Static and dynamic human flexor tendon–pulley interaction

The aim of the study was to investigate the influence of a preceding flexion or extension movement on the static interaction of human finger flexor tendons and pulleys concerning flexion torque being generated. Six human fresh frozen cadaver long fingers were mounted in an isokinetic movement device for the proximal interphalangeal (PIP) joint. During flexion and extension movement both flexor tendons were equally loaded with 40 N while the generated moment was depicted simultaneously at the fingertip. The movement was stopped at various positions of the proximal interphalangeal joint to record dynamic and static torque. The static torque was always greater after a preceding extension movement compared to a preceding flexion movement in the corresponding same position of the joint. This applied for the whole arc of movement of 0–105°. The difference between static extension and flexion torque was maximal 11% in average at about 83° of flexion. Static torque was always smaller than dynamic torque during extension movement and always greater than dynamic torque during flexion movement. The kind of preceding movement therefore showed an influence to the torque being generated in the proximal interphalangeal joint. The effect could be simulated on a mechanical finger device.     

The influence of concentric and eccentric loading on the finger pulley system

In this study we investigated the influence of the loading condition (concentric vs. eccentric loading) on the pulley system of the finger. For this purpose 39 cadaver finger (14 hands, 10 donors) were fixed into an isokinetic loading device. The forces in the flexor tendons and at the fingertip were recorded. In the concentric loading condition A2 and A4 ruptures as well as alternative events such as fracture of a phalanx or avulsion of the flexor tendons were almost equally distributed, whereas the A2 pulley rupture was the most common event (59%) in the eccentric loading condition and alternative events were rare (23.5%). The forces in the deep flexor tendon, the fingertip and in the pulleys were significantly lower in the eccentric loading condition. As the ruptures occurred at lower loads in the eccentric than in the concentric loading condition it can be concluded that friction may be an advantage for climbers, supporting the holding force of their flexor muscles but may also increase the susceptibility to injury.     

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.     

Biomechanical model for the determination of the forces acting on the finger pulley system

A mathematical model proposed by Hume et al., 1991. Journal of Hand Surgery-American Volume 16, 722-730 for the determination of the forces acting on the A2 and A4 pulley was used. The parameters necessary for this determination include the angle of flexion, the positioning of the pulley with respect to the centre of rotation in the proximal interphalangeal joint (PIP), the relative mismatch between bone and tendon width at the location of the respective pulleys as well as the tendon height at this position. This model was further developed to include the stiffness of the respective pulley, as well as the fact, that there are two flexor tendons of which only one passes through both pulleys. Each parameter was then evaluated using a sensitivity analysis proposed by Fasham et al., 1990. Journal of Marine Research 48, 591-639 in order to determine their relative importance for the outcome of the model. The most important parameter proofed to be the positioning of the pulley with respect to the centre of rotation in the PIP joint. This observation enabled us to give the best possible placement for a pulley graft after pulley rupture.     

Effects of movement speed and joint position on knee flexor torque in healthy and post-surgical subjects

Coactivation of knee flexors during knee extension assists in joint stability by exerting an opposing torque to the anterior tibial displacement induced by the quadriceps. This opposing torque is believed to be generated by eccentric muscle actions that stiffen the knee, thereby attenuating strain to joint ligaments, particularly the anterior cruciate ligament (ACL). However, as the lengths of knee muscles vary with changes in joint position, the magnitude of flexor/extensor muscle force coupling may likewise vary, possibly affecting the capacity for active knee stabilization. The purpose of this study was to assess the effect of changes in movement speed and joint position on eccentric/concentric muscle action relationships in the knees of uninjured (UNI) and post-ACL-surgery (INJ) subjects (n = 14). All subjects were tested for maximum eccentric and concentric torque of the contralateral knee flexors and extensor muscles at four isokinetic speeds (15 degrees-60 degrees x s(-1)) and four joint position intervals (20 degrees-60 degrees of knee flexion). Eccentric flexor torque was normalized to the percentage of concentric flexor torque generated at each joint position interval for each speed tested (flexor E-C ratio). In order to estimate the capacity of the knee flexors to resist active knee extension, the eccentric-flexor/concentric-extensor ratios were also computed for each joint position interval and speed (flexor/extensor E-C ratio). The results revealed that eccentric torque surpassed concentric torque by 3%-144% across movement speeds and joint position intervals. The magnitude of the flexor E-C ratio and flexor/extensor E-C increased significantly with speed in both groups of subjects (P < 0.05) and tended to rise with muscle length as the knee was extended; peak values were generated at the most extended joint position (20 degrees-30 degrees). Although torque development patterns were symmetrical between the contralateral limbs in both groups, between-group comparisons revealed significantly higher flexor/extensor E-C ratios for the INJ group compared to the UNI group (P < 0.05), particularly at the fastest speed tested (60 degrees x s(-1)). The results indicate that joint position and movement speed influence the eccentric/concentric relationships of knee flexors and extensors. The INJ subjects appeared to accommodate to surgery by developing the eccentric function of their ACL and normal knee flexors, particularly at higher speeds and at more extended knee joint positions. This may assist in the dynamic stabilization of the knee at positions where ACL grafts have been reported to be most vulnerable to strain.     

