Share this article on:

Quantification of Hand and Forearm Muscle Forces during a Maximal Power Grip Task


Medicine & Science in Sports & Exercise: October 2012 - Volume 44 - Issue 10 - p 1906–1916
doi: 10.1249/MSS.0b013e31825d9612
Applied Sciences

Purpose The aim of this study was to estimate muscle and joint forces during a power grip task. Considering the actual lack of quantification of such internal variables, this information would be essential for sports sciences, medicine, and ergonomics. This study also contributed to the advancement of scientific knowledge concerning hand control during power grip.

Methods A specially designed apparatus combining both an instrumented handle and a pressure map was used to record the forces at the hand/handle interface during maximal exertions. Data were processed such that the forces exerted on 25 hand anatomical areas were determined. Joint angles of the five fingers and the wrist were also computed from synchronized kinematic measurements. These processed data were used as input of a hand/wrist biomechanical model, which includes 23 degrees of freedom and 42 muscles to estimate muscle and joint forces.

Results Greater forces were applied on the distal phalanges of the long fingers compared with the middle and the proximal ones. Concomitantly, high solicitations were observed for FDP muscles. A large cocontraction level of extensor muscles was also estimated by the model and confirmed previously reported activities and injuries of extensor muscles related to the power grip. Quantifying hand internal loadings also resulted in new insights into the thumb and the wrist biomechanics. Output muscle tension ratios were all in smaller ranges than the ones reported in the literature.

Conclusions Including wrist and finger interactions in this hand model provided new quantification of muscle load sharing, cocontraction level, and biomechanics of the hand. Such information could complete future investigations concerning handle ergonomics or pathomechanisms of hand musculoskeletal disorders.

1Institute of Movement Sciences, CNRS UMR 6233, Aix-Marseille University, Marseille, FRANCE; and 2Oxylane Research, Department of Movement Sciences, Villeneuve d’Ascq, FRANCE

Address for correspondence: Benjamin Goislard de Monsabert, MSc, Institut des Sciences du Mouvement, 163 Ave. de Luminy, BP910, 13288 Marseille, cedex 09, France; E-mail:

Submitted for publication September 2011.

Accepted for publication May 2012.

Gripping tasks, and particularly power grip tasks, are essential for most of daily living, working, or sports activities. During power grip, objects are gripped by the entire hand so that grip forces are exerted on the entire circumference of the handle by the palm, the fingers, and the thumb. Power grip is mostly associated with activities involving forceful exertions and is preferably used when manipulating heavy tools or handles. A long-term practice of those high-grip force activities may lead to musculoskeletal disorders such as tennis elbow (31), osteoarthritis (7), and localized fatigue (20). To prevent these disorders, several studies were performed to improve the ergonomic design of hand tools and determine optimal grasping configurations. Among the grasped object’s characteristics, the size (19) and the shape (18) as well as the friction coefficient (13,38) appeared crucial for maximal force capacities.

Although contributions of such studies represent important information, ergonomists and clinicians are facing a lack of knowledge concerning the mechanisms of pathologic conditions associated with high-power grip forces. The first need for further explanation concerns the fingers’ muscle forces that are still not accurately quantified so that the coordination of flexor muscles, which include both extrinsic and intrinsic muscles, is partly unexplored. A second lack of investigation is related to the activation of extensor muscles. Because the power grip is a finger flexion task, it is not well understood why extensor muscles are highly activated so that they are often affected by pathologic conditions such as tennis elbow (31). Finally, the forces applied to all hand joints during power grip have not been fully investigated, whereas a correlation between an increased risk of hand osteoarthritis and high-power grip strength has been identified (7). Providing new data concerning these internal forces is of great importance because it could help ergonomists and clinicians to accurately evaluate the effects of power grip on the joints and the muscles affected by the musculoskeletal disorders cited previously. Furthermore, quantification of such variables would be useful in the understanding of hand control and muscle coordination of the hand used during the power grip.

However, investigating hand muscle and joint forces is confronted with two main scientific challenges. First, the measurements of the external forces exerted at the hand/handle interface is experimentally difficult because the handle needs to be instrumented with sensors imbedded all around the circumference and on the entire area covered by the hand. Most developed devices used a split handle instrumented with strain gauges and/or a pressure map enrolled around the handle (6,26,30,37). However, hand kinematics should also be considered for attributing the measured external forces to each anatomical area of the hand palm. The second challenge is to understand how these external grip forces affect the repartition of internal muscle tensions and joint forces. Because direct measurements of hand joint forces and all hand muscle forces are technically and ethically impossible, a biomechanical model is needed to estimate those internal forces. Two studies investigated power grip tasks using a hand biomechanical model. Sancho-Bru et al. (27) used a four-finger model to simulate maximal grip forces and the effect of handle size. However, the model used by these authors did not take into account that some muscles simultaneously act on several fingers and their finger models were not interdependent. Moreover, the thumb and the wrist joint were not considered. As a consequence, model outputs were not totally realistic: as an example, no antagonist activities were predicted, whereas EMG of these muscles was reported to be significant during power grip (24,31). Wu et al. (38) developed a model to predict the effect of friction during handle manipulation, but they also did not consider the thumb and the wrist joint, and they only focused on the net joint moments.

Thus, the aim of the current study was to investigate the muscle tensions and the joint forces of the hand during a maximal power grip task. To reach this objective, an experimental protocol was conducted to record the external grip forces and the hand and wrist kinematics when grasping a cylindrical handle. These data were used as input of a hand biomechanical model, which includes the wrist, the fingers, and the thumb joints to estimate internal forces.

