John H. Challis

A procedure for determining rigid body transformation parameters

For many biomechanical applications it is necessary to determine the parameters which describe the transformation of a rigid body from one reference frame to another. These parameters are a scaling factor, an attitude matrix, and a translation vector. The paper presents a new procedure for the determination of these parameters incorporating the work of Arun et al. [IEEE Trans. Pattern Anal. Machine Intell, 9, 698-700 (1987)] but expanding their analysis to allow for the determination of a scale factor, the scalar weighting of the least-squares problem, and the problem of obtaining the incorrect determinant when determining the attitude matrix. The procedure, which requires the coordinates of three or more non-collinear points, is based around the singular value decomposition, and provides a least-squares estimate of the rigid body transformation parameters. Examples are presented of the use of this procedure for determining the attitude of a rigid body, and for osteometric scaling. When used for osteometric scaling mirror transformations are possible, therefore a right-hand specimen can be scaled to the left-hand side of another specimen.

Visual and non-visual control of landing movements in humans

1 The role of vision in controlling leg muscle activation in landing from a drop was investigated. Subjects (n= 8) performed 10 drops from four heights (0.2, 0.4, 0.6 and 0.8 m) with and without vision. Drop height was maintained constant throughout each block of trials to allow adaptation. The aim of the study was to assess the extent to which proprioceptive and vestibular information could substitute for the lack of vision in adapting landing movements to different heights. 2 At the final stages of the movement, subjects experienced similar peak centre of body mass (CM) displacements and joint rotations, regardless of the availability of vision. This implies that subjects were able to adapt the control of landing to different heights. The amplitude and timing of electromyographic signals from the leg muscles scaled to drop height in a similar fashion with and without vision. 3 However, variables measured throughout the execution of the movement indicated important differences. Without vision, landings were characterised by 10 % larger ground reaction forces, 10 % smaller knee joint rotations, different time lags between peak joint rotations, and more variable ground reaction forces and times to peak CM displacement. 4 We conclude that non‐visual sensory information (a) could not fully compensate for the lack of continuous visual feedback and (b) this non‐visual information was used to reorganise the motor output. These results suggest that vision is important for the very accurate timing of muscle activity onset and the kinematics of landing.

Learning to coordinate redundant degrees of freedom in a dynamic balance task.

The present study investigated Bernsteins [The co-ordination and regulation of movements, 1967] proposal regarding the three stages of learning in the changing coordination and control of redundant joint-space degrees of freedom. Six participants practiced maintaining balance on a moving platform that was sinusoidally translated in the anterior-posterior direction for 30 trials on day 1 and 10 trials on day 2. At the beginning of practice, the motion of the torso and limb segments was less coherent in the attempt to compensate for the movement of the support surface in retaining a balanced posture. However, with practice, the organization of a compensatory postural coordination mode became highly coherent and also progressively utilized the passive, inertial forces generated by the movement of the support surface. The findings support the propositions that: (a) the pathway of change over time in the coordination pattern of the torso and joint motions depends on the task goal and constraints to action and (b) the changes in limb and torso motion are in support of the learning of a global body center of mass/platform dynamic.

The role of the heel pad and shank soft tissue during impacts: a further resolution of a paradox

The aim of this study was to test the hypothesis that the motion of the soft tissue of the lower leg contributes significantly to the attenuation of the forces during heel impacts. To examine this, a two-dimensional model of the shank and heel pad was developed using DADS. The model contained a heel pad element and a rigid skeleton to which was connected soft tissue which could move relative to the bone. Simulations permitted estimation of heel pad properties directly from heel pad deformations, and from the kinematics of an impacting pendulum. These two approaches paralleled those used in vitro and in vivo, respectively. Measurements from the pendulum indicated that heel pad properties changed from those found in vitro to those found in vivo as relative motion of the bone and soft tissue was allowed. This would indicate that pendulum measures of the in vivo heel pad properties are also measuring the properties of the whole lower leg. The ability of the wobbling mass of the shank to dissipate energy during an impact was found to be significant. These results demonstrate the important role of both the heel pad and soft tissue of the shank to the dissipation of mechanical energy during impacts. These results provide a further clarification of the paradox between the measurements of heel pad properties made in vivo and in vitro.