Moment arms of the human digital flexors

For the extrinsic hand flexors (flexor digitorum profundus, FDP; flexor digitorum superficialis, FDS; flexor pollicis longus, FPL), moment arm corresponds to the tendon's distance from the center of the metacarpalphalangeal (MP), proximal interphalangeal (PIP), or distal interphalangeal (DIP) joint. The clinical value of establishing accurate moment arms has been highlighted for biomechanical modeling, the development of robotic hands, designing rehabilitation protocols, and repairing flexor tendon pulleys (Brand et al., 1975; An et al., 1983; Thompson and Giurintano, 1989; Deshpande et al., 2010; Wu et al., 2010). In this study, we define the moment arms for all of the extrinsic flexor tendons of the hand across all digital joints for all digits in cadaveric hands.     

Biomechanical properties of the crimp grip position in rock climbers

Rock climbers are often using the unique crimp grip position to hold small ledges. Thereby the proximal interphalangeal (PIP) joints are flexed about 90 degrees and the distal interphalangeal joints are hyperextended maximally. During this position of the finger joints bowstringing of the flexor tendon is applying very high load to the flexor tendon pulleys and can cause injuries and overuse syndromes. The objective of this study was to investigate bowstringing and forces during crimp grip position. Two devices were built to measure the force and the distance of bowstringing and one device to measure forces at the fingertip. All measurements of 16 fingers of four subjects were made in vivo. The largest amount of bowstringing was caused by the flexor digitorum profundus tendon in the crimp grip position being less using slope grip position (PIP joint extended). During a warm-up, the distance of bowstringing over the distal edge of the A2 pulley increased by 0.6mm (30%) and was loaded about 3 times the force applied at the fingertip during crimp grip position. Load up to 116N was measured over the A2 pulley. Increase of force in one finger holds by the quadriga effect was shown using crimp and slope grip position.     

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.     

Wrist and digital joint motion produce unique flexor tendon force and excursion in the canine forelimb

The force and excursion within the canine digital flexor tendons were measured during passive joint manipulations that simulate those used during rehabilitation after flexor tendon repair and during active muscle contraction, simulating the active rehabilitation protocol. Tendon force was measured using a small buckle placed upon the tendon while excursion was measured using a suture marker and video analysis method. Passive finger motion imposed with the wrist flexed resulted in dramatically lower tendon force (approximately 5 N) compared to passive motion imposed with the wrist extended (approximately 17 N). Lower excursions were seen at the level of the proximal interphalangeal joint with the wrist flexed (approximately 1.5 mm) while high excursion was observed when the wrist was extended or when synergistic finger and wrist motion were imposed (approximately 3.5 mm). Bivariate discriminant analysis of both force and excursion data revealed a natural clustering of the data into three general mechanical paradigms. With the wrist extended and with either one finger or four fingers manipulated, tendons experienced high loads of approximately 1500 g and high excursions of approximately 3.5 mm. In contrast, the same manipulations performed with the wrist flexed resulted in low tendon forces (4-8 N) and low tendon excursions of approximately 1.5 mm. Synergistic wrist and finger manipulation provided the third paradigm where tendon force was relatively low (approximately 4 N) but excursion was as high as those seen in the groups which were manipulated with the wrist extended. Active muscle contraction produced a modest tendon excursion (approximately 1 mm) and high or low tendon force with the wrist extended or flexed, respectively. These data provide the basis for experimentally testable hypotheses with regard to the factors that most significantly affect functional recovery after digital flexor tendon injury and define the normal mechanical operating characteristics of these tendons.     

Update on the anatomy of the pulley system in the chicken foot long digit

The pulley system in the flexor sheath of the long toe of the white leghorn chicken foot was studied. Histologic sections of the pulleys were prepared, and the mechanics of flexion of the long toe was analyzed. An annular flexor pulley that attached to the third phalanx was identified. This pulley, which has not been described previously, was found to be essential for proper flexion of the third interphalangeal joint.     