Back to Top | Article Outline


Biomechanical Model

A biomechanical model of the five fingers (thumb, index, middle, ring, and little fingers) and the forearm was used to estimate muscle and joint forces. This hand model was developed from two other studies: the solving method and the computation of external moments were based on the model of Vigouroux et al. (35) and the computation of moment arms and the data associated were taken from the study of Chao et al. (8). The segments were modeled as rigid bodies whose dimensions were determined from anthropometric tables of Buchholz et al. (5). Sixteen articulations were included to the model and were modeled as frictionless joints. In total, 23 degrees of freedom (DoF) were considered. Four DoFs were considered for long fingers: metacarpophalangeal (MCP) joints were modeled as condyloid joints with two DoFs in flexion–extension (F–E) and adduction–abduction (A–A), whereas distal (DIP) and proximal (PIP) interphalangeal joints were modeled as hinges with one DoF in F–E. Five DoFs were considered for the thumb: interphalangeal (IP) and metacarpophalangeal (MP) were considered as hinge (one DoF) and condyloid joints (two DoFs), respectively, whereas trapeziometacarpal (TMC) joint was considered as a saddle joint with two DoFs (11). The wrist has been modeled as a two-DoF joint that is capable of F–E and A–A. Forty-two muscles have been included in this model to mobilize these articulations. For all joints, it was considered that the pronation–supination (P–S) movements were not mobilized by muscle actions and were thus not included in the DoFs of the model.

Back to Top | Article Outline

Mechanical equilibrium equations

For the estimation of muscle and tendon forces, the static moment equilibrium equations for each DoF of each finger were considered:

This equation states that external force moments about one joint are counterbalanced by muscle tendon tensions and ligament passive moments. [R] is a 23 × 42 matrix containing moment potentials of the 42 muscles for the 23 DoFs of the model and was obtained from moment arms, unit direction vectors, and coefficients of extensor mechanism (described in a section below). {t} is a 42 × 1 vector containing the unknown muscle tendon tensions. {mL} is a 42 × 1 vector containing eight nonzero elements that are the ligament passive moments in A–A and F–E about the four MCP joints of the long fingers (described in a section below). {mF} is a 42 × 1 vector containing moment of external forces at each DoF of the model.

Back to Top | Article Outline


Because of the muscular redundancy, the moment equilibrium equation system (equation 1) was underdetermined and was solved using an optimization process. After preliminary tests and according to the literature (28), the “muscle stress” criterion was used because it appears to be the most adapted for finger musculoskeletal models:

where (tm)s is the muscle tendon tension of the m muscle from the s solution. PCSAm is the physiological cross-sectional area of the m muscle. For the five fingers, the PCSA were taken from the study of Chao et al. (8) and scaled for each subject using methods described by Sancho-Bru et al. (29). Data from Ramsay et al. (25) were used for wrist muscle PCSA. Muscle forces were also constrained as follows:

where σ max is the maximal muscle stress and c is a coefficient specifically chosen for this study. Initially, the upper boundary was determined, as recommended in the finger modeling literature, by using only PCSA and a σ max value of 35.4 N·cm−2 (32). Initially, no muscle tension estimation was possible because of too low upper boundaries. In response to the several factors (further described in the Discussion section) leading to this limitation, an additional coefficient (c) was added as defined in the inequality (equation 3). The c coefficient was chosen by increasing it by step of 1 starting from 1 until the optimization process converged for every subject. The obtained value for the present study was 6 and was the same for all muscles and all subjects.

Back to Top | Article Outline

Muscle moment arms and unit direction vector

The [R] matrix (equation 1) represents the actions of muscles on joints and is computed using the moment arm and the unit direction vectors of each muscle. For the five fingers, insertion point data were taken from Chao et al. (8). To compute these two muscle vectors with respect to the hand posture, coordinate transformation was used for flexor muscles (8), whereas the first model of Landsmeer (21) was used for extensors. For the wrist, the study of Lemay and Crago (23) provided a relation between moment arms of each muscle and wrist angles.

Back to Top | Article Outline

Extensor mechanism

Extensor muscles acting on DIP and PIP joints of long fingers and on IP and MP joints of the thumb do not have direct insertions on phalangeal bones but join in an extensible tendon hood. Geometrical relations were used to model the force transmission among the different parts of the mechanism (3,35). As an example, equation 4 illustrates the relations between tendon tensions in the extensor mechanism of the ring finger:

The different muscles, tendons, or tendon bands involved in the equation 4 are as follows: terminal extensor (TE), radial band (RB), ulnar band (UB), extensor digitorum communis (EDC), third lumbricales (LU3), radial interossei (RI), ulnaris interossei (UI), and extensor slip (ES). tm represents the tension of the m muscle/tendon with m = {TE, RB, UB, EDC, LU3, RI, UI, ES}. βm coefficients was defined by Brook et al. (3) and was used to model the changes associated to joint posture. As muscle tendon tensions, βm coefficients are unknown variables evaluated by the optimization process.

Back to Top | Article Outline

Ligament passive moment about MCP joints

As previously used in the study of Sancho-Bru et al.(28), our model included passive actions of ulnar (UCL) and radial (RCL) collateral ligaments relative to the MCP joint posture. UCL and RCL insertion point coordinate data were taken from Chao et al. (8). A nonlinear second-order relationship has been used to characterize its elasticity. The complete description of these equations is provided in the study of Vigouroux et al. (35).

Back to Top | Article Outline

Hand and handle weights

Hand and handle weights were taken into account in the wrist joint equilibrium. Center of mass (CoM) and mass of the handle were provided by the manufacturer. Hand mass was computed with anthropometric tables (40) using length and width of the hand and wrist and hand circumferences. For the anatomical position, the hand CoM is located at approximately one-quarter of the third metacarpal bone from the MCP joint center (40). On the basis of this last value, we defined that the position of the hand CoM for the power grip posture was situated at half of the third metacarpal bone in axial and transversal directions and at the hand/handle interface in the anteroposterior direction.

Back to Top | Article Outline

Muscle interactions

Previous works on hand modeling considered only one finger (2,3,9,10,14,28,32) or several long fingers independently (27,35). Because the current hand model solves all equilibrium equations of the 16 articulations in the same computation process, finger and wrist muscle interactions were included. Particularly, forces of extrinsic fingers muscles were included in the wrist moment equilibrium equations and hence “linked” the five fingers. In a same approach, the lumbrical (LU) muscles have insertions on flexor digitorum profundus (FDP) tendons from various fingers; this means that the force of one LU muscle induces moments about different finger joints at the same time (Fig. 1A). Equation 5 describes how those muscular interactions were computed. For simplification, only the DIP moment equations are displayed, but the same principle was used for MCP and PIP joints.



