A joint coordinate system proposal for the study of the trapeziometacarpal joint kinematics

The International Society of Biomechanics (ISB) has recommended a standardisation for the motion reporting of almost all human joints. This study proposes an adaptation for the trapeziometacarpal joint. The definition of the segment coordinate system of both trapezium and first metacarpal is based on functional anatomy. The definition of the joint coordinate system (JCS) is guided by the two degrees of freedom of the joint, i.e. flexion-extension about a trapezium axis and abduction-adduction about a first metacarpal axis. The rotations obtained using three methods are compared on the same data: the fixed axes sequence proposed by Cooney et al., the mobile axes sequence proposed by the ISB and our alternative mobile axes sequence. The rotation amplitudes show a difference of 9 degrees in flexion-extension, 2 degrees in abduction-adduction and 13 degrees in internal-external rotation. This study emphasizes the importance of adapting the JCS to the functional anatomy of each particular joint.     

Method for the estimation of a double hinge kinematic model for the trapeziometacarpal joint using MR imaging

In this paper, we propose a method to estimate the parameters of a double hinge model of the trapeziometacarpal joint (TMC) by MRI-based motion analysis. The model includes two non-orthogonal and non-intersecting rotation axes accounting for flexion–extension (F–E) and adduction–abduction (A–A). We evaluated the quality of the estimated model parameters in the prediction of the relative motion of the first metacarpal bone with respect to the trapezium. As a result, we obtained that: (a) the estimated location and orientation of the F–E and A–A axes were in agreement with previous in vitro studies, (b) the motion of the first metacarpal predicted by the 2 degrees of freedom (2DoF) model exhibits a maximum surface distance error in the range of about 2 mm and (c) four thumb postures at the boundary of the TMC range of motion are sufficient to provide a good estimation of the 2DoF TMC kinematic model and good reproducibility (～1.7 mm) of the real thumb motion at TMC level.     

Determination of the number of degrees of freedom of the trapeziometacarpal joint–An in vitro study

ObjectiveMost of the studies about trapeziometacarpal joint assume that it exhibits only two independent degrees of freedom, but the experimental or theoretical support for considering a two-degrees of freedom model is not always clear.Materials and methodsTherefore, an in vitro kinematic study has been designed to demonstrate, from experimental data, that only two of the trapeziometacarpal degrees of freedom (i.e., flexion/extension and adduction/abduction) are non-null and independent. Several movements of maximal amplitude in flexion, abduction and circumduction have been realized and the relative position and orientation of the segment coordinate system embedded on the first metacarpal with respect to that embedded on the trapezium have been collected using electromagnetic sensors. The trapeziometacarpal rotations have been described using a joint coordinate system and the joint displacements have been evaluated on the axes of this coordinate system.ResultsThe root mean square (RMS) values of the joint displacement components have been found small enough to assume that the trapeziometacarpal joint has no translation degrees of freedom. A paraboloid coupling equation has been found between the internal/external rotation angle and the two other, flexion/extension and adduction/abduction, angles.ConclusionThus, this study demonstrates that the trapeziometacarpal joint has only two independent rotational degrees of freedom, and further, the described methodology could also be used to determine the coupling laws between degrees of freedom of various joints.     

Signaling of Ankle Joint Position by Receptors in Different Muscles

Plots were made of multiunit activity versus ankle joint position for receptors in each of the 12 muscles crossing the cat ankle joint, except peroneus tertius, by recording from populations of afferent fibers in muscle nerves. The discharge was measured 15 or 30 sec after terminating the movements that altered the position of the joint. These recordings were dominated by large-spike activity that would be expected to originate mainly from primary spindle endings. Seven of the 12 muscles also cross other joints. Their responses at a given ankle joint position were so altered by changes in the position of the knee or toe joints that they could not reliably signal the position of the ankle joint. As judged from multiunit recording, receptors in each of the five muscles specific to the ankle joint were influenced by more than one axis of ankle joint displacement.

Single-unit recording from dorsal root filaments was used to determine whether primary or secondary spindle receptors in soleus and tibialis anterior could selectively signal one axis of ankle joint rotation. Individual soleus receptors were tested both on the flexion extension axis and with a combined adduction–eversion movement.

For 38 of the 70 soleus receptors examined (54%), firm adduction–eversion produced a level of activity greater than that caused by 10° of flexion, and for 77% the level of activity was greater than that caused by 5° of flexion. For 168 of the 184 tibialis anterior receptors studied (91%), firm abduction inversion produced a level of activity greater than that caused by 10° of extension. Thus few receptors were found that responded exclusively to one axis of rotation.

