Representation and calculation of 3-D joint movement

doi:10.1016/0167-9457(91)90048-3

Human Movement Science

Volume 10, Issue 5, October 1991, Pages 603-616

https://doi.org/10.1016/0167-9457(91)90048-3 Get rights and content

Abstract

While clinical investigation of segment and joint motion on the examination table is usually confined to purely ‘planar’ movement about and along major co-ordinate axes, functional movement analysis requires unambiguous definitions of compound, 3-D segment and joint movement. These are not available in current handbooks.

The present paper describes some properties of various angular parameterizations currently in use, and it proposes the so-called helical angles as a suitable candidate, since it avoids the disadvantages of other angular parameterizations.

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Cited by (108)

The signed helical angle: A technique for characterizing midfoot motion during gait
2023, Journal of Biomechanics
Quantifying motion in the midfoot during gait and other movements is important for a variety of applications, but challenging due to the complexity of the multiple small articulations involved. The most common motion capture based techniques are limited in their ability to characterize the non-planar nature of the midfoot joint axes. In this study we developed a novel Signed Helical Angle (SHA) to quantify midfoot angular displacement. Motion capture data from 40 healthy subjects walking at a controlled speed were used to calculate finite helical axes and angles from a two-segment foot model. Axes were classified as either pronation or supination based on their orientation, and given a sign, thus either adding to or subtracting from the angular displacement. Analysis focused on insights from axis orientation and comparisons to other techniques. Results showed that when transitions were excluded, pronation and supination axes were fairly well clustered in the transverse plane. The resulting SHA midfoot angle waveform was comparable to sagittal plane Euler and helical component waveforms, but with 39% (approximately 3°) greater range of motion in pronation and 25% (approximately 4°) greater in supination, due to the direct measurement of the motion path and the influence of the other planes. The proposed SHA method may provide an intuitive and useful method to analyze midfoot motion for a variety of applications, particularly when interventions cause subtle changes that may be diluted in planar analyses.
Analysis of the spinal 3D motion of postmortem human surrogates in nearside oblique impacts
2023, Traffic Injury Prevention
Objective: The objective of this study is to analyze the 6 degrees of freedom (DOF) motion of the spine using the finite helical axis (FHA) in three postmortem human surrogates (PMHS) sled tests.
Methods: The sled test configurations corresponded to a 30° nearside oblique impact at 35 km/h. Two different restraint system versions (RSv) were used. RSv1 was used for PMHS A and B while RSv2 was used for PMHS C. The 6 DOF motion of the head and three selected vertebrae have been analyzed using the FHA which describes the 3 D motion of a rigid body between two instants of time as a rotation about and a translation along a unit vector. A minimal amount of rotation is necessary to the FHA calculation, thus the FHA components have been calculated based on a pre-defined interval of 8° of rotation.
Results: The analysis of the FHA components demonstrated right lateral bending until around 100 ms, when the rebound phase was reached and the head and the lower spine undergoes left lateral bending. The three PMHS exhibited, in general, flexion movement of the whole body and torsion to the right side of the occupant. This general motion can be associated to the effect of the seatbelt acting as a fulcrum of the rotational movement of the bony landmarks. The interaction of the PMHS with the retention system can be noted by analyzing the time in which the head and the upper spine initiated the rotation and the sudden changes of rotational direction of the three PMHS’s head.
Conclusions: The rotational analyses have shown to be more sensitive to experimental events than the trajectory analyses for the studied physical tests. Additionally, the results presented in the present study contributes to the analysis of the body kinematics during an oblique impact and adds new experimental data for Human Body Models (HBM) and Anthropometric Test Devices (ATD) benchmarking.
Correspondence between scapular anatomical coordinate systems and the 3D axis of motion: A new perspective on an old challenge
2022, Journal of Biomechanics
Citation Excerpt :