M musc(f)|DIP is the muscle moment about the DIP joint of the f finger, where f = {I (index), M (middle), R (ring), L (little)}. tm ( f ) represents the muscle tendon tension of the m muscle/tendon from the f finger where m = {TE, FDP, LU1, LU2, LU3, LU4}. rm ( f )|DIP represents the moment potential element of the m muscle/tendon from the f finger about the DIP joint (element of moment potential matrix [R] in equation 1). The first lumbrical (LU1) inserts on the index finger FDP tendon; in consequence, LU1 activation modifies the tension of the FDP muscle (equation 5a). A similar mechanism is observed for the middle finger during the solicitation of the second lumbrical (LU2) (equation 5b). The third lumbrical (LU3) originates on both the middle and ring fingers’ FDPs and is consequently involved in both equations 5b and c. Half of the LU3 global action was allocated in each finger. In addition, the action of the index finger RI muscle on the thumb TMC joint was taken into account according to results of Domalain (12).

Back to Top | Article Outline

Joint forces

Once muscle tensions have been estimated using the optimization process, force mechanical equilibrium (Fig. 1B) equation was used to compute joint forces:

where F joint ,j represents the force acting on the j articulation. tm represents muscle tension of the m muscle. F ext, p represents the external force applied on the p point of the finger. F lig, l is the l ligament passive force acting on MCP joints. The output joint forces were reconciled in three dimensions with dorsal bony landmarks (BLM) to inspect their orientations regarding phalanges. The amount of compressive force was also checked regarding the other joint force components.

Back to Top | Article Outline

Experimental Setup and Protocol


Eleven healthy right-handed male volunteers were recruited for this experiment (age = 25.8 ± 3.2 yr, height = 178.3 ± 5.9 cm, weight = 71.5 ± 6.9 kg, hand length = 19.0 ± 0.7 cm, hand width = 8.6 ± 0.4 cm). All participants reported no traumas to right upper extremity and signed an informed consent according to university guideline that was approved by ethics committee of Aix-Marseille University. Subjects were seated with a cylindrical handle (33 mm in diameter) on a table in front of them. Participants were asked to use a power grip posture to grasp, with their right hand, and then raise the handle at a comfortable altitude (Fig. 2A). Then they were required to exert their maximal voluntary force during 6 s. The handle was raised instead of fixed to the table to avoid any secondary loads regarding grip force exertion such as push or pull forces or external torques. Each subject repeated this task three times and rested during 3 min before each trial to prevent from any effect of fatigue. Only the data corresponding to the trial presenting the highest grip force value were used.



Back to Top | Article Outline

Force analysis

External forces applied on anatomical areas of the hand were computed by combining two systems. First, a cylindrical handle (Handle Dynamometer; Sixaxes, Argenteuil, France) split into six beams, each one instrumented with strain gauges, permitted to record the grip force at 1875 Hz. This dynamometer has already been presented in the literature (26,36) and is similar to the one developed by Chadwick and Nicol (6) with the same arrangement of strain gauges and measurement principle. Second, the pressure repartition at the hand/handle interface was recorded at 125 Hz with a pressure map (Hoof no. 3200; TekScan, Boston, MA) consisting in 1089 transducers (33 rows × 33 columns). The pressure map was wrapped around the handle, and they were both squeezed during all the trials. This special design was previously validated in a study of Rossi et al. (26). Grip force and kinematic data were acquired by a Nexus acquisition system (MX Giganet, Vicon, Oxford, United Kingdom), whereas an F-scan mobile unit was used for the pressure map (TekScan). These two acquisition systems were synchronized with an external trigger. As recommended by the furnisher, the pressure map was calibrated before the experiment. For this purpose, two calibration loads were applied with a pneumatic dynamometer and corresponded to 20% and 65% of the sensor measuring range which was 100 psi in this study.

Signals from the six-beam handle were filtered with a zero-phase low-pass filter (fourth-order Butterworth filter, cutoff frequency = 20 Hz) and then resampled at 125 Hz. First, the grip force was computed as the sum of the six signals from the six-beam handle. Then, the maximal handle force (MHF) was computed as the mean of the grip force during a 750-ms window centered on the grip force peak. Mean of the pressure map data was computed on the same window.

To input the recorded forces in the model, the proportion of MHF corresponding to each segment was determined by combining the data from the pressure map and the six-beam handle. With each of the 1089 transducers having a measuring range of 255 values, the pressure map was used to provide an estimation of the load distribution on the hand palm. The intensity of the grip force (MHF value) was only measured with the six-beam handle. Twenty-five anatomical areas were defined on the hand palm surface and were considered as force application points (Fig. 3A). The 25 corresponding input forces were each defined by three parameters: the force intensity, the direction vector, and the application point location. The force intensities were computed by combining the processed data of the pressure map and the six-beam handle using the following equation:

where F map, i is the “corrected” force intensity of the i point on the map, with i ∈ [1,1089]. P map, i is the initial pressure value of the same i point on the map. The MHF value represents the grip force (as explained above). Overall, this computation stated that the sum of all pressure values from the map corresponded to the MHF value measured with the six-beam handle. This way, a percentage map has been first computed from the pressure map data by normalizing each pressure value (P map, i) by the sum of all pressure values. Then, a “corrected” force map was obtained (Fig. 3B) by allocating the MHF value among all points of the percentage map. Equation 7 provided a force map at the hand/handle interface, which was accurate both in localization and in intensity. This “corrected” force map was then used to compute the 25 input force intensities (Fig. 3B): for each anatomical area, we first manually drew a polygon on the map, which represented the limits of the concerned area. Input force intensities were then computed as the sum of all the individual force values (F map, i in equation 7) of the map points, which are inner the polygon limits.



