A musculoskeletal model to estimate the relative changes in wrist strength due to interacting wrist and forearm postures

Wrist rotations about one wrist axis (e.g. flexion/extension) can affect the strength about another wrist axis (e.g. radial/ulnar deviation). This study used a musculoskeletal model of the distal upper extremity, and an optimization approach, to quantify the interaction effects of wrist flexion/extension (FE), radial/ulnar deviation (RUD) and forearm pronation/supination (PS) on wrist strength. Regression equations were developed to predict the relative changes in strength from the neutral posture, so that the changes in strength, due to complex and interacting wrist and forearm rotation postures, can be incorporated within future ergonomics assessments of wrist strength.     

Extrinsic flexor muscles generate concurrent flexion of all three finger joints

The role of the forearm (extrinsic) finger flexor muscles in initiating rotation of the metacarpophalangeal (MCP) joint and in coordinating flexion at the MCP, the proximal interphalangeal (PIP), and distal interphalangeal (DIP) joints remains a matter of some debate. To address the biomechanical feasibility of the extrinsic flexors performing these actions, a computer simulation of the index finger was created. The model consisted of a planar open-link chain comprised of three revolute joints and four links, driven by the change in length of the flexor muscles. Passive joint characteristics, included in the model, were obtained from system identification experiments involving the application of angular perturbations to the joint of interest. Simulation results reveal that in the absence of passive joint torque, shortening of the extrinsic flexors results in PIP flexion (80°), but DIP (8°) and MCP (7°) joint extension. The inclusion of normal physiological levels of passive joint torque, however, results in simultaneous flexion of all three joints (63° for DIP, 75° for PIP, and 43° for MCP). Applicability of the simulation results was confirmed by recording finger motion produced by electrical stimulation of the extrinsic flexor muscles for the index finger. These findings support the view that the extrinsic flexor muscles can initiate MCP flexion, and produce simultaneous motion at the MCP, PIP, and DIP joints.     

A kinematic model of the human hand to evaluate its prehensile capabilities.

A kinematic model has been developed for simulation and prediction of the prehensile capabilities of the human hand. The kinematic skeleton of the hand is characterized by ideal joints and simple segments. Finger-joint angulation is characterized by yaw (abduction-adduction), pitch (flexion-extension) and roll (axial rotation) angles. The model is based on an algorithm that determines contact between two ellipsoids, which are used to approximate the geometry of the cutaneous surface of the hand segments. The model predicts the hand posture (joint angles) for power grasp of ellipsoidal objects by 'wrapping' the fingers around the object. Algorithms for two grip types are included: (1) a transverse volar grasp, which has the thumb abducted for added power; and (2) a diagonal volar grasp, which has the thumb adducted for an element of precision. Coefficients for estimating anthropometric parameters from hand length and breadth are incorporated in the model. Graphics procedures are included for visual display of the model. In an effort to validate the predictive capabilities of the model, joint angles were measured on six subjects grasping circular cylinders of various diameters and these measured joint angles were compared with angles predicted by the model. Sensitivity of the model to the various input parameters was also determined. On an average, the model predicted joint flexion angles that were 5.3% or 2.8 degrees +/- 12.2 degrees larger than the measured angles. Good agreement was found for the MCP and PIP joints, but results for DIP were more variable because of its dependence on the predictions for the proximal joints.     

Muscle moment arm and normalized moment contributions as reference data for musculoskeletal elbow and wrist joint models

A geometric musculoskeletal model of the elbow and wrist joints was developed to calculate muscle moment arms throughout elbow flexion/extension, forearm pronation/supination, wrist flexion/extension and radial/ulnar deviation. Model moment arms were verified with data from cadaver specimen studies and geometric models available in the literature. Coefficients of polynomial equations were calculated for all moment arms as functions of joint angle, with special consideration to coupled muscles as a function of two joint angles. Additionally, a “normalized potential moment (NPM)” contribution index for each muscle across the elbow and wrist joints in four degrees-of-freedom was determined using each muscle's normalized physiological cross-sectional area (PCSA) and peak moment arm (MA). We hypothesize that (a) a geometric model of the elbow and wrist joints can represent the major attributes of MA versus joint angle from many literature sources of cadaver and model data and (b) an index can represent each muscle's normalized moment contribution to each degree-of-freedom at the elbow and wrist. We believe these data serve as a simple, yet comprehensive, reference for how the primary 16 muscles across the elbow and wrist contribute to joint moment and overall joint performance.     