The future of performance‐related sports biomechanics research

An overview of performance-related research in sports biomechanics is presented describing the relevant techniques of data analysis and data processing together with the methods used in experimental and theoretical studies. Advances in data collection and processing techniques which are necessary for the future development of sports biomechanics research are identified. The difficulties associated with experimental studies in sports biomechanics are described with examples of the different approaches that have been used. The strengths and weaknesses of theoretical studies are discussed with examples drawn from a number of sports. It is concluded that progress in performance-related research will result from the application of a suitable combination of theoretical and experimental approaches to those sports in which technique is the primary requirement for success.

Accuracy assessment and control point configuration when using the DLT for photogrammetry

The direct linear transformation (DLT) is a common technique used to calibrate cameras and subsequently reconstruct points filmed with two or more cameras in a three-dimensional object space. The assessment of the accuracy of this technique, and of the influence of the distribution of control points on accuracy were examined. It was concluded that to obtain a true estimation of reconstruction accuracy, an independent assessment criterion is required, and that the use of control points distributed around the outside, rather than within the space to be calibrated, is preferred.

Stability and the time-dependent structure of gait variability in walking and running

Participants were asked to walk and run continuously (5 min trials) at speeds associated with preferred gait transition speeds. During slow running the local dynamic stability of the head was decreased compared with fast walking, with the reverse being true for the local dynamic stability of the ankle. The standard deviation of relative phase of the knee and ankle also was greater during slow running than fast walking. These findings for stability were mirrored in the detrended fluctuation analysis of the peak to peak interval of the head and ankle. Taken collectively these results support the proposition that larger long range correlations in the stride interval are associated with decreases in measures of stability.

An objective evaluation of a segmented foot model

Segmented foot and ankle models divide the foot into multiple segments in order to obtain more meaningful information about its functional behavior in health and disease. The goal of this research was to objectively evaluate the fidelity of a generalized three-segment foot and ankle model defined using externally mounted markers. An established apparatus that reproduces the kinematics and kinetics of gait in cadaver lower extremities was used to independently examine the validity of the rigid body assumption and the magnitude of soft tissue artifact induced by skin-mounted markers. Stance phase simulations were conducted on ten donated limbs while recording the three-dimensional kinematic trajectories of skin-mounted and then bone-mounted marker constructs. Segment kinematics were compared to underlying bone kinematics to examine the rigid body assumption. Virtual markers were calculated from the bone mounted marker set and then compared to the skin-mounted markers to examine soft tissue artifact. The shank and hindfoot segments behaved as rigid bodies. The forefoot segment violated the rigid body assumption, as evidenced by significant differences between motions of the first metatarsal and the forefoot segment, and relative motion between the first and fifth metatarsals. Motion vectors of the external skin markers relative to their virtual counterparts were no more than 3mm in each direction, and 3-7 mm overall. Artifactual marker motion had mild affects on inter-segmental kinematics. Despite errors, the segmented model appeared to perform reasonably well overall. The data presented here enable more informed interpretations of clinical findings using the segmented model approach.

An Analytical Examination of Muscle Force Estimations Using Optimization Techniques

Muscle forces are often estimated during human movement using optimization procedures. The optimization procedures involve the minimization of an objective function relating to the muscle forces. In this study 15 different objective functions were evaluated by examining the analytical solutions to the objective functions and by comparing their force predictions with the forces estimated using a validated muscle model. The muscle forces estimated by the objective functions were shown to give poor correspondence with the muscle model predicted muscle forces. The objective function estimates were criticized for not taking sufficient account of the physiological properties of the muscles. As a consequence of the analysis of the objective functions an alternative, simpler function was presented with which to estimate muscle forces in vivo. This function required that to satisfy a given joint moment, the force exerted by each of the muscles divided by the maximum force possible by the muscle was constant for all muscles. For this function the maximum muscle force was determined using a muscle model assuming maximal activation.

Quantification of the uncertainties in resultant joint moments computed in a dynamic activity

Resultant joint moments are an important variable with which to examine human movement, but the uncertainty with which resultant joint moments are calculated is often ignored. This paper presents a procedure for examining the uncertainty with which resultant joint moments are calculated. The uncertainty was calculated by changing the parameters and variables required to compute the resultant joint moments, by amounts relating to their estimated uncertainties, and then quantifying the resulting change in the resultant joint moments. The procedure was applied to the elbow joint during loaded elbow flexion executed at maximum volitional speed. For this activity, the estimated moments were most sensitive to uncertainties in the derivatives of the position data. A number of other sources of error and uncertainty were identified which warrant further investigation. The protocols outlined in this study are applicable to other activities.