Contrary to force intensities, the direction vectors and the application point locations were defined following a common scheme for all subjects and were independent from the subjects’ force performance. In direct correspondence with the anatomical area (Fig. 3A), the application point locations were either the middle of a segment or a joint rotation center. For long fingers, the force direction was considered as the abduction (y) axis of the subject-specific segment coordinate system (SCS), which is defined below; when the application point location was a joint rotation center, the direction was the sum vector of the force directions of the proximal and the distal segments. A common scheme was used to input forces in the model because pretests showed that, in the context of our experimental setup, the calculation of such parameters for each subject was a lot more complex without improving the results. Especially, uncertainties appeared when locating each pressure map cell sensor regarding beams of the handle to estimate application point locations. Only for the thumb, the markers of each subject were reconciled in three dimensions with those of the handle, and the force direction vectors were all orthogonal to the longitudinal axis of the six-beam handle and passing through the force application point.

Back to Top | Article Outline

Kinematic analysis

Kinematic data were recorded at 125 Hz with a system including six optoelectronic cameras (Vicon MX T40; Vicon). A set of 30 spherical reflecting markers (6 mm in diameter) was used to record three-dimensional positioning of hand and forearm segments (Fig. 2B). The marker set was based on the kinematic tracking of dorsal BLM. Two additional markers were placed on the thumb to compute TMC and MP joint angles with results of Cooney et al. (11). Three other markers were fixed on the handle (Fig. 2A) for both analyzing the hand posture relative to the handle and determining the external force directions of the thumb anatomical areas. SCS were defined so that x was the P–S axis and was proximally oriented, y was the A–A axis and was dorsally oriented, and z was the F–E axis and was radially oriented. With these orientations, pronation, abduction, and flexion corresponded to positive joint angles.

To compute all F–E and A–A joint angles, averaged marker position data during a 750-ms window centered on the grip force peak was used. First, we computed each SCS using BLM. For all segments, the proximal and the distal BLM were used to compute a longitudinal (x) axis. For the finger metacarpals, a coronal plane was built using the x axis and the distal BLM of the adjacent metacarpal in the radial direction. However, the third metacarpal distal BLM was also used for the computation of the second metacarpal SCS (Fig. 2B). The A–A (y) axis was defined orthogonally to that coronal plane. Finally, the F–E (z) axis was orthogonal to both x and y axes. For the finger phalanges, the coronal plane was computed using the previous z axis. For the thumb, T markers were used for both the metacarpal and the proximal phalanx so that a coronal plane was directly built with a “radial” marker. The process for the thumb distal phalanx was the same as that for the finger phalanges. Then, for each of the 16 joints, the orientation matrix containing the vectors of the distal SCS (moving system) regarding the proximal SCS (fixed system) was computed. Finally, Euler angles were used for the calculation of joint angles with a rotation sequence z (F–E), y (A–A), and x (P–S) around fixed axes. In contrast to the other hand joints, the thumb TMC joint kinematics is more complex and is controversial (12,13,31,32). In the present study, TMC joint angles were defined as the rotations between the trapezium and first metacarpal bone. Results from the study of Cooney et al. (11) were used for the orientation of the trapezium: the authors found that trapezium was deviated from the third metacarpal at angles of 46° of flexion, 35° of abduction, and 82° of supination.

Back to Top | Article Outline

Result analysis

Using external forces and joint angles as input data, the muscle forces and the joint forces were computed for the maximal test performed by each subject. Muscle tension–external force ratios were computed by dividing each muscle tension by the total finger force computed by summing the forces of all the areas of the concerned finger. Descriptive statistics are mean ± SD computed for all subjects. To identify the effect of joint (proximal, medial, or distal) on joint forces for each finger, five repeated-measures ANOVAs were used. When significant effect was observed (P < 0.05), Tukey post hoc was performed to determine the significance of differences.

Back to Top | Article Outline


During our experimentations, the mean MHF was 804.0 ± 117.9 N. Figure 3C shows the mean values (N) of external forces applied on the 25 anatomical areas considered and used as input of the biomechanical model. The resultant force of all the five fingers’ areas represented 66.8% of the MHF, or a 537.4-N force, whereas the other 33.2% were exerted on the hand palm. No force was measured on the areas corresponding to the thumb distal phalanx and the little finger distal joint. For the thumb, the greatest forces were applied by the most proximal areas with 36.2 ± 23.3 and 57.7 ± 22.9 N for metacarpal and MP joint areas, respectively, against 14.2 ± 12.0, 17.6 ± 14.2, and 0 N for other areas. The inverse phenomenon was observed for long fingers because the highest forces were bore by the distal phalanx, with 49.0 ± 18.6, 55.9 ± 20.6, 37.3 ± 22.1, and 34.8 ± 15.7 N for the index, middle, ring, and little fingers, respectively. However, one should note that the force exerted by the index finger proximal phalanx was as high as that on the distal phalanx, with 49.4 ± 22.9 N. Concerning the distribution of the resultant force for all areas, the greatest force was applied by the index finger with 25.5% of the resultant followed by the thumb, middle, ring, and little fingers with 23.8%, 22.4%, 17.8%, and 10.5%, respectively.

MCP joints of the four long fingers were highly flexed, with a mean F–E angle among the four fingers of 77.6° ± 3.4° and slightly adducted with a mean A–A angle among the four fingers of −2.2° ± 1.6°. The flexion angles of the PIP joints were greater than those of the DIP joints, with mean values among the four fingers of 59.7° ± 12.8° and 49.8° ± 3.7°, respectively. Only the little finger did not follow this trend with 41.6° ± 10.0° for the PIP joint and 52.9° ± 7.4° for the DIP joint. TMC joint is slightly extended and adducted with F–E and A–A angles of −9.5° ± 9.0° and −10.4° ± 6.5°, respectively. The IP and MP joints were largely flexed with 56.5° ± 14.9° and 43.9° ± 11.4°, respectively. MP joint showed a slight adduction with −7.3° ± 11° in A–A. The wrist joint was extended and slightly abducted with F–E and A–A angles of −34.3° ± 10.0° and 4.8° ± 9.5°, respectively.