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.     

Interdependency of the maximum range of flexion–extension of hand metacarpophalangeal joints

Mobility of the fingers metacarpophalangeal (MCP) joints depends on the posture of the adjacent ones. Current Biomechanical hand models consider fixed ranges of movement at joints, regardless of the posture, thus allowing for non-realistic postures, generating wrong results in reach studies and forward dynamic analyses. This study provides data for more realistic hand models. The maximum voluntary extension (MVE) and flexion (MVF) of different combinations of MCP joints were measured covering their range of motion. Dependency of the MVF and MVE on the posture of the adjacent MCP joints was confirmed and mathematical models obtained through regression analyses (RMSE 7.7°).     

Influence of knee angle and individual flexibility on the flexion-relaxation response of the low back musculature.

In many occupational settings (e.g. agriculture and construction) workers are asked to maintain static flexed postures of the low back for extended periods of time. Recent research indicates that the resulting strain in the viscoelastic, ligamentous tissues may have a deleterious effect on the stability of the spine and the normal reflex response of spinal tissues. The purpose of this study was to evaluate the previously described flexion-relaxation response in terms of the interactive effect of trunk flexion angle (30 degrees, 50 degrees, 70 degrees, 90 degrees ), knee flexion angle (0 degrees (straight knees), 20 degrees, 40 degrees ) and individual flexibiliteky (low, medium, and high). These conditions were tested under two levels of loading: no load (just supporting the weight of the torso) and trunk extension moment equal to 50% of the subject's posture-specific maximum voluntary trunk extension capacity. Surface electromyographic (EMG) data were collected from the multifidus, the longissimus, the iliocostalis, the vastus medialis, the rectus femoris, the vastus lateralis, the biceps femoris, and the gastrocnemius-soleus group from a sample of eight male participants as they performed isometric weight holding tasks in the postures defined by the combinations of trunk angle and knee angle. The results of this study showed that knee angle did have a significant effect on the lumbar extensor muscle activity but only consistently at the 90 degrees trunk angle. Participant flexibility showed a consistent trend of decreasing lumbar extensor muscle activity with decreased flexibility across all trunk angle values. Most interesting was the interactive response of flexibility and knee angle, wherein the flexibility of the participant influenced the trunk angles at which the knee flexion angle affected the flexion-relaxation response. Highly flexible subjects showed an effect of knee angle on the flexion-relaxation response only at the 90 degrees trunk angle; subjects in the medium flexibility category showed a similar response in both the 70 degrees and 90 degrees trunk angles; subject in the low flexibility group showed no knee angle effect on the flexion-relaxation response. Overall the results confirm previous results with regard to the contribution of the passive tissues to the overall trunk extension moment but also show that the tension in the bi-articular biceps femoris, which was influenced by knee flexion angle and flexibility, affects the ratio of active extensor moment contributions of the lumbar extensor musculature to passive extensor moment contributions from the muscular and ligamentous tissues. The results of this study provide empirical data describing this complicated, interactive response.     

Comparison of measurement accuracy between two wrist goniometer systems during pronation and supination.

Pronation and supination have been shown to affect wrist goniometer measurement accuracy. The purpose of this study was to compare differences in measurement accuracy between a commonly used biaxial, single transducer wrist goniometer (System A) and a biaxial, two-transducer wrist goniometer (System B) over a wide range of pronation and supination (P/S) positions. Eight subjects moved their wrist between -40 and 40 degrees of flexion/extension (F/E) and -10 and 20 degrees of radial/ulnar (R/U) deviation in four different P/S positions: 90 degrees pronation; 45 degrees pronation; 0 degrees neutral and 45 degrees supination. System A was prone to more R/U crosstalk than System B and the amount of crosstalk was dependent on the P/S position. F/E crosstalk was present with both goniometer systems and was also shown to be dependent on P/S. When moving from pronation to supination, both systems experienced a similar extension offset error; however R/U offset errors were roughly equal in magnitude but opposite in direction. The calibration position will affect wrist angle measurements and the magnitude and direction of measurement errors. To minimize offset errors, the goniometer systems should be calibrated in the P/S posture most likely to be encountered during measurement. Differences in goniometer design and application accounted for the performance differences.     