One way in which the position of the ankle joint could be specified in the face of multiaxial receptor activity is by examining the receptor discharge from more than one muscle. A suggestion for how the nervous system might do this is given in the discussion.     

On the estimation of joint kinematics during gait.

In gait analysis, the concepts of Euler and helical (screw) angles are used to define the three-dimensional relative joint angular motion of lower extremities. Reliable estimation of joint angular motion depends on the accurate definition and construction of embedded axes within each body segment. In this paper, using sensitivity analysis, we quantify the effects of uncertainties in the definition and construction of embedded axes on the estimation of joint angular motion during gait. Using representative hip and knee motion data from normal subjects and cerebral palsy patients, the flexion-extension axis is analytically perturbed +/- 15 degrees in 5 degrees steps from a reference position, and the joint angles are recomputed for both Euler and helical angle definitions. For the Euler model, hip and knee flexion angles are relatively unaffected while the ab/adduction and rotation angles are significantly affected throughout the gait cycle. An error of 15 degrees in the definition of flexion-extension axis gives rise to maximum errors of 8 and 12 degrees for the ab/adduction angle, and 10-15 degrees for the rotation angles at the hip and knee, respectively. Furthermore, the magnitude of errors in ab/adduction and rotation angles are a function of the flexion angle. The errors for the ab/adduction angles increase with increasing flexion angle and for the rotation angle, decrease with increasing flexion angle. In cerebral palsy patients with flexed knee pattern of gait, this will result in distorted estimation of ab/adduction and rotation. For the helical model, similar results are obtained for the helical angle and associated direction cosines.(ABSTRACT TRUNCATED AT 250 WORDS)     

An improved OpenSim gait model with multiple degrees of freedom knee joint and knee ligaments

Musculoskeletal models are widely used to investigate joint kinematics and predict muscle force during gait. However, the knee is usually simplified as a one degree of freedom joint and knee ligaments are neglected. The aim of this study was to develop an OpenSim gait model with enhanced knee structures. The knee joint in this study included three rotations and three translations. The three knee rotations and mediolateral translation were independent, with proximodistal and anteroposterior translations occurring as a function of knee flexion/extension. Ten elastic elements described the geometrical and mechanical properties of the anterior and posterior cruciate ligaments (ACL and PCL), and the medial and lateral collateral ligaments (MCL and LCL). The three independent knee rotations were evaluated using OpenSim to observe ligament function. The results showed that the anterior and posterior bundles of ACL and PCL (aACL, pACL and aPCL, pPCL) intersected during knee flexion. The aACL and pACL mainly provided force during knee flexion and adduction, respectively. The aPCL was slack throughout the range of three knee rotations; however, the pPCL was utilised for knee abduction and internal rotation. The LCL was employed for knee adduction and rotation, but was slack beyond 20° of knee flexion. The MCL bundles were mainly used during knee adduction and external rotation. All these results suggest that the functions of knee ligaments in this model approximated the behaviour of the physical knee and the enhanced knee structures can improve the ability to investigate knee joint biomechanics during various gait activities.     

The effect of using different coordinate systems on in-vivo hip angles can be estimated from computed tomography images

Measurements of hip kinematics inherently depend on the coordinate system in which they are derived, yet the effect of the coordinate system definition on calculations of hip angles is not well-understood. Herein, hip angles calculated during dynamic activities were compared using coordinate systems described in the literature. In-vivo kinematic data of 24 participants (13 males) were analyzed during gait and the anterior impingement test using dual fluoroscopy and model-based tracking. Two coordinate systems for the pelvis (anterior pelvic plane, International Society of Biomechanics [ISB]) and three coordinate systems for the femur (table top plane with two definitions of the superior-inferior axis, ISB) were evaluated. Bony landmarks visible on computed tomography (CT) images were identified to establish each coordinate system and used as the basis to calculate differences in hip angles between coordinate system pairs. In the analysis during gait, the maximum differences derived from various coordinate system definitions were 6.7° ± 5.5° for flexion, 7.7° ± 2.1° for rotation, and 5.5° ± 0.7° for adduction. For the anterior impingement test, the differences were 8.1° ± 5.9°, 7.1° ± 1.2°, and 5.3° ± 0.7°, respectively. Landmark-based analysis using CT images could estimate these dynamic differences with errors less than 1.0°. Our results indicate that hip angles can be accurately transformed to angles calculated in different coordinate systems by accounting for the inherent bony anatomy. This information may aid in the interpretation of results across biomechanical studies of the hip.     

