- Artefato de Tecidos Moles - Soft Tissue Artifact (STA)
- IMMU - Inertial and Magnetic Measurement Unit Systems
- Measurement of errors in quantitative gait data
- Membros Superiores - Upper Limbs
- Modelos Musculoesqueléticos - OpenSim
- Modelos do Pé - Foot Models
- Sistemas e Instrumentação ■Systems, Instrumentation and Devices ■Depth Camera Motion Assessment and Markerless MoCap System ■Massachusetts General Hospital, Biomotion Laboratory: Gait Analysis Using a Wireless Shoe-Integrated Sensor System
- Torção Tibial - Tibial Torsion
Standardization and Terminology Committee (STC)
International Society of Biomechanics (ISB):
- ISB recommendation on definitions of joint coordinate system ISB recommendation on definitions of joint coordinate system of various joints for the reporting of human joint motion—part I:
- ISB recommendation on definitions of joint coordinate system ISB recommendation on definitions of joint coordinate systems of various joints for the reporting of human joint motion—Part II:
ankle, hip, and spine
shoulder, elbow, wrist and hand
Clinical Gait Analysis:
- Automatic real-time gait event detection in children using deep neural networks "Annotation of foot-contact and foot-off events is the initial step in post-processing for most quantitative gait analysis workflows. If clean force plate strikes are present, the events can be automatically detected. Otherwise, annotation of gait events is performed manually, since reliable automatic tools are not available. Automatic annotation methods have been proposed for normal gait, but are usually based on heuristics of the coordinates and velocities of motion capture markers placed on the feet. These heuristics do not generalize to pathological gait due to greater variability in kinematics and anatomy of patients, as well as the presence of assistive devices. In this paper, we use a data-driven approach to predict foot-contact and foot-off events from kinematic and marker time series in children with normal and pathological gait." Project: event-detector: Machine Learning model for detecting gait events in mocap data
- Can biomechanical variables predict improvement in crouch gait? "In this study, we developed a multivariable regression model to determine if biomechanical variables and other subject characteristics measured during a physical exam and gait analysis can predict which subjects with crouch gait will demonstrate improved knee kinematics on a follow-up gait analysis."
- Comprehensive non-dimensional normalization of gait data "Normalizing clinical gait analysis data is required to remove variability due to physical characteristics such as leg length and weight. This is particularly important for children where both are associated with age. In most clinical centres conventional normalization (by mass only) is used whereas there is a stronger biomechanical argument for non-dimensional normalization. This study used data from 82 typically developing children to compare how the two schemes performed over a wide range of temporalspatial and kinetic parameters by calculating the coefficients of determination with leg length, weight and height. 81% of the conventionally normalized parameters had a coefficient of determination above the threshold for a statistical association (p<0.05) compared to 23% of those normalized non-dimensionally."
- Development of temporal and distance parameters of gait in normal children "Temporal and distance parameters of 33 normal children were obtained from instrumented gait analysis prospectively over five consecutive years. The parameters were normalised to minimise the confounding effects of increasing height and leg length."
- Detection of gait events and intervals "Assessment and validation of a simple automated method for the detection of gait events and intervals
- Fixating the pelvis in the horizontal plane affects gait characteristics "In assistive devices for neuro-rehabilitation, natural human motions are partly restricted by the device. This may affect the normality of walking during training. This research determines effects on gait of fixating the pelvis translations in the horizontal plane during treadmill walking. Direct effects on the motion of the pelvis and external forces acting on the pelvis were measured. Several gait descriptors (step parameters, trunk angles and a ground reaction force parameter) were defined and measured to indicate changes."
- Human movement analysis using stereophotogrammetry "Human movement analysis using stereophotogrammetry Part 4: assessment of anatomical landmark misplacement and its effects on joint kinematics"
- Muscle synergies and complexity of neuromuscular control during gait in cerebral palsy AIM: "Individuals with cerebral palsy (CP) have impaired movement due to a brain injury near birth. Understanding how neuromuscular control is altered in CP can provide insight into pathological movement. We sought to determine if individuals with CP demonstrate reduced complexity of neuromuscular control during gait compared with unimpaired individuals and if changes in control are related to functional ability." METHOD: "Muscle synergies during gait were retrospectively analyzed for 633 individuals (age range 3.9–70y): 549 with CP (hemiplegia, n=122; diplegia, n=266; triplegia, n=73; quadriplegia, n=88) and 84 unimpaired individuals. Synergies were calculated using non-negative matrix factorization from surface electromyography collected during previous clinical gait analyses. Synergy complexity during gait was compared with diagnosis subtype, functional ability, and clinical examination measures."