Measurements of wrist and forearm positions and movements: effect of, and compensation for, goniometer crosstalk.

Flexible biaxial goniometers are extensively used for measuring wrist positions and movements. However, they display an inherent crosstalk error. The aim was to evaluate the effect, of this error, on summary measures used for characterizing manual work. A goniometer and a torsiometer were combined into one device. An algorithm that effectively compensated for crosstalk was developed. Recordings from 25 women, performing five worktasks, were analyzed, both with and without compensation for crosstalk. The errors in the 10th, 50th and 90th percentiles of the flexion/extension distributions were small, on average <1 degrees. The ulnar/radial deviation distributions were weakly dependent on forearm position. The flexion/extension velocity measures were, for the 50th and 90th percentiles, as well as the mean velocity, consistently underestimated by, on average, 3.9%. For ulnar/radial deviation, the velocity errors were less consistent. Mean power frequency, which is a measure of repetitiveness, was insensitive (error <1%) to crosstalk. The forearm supination/pronation angular distributions were wider, and the velocities higher, than for the wrists. Considering wrist/hand exposure in epidemiologic studies, as well as for establishing and surveillance of exposure limits for prevention of work-related upper extremity musculoskeletal disorders, the crosstalk error can, when considering other errors and sources to variation, be disregarded.     

Quantitative assessment of the accuracy for three interpolation techniques in kinematic analysis of human movement

Marker obstruction during human movement analyses requires interpolation to reconstruct missing kinematic data. This investigation quantifies errors associated with three interpolation techniques and varying interpolated durations. Right ulnar styloid kinematics from 13 participants performing manual wheelchair ramp ascent were reconstructed using linear, cubic spline and local coordinate system (LCS) interpolation from 11-90% of one propulsive cycle. Elbow angles (flexion/extension and pronation/supination) were calculated using real and reconstructed kinematics. Reconstructed kinematics produced maximum elbow flexion/extension errors of 37.1 (linear), 23.4 (spline) and 9.3 (LCS) degrees. Reconstruction errors are unavoidable [minimum errors of 6.7?mm (LCS); 0.29?mm (spline); 0.42?mm (linear)], emphasising careful motion capture system setup must be performed to minimise data interpolation. For the observed movement, LCS-based interpolation (average error of 14.3?mm; correlation of 0.976 for elbow flexion/extension) was most suitable for reconstructing durations longer than 200?ms. Spline interpolation was superior for shorter durations.     

A demonstration of the validity of a 3-D video motion analysis method for measuring finger flexion and extension

This study demonstrates the validity of using 3-D video motion analysis to measure hand motion. Several researchers have devised ingenious methods to study normal and abnormal hand movements. Although very helpful, these earlier studies are static representations of a dynamic phenomenon. Despite the many studies of hand motion using scientifically impeccable techniques, little is known about digital motion, and there are still few researchers investigating dynamic three-dimensional motion of the hand. Results from a three-camera video motion analysis system were compared to those from the “gold standard”, 2-D lateral view fluoroscopy. We used these two methods to record hand motion simultaneously during unrestricted flexion and extension of the index finger of the dominant hand in 6 neurologically normal, healthy volunteers. After collection and post-processing, the waveforms of the PIP, DIP and MCP joint angles were compared using the adjusted coefficient of multiple determination (R²_a, or CMD). The mean CMD values for the MCP, PIP and DIP joint angle waveforms were 0.96, 0.98 and 0.94, respectively, suggesting a close similarity between motion of comparable joints analyzed by the 2-D and 3-D methods. This shows that the method of 3-D motion analysis is capable of accurately quantifying digital joint motion.

