Ten right-handed healthy adults (five males and five females) gave an informed consent to participate in this study. All protocols were approved by the Review Board of Tohoku Bunka Gakuen University. They had no neurological, musculoskeletal, or visual disorders by self-report. The subject's age ranged from 20 to 22 years (average 21 yrs).

The subjects sat on a stool with their shoulder 0° flexed, 0° adducted and 0° outward rotated. Their right elbow joint and hand were flexed 90° and at a middle position to supination and pronation, respectively. The subjects were asked to reach their right hand by pointing at a small target in the sagittal plane while keeping their trunk in the initial position. Each target was 1 cm in width and wrapped around a stick of 1.5 cm diameter that stood in front of the right shoulder joint. The subjects were verbally instructed to reach at fast, natural (comfortable), and slow speed. Accuracy of the pointing was not required.

As shown in Figure. 1, we used five targets that required subjects to flex their shoulder from 45 to 105 degrees at 15 degrees intervals (i.e., 45 degrees (T45), 60 degrees (T60), 75 degrees (T75), 90 degrees (T90), and 105 degrees (T105)). The distance of the target from the shoulder was adjusted to 80% of their upper arm length.

Subjects were allowed to practice several times by reaching at T45 to familiarize themselves with the task. All subjects first reached to T60 under a slow speed condition, and then target and motion speed were randomly assigned. The subjects performed a total of 15 trails (5 targets × 3 speeds).

Adhesive infra-red reflex markers were placed on the acromion, the lateral epicondyle of the humerus, and middle point between styloid process of the ulnaris and radius of the right arm, and positions were collected using a three-dimension motion analysis device (ELITE puls, BTS, 50 Hz). Position data of each joint was smoothed with a cutoff frequency of 3 Hz for natural and slow speed conditions, and 1 Hz for the very slow speed condition using a second order Butterworth filter 22. Using these position data, joint angle, velocity, and acceleration were calculated for the shoulder and elbow joints.

As described earlier, there was an invariant relationship in trajectory (Figure 2) and joint movement (Figure 3). Figure 10 illustrates the relationship between the magnitude of torque impulses and peak angular velocity for all targets from one subject. As expected, a high correlation between iNET and peak angular velocity were observed in each joint (r = 0.999, p < 0.01 for both joints). The correlations between iDMUS and peak angular velocity were also high for the shoulder (r = 0.970 p < 0.01), but the correlation was greatly reduced in the elbow (r = 0.457(n.s.)). The correlation coefficients averaged across all subjects are shown in Table 2. Table 2 demonstrates that iDMUS in the elbow, in contrast to the shoulder joint, had only a weak correlation with peak elbow velocity as compared to other torque components. The correlation of torque impulse to peak angular velocity at the elbow joint was held in terms of NET but not in DMUS. Note that the direction of DMUS was always opposed to the movement direction, except at T45.

The experimental setting adopted in the present study was designed to simulate every day reaching in which subjects performed forward reaching in a vertical plane. Reaching targets differed both in direction and distance. The distance increased as the target got higher from T45 to T105 (Figure 2), but movement time remained the constant among targets (Table 1) because of a corresponding increase in the velocity of reach. Since increases in shoulder velocity with higher targets were compensated by decreases in elbow velocity (Figure 4), movement time was kept constant independent of the target position. The changes in angular velocity were directly related to the amount of net torque (iNET) required for reaching in the shoulder and elbow (Figure 8).

In addition, differences in target direction corresponded to gravity torque loaded on the both joints. Whereas gravity torque on the shoulder joint increased steadily with the target height, gravity on the elbow changed little (Figure 8). The effect of gravity on the trajectory generation has been examined by some researchers. A series of studies by Papaxanthis et al. showed that the direction of pointing movement was a determinant for arm trajectory generation in a vertical plane 26272829. The result of the present study is in agreement with their result, that is, the linearity of hand trajectory varied with the direction of reach. In particular, the trajectories of reaching movement to upper targets in this study, i.e., T90 and T105, were curved more greatly than the lower targets. This result implies that gravity affects the trajectory in vertical reaching.

Further, the present study suggests gravity and interaction torque both relate to wrist trajectory generation in multijoint movement. If the absolute magnitude of interaction torque was a major factor for trajectory generation, changes in the linearity of wrist trajectory would appear under different speed conditions. While the magnitude of the interaction torque (iINT) decreased as the reach got slower (Figure 8), the linearity of trajectory to a target was independent of the speed. Because of the speed-independency of the trajectory, it is suggested that the interaction torque contributed to the trajectory formation even at slow speed. This point will be discussed below.

We believe that the most remarkable finding of this study was that the contribution of INT to NET was important when reaching at slow speed. The contribution index of INT to NET was independent of speed for every target in the shoulder and elbow joints (Figure 9). As the velocity of reach decreases, the magnitude of INT and NET at the joints also decrease. This relation might be the reason for the fact that the relative contribution of INT to NET was independent of the speed. A recent study from our laboratory examined squatting and also showed the same speed-independency of the relative contribution of INT to NET (manuscript in preparation). It has been postulated that the speed of reaching is crucial for the effects of interaction torque, and therefore may be negligible for multi-joint movements at slow speed 30. Consequently, most recent studies have examined the effects of INT on fast movements.