Orientation and location of the finite helical axis of the equine forelimb joints

To reduce anatomically unrealistic limb postures in a virtual musculoskeletal model of a horse's forelimb, accurate knowledge on forelimb joint constraints is essential. The aim of this cadaver study is to report all orientation and position changes of the finite helical axes (FHA) as a function of joint angle for different equine forelimb joints. Five horse cadaver forelimbs with standardized cuts at the midlevel of each segment were used. Bone pins with reflective marker triads were drilled into the forelimb bones. Unless joint angles were anatomically coupled, each joint was manually moved independently in all three rotational degrees of freedom (flexion–extension, abduction–adduction, internal–external rotation). The 3D coordinates of the marker triads were recorded using a six infra-red camera system. The FHA and its orientational and positional properties were calculated and expressed against joint angle over the entire range of motion using a finite helical axis method. When coupled, joint angles and FHA were expressed in function of flexion–extension angle. Flexion–extension movement was substantial in all forelimb joints, the shoulder allowed additional considerable motion in all three rotational degrees of freedoms. The position of the FHA was constant in the fetlock and elbow and a constant orientation of the FHA was found in the shoulder. Orientation and position changes of the FHA over the entire range of motion were observed in the carpus and the interphalangeal joints. We report FHA position and orientation changes as a function of flexion–extension angle to allow for inclusion in a musculoskeletal model of a horse to minimize calculation errors caused by incorrect location of the FHA.     

Influence of kinematic analysis methods on detecting ankle and subtalar joint instability

Patients with subtalar joint instability may be misdiagnosed with ankle instability, which may lead to chronic instability at the subtalar joint. Therefore, it is important to understand the difference in kinematics after ligament sectioning and differentiate the changes in kinematics between ankle and subtalar instability. Three methods may be used to determine the joint kinematics; the Euler angles, the Joint Coordinate System (JCS) and the helical axis (HA). The purpose of this study was to investigate the influence of using either method to detect subtalar and ankle joints instability. 3D kinematics at the ankle and subtalar joint were analyzed on 8 cadaveric specimens while the foot was intact and after sequentially sectioning the anterior talofibular ligament (ATFL), the calcaneofibular ligament (CFL), the cervical ligament and the interosseous talocalcaneal ligament (ITCL). Comparison in kinematics calculated from sensor and anatomical landmarks was conducted as well as the influence of Euler angles and JCS rotation sequence (between ISB recommendation and previous research) on the subtalar joint. All data showed a significant increase in inversion when the ITCL was sectioned. There were differences in the data calculated using sensors coordinate systems vs. anatomic coordinate systems. Anatomic coordinate systems were recommended for these calculations. The Euler angle and JCS gave similar results. Differences in Euler angles and JCS sequence lead to the same conclusion in detecting instability at the ankle and subtalar joint. As expected, the HA detected instability in plantarflexion at the ankle joint and in inversion at the subtalar joint.     

Repeatability assessment of functional methods to estimate the glenohumeral joint centre

Functional methods can be used to determine the centre of rotation (CoR) of a ball-and-socket joint. The algorithms are used to locate rather the hip joint centre than the glenohumeral joint centre. The choice of the most suitable method depends especially on the intra- and inter-session repeatability of these methods. This paper aims at evaluating the intra- and inter-session repeatability of functional methods with which the glenohumeral joint rotation centre (GHRC) can be estimated in vivo. It also estimates the most suitable amplitude of functional movements. Five functional methods were tested: the algorithms of Gamage and Lasenby, bias compensation, symmetrical CoR estimation, normalisation method and helical axis. Ten subjects performed three cycles of three different movements (flexion–extension, abduction–adduction and circumduction). These movements were repeated three times with three different ranges of motion. Six subjects came back in order to evaluate the inter-session repeatability. For each test, the location of the GHRC was estimated by the five methods. The method to solve the functional problem and the range of functional movement affected the GHRC location. The results showed a good to excellent intra-session repeatability. The lowest repeatability error was found for the high amplitude whatever the methods used. The inter-session reliability was moderate. Finally, we suggest the use of functional methods with high amplitude movement in order to locate the GHRC with the best reliability.     