It is anticipated that 3-D motion analysis, in addition to being used as a research tool, will also have clinical applications such as surgical planning in neuromuscular disorders and the documentation of abnormal motion in many other pathological hand conditions.     

Posture-dependent trunk extensor EMG activity during maximum isometrics exertions in normal male and female subjects.

Posture-dependent trunk function data are important for appropriate normalization of submaximal trunk exertions, and is also necessary to define a more precise and specific use for strength testing in the prevention and diagnosis of spinal disorders. The aim of the current study was to quantify maximal effort trunk muscle extensor activity and trunk isometric extension torque over a functional range of sagittal standing postures. Twenty healthy, young adult male and female subjects performed isometric extension tasks over a sagittal posture range of -20 degrees extension to +50 degrees flexion, in 10 degrees increments. Erector spinae muscle activity was recorded bilaterally at the level of L3 using surface EMG electrodes. Isometric trunk extension torque was measured using a trunk dynamometer. EMG and trunk torque differed significantly between genders, but there were no differences between male and female subjects when the data were normalized with respect to the upright posture. For the combined male and female population, upright posture normalized L3 EMG activity (EMGn) and trunk extension torque (Tn) increased 1.7-fold and 3.5-fold, respectively, over the 70 degrees range of sagittal postures examined. The ratio (Tn/EMGn) increased two-fold (0.83 to 1.67) from -20 degrees extension to +50 degrees flexion, indicating that the neuromuscular efficiency increases with flexion. Trunk extension torque normalized with respect to the upright posture was linearly and positively correlated (r = 0.59, P < 0.001) to similarly normalized L3 EMG activity. This relatively weak correlation suggests that trunk muscle synergism and/or intrinsic muscle length-tension relationships are also modulated by posture. This study provides data that can be used to estimate trunk extensor muscle function over a broad range of sagittal postures. Our findings indicate that appropriate postural normalization of trunk extensor EMG activity is necessary for studies where submaximal trunk exertions are performed over a range of upright postures.     

Quantitative assessment of the accuracy for three interpolation techniques in kinematic analysis of human movement

Marker obstruction during human movement analyses requires interpolation to reconstruct missing kinematic data. This investigation quantifies errors associated with three interpolation techniques and varying interpolated durations. Right ulnar styloid kinematics from 13 participants performing manual wheelchair ramp ascent were reconstructed using linear, cubic spline and local coordinate system (LCS) interpolation from 11–90% of one propulsive cycle. Elbow angles (flexion/extension and pronation/supination) were calculated using real and reconstructed kinematics. Reconstructed kinematics produced maximum elbow flexion/extension errors of 37.1 (linear), 23.4 (spline) and 9.3 (LCS) degrees. Reconstruction errors are unavoidable [minimum errors of 6.7 mm (LCS); 0.29 mm (spline); 0.42 mm (linear)], emphasising careful motion capture system setup must be performed to minimise data interpolation. For the observed movement, LCS-based interpolation (average error of 14.3 mm; correlation of 0.976 for elbow flexion/extension) was most suitable for reconstructing durations longer than 200 ms. Spline interpolation was superior for shorter durations.     

A demonstration of validity of 3-D video motion analysis method for measuring finger flexion and extension

This study demonstrates the validity of using 3-D video motion analysis to measure hand motion. Several researchers have devised ingenious methods to study normal and abnormal hand movements. Although very helpful, these earlier studies are static representations of a dynamic phenomenon. Despite the many studies of hand motion using scientifically impeccable techniques, little is known about digital motion, and there are still few researchers investigating dynamic three-dimensional motion of the hand. Results from a three-camera video motion analysis system were compared to those from the "gold standard", 2-D lateral view fluoroscopy. We used these two methods to record hand motion simultaneously during unrestricted flexion and extension of the index finger of the dominant hand in 6 neurologically normal, healthy volunteers. After collection and post-processing, the waveforms of the PIP, DIP and MCP joint angles were compared using the adjusted coefficient of multiple determination (R2(a), or CMD). The mean CMD values for the MCP, PIP and DIP joint angle waveforms were 0.96, 0.98 and 0.94, respectively, suggesting a close similarity between motion of comparable joints analyzed by the 2-D and 3-D methods. This shows that the method of 3-D motion analysis is capable of accurately quantifying digital joint motion. It is anticipated that 3-D motion analysis, in addition to being used as a research tool, will also have clinical applications such as surgical planning in neuromuscular disorders and the documentation of abnormal motion in many other pathological hand conditions.     