Effects of wrist position and contraction on wrist flexors H-reflex, and its functional implications.

In order to determine whether joint position exerts a powerful influence on length-tension regulation in multiarticulate wrist flexors, three wrist positions (neutral, flexion and extension) and four levels of flexor contraction [0%, 10%, 20% and 30% maximum voluntary contraction (MVC)] were manipulated. There were significant differences in H-reflex amplitudes according to wrist positions and levels of flexor contraction. H-reflex increased linearly as a function of contraction in all three wrist positions. H-reflex was consistently larger in the wrist flexion than in the wrist extension position. The strength of the relationship (omega2) indicated that wrist position had a greater effect on H-reflex than force of muscle contraction. The interaction between wrist flexors contraction and joint position was significant only in the wrist flexion position. Trend analysis showed that, in the wrist flexion position, a low level of contraction was sufficient to maximally facilitate the H-reflex; however, a quadratic component was seen at higher contraction levels. The above findings may reflect the length-tension relationship of the multiarticulate wrist flexors. Therefore, this paper will discuss the functional implications related to the larger H-reflex in flexion position and the depressed H-reflex in the wrist extension position.     

Kinetics of crimp and slope grip in rock climbing

The aim was to investigate differences of the kinetics of the crimp and the slope grip used in rock climbing. Nine cadaver fingers were prepared and fixated with the proximal phalanx in a frame. The superficial (FDS) and deep (FDP) flexor tendons were loaded selectively and together with 40 N in the crimp grip (PIP joint flexed 90°/DIP joint hyperextended) and the slope grip position (<25° flexed/50° flexed respectively). Five different grip sizes were tested and the flexion force which was generated to the grip was measured. In the crimp grip the FDP generated more flexion force in small sized holds whereas the FDS generated more force in the larger holds. During the slope grip the FDP was more effective than the FDS. While both tendons were loaded, the flexion force was always greater during crimp grip compared with the slope grip. The FDP seems to be most important for very small holds using the crimp grip but also during slope grip holds whereas the FDS is more important for larger flat holds.     

The effect of tendon loading on in-vitro carpal kinematics of the wrist joint

Measurements of in-vitro carpal kinematics of the wrist provide valuable biomechanical data. Tendon loading is often applied during cadaver experiments to simulate natural stabilizing joint compression in the wrist joint. The purpose of this study was to investigate the effect of tendon loading on carpal kinematics in-vitro.A cyclic movement was imposed on 7 cadaveric forearms while the carpal kinematics were acquired by a 4-dimensional rotational X-ray imaging system. The extensor- and flexor tendons were loaded with constant force springs of 50 N, respectively. The measurements were repeated without a load on the tendons. The effect of loading on the kinematics was tested statistically by using a linear mixed model.During flexion and extension, the proximal carpal bones were more extended with tendon loading. The lunate was on the average 2.0° (p=0.012) more extended. With tendon loading the distal carpal bones were more ulnary deviated at each angle of wrist motion. The capitate was on the average 2.4° (p=0.004) more ulnary deviated.During radioulnar deviation, the proximal carpal bones were more radially deviated with the lunate 0.7° more into radial deviation with tendon loading (p<0.001). Conversely, the bones of distal row were more flexed and supinated with the capitate 1.5° more into flexion (p=0.025) and 1.0° more into supination (p=0.011).In conclusion, the application of a constant load onto the flexor and extensor tendons in cadaver experiments has a small but statistically significant effect on the carpal kinematics during flexion–extension and radioulnar deviation.     

Estimation of finger muscle tendon tensions and pulley forces during specific sport-climbing grip techniques

The present work displayed the first quantitative data of forces acting on tendons and pulleys during specific sport-climbing grip techniques. A three-dimensional static biomechanical model was used to estimate finger muscle tendon and pulley forces during the "slope" and the "crimp" grip. In the slope grip the finger joints are flexed, and in the crimp grip the distal interphalangeal (DIP) joint is hyperextended while the other joints are flexed. The tendons of the flexor digitorum profundus and superficialis (FDP and FDS), the extensor digitorum communis (EDC), the ulnar and radial interosseus (UI and RI), the lumbrical muscle (LU) and two annular pulleys (A2 and A4) were considered in the model. For the crimp grip in equilibrium conditions, a passive moment for the DIP joint was taken into account in the biomechanical model. This moment was quantified by relating the FDP intramuscular electromyogram (EMG) to the DIP joint external moment. Its intensity was estimated at a quarter of the external moment. The involvement of this parameter in the moment equilibrium equation for the DIP joint is thus essential. The FDP-to-FDS tendon-force ratio was 1.75:1 in the crimp grip and 0.88:1 in the slope grip. This result showed that the FDP was the prime finger flexor in the crimp grip, whereas the tendon tensions were equally distributed between the FDP and FDS tendons in the slope grip. The forces acting on the pulleys were 36 times lower for A2 in the slope grip than in the crimp grip, while the forces acting on A4 were 4 times lower. This current work provides both an experimental procedure and a biomechanical model that allows estimation of tendon tensions and pulley forces crucial for the knowledge about finger injuries in sport climbing.     