Sensitivity of the knee joint kinematics calculation to selection of flexion axes

Various flexion axes have been used in the literature to describe knee joint kinematics. This study measured the passive knee kinematics of six cadaveric human knee specimens using two widely accepted flexion axes; transepicondylar axis and the geometric center axis. These two axes were found to form an angle of 4.0 degrees +/- 0.8 degrees. The tibial rotation calculated using the transepicondylar axis was significantly different than the rotation obtained using the geometric center axis for the same knee motion. At 90 degrees of flexion, the tibial rotation obtained using the transepicondylar axis was 4.8 degrees +/- 9.4 degrees whereas the rotation recorded using the geometric center axis at the same flexion angle was 13.8 degrees +/- 10.2 degrees. At 150 degrees of knee flexion, the rotations obtained from the transepicondylar and the geometric center axes were 7.2 degrees +/- 5.7 degrees and 19.9 degrees +/- 6.9 degrees, respectively. The data suggest that a clear definition of the flexion axis is necessary when reporting knee joint kinematics.     

Expressing the joint moments of drop jumps and sidestep cutting in different reference frames – does it matter?

Joint moments help us understand joint loading and muscle function during movement. However, the interpretation depends on the choice of reference frame, but the different reference frames have not been compared in dynamic, high-impact sporting movements. We have compared the magnitude and the resulting ranking of hip and knee joint moments expressed in the laboratory coordinate system, the local system of the distal segment and projected or decomposed to the Joint Coordinate System (JCS) axes. Hip and knee joint moments of drop jumps and sidestep cutting in 70 elite female handball players were calculated based on recordings from an eight-camera 240 Hz system and two force platforms and expressed with the four methods. The greatest variations in magnitude between conditions were seen for drop jump hip internal rotation (range: 0.31–0.71 Nm/kg) and sidestep cutting knee flexion (2.87–3.39 Nm/kg) and hip internal rotation (0.87–2.36 Nm/kg) and knee internal rotation (0.10–0.40 Nm/kg) moments. The rank correlations were highest between conditions for flexion moments (0.88–1.00) and sidestep cutting abduction moments (0.71–0.98). The rank correlations ranged from 0.64 to 0.73 for drop jump knee abduction moments and between −0.17 and 0.67 for hip and knee internal rotation moments. Expression of joint moments in different reference systems affects the magnitude and ranking of athletes. This lack of consistency may complicate the comparison and combination of results. Projection to the JCS is the only method where joint moments correspond to muscle and ligament loading. More widespread adoption of this convention could facilitate comparison of studies and ease the interpretation of results.     

Expression of joint moment in the joint coordinate system

The question of using the nonorthogonal joint coordinate system (JCS) to report joint moments has risen in the literature. However, the expression of joint moments in a nonorthogonal system is still confusing. The purpose of this paper is to present a method to express any 3D vector in a nonorthogonal coordinate system. The interpretation of these expressions in the JCS is clarified and an example for the 3D joint moment vector at the shoulder and the knee is given. A nonorthogonal projection method is proposed based on the mixed product. These nonorthogonal projections represent, for a 3D joint moment vector, the net mechanical action on the JCS axes. Considering the net mechanical action on each axis seems important in order to assess joint resistance in the JCS. The orthogonal projections of the same 3D joint moment vector on the JCS axes can be characterized as "motor torque." However, this interpretation is dependent on the chosen kinematic model. The nonorthogonal and orthogonal projections of shoulder joint moment during wheelchair propulsion and knee joint moment during walking were compared using root mean squares (rmss). rmss showed differences ranging from 6 N?m to 22.3 N?m between both projections at the shoulder, while differences ranged from 0.8 N?m to 3.0 N?m at the knee. Generally, orthogonal projections were of lower amplitudes than nonorthogonal projections at both joints. The orthogonal projection on the proximal or distal coordinates systems represents the net mechanical actions on each axis, which is not the case for the orthogonal projection (i.e., motor torque) on JCS axes. In order to represent the net action at the joint in a JCS, the nonorthogonal projection should be used.     

ISB recommendation on definitions of joint coordinate systems of various joints for the reporting of human joint motion--Part II: shoulder, elbow, wrist and hand

In this communication, the Standardization and Terminology Committee (STC) of the International Society of Biomechanics proposes a definition of a joint coordinate system (JCS) for the shoulder, elbow, wrist, and hand. For each joint, a standard for the local axis system in each articulating segment or bone is generated. These axes then standardize the JCS. The STC is publishing these recommendations so as to encourage their use, to stimulate feedback and discussion, and to facilitate further revisions. Adopting these standards will lead to better communication among researchers and clinicians.     