A simple and rapid automatic method for detection of gait events at the foot could speed up and possibly increase the repeatability of gait analysis and evaluations of treatments fo rpathological gaits. The aim of this study was to compare and validate a kinematic-based algorithm used in the detection of four gait events, heel contact, heel rise, toe contact and toe off."
Biomechanics Models:
Ankle, Knee, Pelvis (Cardan angle), Filters, Correction Methods (PCA)
- A method to calculate the centre of the ankle joint A method to calculate the centre of the ankle joint: A comparison with the Vicon Plug-in-Gait model. "In gait analysis, calculation of the ankle joint centre is a difficult task. The conventional way to calculate the ankle joint centre is using the Vicon Plug-in-Gait model. The present study proposes a new model, which calculates the joint centre from two markers positioned over the medial and lateral malleoli (i.e. Two-marker-model)."
- Defining the knee joint flexion–extension axis Defining the knee joint flexion–extension axis for purposes of quantitative gait analysis: An evaluation of methods "Minimising measurement variability associated with hip axial rotation and avoiding knee joint angle cross-talk are two fundamental objectives of any method used to define the knee joint flexion–extension axis for purposes of quantitative gait analysis. The aim of this experiment was to compare three different methods of defining this axis: the knee alignment device (KAD) method, a method based on the transepicondylar axis (TEA) and an alternative numerical method (Dynamic)."
- Kalman smoothing Kalman smoothing improves the estimation of joint kinematics and kinetics in marker-based human gait analysis "We developed a Kalman smoothing algorithm to improve estimates of joint kinematics from measured marker trajectories during motion analysis. Kalman smoothing estimates are based on complete marker trajectories. This is an improvement over other techniques, such as the global optimisation method (GOM), Kalman filtering, and local marker estimation (LME), where the estimate at each time instant is only based on part of the marker trajectories."
- The impact of thigh and shank marker quantity The impact of thigh and shank marker quantity on lower extremity kinematics using a constrained model "Abstract Background: Musculoskeletal models are commonly used to quantify joint motions and loads during human motion. Constraining joint kinematics simplifies these models but the implications of the placement and quantity of markers used during data acquisition remains unclear. The purpose of this study was to establish the effects of marker placement and quantity on lower extremity kinematics calculated using a constrained-kinematic model. We hypothesized that a constrained-kinematic model would produce lower-extremity kinematics errors that correlated with the number of tracking markers removed from the thigh and shank. Methods: Healthy-young adults (N = 10) walked on a treadmill at slow, moderate, and fast speeds while skin-mounted markers were tracked using motion capture. Lower extremity kinematics were calculated for 256 combinations of leg and shank markers to establish the implications of marker placement and quantity on joint kinematics. Marker combinations that yielded differences greater than 5 degrees were tested with paired t-tests and the relationship between number of markers and kinematic errors were modeled with polynomials to determine goodness of fit (R2). Results: Sagittal joint and hip coronal kinematics errors were smaller than documented errors caused by soft-tissue artifact, which tends to be approximately 5 degrees, when excluding thigh and shank markers. Joint angle and center kinematic errors negatively correlated with the number of markers included in the analyses (R2 > 0.97) and typically showed the greatest error reductions when two markers were included on the thigh or shank segments. Further, we demonstrated that a simplified marker set that included markers on the pelvis, lateral knee condyle, lateral malleolus, and shoes produced kinematics that strongly agreed with the traditional marker set that included 3 tracking markers for each segment. Conclusion: Constrained-kinematic models are resilient to marker placement and quantity, which has implications on study design and post-processing workflows."
- A Principal Component Analysis Approach to Correcting the Knee Flexion Axis during Gait "Accurate and precise knee flexion axis identification is critical for prescribing and assessing tibial and femoral derotation osteotomies, but is highly prone to marker misplacement-induced error. The purpose of this study was to develop an efficient algorithm for post hoc correction of the knee flexion axis and test its efficacy relative to other established algorithms. Gait data were collected on twelve healthy subjects using standard marker placement as well as intentionally misplaced lateral knee markers. The efficacy of the algorithm was assessed by quantifying the reduction in knee angle errors."