Muscle tensions of the five fingers and the forearm are shown in Figure 4. From an overall point of view, values ranged from 0 N for lumbrical muscles to nearly 370 N for the opponent muscle of the thumb. Muscle tensions–external forces ratios are presented in Table 1. These ratios ranged from 0 for lumbrical muscles to 2.83 for the opponent muscle. Interestingly, muscle tensions of the long fingers showed high values for the FDP and the extensors. FDP muscle tensions of the index, middle, ring, and little fingers were 84.3 ± 39.5, 170.8 ± 58.0, 103.8 ± 59.0, and 83.0 ± 36.0 N, respectively. FDP ratios ranged from 0.65 and 1.52. In comparison with FDP muscles, FDS muscles were less solicited, with a mean tension and a mean ratio among the four fingers of 58.1 ± 29.2 N and 0.59 ± 0.24, respectively. The tension values of all lumbrical muscles were lower than 0.1 N, except for the ring finger with 0.4 ± 1.5 N. Radial (RI) and ulnar (UI) interossei muscles were activated differently among long fingers without any real trend; from an overall point of view, their tension in the index finger was higher than that in the middle, ring, and little fingers. Concerning extensors, for the middle and ring fingers, EDC muscles showed tensions of 120.9 ± 54.0 and 60.0 ± 53.4 N, respectively, and ratios of 1.01 ± 0.40 and 0.60 ± 0.47, respectively. The index and little fingers EDC muscle ratios were lower than those of the middle and ring fingers, but they have both one own extensor muscle: EDI for the index finger and EDQ for the little finger. For comparison with other fingers, the sum of both extensor values was thus considered for these two fingers. Index extensor tension sum (EDC and EDI) was 145.7 ± 59.1 N. The sum of little finger EDC and EDQ muscle tensions was 39.5 ± 32.2 N. For the thumb, opponent muscle was highly implicated and showed the greatest values of tension and ratio among all the 42 muscles of the model with 366.5 ± 154.2 N and 2.83 ± 0.3, respectively. EPL and ADPo muscle tensions were relatively high with 125.5 ± 47.5 and 104.5 ± 76.7 N, respectively, and associated ratios were 1.0 ± 0.25 and 0.83 ± 0.51, respectively. APB, FPB, FPL, ADPt, and EPB muscles were slightly solicited with ratio ranged from 0.13 to 0.44 and tensions of 54.9 ± 45.3, 53.2 ± 35.3, 47.0 ± 45.2, 28.2 ± 20.7, and 16.0 ± 32.6 N, respectively. APL was found to be nonactivated with a tension and a ratio close to null values. For the wrist, results showed flexor (PL, FCR, FCU) muscle tensions close to zero, whereas those of extensor muscles (ECRB, ECRL, ECU) were relatively high with 106.0 ± 50.5, 50.9 ± 23.3, and 98.1 ± 59.4 N, respectively.





Figure 5 shows the joint forces for each finger. Values ranged from 59.8 ± 24.9 N for the little finger DIP joint to 624.2 ± 251.1 N for the thumb TMC joint. For each finger, there was a significant effect of joint on joint forces (thumb finger: F 2,20 = 52.3, P < 0.05; index finger: F 2,20 = 40.9, P < 0.05; middle finger: F 2,20 = 43.5, P < 0.05; ring finger: F 2,20 = 36.6, P < 0.05; little finger: F 2,20 = 38.7, P < 0.05). For all fingers, the force applied on the “distal” (thumb IP or finger DIP) joint was significantly lower than that applied on the “proximal” (thumb TMC or finger MCP) joint (P < 0.05). Results showed that little finger joint forces progressively increased in the proximal direction because PIP joint force was significantly higher than that applied on the DIP joint and significantly lower than that applied on the MCP joint (P < 0.05). Results concerning other “medial” (thumb MP or finger PIP) joints varied among fingers. For the thumb and index fingers, the force applied on the medial joint was lower than that applied on the proximal joint (P < 0.05) but was not higher than that applied on the distal one (P = 0.094 and P = 0.38 for the thumb and index fingers, respectively). For the middle finger, the PIP joint force was higher than that applied on the MCP and the DIP joints (P < 0.05). Finally, the ring finger PIP joint force was only higher than that of the DIP joint (P < 0.05).



Back to Top | Article Outline


In this study, a method has been developed to measure and input the forces associated to 25 anatomical areas of the hand during a power grip task. These forces were determined by combining the signals obtained from a pressure map, which provided the force distribution at the hand/handle interface, and from a six-beam handle sensor, which recorded the grip force intensity. The major advantage of this measurement design was to provide accurate data both in localization and intensity. Unlike to dynamometric pincers typically used, the system presented in this study records external forces not only in one direction but all around the circumference of the handle. It was already shown in a study of Wimer et al. (37) that, by splitting a cylindrical dynamometer into six beams, the measured force value represents 95.5% of the real grip force, whereas with two beams, this rate is only of 63.7%. In addition, the present results showed an MHF of approximately 800 N, which is in good accordance with the results of Wimer et al. (37) who used a similar device. In the current results, the resultant force of all the five fingers’ areas reached 537.4 N and was distributed so that 23.8%, 25.5%, 22.4%, 17.8%, and 10.5% was applied by the thumb, the index, the middle, the ring, and the little finger, respectively. Comparable values were observed by Kong and Lowe (19), Lee and Rim (22), and Amis (1) for similar cylinder diameters, although they did not measure the thumb forces. The force distribution among fingers during power grip was previously investigated and seems to be related to wrist equilibrium conditions and also to the thumb opposition (26,36). It should be noted, however, that only few authors recorded the thumb forces when grasping a cylindrical handle (13,30) and none of them took into account its proximal anatomical areas. Therefore, the measurement system presented in this study is also providing new insight on the force balance between the fingers, and such information is important for the understanding of hand control during power grip. Moreover, because previous studies showed that handle size and shape have direct effects on the force distribution among fingers and phalanges (18,19), further studies should investigate these parameters to improve handle design.