Static optimization underestimates antagonist muscle activity at the glenohumeral joint: A musculoskeletal modeling study

Static optimization is commonly employed in musculoskeletal modeling to estimate muscle and joint loading; however, the ability of this approach to predict antagonist muscle activity at the shoulder is poorly understood. Antagonist muscles, which contribute negatively to a net joint moment, are known to be important for maintaining glenohumeral joint stability. This study aimed to compare muscle and joint force predictions from a subject-specific neuromusculoskeletal model of the shoulder driven entirely by measured muscle electromyography (EMG) data with those from a musculoskeletal model employing static optimization. Four healthy adults performed six sub-maximal upper-limb contractions including shoulder abduction, adduction, flexion, extension, internal rotation and external rotation. EMG data were simultaneously measured from 16 shoulder muscles using surface and intramuscular electrodes, and joint motion evaluated using video motion analysis. Muscle and joint forces were calculated using both a calibrated EMG-driven neuromusculoskeletal modeling framework, and musculoskeletal model simulations that employed static optimization. The EMG-driven model predicted antagonistic muscle function for pectoralis major, latissimus dorsi and teres major during abduction and flexion; supraspinatus during adduction; middle deltoid during extension; and subscapularis, pectoralis major and latissimus dorsi during external rotation. In contrast, static optimization neural solutions showed little or no recruitment of these muscles, and preferentially activated agonistic prime movers with large moment arms. As a consequence, glenohumeral joint force calculations varied substantially between models. The findings suggest that static optimization may under-estimate the activity of muscle antagonists, and therefore, their contribution to glenohumeral joint stability.     

Effect of axis alignment on in vivo shoulder kinematics

Background. To describe 3D shoulder joint movements, the International Society of Biomechanics (ISB) recommends using segment coordinate systems (SCSs) on the humerus, scapula and thorax, and joint coordinate systems (JCSs) on the shoulder. However, one of the remaining problems is how to define the zero angles when the arm is in an initial reference position. The aim of this paper is to compare various methods of determining the JCSs of the shoulder that make it possible to define the zero angles of the arm in the resting position.

Methods. Able-bodied subjects performed elevation movements in the scapular plane, specifically neutral, internal and external rotations of the humerus. The initial humerus position (at the beginning of the arm movement) and range of motion were analysed for the purpose of clinical interpretation of arm attitude and movement. The following four different JCSs were explored: (1) the standard JCS, defined as recommended by the ISB, (2) a first aligned JCS, where the humerus SCS is initially aligned with the scapula SCS, (3) a second aligned JCS, where the opposite operation is performed and 4) a third aligned JCS, where both the humerus and the scapular SCS are initially aligned with the thorax SCS.

Findings. The second aligned JCS was the only method that did not produce any exaggerated range of movement in either anatomical plane.

Interpretation. Mathematical JCS alignment allows clearer clinical interpretation of arm attitude and movement.     

A motion-decomposition approach to address gimbal lock in the 3-cylinder open chain mechanism description of a joint coordinate system at the glenohumeral joint

In this study, the standard-sequence properties of a joint coordinate system were implemented for the glenohumeral joint by the use of a set of instantaneous geometrical planes. These are: a plane that is bound by the humeral long axis and an orthogonal axis that is the cross product of the scapular anterior axis and this long axis, and a plane that is bounded by the long axis of the humerus and the cross product of the scapular lateral axis and this long axis. The relevant axes are updated after every decomposition of a motion component of a humeral position. Flexion, abduction and rotation are then implemented upon three of these axes and are applied in a step-wise uncoupling of an acquired humeral motion to extract the joint coordinate system angles. This technique was numerically applied to physiological kinematics data from the literature to convert them to the joint coordinate system and to visually reconstruct the motion on a set of glenohumeral bones for validation.     

