3-D attitude representation of human joints: a standardization proposal.

In view of the singularities, asymmetries and other adverse properties of existing, three-dimensional definitions for joint and segment angles, the present paper proposes a new convention for unambiguous and easily interpretable, 3-D joint angles, based on the concept of the attitude 'vector' as derived from Euler's theorem. The suggested standard can be easily explained to non-mathematically trained clinicians, is readily implemented in software, and can be simply related to classical Cardanic/Eulerian angles. For 'planar' rotations about a coordinate system's axes, the proposed convention coincides with the Cardanic convention. The attitude vector dispenses with the 'gimbal-lock' and non-orthogonality disadvantages of Cardanic/Eulerian conventions; therefore, its components have better metrical properties, and they are less sensitive to measurement errors and to coordinate system uncertainties than Cardanic/Eulerian angles. A sensitivity analysis and a physical interpretation of the proposed standard are given, and some experimental results that demonstrate its advantages.

Instantaneous helical axis estimation from 3-D video data in neck kinematics for whiplash diagnostics.

To date, the diagnosis of whiplash injuries has been very difficult and largely based on subjective, clinical assessment. The work by Winters and Peles Multiple Muscle Systems--Biomechanics and Movement Organization. Springer, New York (1990) suggests that the use of finite helical axes (FHAs) in the neck may provide an objective assessment tool for neck mobility. Thus, the position of the FHA describing head-trunk motion may allow discrimination between normal and pathological cases such as decreased mobility in particular cervical joints. For noisy, unsmoothed data, the FHAs must be taken over rather large angular intervals if the FHAs are to be reconstructed with sufficient accuracy; in the Winters and Peles study, these intervals were approximately 10 degrees. in order to study the movements' microstructure, the present investigation uses instantaneous helical axes (IHAs) estimated from low-pass smoothed video data. Here, the small-step noise sensitivity of the FHA no longer applies, and proper low-pass filtering allows estimation of the IHA even for small rotation velocity omega of the moving neck. For marker clusters mounted on the head and trunk, technical system validation showed that the IHAs direction dispersions were on the order of one degree, while their position dispersions were on the order of 1 mm, for low-pass cut-off frequencies of a few Hz (the dispersions were calculated from omega-weighted errors, in order to account for the adverse effects of vanishing omega). Various simple, planar models relating the instantaneous, 2-D centre of rotation with the geometry and kinematics of a multi-joint neck model are derived, in order to gauge the utility of the FHA and IHA approaches. Some preliminary results on asymptomatic and pathological subjects are provided, in terms of the 'ruled surface' formed by sampled IHAs and of their piercing points through the mid-sagittal plane during a prescribed flexion-extension movement of the neck.

A least-squares algorithm for the equiform transformation from spatial marker co-ordinates.

The present paper describes an algorithm for estimating the translation vector and the rotation matrix of a moving body from noisy measurements on the spatial co-ordinates of at least three non-collinear markers. A sensitivity analysis of the estimated parameters and of the helical axis is presented in terms of characteristics of the marker distribution. The implementation of the proposed algorithm in a FORTRAN-subroutine is appended.

Analytical stereophotogrammetric determination of three-dimensional knee-joint geometry.

An analytical stereophotogrammetric method is introduced to measure the three-dimensional geometry of articular surfaces in vitro. Information of this kind is particularly useful for mathematical joint models and anthropological studies. The method requires no specific equipment, such as a stereocomparator, contrarily to other techniques reported (e.g. Ghosh, 1983) and is relatively simple and inexpensive. The background of the method is outlined in the present paper, and results of accuracy and precision tests are presented. It is shown that an accuracy on the order of 0.2 mm (95% confidence interval) is well feasible in actual knee-joint evaluations, if the measuring procedure is conducted carefully. The method is illustrated by measuring and comparing the articular surface geometries of a bilateral pair of knee joints.

Finite centroid and helical axis estimation from noisy landmark measurements in the study of human joint kinematics.

Recent work on joint kinematics indicates that the finite centroid (centre of rotation) and the finite helical axis (axis of rotation, screw axis, twist axis) are highly susceptible to measurement errors when they are experimentally determined from landmark position data. This paper presents an analytical model to describe these effects, under isotropic conditions for the measurement errors and for the spatial landmark distribution. It appears that the position and direction errors are inversely proportional to the rotation magnitude, and that they are much more error-prone than the relatively well-determined rotation and translation magnitudes. Furthermore, the direction and rotation magnitude errors are inversely proportional to the landmark distribution radius, and the position and translation magnitude errors are minimal if the mean position of the landmarks coincides with the centroid or helical axis. For the planar centroid, the use of rigid-body constraints results in considerable precision improvement relative to the classical, finite Reuleaux method for centroid reconstruction. These analytical results can be used to define suitable measurement configurations, and they are used in this paper to explain experimental results on Röntgenphotogrammetrically acquired in vitro wrist joint movement.

Optoelectric (Selspot) gait measurement in two- and three-dimensional space--a preliminary report.

Traditional studies of human movement by photographic methods require tedious, error-prone, and expensive data reduction. Various optoelectronic methods have been designed. A commercially available system, SELSPOT, purchased for the Cleveland VAMC Motion Study Laboratory, is described. Sequentially pulsed light-emitting-diode targets on the subject are observed, with data fed into a computer for combination with force plate data (Cohen, Orin, and Marsolais, Technical Note, BPR 10-33). Calibration methods, errors, and practical difficulties are described. Though problems remain after revisions (see progress reports in BPR), it is believed that SELSPOT offers potential for clinically useful real-time acquisition and analysis of three-dimensional data.

Calibration and measurement in 3-dimensional monitoring of human motion by optoelectronic means. I. Preliminaries and theoretical aspects.

By combinding the obervations from a number of independent direction sensors, the spatial positions of one or more targets may be reconstructed. The theory of calibration and measurement in a computerized, interactive environment is discussed in the terminology of analytical photogrammetry, for applications in the field of biomechanics. The discussion is focussed upon optoelectronic system for movement monitoring in real-time rather than upon photography as is the conventional photogrammetric implementation.