Effect of knee joint flexion and femur rotation on retropatellar contact of the human knee joint]

The aim of the present study was to evaluate retropatellar contact characteristics at different angles of flexion of the knee joint. To this end, 6 cadaveric legs were examined using pressure sensitive film (Fuji Prescale type "super low") at angles of flexion of 45 degrees, 60 degrees, 90 degrees and 120 degrees both in neutral rotation and 10 degrees internal and external rotation of the femur in the same knee joints. A force of 140 N was applied to both the vastus medialis and lateralis, and a comparison made with a medially and a laterally dominating muscle force. The contact areas decreased with increasing angles of flexion. The medially dominating muscle traction increased the contact area. Comparison between internal and external rotation revealed a decrease in contact area on internal rotation. The pressure measurements were comparable in all loading situations. Comparison between neutral and medial traction revealed significant differences in contact area, pressure and force. The influence of femoral rotation showed no significant difference. A comparison of the different angles of flexion revealed only few significant differences. To prevent the development of retropatellar arthrosis, maximum contact areas are necessary. The study has shown an advantage for medially dominating muscle traction, and external rotation of the femur.     

Normal force distribution and posture of a hand pressing on a flat surface

Hand strength data are needed to understand and predict hand postures and finger loads while placing the hand on an object or surface. This study aims to analyze the effect of hand posture and surface orientation on hand force while pressing a flat surface. Twelve participants, 6 females and 6 males ages 19–25, performed three exertions (100%, 30% and 10% MVC- Maximum Voluntary Contraction) perpendicular to a plate in 4 angles (−45°, 0°, 45° and 90° with respect to the horizontal plane) at elbow height. Exertions involved pushing in two postures: (1) whole hand and (2) constrained to only using the fingertips. Inter-digit joint angles were recorded to map hand and finger motions and estimate joint moments for each condition. Participants exerted twice the force when pushing with whole hand vs. fingertips. 72–75% of the total force was exerted over the base of the palm, while only 11–13% with the thumb for exertions at 90°, 45° or 0° plate angles. Males maximum force for pushing at 0°, 45° and 90° plates averaged 49% higher than females for the whole hand and 62% for the fingertips (p < 0.01). There was no significant sex difference (p > 0.05) for the −45° plate. Thumb joint loads were generally higher than the other individual fingers (p < 0.05) in all % MVC and accounted for 12% of total force during whole hand exertions. On average, joint moments were 30% higher during fingertip conditions vs. whole hand. Thumb and finger joint moment magnitudes when pushing the plate at 100% MVC indicated that Metacarpophalangeal (MCP) joint moments were higher (p < 0.05) than Distal Interphalangeal joints (DIP) and Proximal Interphalangeal joints (PIP) under whole hand and fingertips conditions.     

The effect of finger extensor mechanism on the flexor force during isometric tasks.

The role of the intrinsic finger flexor muscles was investigated during finger flexion tasks. A suspension system was used to measure isometric finger forces when the point of force application varied along fingers in a distal-proximal direction. Two biomechanical models, with consideration of extensor mechanism Extensor Mechanism Model (EMM) and without consideration of extensor mechanism Flexor Model (FM), were used to calculate forces of extrinsic and intrinsic finger flexors. When the point of force application was at the distal phalanx, the extrinsic flexor muscles flexor digitorum profundus, FDP, and flexor digitorum superficialis, FDS, accounted for over 80% of the summed force of all flexors, and therefore were the major contributors to the joint flexion at the distal interphalangeal (DIP), proximal interphalangeal (PIP), and metacarpophalangeal (MCP) joints. When the point of force application was at the DIP joint, the FDS accounted for more than 70% of the total force of all flexors, and was the major contributor to the PIP and MCP joint flexion. When the force of application was at the PIP joint, the intrinsic muscle group was the major contributor for MCP flexion, accounting for more than 70% of the combined force of all flexors. The results suggest that the effects of the extensor mechanism on the flexors are relatively small when the location of force application is distal to the PIP joint. When the external force is applied proximally to the PIP joint, the extensor mechanism has large influence on force production of all flexors. The current study provides an experimental protocol and biomechanical models that allow estimation of the effects of extensor mechanism on both the extrinsic and intrinsic flexors in various loading conditions, as well as differentiating the contribution of the intrinsic and extrinsic finger flexors during isometric flexion.     