- Cross-Talk Correction Method for Knee Kinematics in Gait Analysis Using PCA Cross-Talk Correction Method for Knee Kinematics in Gait Analysis Using Principal Component Analysis (PCA): A New Proposal "Background: In 3D gait analysis, the knee joint is usually described by the Eulerian way. It consists in breaking down the motion between the articulating bones of the knee into three rotations around three axes: flexion/extension, abduction/adduction and internal/external rotation. However, the definition of these axes is prone to error, such as the "cross-talk" effect, due to difficult positioning of anatomical landmarks. This paper proposes a correction method, principal component analysis (PCA), based on an objective kinematic criterion for standardization, in order to improve knee joint kinematic analysis. Methods: The method was applied to the 3D gait data of two different groups (twenty healthy subjects and four with knee osteoarthritis). Then, this method was evaluated with respect to three main criteria: (1) the deletion of knee joint angle cross-talk (2) the reduction of variance in the varus/valgus kinematic profile (3) the posture trial varus/valgus deformation matching the X-ray value for patients with knee osteoarthritis. The effect of the correction method was tested statistically on variabilities and cross-talk during gait. Results: Cross-talk was lower (p,0.05) after correction (the correlation between the flexion-extension and varus-valgus kinematic profiles being annihilated). Additionally, the variance in the kinematic profile for knee varus/valgus and knee flexion/extension was found to be lower and higher (p,0.05), respectively, after correction for both the left and right side. Moreover, after correction, the posture trial varus/valgus angles were much closer to x-ray grading. Conclusion: The results show that the PCA correction applied to the knee joint eliminates the cross-talk effect, and does not alter the radiological varus/valgus deformation for patients with knee osteoarthritis. These findings suggest that the proposed correction method produces new rotational axes that better fit true knee motion."
- Reducing knee joint crosstalk using PCA correction O99: Reducing knee joint crosstalk using PCA correction Gait & Posture, Volume 57, Supplement 1, September 2017, Pages 173-174 doi.org/10.1016/j.gaitpost.2017.06.352 "Multiple marker protocols exist for analysing gait kinematics, however most models show crosstalk, particularly in the knee joint due to difficulties in aligning the flexion/extension (F/E) axis. These difficulties are enlarged in patient groups, such as children with cerebral palsy (CP) due to difficulties in palpation and deviations from model assumptions. Functional calibration might be effective in improving knee axes alignment, but is time consuming and difficult to perform. Therefore post hoc optimisation methods are preferable. The aim of this study is to outline the effects of a newly proposed post hoc method based on principal component analysis (PCA) to reduce crosstalk in commonly used models for gait analysis."
- A comparison of two sequences of pelvic angle calculation A comparison of two sequences of pelvic angle calculation in patients with a stiff hip "The results from a study, comparing the conventional cardan angle sequence of rotations for pelvic angle definition (tilt, obliquity, rotation, TOR) and the sequence of rotation, obliquity, tilt (ROT) are presented for 13 patients with femoral head avascular necrosis (AVN). Pelvic angle alignment and excursion were compared and evaluated against visual observation and examined fixed hip deformities. Differences in pelvic waveforms were identified in six cases for whom the ROT sequence reflected the visual and clinical findings more accurately. There were minimal or no differences in eight cases. These results support the use of the ROT sequence in this population."
- Pelvic angles: a mathematically rigorous definition Pelvic angles: a mathematically rigorous definition which is consistent with a conventional clinical understanding of the terms "The most common definition of pelvic angles in conventional gait analysis uses the sequence tilt, obliquity, rotation. This is used in most commercially available gait analysis software. This definition of angles, however, is not in agreement with the conventional clinical understanding of the terms when both tilt and rotation are large. This paper shows that by using the sequence rotation, obliquity, tilt it is possible to make a mathematically rigorous definition of pelvic angles which it is consistent with that conventional clinical usage."