For the ISB-recommended Y-X’-Z’’ sequence for scapulothoracic kinematics (Wu et al., 2005), gimbal lock will occur when upward/downward rotation approaches 90°. Although this magnitude of upward rotation may not be often observed, even positions nearing gimbal lock (±20°) will be affected by high kinematic variability (van der Helm, 1997; Woltring, 1991). Fig. 3 illustrates an example from the current study in which the participant’s upward rotation exceeded 70° based on the original convention.
Several scapular anatomical coordinate systems have been reported in the literature to describe shoulder kinematics. Unfortunately, the use of different conventions hinders comparison across studies. Further, inconsistencies between a coordinate system and the scapula’s 3D axis of motion means that scapular motion will be incorrectly attributed to axes about which it did not rotate. The objectives of this study were to: 1) determine the extent to which the axes of four common scapular coordinate system conventions correspond to the 3D axis of scapular motion (i.e., instantaneous helical axis, IHA), and 2) report the prevalence of scapulothoracic gimbal lock for each convention. Shoulder kinematics were tracked during scapular plane abduction in 45 participants using biplane videoradiography. Scapulothoracic kinematics were described using the original convention proposed by van der Helm, the convention recommended by the International Society of Biomechanics (ISB), a glenoid-based coordinate system, and a glenoid-oriented coordinate system. The 3D angle was calculated between the IHA and each axis of the four conventions (IHA-axis angular deviations). A repeated measures ANOVA was used to compare IHA-axis angular deviations between conventions. The glenoid-oriented and ISB conventions resulted in the smallest and largest IHA-axis angular deviations, respectively (21.7°±3.6° vs. 30.5°±5.2°, p < 0.01). Gimbal lock was approached in 17.8% of participants when using the original convention, 2.2% when using the ISB convention, and 0% when using the glenoid-based or -oriented conventions. These findings suggest the glenoid-oriented coordinate system may be worthy of further consideration when investigating shoulder kinematics during scapular plane abduction.
The biomechanical effects of 3D printed and traditionally made foot orthoses in individuals with unilateral plantar fasciopathy and flat feet
2022, Gait and Posture
Citation Excerpt :
For each trial, 3D marker trajectories were reconstructed, missing frames (gaps < 10 frames) were manually reviewed and filled using a pattern gap-fill function. Data was smoothed with a Woltring filter (mean square error =20) [30] and modelled according to the Vicon Nexus Plug-in gait Lower Limb and the Oxford Foot Model [27]. The joint angles were computed according to the Cardan sequence: sagittal, transverse and frontal.
Foot orthoses (FOs) are used to manage foot pathologies such as plantar fasciopathy. 3D printed custom-made FOs are increasingly being manufactured. Although these 3D-printed FOs look like traditionally heat-moulded FOs, there are few studies comparing FOs made using these two different manufacturing processes.
How effective are 3D-printed FOs (3D-Print) compared to traditionally-made (Traditional) or no FOs (Control), in changing biomechanical parameters of flat-footed individuals with unilateral plantar fasciopathy?
Thirteen participants with unilateral plantar fasciopathy walked with shoes under three conditions: Control, 3D-print, and Traditional. 2 × 3 repeated measures analysis of variance (ANOVAs) with Bonferroni post-hoc tests were used to compare discrete kinematic and kinetic variables between limbs and conditions. Waveform analyses were also conducted using statistical parametric mapping (SPM).
There was a significant condition main effect for arch height drop (p = 0.01; ηp² =0.54). There was 0.87 mm (95% CI [−1.84, −0.20]) less arch height drop in 3D-print compared to Traditional. The SPM analyses revealed condition main effects on ankle moment (p < 0.001) and ankle power (p < 0.001). There were significant differences between control condition and both 3D-print and Traditional conditions. For ankle moment and power, there were no differences between 3D-print and Traditional conditions.
3D-printed FOs are more effective in reducing arch height drop, whist both FOs lowered ankle plantarflexion moment and power compared to no FOs. The results support the use of 3D-printed FOs as being equally effective as traditionally-made FOs in changing lower limb biomechanics for a population of flat-footed individuals with unilateral plantar fasciopathy.
Anatomical Nomenclature: Conundrums of Nonstandardized Foot and Ankle Terminology
2022, Foot and Ankle Biomechanics