The repartition of grip force among finger phalanges indicated a great implication of distal phalanges of the long fingers compared with their proximal and medial ones. This distribution is in agreement with previous force measurements during power grip tasks (19,22). Interestingly, an inverse phenomenon was observed for the thumb for which proximal areas bore the lowest forces. This antagonism could be explained by the geometrical opposition around the handle circumference between the thumb proximal anatomical areas and the long fingers’ distal phalanges. As a consequence, proximal areas of the thumb are more inclined to equilibrate high forces applied by distal phalanges of the long fingers. Thus, despite a large contact area between the hand palm surface and the handle, the repartition of grip forces resulted in high-intensity forces located on precise points instead of being homogenously distributed. Such organization could induce many discomfort problems (blisters, burnings, or friction) and could also lead to pathologic conditions associated to the oversolicitation of particular muscles (discussed below). For these reasons, it could be interesting for ergonomists to modify the shape at hand/handle interface to obtain a repartition of external forces among phalanx more homogeneous than for a cylinder.

Back to Top | Article Outline

Muscle tensions

Muscle tension–external force ratios values obtained in our study were coherent with those observed in the literature for various hand/finger tasks. In fact, all our ratios were lower than 3, whereas previously reported values ranged from 0 to 7 (2,9,10,14,34). Without going into a detailed description of each muscle, the most interesting results related to muscle tensions concern deep flexor (FDP) and extensor muscles. High FDP tensions of the index, middle, ring, and little fingers were induced by the high external force values exerted on the distal phalanges. FDP is indeed the only muscle that can develop a flexion moment about the distal (DIP) joint and was consequently highly solicited. In the literature, the biomechanical models used for the study of power grip did not provide the same organization of muscle tensions (2,14,27). In those previous studies, FDP muscles were also highly solicited, but in contrast to the present results, extensor muscle ratios were null and FDS muscles were always implicated to a similar or higher level than FDP. Such differences are probably due to the use of models that considered only one finger (2,14) or neglected the interdependence between fingers (27). By including wrist and finger interactions in this hand model, new quantification and information regarding muscle tension organization were provided here and could help to better understand the pathomechanisms of musculoskeletal disorders related to high-power grip force activities. The high solicitations of FDP muscles estimated by the model seem to indicate that the practice of high-power grip force put the muscle belly and tendons of FDP and the surrounding tissues at risk of damages. This exposition to inflammation, thickening, or even rupture is increased when the power grip task is repetitive as it could be in industrial workplaces (15). One possible way to prevent injuries would be to adapt the handle ergonomics to obtain a more homogeneous load sharing among muscles.

Interestingly, extensor muscles of the long fingers (EDI, EDQ and the four EDC) and the wrist (ECRB, ECRL, ECU) were also much implicated during the power grip task with sometimes similar activation levels than those of flexors. This phenomenon is associated to the power grip task itself. As Snijders et al. (31) explained, the great activations of FDP muscles lead to a high-flexion muscle moment about the wrist joint, whereas external force moments are slight because of the force equilibrium all around the hand/handle interface. Therefore, high actions of extensor muscles are required to maintain the wrist moment equilibrium. By considering all articulations, including the wrist, and by taking into account the fingers in close interaction, this biomechanical model revealed and quantified cocontraction states. Keir and Wells (17) also described such phenomenon with a one-finger/wrist model. However, the cocontraction was not fully investigated because only net muscle moments were observed, and muscles were grouped so that the wrist was only mobilized by one extensor and one flexor. Besides, all muscle tensions were not estimated in the same process because the finger and the wrist were simulated by two different models. More generally, Jinha et al. (16) also observed that polyarticulated models result in a better prediction of cocontraction. Previous studies focused on power grip (2,14,27) did not include wrist in their model so that they never identified this phenomenon. These particular wrist equilibrium and cocontraction level could explain why extensors are frequently affected by tendon pathologic conditions, such as “tennis elbow,” whereas power grip is a flexion task (31). In addition, this muscle load sharing directly supports motor control theories, which suggest that finger force sharing is strongly associated with the wrist equilibrium (36,39).

The most remarkable result concerning the thumb muscles was that flexors were not much implicated. Those low solicitations are coherent with the absence of force recording on the distal phalanx. Unlike other fingers of the present model, the directions of force vectors applied on the thumb segments were orthogonal to the longitudinal axis of the handle. These particular force orientations leaded to external force moments with similar actions on abduction–adduction and on flexion–extension DoF of the thumb joints. Thus, a dissimilar muscle load sharing was observed for the thumb compared with other fingers. In the same way, the high values obtained for ADPo seems realistic because the inputted external forces represent abduction joint moments. As observed for extensor muscles of the long fingers, EPL was also highly activated to participate in the wrist joint equilibrium. The opponent muscle showed the highest tensions and ratios among all the 42 muscles considered. Nevertheless, this result might not be physiologically realistic because Vigouroux et al. (33) showed that tension of the opponent muscle could be overestimated by biomechanical models. Those nonphysiological estimations are probably due to the complexity and the hypothesis related to the TMC joint kinematics (12,32,33). Cooney and Chao (10) are the only authors who studied muscle tensions of the thumb during a power grip task. They observed very different tension distribution from ours. However, only one effort was assumed to act on the thumb and was applied on the distal phalanx, whereas no force was recorded on this area during our experimentations. Besides, to simplify the muscle tension estimations, they neglected the actions of extensors. Therefore, by using experimentally measured force input and by considering the thumb in interaction with other fingers and with the wrist, the present study provided a more complete and new insight into the thumb biomechanics during power grip.