PCA: Principal Component Analysis
Pelvis/Cardan angle sequence of rotations
'The' CGM 2.i Project:
- PyCGM2 (Conventional Gait Model 2) - 2018 (update: 2022) Fabien Leboeuf, Julie Reay, Richard Baker (University of Salford - UK)
Morgan Sangeux (University of Melbourne, Murdoch Childrens Research Institute,
The Royal Children's Hospital (RCH) - AU)
Derek Potter (Commercial Partner: Vicon - UK)
"The Conventional Gait Model is the most widely used biomechanical model for clinical gait analysis. It was first developed in the 1980s and although, it has many strengths, it has several well-known weaknesses.
The overall aim of this project is to develop and validate a new version, CGM 2, which maintains the current model's strengths but addresses its weaknesses. The new version will allow robust, efficient and standardised data capture by people whose primary interest is in using the results of the gait analysis.
Although the project aims to make the new model as compatible as possible with the old it cannot be identical. It is therefore important that future users know exactly how the new version differs from the old. This will be ensured by developing the model in a series of iterations each addressing a specific weakness and each fully validated to understand the behaviour of the new model in comparison to the old one.
We want the new model to be as open and transparent as possible. All code will be developed in python and made available through GitHub. The project is part-funded by Vicon and we will focus first on implementations to support use of the new models with Vicon's suite of clinical gait analysis software. We are open to developing similar relationships with other manufacurers."
- The conventional gait model, an open-source implementation The conventional gait model, an open-source implementation that reproduces the past but prepares for the future "The Conventional Gait Model (CGM), known by a variety of different names, is widely used in clinical gait analysis. We present pyCGM2, an open-source implementation of the CGM with two versions. The first, CGM1.0, is a clone of Vicon Plug In Gait (PiG) with all its variants. CGM1.0 provides a platform to test the effect of modifications to the CGM on data collected and processed retrospectively or to provide backward compatibility. The second version, CGM1.1, offers some practical modifications and includes three well documented improvements."
- The effect of subject measurement error on joint kinematics in the CGM - (open access) The effect of subject measurement error on joint kinematics in the conventional gait model: Insights from the open-source pyCGM tool using high performance computing methods "The conventional gait model (CGM) is a widely used biomechanical model which has been validated over many years. This paper introduces a Python implementation for the CGM, referred to as pyCGM, which is an open-source, easily modifiable, cross platform, and high performance computational implementation. The aims of pyCGM are to (1) reproduce joint kinematic outputs from the Vicon CGM and (2) be implemented in a parallel approach to allow integration on a high performance computer. The aims of this paper are to (1) demonstrate that pyCGM can systematically and efficiently examine the effect of subject measurements on joint angles and (2) be updated to include new calculation methods suggested in the literature."
Dynakad:
Musgrave Park Hospital, Gait Analysis Service (UK) School of Mechanical and Manufacturing Engineering The Queen's University of Belfast (UK)
- A new approach to determining the hip rotation profile from clinical gait analysis data "Conventional models for determining joint rotation angles from marker positions as part of three-dimensional clinical gait analysis are susceptible to errors arising from mis-placement of the thigh markers. An analysis of idealised data reveals how the measured variables are affected by different angular offsets of the thigh marker from its true position. An artefact on the varus-valgus signal arising from the projection true knee flexion onto a mal-aligned thigh segment axes is the most characteristic feature of this problem. If this is observed then the hip rotation profiles are also erroneous.
A technique is proposed to determine a correction factor which can be applied to gait data to correct for this mal-alignment. Its use is demonstrated on a single case study and a subjective assessment of its use on a cohort of 40 patients is reported. A detailed discussion of the assumptions on which the method is founded is included as well as guidelines as to when the technique is likely to be successful.
The technique used is perhaps best used as an aid to training staff in marker placement."
Kinematically Constrained Joint Parameters (KC Method):
Gillette Children's Specialty Healthcare Center for Gait and Motion Analysis (USA)
- A kinematically constrained method for determining subject specific joint parameters
- Kinematically Constrained Joint Parameters I: Method, Repeatability and Objectivity
- Kinematically Constrained Joint Parameters part II: Accuracy and Kinematics Results
- Performance of the kinematically constrained method for joint parameter estimation
- A new method for estimating joint parameters from motion data "This article describes a new method for joint parameter estimation. The new method can be summarized as follows: (i) the motions of two adjacent segments spanning a single joint are tracked, (ii) the axis of rotation between every pair of observed segment configurations is computed, (iii) the most likely intersection of all axes (effective joint center) and most likely orientation of the axes (effective joint axis) is found. Initial validation of the method was conducted on a hinged mechanical analog and a single healthy adult subject."