Messier et al. 20 reported that patients with complete loss of proprioception experience a deficit in accuracy during slow reaching, and also suggested that the proprioceptive information providing cues for the predictive control of interaction torque is important, even when interaction torques are very small. Also, Hollerbach and Flash 1 demonstrated qualitatively that the effects of interaction torque may be relatively independent of speed. Our result is consistent with these works and suggests that the contribution of interaction torque to multi-joint movement may be significant irrespective of speed.

The contribution index of INT consistently depended on the target direction at both joints. This result is consistent with data presented in previous studies demonstrating that the magnitude of INT gradually changes with the direction of reaching 91012. As a larger shoulder flexion was required for the elbow extension (e.g., reaching toward T105), the contribution of iDMUS became more dominant than that of INT at the shoulder, while the INT contributed excessively to NET at the elbow. In contrast, when reaching toward T45 the contribution of INT became dominant when compared to iDMUS at the shoulder. The dependence of INT on the target position shown in our study could be attributed to changes in the joint angular velocities of the shoulder and elbow joints. For instance, the peak angular velocity at the shoulder during reaching toward T105 was faster than the others (see Figure 4), thus resulted in more interaction torque produced at the elbow (Figure 8).

For every target, flexion DMUS and flexion INT always contributed in an additive fashion to flexion movement at the shoulder (i.e., INT assisted the shoulder movement). In other words, DMUS utilized the INT to produce a specific shoulder movement over a range of movement speeds. This can especially be seen by the contribution of DMUS to joint movement during T105 reaching. On the other hand, the contribution of DMUS also counteracted elbow movement. Because the INT overwhelmingly contributed to net torque production, DMUS was forced to compensate for the magnitude of the INT. Interestingly, when reaching to T45 and T60 the contribution of the DMUS to NET was quite low and the joint motion was produced solely by passive interaction torques caused by the shoulder joint.

Our results were consistent with the "shoulder-centered pattern" 12 or "leading joint hypothesis" 30, in which shoulder muscle torque predominates in the production of movement while the elbow muscles play a minor role. The torque profiles at the elbow (Figure 7) showed that DMUS was generated prior to NET. This result is consistent with the notion that the central nervous system (CNS) can predict coming interaction torque during multi-joint movement in a feed-forward manner 3456831.

The trajectory of reach examined in the present study was always linear to each target and the linearity was preserved regardless of movement speed (Figure 2). The linear trajectory of reach has been generally observed in planar reaching, except in the extreme margins of the work space 21. Therefore, the angular movements of joints involved in reaching should be also coordinated so that a linear trajectory is produced. This inter-joint coordination is demonstrated in Figure 3 for our reaching task. The relationship between shoulder and elbow joints is the result of inverse kinematics from the linear trajectory.

The question then arises as to how muscular torque acts on each joint in order to produce coordinated joint movement, or "By what rule has the CNS selected an appropriate muscle activation pattern to achieve the inter-joint coordination?" 2. If interaction torque can be neglected in multi-joint reaching, then the inter-joint coordination should closely correspond to the invariant relationship between the muscle torques of each joint. However, the joint net torque that produces inter-joint coordination cannot be determined solely by muscle torque (or dynamic muscle torque), because of the essential contribution of INT to NET. Consequently, muscle torques per se may be variable from trial to trial without corresponding to joint kinematics. This indeterminacy of muscle torque is indeed demonstrated in Figure 10 and Table 2 for the elbow joint in our reaching task. Also, the dynamic muscle torque could not predict the elbow peak velocity. In addition, the elbow muscle torque was opposed to the direction of the elbow movement.

Gottlieb et al. 3233 previously reported data indicating that shoulder and elbow torques keep a linear relation in averaged trials of their reaching task (i.e., "linear synergy"). Based on this data, Gottlieb et al. postulated that the CNS uses a single command that is transmitted to the muscle at two joints in a predetermined proportion, thereby reducing the degree of freedom for movement. However, their later work failed to provide evidence that shows the generality of "linear synergy" for reaching 24. Their studies on elbow muscle torque appeared to show linear relationship with shoulder torque, but it was often opposed to the direction of elbow movement depending on the target direction. The central command must designate the direction of elbow torque in this case, thereby requiring an additional degree of freedom.

The indeterminacy of motor command to produce inter-joint coordination has been previously suggested 34 (i.e., "functional non-univocality of the connections between the motor center and the periphery"). Bernstein stressed that "movements are not completely determined by effector process" (P105). Consistent with this idea, the findings in this study suggest that the traditional notion of deterministic connection from motor command (and hence, muscle activation) to the coordinated movement is no longer holds true for multi-joint movements. Alternatively, our data indicate that motor command must adjust the direction and magnitude of dynamic muscle torque to passive torques on a trial to trial basis so that the coordinated joint movements are organized. A possible connection between muscle and passive torque, and the joint coordination in multi-joint movement, is illustrated in Figure 11. The passive torques in Figure 11 include interaction and gravity torques, and also the torque due to visco-elastic forces within muscle tissue 35. Of particular interest is the behavior of elbow muscle torque examined in this study. Dynamic muscle torque at the elbow tended towards an opposite direction of elbow movement (Figure 9), and its magnitude varied from trial to trial in order to compensate for the variability of interaction torques at the joint (Figure 10). Nevertheless, the joint coordination was kept invariant irrespective of motion speed. We speculate that motor command does not control muscle activity by a rigid computational rule, and the CNS may instead have to learn through everyday experience to adjust muscle torque production against the perturbation caused by these passive torques.