Concentric and eccentric muscle strength before, during and after fatigue in 13 year-old boys

The purpose of this study was to investigate the force-producing characteristics of boys aged 13 years in relation to fatigue of elbow flexor muscles. Maximal voluntary force in elbow flexion was measured before and after a muscle endurance test (MET) by using an isokinetic dynamometer isometrically, concentrically and eccentrically at three velocities, i.e. 0.21, 0.52, and 1.05 rad · s^–1. The MET consisted of maximal concentric and eccentric muscle actions performed alternately at 0.52 rad · s^–1 for 50 consecutive trials. Muscle cross-sectional area (CSA) of elbow flexor muscles (biceps brachii and brachialis) was measured by a B-mode ultrasound apparatus. Although eccentric force showed significantly higher values than concentric force during MET, there was no significant difference in the rate of decline in force between the two actions. There was no significant difference in the rate of decline in force after MET for each velocity and muscle action. Isometric, concentric and eccentric force before MET was significantly related to muscle CSA whereas, after MET, concentric force significantly correlated with muscle CSA but there was no significant correlation between muscle CSA and isometric or eccentric force. From our study, it is therefore suggested that in development to maturity, isometric, concentric and eccentric force decrease at the same rate with advancing muscle fatigue; however, there might be differences among muscle actions in facors affecting force development.     

Eccentric exercise increases EMG amplitude and force fluctuations during submaximal contractions of elbow flexor muscles.

The purpose of this study was to determine the effect of eccentric exercise on the ability to exert steady submaximal forces with muscles that cross the elbow joint. Eight subjects performed two tasks requiring isometric contraction of the right elbow flexors: a maximum voluntary contraction (MVC) and a constant-force task at four submaximal target forces (5, 20, 35, 50% MVC) while electromyography (EMG) was recorded from elbow flexor and extensor muscles. These tasks were performed before, after, and 24 h after a period of eccentric (fatigue and muscle damage) or concentric exercise (fatigue only). MVC force declined after eccentric exercise (45% decline) and remained depressed 24 h later (24%), whereas the reduced force after concentric exercise (22%) fully recovered the following day. EMG amplitude during the submaximal contractions increased in all elbow flexor muscles after eccentric exercise, with the greatest change in the biceps brachii at low forces (3-4 times larger at 5 and 20% MVC) and in the brachialis muscle at moderate forces (2 times larger at 35 and 50% MVC). Eccentric exercise resulted in a twofold increase in coactivation of the triceps brachii muscle during all submaximal contractions. Force fluctuations were larger after eccentric exercise, particularly at low forces (3-4 times larger at 5% MVC, 2 times larger at 50% MVC), with a twofold increase in physiological tremor at 8-12 Hz. These data indicate that eccentric exercise results in impaired motor control and altered neural drive to elbow flexor muscles, particularly at low forces, suggesting altered motor unit activation after eccentric exercise.     

Modelling tendon excursions and moment arms of the finger flexors: anatomic fidelity versus function

A detailed musculoskeletal model of the human hand is needed to investigate the pathomechanics of tendon disorders and carpal tunnel syndrome. The purpose of this study was to develop a biomechanical model with realistic flexor tendon excursions and moment arms. An existing upper extremity model served as a starting point, which included programmed movement of the index finger. Movement capabilities were added for the other fingers. Metacarpophalangeal articulations were modelled as universal joints to simulate flexion/extension and abduction/adduction while interphalangeal articulations used hinges to represent flexion. Flexor tendon paths were modelled using two approaches. The first method constrained tendons with control points, representing annular pulleys. The second technique used wrap objects at the joints as tendon constraints. Both control point and joint wrap models were iteratively adjusted to coincide with tendon excursions and moment arms from a anthropometric regression model using inputs for a 50th percentile male. Tendon excursions from the joint wrap method best matched the regression model even though anatomic features of the tendon paths were not preserved (absolute differences: mean<0.33 mm, peak<0.74 mm). The joint wrap model also produced similar moment arms to the regression (absolute differences: mean<0.63 mm, peak<1.58 mm). When a scaling algorithm was used to test anthropometrics, the scaled joint wrap models better matched the regression than the scaled control point models. Detailed patient-specific anatomical data will improve model outcomes for clinical use; however, population studies may benefit from simplified geometry, especially with anthropometric scaling.     