- ESMAC 2018: O 007—Inclusion of a patella marker to improve functional model hip rotation tracking Gait & Posture, Volume 65, Supplement 1, September 2018, Pages 13-14 "Hip rotation, as measured by 3-dimensional motion capture, has been shown to detect only 50-70% of true hip rotation [1]. Previous studies by Wren and McMulkin have shown that utilizing a patellar marker significantly improves conventional model tracking of hip rotation and reduces errors caused static calibration misalignment [2,3]. No studies have evaluated a similar methodology for models with functionally defined hip and knee axes (functional models)."
OLGA - Vicon (UK)
- Sensitivity of the OLGA and VCM models to erroneous marker placement: Effects on 3D-gait kinematics "Gait data need to be reliable to be valuable for clinical decision-making. To reduce the impact of marker placement errors, the Optimized Lower Limb Gait Analysis (OLGA) model was developed. The purpose of this study was to assess the sensitivity of the kinematic gait data to a standard marker displacement of the OLGA model compared with the standard Vicon Clinical Manager (VCM) model and to determine whether OLGA reduces the errors due to the most critical marker displacements."
- Repeatability of an optimised lower body model - Vicon/OLGA "The optimisation technique, optimised lower-limb gait analysis (OLGA), is described together with a preliminary study of repeatability compared to an implementation of the Newington–Helen Hayes gait model."
Pelvis/Hip Joint Centers (HJC):
- A comparison of hip joint centre localisation techniques with 3-DUS A comparison of hip joint centre localisation techniques with 3-DUS for clinical gait analysis in children with cerebral palsy "Functional calibration techniques have been proposed as an alternative to regression equations for estimating the position of the hip within the pelvic co-ordinate system for clinical gait analysis. So far validation of such techniques has focussed on healthy adults. This study evaluated a range of techniques based on regression equations or functional calibration procedures techniques in 46 children representative of those attending a major clinical gait analysis service against previously validated 3-D ultrasound techniques for determining the hip joint centre."
- Accuracy of the functional method of hipjoint center location Accuracy of the functional method of hipjoint center location: effects of limited motion and varied implementation "Accurate location of the hipjoint center is essential for computation of hip kinematics and kinetics as well as for determination of the moment arms of muscles crossing the hip. The functional method of hip joint center location involves fitting a pelvis-fixed sphere to the path traced by a thigh-fixed point while a subject performs hip motions; the center of this sphere is the hip joint center. The aim of the present study was to evaluate the potential accuracy of the functional method and the dependence of its accuracy on variations in its implementation and the amount of available hip motion."
- Alternative modelling procedures for pelvic marker occlusion during motion analysis "Motion analysis of participants with different body shapes under diverse conditions can be problematic when vitalmarkers are occluded. The markers located over the anterior superior iliac spines are commonly occluded in older patients and during analysis of activities with trunk and hip flexion which can prevent accurate calculation of lower limb joint kinematics. Options to modify standard body models exist but have not been described in detail, and the effects on the lower limb kinematics are not known."
- Evaluation of alternative technical markers for the pelvic coordinate system "In this study, we evaluated alternative technical markers for the motion analysis of the pelvic segment. Thirteen subjects walked eight times while tri-dimensional kinematics were recorded for one stride of each trial. Five marker sets were evaluated, and we compared the tilt, obliquity, and rotation angles of the pelvis segment: (1) standard: markers at the anterior and posterior superior iliac spines (ASIS and PSIS); (2) markers at the PSIS and at the hip joint centers, HJCs (estimated by a functional method and described with clusters of markers at the thighs); (3) markers at the PSIS and HJCs (estimated by a predictive method and described with clusters of markers at the thighs); (4) markers at the PSIS and HJCs (estimated by a predictive method and described with skin-mounted markers at the thighs based on the Helen-Hayes marker set); (5) markers at the PSIS and at the iliac spines."
- Hip joint centre localization Hip joint centre localization: Evaluation on normal subjects in the context of gait analysis "Locating the position of the hip joint centre (HJC) is an important part of lower limb modeling for gait analysis. Regression equations have been used in the past but a range of functional calibration methods are now available. This study compared the accuracy of HJC localization from two sets of regression equations and five different functional calibration methods against three dimensional ultrasound (3-DUS) on a population of 19 able bodied subjects. Results show that the geometric sphere fitting technique was the best performer with mean absolute distance error of 15 mm and 85% of measurements being within 20 mm."
