based on a special nine-accelerometer configuration is proposed. The stability and superiority of this approach are shown by the use of hypothetical as well as experimental data.