The optimization process has been adapted here by adding the c coefficient (equation 3) because no possible muscle load distribution was initially found for balancing the recorded force performances. In fact, the optimization process was “overconstrained” by the muscle force capabilities classically reported in the literature. Although such limitation has no consequences when studying low-force tasks, not a single solution was feasible in our study because the input data concerned maximal voluntary contractions. Several inconsistencies inherent to hand musculoskeletal modeling could explain this problem, especially the hypotheses related to the PCSA and the maximum muscle stress. The PCSA values used here might have been underestimated because they were adapted from elderly cadaver specimens. Besides, the scaling relationship was only based on subject’s hand size (29) and was the same for all muscles. As for PCSA, the maximum muscle stress value could be different for every person, but to our knowledge, no studies investigated the individualization of these parameters according to individual training, health, gender, or age. In addition, the maximum muscle stress probably varies among muscles (4), whereas the same 35.4 N·cm−2 value is always used for all the finger muscles in the literature (28,32). All these inconsistencies were particularly highlighted during the present study because the inputs corresponded to maximal grip forces of healthy young subjects. To counteract all these limitations, we increased the muscle force capabilities usually reported in the literature by adding the c coefficient in the upper boundary of the optimization process (equation 3). Regardless of this adjustment, the obtained estimations were still physiologically coherent because all muscle tension–external force ratios were smaller than 3 and in a similar range than values reported with other modeling (14) and in vitro direct tendon force measurements (15).

Back to Top | Article Outline

Joint forces

Previously, the joint forces were only investigated through index finger (2,9,14) or thumb (10) models. Data obtained in the present study are thus of great importance because all finger joint forces have been considered during a power grip task. Except for the middle finger, results showed that joint forces increased in the distoproximal direction along each finger. This trend is caused by muscle tensions. For each finger, the number of muscles crossing a joint is incrementing proximally; consequently, a compression effort is increasing in the same direction (34). This joint compression was particularly pronounced here because muscle tensions were relatively high, and almost all muscles were implicated because of the cocontraction phenomenon. In the literature, Cooney and Chao (10) studied joint forces of the thumb, whereas Fok and Chou (14) and Chao et al. (9) focused on the index finger. All of them indicated a similar direction of increasing during power grip tasks. Vigouroux et al. (34) used a similar biomechanical modeling to that presented here to analyze forces in the thumb and index fingers during a pulp pinch grip task. In this study, the joint forces also increased proximally along the two modeled fingers. Therefore, this trend seems to be more related to intrinsic factors than to the conditions of the gripping tasks. However, when normalizing the joint forces by the exerted external forces, higher joint loadings were observed for the pinch grip than for the power grip: joint forces were 15 times higher than external forces in the study of Vigouroux et al. (34) against only 5 times higher in the current study. Further studies should thus investigate the influence of the gripping task on the joint and muscle forces. From a clinical point of view, our data could be used by orthopedics designers to simulate mechanical behavior of prosthesis under maximal loadings for instance.

Back to Top | Article Outline


Some limitations should be considered for this study. Among them, the ones related to biomechanical modeling concerns the simplified kinematic model of TMC joint, the hypothesis associated to the optimization process, and the use of generic anthropometric data. Especially, normative models have been used for muscle, tendon, and ligament parameters with only few individualization factors. An adjustment (coefficient c) of the muscle force capabilities was also necessary to find a feasible muscle load distribution, but output muscle ratio values were in similar ranges as the ones reported in the literature. In the same way, force/length and force/speed relationships should be taken into account because the actual assumption was that muscles were able to provide their maximal force in any situation. For these reasons, improvements are necessary in the individualization of muscle modeling and could result in more physiological estimations. Other limitations concern the force measurements system, which superposed two acquisition systems. However, at the current state of knowledge, no other acquisition system exists to accurately determine forces applied on 25 anatomical areas of the five fingers. Thus, despite these limitations, the measurements and the estimations performed in this study gave new insights on the muscle and joint forces during power grip tasks. These data could complete clinical and ergonomic investigations on musculoskeletal disorders such as lateral epicondylalgia or thumb base osteoarthritis.

The Institute of Movement Sciences is using equipment of Oxylane Research for data acquisition.

There were no external funding sources used in the preparation of this article.

There is no conflict of interests concerning the preparation of this article.

The publication of this article does not constitute endorsement by the American College of Sports Medicine.