Measurement of the screw-home motion of the knee is sensitive to errors in axis alignment

Measurements of joint angles during motion analysis are subject to error caused by kinematic crosstalk, that is, one joint rotation (e. g., flexion) being interpreted as another (e.g., abduction). Kinematic crosstalk results from the chosen joint coordinate system being misaligned with the axes about which rotations are assumed to occur. The aim of this paper is to demonstrate that measurement of the so-called "screw-home" motion of the human knee, in which axial rotation and extension are coupled, is especially prone to errors due to crosstalk. The motions of two different two-segment mechanical linkages were examined to study the effects of crosstalk. The segments of the first linkage (NSH) were connected by a revolute joint, but the second linkage (SH) incorporated gearing that caused 15 degrees of screw-home rotation to occur with 90 degrees knee flexion. It was found that rotating the flexion axis (inducing crosstalk) could make linkage NSH appear to exhibit a screw-home motion and that a different rotation of the flexion axis could make linkage SH apparently exhibit pure flexion. These findings suggest that the measurement of screw-home rotation may be strongly influenced by errors in the location of the flexion axis. The magnitudes of these displacements of the flexion axis were consistent with the inter-observer variability seen when five experienced observers defined the flexion axis by palpating the medial and lateral femoral epicondyles. Care should be taken when interpreting small internal-external rotations and abduction-adduction angles to ensure that they are not the products of kinematic crosstalk.     

A reproducible method for studying three-dimensional knee kinematics

The methods used in movement analysis often rely on the definition of joint coordinate systems permitting three-dimensional (3D) kinematics. The first aim of this research project was to present a functional and postural method (FP method) to define a bone-embedded anatomical frame (BAF) on the femur and tibia, and, subsequently, a knee joint coordinate system. The repeatability of the proposed method was also assessed. Using FP method to define the BAFs, 4 kinematic parameters (flexion/extension, abduction/adduction, tibial internal/external rotation, and antero-posterior translation) were computed for 15 subjects walking on a treadmill. The repeatability for all four kinematic parameters was then assessed, using intra- and inter-observer settings. After pooling the results for all observers, the mean repeatability value ranged between 0.4 degrees and 0.8 degrees for rotation angles and between 0.8 and 2.2 mm for translation.     

Registration of 6-DOFs electrogoniometry and CT medical imaging for 3D joint modeling

The paper describes a method in which two data-collecting systems, medical imaging and electrogoniometry, are combined to allow the accurate and simultaneous modeling of both the spatial kinematics and the morphological surface of a particular joint. The joint of interest (JOI) is attached to a Plexiglas jig that includes four metallic markers defining a local reference system (R(GONIO)) for the kinematics data. Volumetric data of the JOI and the R(GONIO) markers are collected from medical imaging. The spatial location and orientation of the markers in the global reference system (R(CT)) of the medical-imaging environment are obtained by applying object-recognition and classification methods on the image dataset. Segmentation and 3D isosurfacing of the JOI are performed to produce a 3D model including two anatomical objects-the proximal and distal JOI segments. After imaging, one end of a custom-made 3D electrogoniometer is attached to the distal segment of the JOI, and the other end is placed at the R(GONIO) origin; the JOI is displaced and the spatial kinematics data is recorded by the goniometer. After recording, data registration from R(GONIO) to R(CT) occurred prior to simulation. Data analysis was performed using both joint coordinate system (JCS) and instantaneous helical axis (IHA).Finally, the 3D joint model is simulated in real time using the experimental kinematics data. The system is integrated into a computer graphics interface, allowing free manipulation of the 3D scene.The overall accuracy of the method has been validated with two other kinematics data collection methods including a 3D digitizer and interpolation of the kinematics data from discrete positions obtained from medical imaging. Validation has been performed on both superior and inferior radio-ulna joints (i.e. prono-supination motion). Maximal RMS error was 1 degrees and 1.2mm on the helical axis rotation and translation, respectively. Prono-supination of the forearm showed a total rotation of 132 degrees for 0.8mm of translation. The method reproducibility using JCS parameters was in average 1 degrees (maximal deviation=2 degrees ) for rotation, and 1mm (maximal deviation=2mm) for translation. In vitro experiments have been performed on both knee joint and ankle joint. Averaged JCS parameters for the knee were 109 degrees, 17 degrees and 4 degrees for flexion, internal rotation and abduction, respectively. Averaged maximal translation values for the knee were 12, 3 and 4mm posteriorly, medially and proximally, respectively. Averaged JCS parameters for the ankle were 43 degrees, 9 degrees and 3 degrees for plantarflexion, adduction and internal rotation, respectively. Averaged maximal translation values for the ankle were 4, 2 and 1mm anteriorly, medially and proximally, respectively.