In vivo motion of the scaphotrapezio-trapezoidal (STT) joint

It has previously been shown that the articulation of the scaphotrapezio-trapezoidal (STT) joint can be modeled such that the trapezoid and trapezium are tightly linked and move together on a single path relative to the scaphoid during all directions of wrist motion. The simplicity of such a model is fascinating, but it leaves unanswered why two distinct carpal bones would have a mutually articulating surface if there were no motion between them, and how such a simplistic model of STT joint motion translates into the more complex global carpal motion. We performed an in vivo analysis of the trapezoids and trapeziums of 10 subjects (20 wrists) using a markerless bone registration technique. In particular, we analyzed the centroid spacing, centroid displacements, kinematics, and postures of the trapezoid and trapezium relative to the scaphoid. We found that, on a gross level, the in vivo STT motion was consistent with that reported in vitro. In addition, we found that the magnitude of trapezoid and trapezium motion was dependent upon the direction of wrist motion. However, we also found that when small rotations and displacements are considered there were small but statistically significant relative motions between the trapezoid and trapezium (0.4 mm in maximum flexion, 0.3 mm in radial deviation and at least 10 degrees in flexion extension and ulnar deviation) as well as slight off-path rotations. The results of this study indicate that the STT joint should be considered a mobile joint with motions more complex than previously appreciated.     

Comparison of strain-gage and fiber-optic goniometry for measuring knee kinematics during activities of daily living and exercise

There is increasing interest in wearable sensor technology as a tool for rehabilitation applications in community or home environments. Recent studies have focused on evaluating inertial based sensing (accelerometers, gyroscopes, etc.) that provide only indirect measures of joint motion. Measurement of joint kinematics using flexible goniometry is more direct, and still popular in laboratory environments, but has received little attention as a potential tool for wearable systems. The aim of this study was to compare two goniometric devices: a traditional strain-gauge flexible goniometer, and a fiberoptic flexible goniometer, for measuring dynamic knee flexion/extension angles during activity of daily living: chair rise, and gait; and exercise: deep knee bends, against joint angles computed from a "gold standard" Vicon motion tracking system. Six young adults were recruited to perform the above activities in the lab while wearing a goniometer on each knee, and reflective markers for motion tracking. Kinematic data were collected simultaneously from the goniometers (one on each leg) and the motion tracking system (both legs). The results indicate that both goniometers were within 2-5 degrees of the Vicon angles for gait and chair rise. For some deep knee bend trials, disagreement with Vicon angles exceeded ten degrees for both devices. We conclude that both goniometers can record ADL knee movement faithfully and accurately, but should be carefully considered when high (>120?deg) knee flexion angles are required.     

Coordination of thumb joints during opposition

Thumb opposition plays a vital role in hand function. Kinematically, thumb opposition results from composite movements from multiple joints moving in multiple directions. The purpose of this study was to examine the coordination of thumb joints during opposition tasks. A total of 15 female subjects with asymptomatic hands were studied. Three-dimensional angular kinematics of the carpometacarpal (CMC), metacarpophalangeal (MCP) and interphalangeal (IP) joints were obtained by a marker-based motion analysis system. Thumb opposition revealed coordination among joints in a specific direction (inter-joint coordination) and among different directions within a joint (intra-joint coordination). In particular, linear couplings existed between the flexion and pronation at the CMC joint, and between the flexion of the CMC joint and flexion of the MCP joint. Principal component analysis showed that only two principal components adequately represented the thumb opposition data of seven movement directions. A term functional degrees of freedom by virtue of principal component analysis was proposed to uncover the extent of movement coordination in functional tasks.