- Prediction of the hip joint centre Prediction of the hip joint centre in adults, children, and patients with cerebral palsy based on magnetic resonance imaging "The location of the hip joint centre (HJC) is required for calculations of hip moments, the location and orientation of the femur, and muscle lengths and lever arms. In clinical gait analysis, the HJC is normally estimated using regression equations based on normative data obtained from adult populations. There is limited relevant anthropometric data available for children, despite the fact that clinical gait analysis is predominantly used for the assessment of children with cerebral palsy. In this study, pelvic MRI scans were taken of eight adults (ages 23–40), 14 healthy children (ages 5–13) and 10 children with spastic diplegic cerebral palsy (ages 6–13). Relevant anatomical landmarks were located in the scans, and the HJC location in pelvic coordinates was found by fitting a sphere to points identified on the femoral head."
- Predicting the location of the hip joint centres, impact of age group and sex "Clinical gait analysis incorporating three-dimensional motion analysis plays a key role in planning surgical treatments in people with gait disability. The position of the Hip Joint Centre (HJC) within the pelvis is thus critical to ensure accurate data interpretation. The position of the HJC is determined from regression equations based on anthropometric measurements derived from relatively small datasets. Current equations do not take sex or age into account, even though pelvis shape is known to differ between sex, and gait analysis is performed in populations with wide range of age. Three dimensional images of 157 deceased individuals (37 children, 120 skeletally matured) were collected with computed tomography. The location of the HJC within the pelvis was determined and regression equations to locate the HJC were developed using various anthropometrics predictors. We determined if accuracy improved when age and sex were introduced as variables."
- Validation of a method to accurately correct anterior superior iliac spine marker occlusion "Anterior superior iliac spine (ASIS) marker occlusion commonly occurs during three-dimensional (3-D) motion capture of dynamic tasks with deep hip flexion. The purpose of this study was to validate a universal technique to correct ASIS occlusion."
- Verification of an improved hip joint center prediction method "A new regression method (Hara) utilizes leg length and has been shown to improve HJC location in cadavers and less error than previous pelvic based regression methods, such as those proposed by Harrington et al. This study compared the accuracy of the HJC location calculated with both of the Harrington methods and the Hara method. The coronal knee angle was calculated for each method using a static motion analysis trial, and compared to the tibiofemoral angle measured on a gold standard digital full-leg coronal radiograph. This study demonstrated that the Hara method was more accurate than either of the Harrington methods."
SARA and SCoRE:
Center for Musculoskeletal Surgery, Charité Universitätsmedizin Berlin (DE)
- A survey of formal methods for determining functional joint axes (SARA) "Axes of rotation e.g. at the knee, are often generated from clinical gait analysis data to be used in the assessment of kinematic abnormalities, the diagnosis of disease, or the ongoing monitoring of a patient’s condition. They are additionally used in musculoskeletal models to aid in the description of joint and segment kinematics for patient specific analyses. Currently available methods to describe joint axes from segment marker positions share the problem that when one segment is transformed into the coordinate system of another, artefacts associated with motion of the markers relative to the bone can become magnified. In an attempt to address this problem, a symmetrical axis of rotation approach (SARA) is presented here to determine a unique axis of rotation that can consider the movement of two dynamic body segments simultaneously, and then compared its performance in a survey against a number of previously proposed techniques."
- A survey of formal methods for determining the centre of rotation of ball joints (SCoRE) "The determination of an accurate centre of rotation (CoR) from segment marker positions is of interest across a wide range of applications, but particularly for clinical gait analysis and for estimating the hip joint centre during surgical intervention of the knee, for limb alignment purposes. For the first time in this survey of formal methods, we classify, analyse and compare different methods (geometric, algebraic, bias compensated algebraic, and Pratt sphere fit methods, as well as the centre transformation technique, the Holzreiter approach, the helical pivot technique, the Schwartz transformation techniques, the minimal amplitude point method and the Stoddart approach) for the determination of spherical joint centres from marker position data. In addition, we propose a new method, the symmetrical CoR estimation or SCoRE, in which the coordinates of the joint centre must only remain constant relative to each segment, thus not requiring the assumption that one segment should remain at rest."