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.

In this paper, we present a real-time algorithm for automatic recognition of not only physical activities, but also, in some cases, their intensities, using five triaxial wireless accelerometers and a wireless heart rate monitor. The algorithm has been evaluated using datasets consisting of 30 physical gymnasium activities collected from a total of 21 people at two different labs. On these activities, we have obtained a recognition accuracy performance of 94.6% using subject-dependent training and 56.3% using subjectindependent training. The addition of heart rate data improves subject-dependent recognition accuracy only by 1.2% and subject-independent recognition only by 2.1%. When recognizing activity type without differentiating intensity levels, we obtain a subjectindependent performance of 80.6%. We discuss why heart rate data has such little discriminatory power.

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The angular acceleration of a rigid body with respect to a body-fixed (moving) frame can be reliably computed from nine acceleration field measurements. Noncommutativity of finite rotations causes computational problems during numerical integration to obtain the transformation matrix, especially when the rotation is three-dimensional and there are errors in the measured linear accelerations. A method based on the orientation vector concept is formulated and tested against hypothetical data. The rigid-body rotations computed from linear accelerometer data from impact acceleration tests are compared against those obtained from three-dimensional analysis of high speed movie films.