Back to Top | Article Outline


1. Amis AA. Variation of finger forces in maximal isometric grasp tests on a range of cylinder diameters. J Biomech Eng. 1987; 9 (4): 313–20.
2. An KN, Chao EY, Cooney WP, Linscheid RL. Forces in the normal and abnormal hand. J Orthop Res. 1985; 3 (2): 202–11.
3. Brook N, Mizrahi J, Shoham M, Dayan J. A biomechanical model of index finger dynamics. Med Eng Phys. 1995; 17 (1): 54–63.
4. Buchanan TS. Evidence that maximum muscle stress is not a constant: differences in specific tension in elbow flexors and extensors. Med Eng Phys. 1995; 17 (7): 529–36.
5. Buchholz B, Armstrong TJ, Goldstein SA. Anthropometric data for describing the kinematics of the human hand. Ergonomics. 1992; 35 (3): 261–73.
6. Chadwick EKJ, Nicol AC. A novel force transducer for the measurement of grip force. J Biomech. 2001; 34 (1): 125–8.
7. Chaisson CE, Zhang Y, Sharma L, Kannel W, Felson DT. Grip strength and the risk of developing radiographic hand osteoarthritis: results from the Framingham Study. Arthritis Rheum. 1999; 42 (1): 33–8.
8. Chao EY, An KN, Cooney WP III, Linscheid RL. Biomechanics of the Hand: A Basic Research Study. Singapore, SG: World Scientific; 1989. p. 5–30, 31–52, 163–178.
9. Chao EY, Opgrande JD, Axmear FE. Three-dimensional force analysis of finger joints in selected isometric hand functions. J Biomech. 1976; 9 (6): 387–96, IN2.
10. Cooney W, Chao E. Biomechanical analysis of static forces in the thumb during hand function. J Bone Joint Surg Am. 1977; 59 (1): 27–36.
11. Cooney W, Lucca M, Chao E, Linscheid R. The kinesiology of the thumb trapeziometacarpal joint. J Bone Joint Surg Am. 1981; 63 (9): 1371–81.
12. Domalain M. Modélisation biomécanique de la main pour l’estimation des contraintes du système musculo-squelettique lors de la préhension pouce-index [dissertation]. Marseille (France): University of Aix-Marseille 2; 2010. p. 97–108.
13. Enders LR, Seo NJ. Phalanx force magnitude and trajectory deviation increased during power grip with an increased coefficient of friction at the hand-object interface. J Biomech. 2011; 44 (8): 1447–53.
14. Fok KS, Chou SM. Development of a finger biomechanical model and its considerations. J Biomech. 2010; 43 (4): 701–13.
15. Freivalds A. Biomechanics of the Upper Extremities: Mechanics, Modeling, and Musculoskeletal Injuries. Boca Raton, FL: CRC Press; 2004. p. 215–227, 233–238, 275–288.
16. Jinha A, Ait-Haddou R, Herzog W. Predictions of co-contraction depend critically on degrees-of-freedom in the musculoskeletal model. J Biomech. 2006; 39 (6): 1145–52.
17. Keir PJ, Wells RP. The effect of typing posture on wrist extensor muscle loading. Hum Factors. 2002; 44 (3): 392–403.
18. Kong Y-K, Lowe BD, Lee S-J, Krieg EF. Evaluation of handle shapes for screwdriving. Appl Ergon. 2008; 39 (2): 191–8.
19. Kong Y-K, Lowe BD. Optimal cylindrical handle diameter for grip force tasks. Int J Ind Ergon. 2005; 35 (6): 495–507.
20. Kramer AM, Knudson DV. Grip strength and fatigue in junior college tennis players. Percept Mot Skills. 1992; 75 (2): 363–6.
21. Landsmeer JM. Studies in the anatomy of articulation. I. The equilibrium of the “intercalated” bone. Acta Morphol Neerl Scand. 1961; 3: 287–303.
22. Lee JW, Rim K. Measurement of finger joint angles and maximum finger forces during cylinder grip activity. J Biomed Eng. 1991; 13 (2): 152–62.
23. Lemay MA, Crago PE. A dynamic model for simulating movements of the elbow, forearm, and wrist. J Biomech. 1996; 29 (10): 1319–30.
24. Mogk J, Keir P. The effects of posture on forearm muscle loading during gripping. Ergonomics. 2003; 46 (9): 956–75.
25. Ramsay JW, Hunter BV, Gonzalez RV. Muscle moment arm and normalized moment contributions as reference data for musculoskeletal elbow and wrist joint models. J Biomech. 2009; 42 (4): 463–73.
26. Rossi J, Berton E, Grélot L, Barla C, Vigouroux L. Characterization of forces exerted by the entire hand during the power grip: effect of the handle diameter. Ergonomics. 2012; 55 (6): 682–92.
27. Sancho-Bru JL, Perez-Gonzalez A, Vergara M, Giurintano DJ. A 3D biomechanical model of the hand for power grip. J Biomech Eng. 2003; 125 (1): 78–83.
28. Sancho-Bru JL, Pérez-González A, Vergara-Monedero M, Giurintano D. A 3-D dynamic model of human finger for studying free movements. J Biomech. 2001; 34 (11): 1491–1500.
29. Sancho-Bru JL, Vergara M, Rodríguez-Cervantes P-J, Giurintano DJ, Pérez-González A. Scalability of the muscular action in a parametric 3D model of the index finger. Ann Biomed Eng. 2008; 36 (1): 102–7.
30. Seo NJ, Armstrong TJ, Ashton-Miller JA, Chaffin DB. The effect of torque direction and cylindrical handle diameter on the coupling between the hand and a cylindrical handle. J Biomech. 2007; 40 (14): 3236–43.
31. Snijders CJ, Volkers AC, Mechelse K, Vleeming A. Provocation of epicondylalgia lateralis (tennis elbow) by power grip or pinching. Med Sci Sports Exerc. 1987; 19 (5): 518–23.
32. Valero-Cuevas FJ, Johanson ME, Towles JD. Towards a realistic biomechanical model of the thumb: the choice of kinematic description may be more critical than the solution method or the variability/uncertainty of musculoskeletal parameters. J Biomech. 2003; 36 (7): 1019–30.
33. Vigouroux L, Domalain M, Berton E. Comparison of tendon tensions estimated from two biomechanical models of the thumb. J Biomech. 2009; 42 (11): 1772–7.
34. Vigouroux L, Domalain M, Berton E. Effect of object width on muscle and joint forces during thumb–index finger grasping. J Appl Biomech. 2011; 27 (3): 173–80.
35. Vigouroux L, Quaine F, Paclet F, Colloud F, Moutet F. Middle and ring fingers are more exposed to pulley rupture than index and little during sport-climbing: a biomechanical explanation. Clin Biomech. 2008; 23 (5): 562–70.
36. Vigouroux L, Rossi J, Foissac M, Grélot L, Berton E. Finger force sharing during an adapted power grip task. Neurosci Lett. 2011; 504 (3): 290–4.
37. Wimer B, Dong RG, Welcome DE, Warren C, McDowell TW. Development of a new dynamometer for measuring grip strength applied on a cylindrical handle. Med Eng Phys. 2009; 31 (6): 695–704.
38. Wu JZ, Dong RG, McDowell TW, Welcome DE. Modeling the finger joint moments in a hand at the maximal isometric grip: the effects of friction. Med Eng Phys. 2009; 31 (10): 1214–8.
39. Zatsiorsky VM, Li Z-M, Latash ML. Coordinated force production in multi-finger tasks: finger interaction and neural network modeling. Biol Cybern. 1998; 79 (2): 139–50.
40. Zatsiorsky VM. Kinetics of Human Motion. Champaign, IL: Human Kinetics; 2002. p. 600.


©2012The American College of Sports Medicine