The terminology of the foot and ankle can be confusing. The fact that several different terms can be associated with each structure or concept complicates their understanding. Many practitioners may assume that terminological differences are associated with specific disciplines, such as clinician versus bioengineer, or basic versus applied researcher. However, that is not the case always. Terminology differences are more complicated. As such, opportunities for collaborations among laboratories, disciplines, languages, and cultures are inadvertently stifled. Different organizations have attempted to address this problem by developing recommended terminological standards. A few of these standards are regularly consulted, but none have been fully successful.
This chapter outlines some of the more common areas of terminological confusion that may be found in discussions of foot and ankle biomechanics. Some confusions arise in the use of unfamiliar words, such as eponyms or different regional names. These words are presumed to provide concise and simple descriptions. But they can sometimes have the opposite effect. Other conceptual terms are common in their use, but complex in their meaning. Important concepts, such as the anatomical position or the anatomical planes, are not associated with simple and consistent meanings. The effect of differing concept meanings can cascade through the understanding of other terms that, on the surface, would have uncomplicated meanings and applications. This problem applies particularly to descriptions of movements, which can be misunderstood because they are related to the irregularly established concepts of the anatomical planes. Finally, there are terms of motion that can have identical definitions, but when their underlying mathematical assumptions differ, they can be associated with widely contrasting values.
Some suggestions are offered to minimize miscommunication within scientific discourse. In the end, however, we must remain on guard for terminology problems. By understanding where, and how, terminological differences can intrude into presentations, we can try to mitigate their influence on the interpretation of results.
The effect of planar constraint on the definition of the wrist axes of rotation
2020, Journal of Biomechanics
Instantaneous helical axes (IHAs) and screw displacement axes (SDAs) are commonly used to investigate joint functional axes of rotation. In the wrist, these have often been obtained through in vitro motion analysis. These definitions are then employed for in vivo applications, such as the design of implants or the development of musculoskeletal models. However, functional unguided joint motions are, by definition, affected by the activity of muscles. Previously published data has disagreed on the relative position and orientation of the two primary axes of rotation of the wrist, i.e. the radioulnar deviation (RUD) axis with respect to the flexion-extension (FE) axis. An in vivo study comparing the FE and RUD IHAs and SDAs of guided motions, to replicate in vitro conditions, and unguided motions of 23 healthy participants was conducted using optical motion capture. Guided motions were performed with the hand and forearm flush against a flat surface. The relative position and orientation of the RUD SDAs with respect to the FE SDAs differed (p = 0.019, p = 0.001) between unguided FE and guided RUD (0.1 ± 4.3 mm, 93.5 ± 16.0°) and guided FE and RUD (1.6 ± 4.0 mm, 107.8 ± 17.7°). This indicates that the use of different constraints, and not physiological differences, is the primary cause of differences in the relative positions and orientations of the FE and RUD axes in the literature. Thus, the practice of using in vitro definitions of the axes of rotation of the wrist for in vivo applications, especially involving FE, may be inappropriate and care must be taken to account for any constraint on wrist motion. It is recommended that investigators define the axes of rotation specifically for their study or refer to literature featuring the desired levels of constraint.

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^☆: Parts of this paper were presented earlier in Woltring and Fioretti (1989).

^†

On leave from Philips Medical Systems, Best, The Netherlands (Co-ordination Development, Science, and Technology) at Eindhoven University of Technology, The Netherlands.

The author wishes to express his gratitude to Prof. P. Eykhoff at Eindhoven University of Technology for his hospitality.

Author's address: H.J. Woltring, Brussellaan 29, 5628 TB Eindhoven, The Netherlands.

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Representation and calculation of 3-D joint movement☆

Abstract

Journal of Biomechanics

Journal of Biomechanics

Human Movement Science

Journal of Biomechanics

Human Movement Science

Journal of Biomechanics

Journal of Biomechanics

A kinematical study of the wrist joint

De immutatione coordinatarum

Introductio in Analysin Infinitorum

A joint co-ordinate system for the clinical description of three-dimensional motions: Application to the knee

Journal of Biomechanical Engng.