Power and work produced in different leg muscle groups when rising from a chair

The aim of this study was to determine the power output and work done by different muscle groups at the hip and knee joints during a rising movement, to be able to tell the degree of activation of the muscle groups and the relationship between concentric and eccentric work. Nine healthy male subjects rose from a chair with the seat at knee level. The moments of force about the hip and knee joints were calculated semidynamically. The power output (P) and work in the different muscle groups surrounding the joints was calculated as moment of force times joint angular velocity. Work was calculated as: work = f Pdt. The mean peak concentric power output was for the hip extensors 49.9 W, hip flexors 7.9 W and knee extensor 89.5 W. This power output corresponded to a net concentric work of 20.7 J, 1.0 J and 55.6 J, respectively. There was no concentric power output from the knee flexor muscles. Energy absorption through eccentric muscle action was produced by the hip extensors and hip flexors with a mean peak power output of 4.8 W and 7.4 W, respectively. It was concluded that during rising, the hip and knee muscles mainly worked concentrically and that the greatest power output and work were produced during concentric contraction of the knee and hip extensor muscles. There was however also a demand for eccentric work by the hip extensors as well as both concentric and eccentric work by the hip flexors. The knee flexor muscles were unloaded.     

In vivo changes in the human patellar tendon moment arm length with different modes and intensities of muscle contraction

The purpose of this study was to examine the effect of different muscle contraction modes and intensities on patellar tendon moment arm length (d(PT)). Five men performed isokinetic concentric, eccentric and passive knee extensions at an angular velocity of 60 deg/s and six men performed gradually increasing to maximum effort isometric muscle contractions at 90( composite function) and 20( composite function) of knee flexion. During the tests, lateral X-ray fluoroscopy imaging was used to scan the knee joint. The d(PT) differences between the passive state and the isokinetic concentric and extension were quantified at 15( composite function) intervals of knee joint flexion angle. Furthermore, the changes of the d(PT) as a function of the isometric muscle contraction intensities were determined during the isometric knee extension at 90( composite function) and 20( composite function) of knee joint flexion. Muscle contraction-induced changes in knee joint flexion angle during the isometric muscle contraction were also taken into account for the d(PT) measurements. During the two isometric knee extensions, d(PT) increased from rest to maximum voluntary muscle contraction (MVC) by 14-15%. However, when changes in knee joint flexion angle induced by the muscle contraction were taken into account, d(PT) during MVC increased by 6-26% compared with rest. Moreover, d(PT) increased during concentric and eccentric knee extension by 3-15%, depending on knee flexion angle, compared with passive knee extension. These findings have important implications for estimating musculoskeletal loads using modelling under static and dynamic conditions.     

Mechanical effect of rat flexor carpi ulnaris muscle after tendon transfer: does it generate a wrist extension moment?

The mechanical effect of a muscle following agonist-to-antagonist tendon transfers does not always meet the surgeon's expectations. We tested the hypothesis that after flexor carpi ulnaris (FCU) to extensor carpi radialis (ECR) tendon transfer in the rat, the direction (flexion or extension) of the muscle's joint moment is dependent on joint angle. Five weeks after recovery from surgery (tendon transfer group) and in a control group, wrist angle-moment characteristics of selectively activated FCU muscle were assessed for progressive stages of dissection: 1) with minimally disrupted connective tissues, 2) after distal tenotomy, and 3) after maximal tendon and muscle belly dissection, but leaving blood supply and innervations intact. In addition, force transmission from active FCU onto the distal tendon of passive palmaris longus (PL) muscle (a wrist flexor) was assessed. Excitation of control FCU yielded flexion moments at all wrist angles tested. Tenotomy decreased peak FCU moment substantially (by 93%) but not fully. Only after maximal dissection, FCU wrist moment became negligible. The mechanical effect of transferred FCU was bidirectional: extension moments in flexed wrist positions and flexion moments in extended wrist positions. Tenotomy decreased peak extension moment (by 33%) and increased peak flexion moment of transferred FCU (by 41%). Following subsequent maximal FCU dissection, FCU moments decreased to near zero at all wrist angles tested. We confirmed that, after transfer of FCU towards a wrist extensor insertion, force can be transmitted from active FCU to the distal tendon of passive PL. We conclude that mechanical effects of a muscle after tendon transfer to an antagonistic site can be quite different from those predicted based solely on the sign of the new moment arm at the joint.