The compensatory synergy concept was further developed to include the notion of gain control (Pigeon & Feldman, 1998; Pigeon et al. 2000). This formulation made the concept applicable to movements in which trunk involvement is determined by the task rather than by instruction, as is the case in movement beyond the reach of the arm. Thus, efficiency of the compensatory synergy is characterized by a coefficient called gain (g), so that g = 1 when the influence of the trunk motion on the hand position is fully compensated and g = 0 when no compensation is made. It is likely that the gain can be specified depending on the distance to the target. For example in movements to remote objects, the gain of the compensatory synergy should be attenuated (g < 1) in order to allow the trunk to contribute to the pointing extent.

Achieving the required movement extent may not be the only aspect of the integration of trunk motion into reaching. In some behavioural situations, the directions of the trunk and hand motion may not coincide. For example when taking a laterally located glass from a dinner table, we can simultaneously lean the trunk forward, in the sagittal plane, to hear a person on the opposite side of the table better. In this case, while producing the trunk motion, control systems should prevent a change in the hand movement direction, which also requires appropriate co-ordination of the arm and trunk motions. Since these motions may be desynchronized in terms of peak velocities, the gain of the arm-trunk co-ordination may not be constant during reaching.

In the present study, we investigated the spatial-temporal aspects of the integration of the trunk motion into reaching towards targets placed beyond the reach of the arm. Specifically, we tested the hypothesis that the arm-trunk compensatory co-ordination, and thus the contribution of the trunk to the movement extent, may substantially vary depending on the phase of reaching.

Subjects made hand movements in a diagonal direction while leaning the trunk sagittally. The trunk movement was thus intentionally constrained to influence not only the hand movement extent but also direction. There are several possible strategies for combining the arm and trunk motion in pointing to targets beyond the reach of the arm. One strategy would be to initiate the trunk contribution to the hand displacement as soon as the trunk begins to move. Another strategy would be to initiate the trunk contribution some time after the trunk movement onset, when the arm has reached the limit of its contribution to hand movement extent. To determine which strategy was actually used by subjects, the trunk motion was blocked in randomly selected trials, making it impossible for the hand to cover the whole pointing distance. This trunk arrest paradigm has previously been used in the analysis of movements within the reach of the arm (Adamovich et al. 2001). In movements beyond the reach, if subjects employed the first strategy in non-perturbed trials, the effect of trunk arrest would be a change in the hand movement direction. In the case of the second strategy, the hand trajectory could remain invariant despite the trunk arrest, up until the arm reached the maximal extent. In addition, the changes in the arm inter-joint co-ordination in response to the trunk arrest may be indicative of the control strategies employed by the nervous system in response to sudden changes in the number of DFs participating in the movement. Some results of the present study have been reported in abstract form (Feldman et al. 2001).

Subjects were seated in a cut-out section of a table limiting the range of possible directions of trunk bending (± 15 deg from the sagittal plane). The initial target (a light-emitting diode embedded in the table; Fig. 1, open circles) was at a distance of 30 cm from the midline of the chest directly in front of the subject. On a ‘ready’ cue (light), subjects lifted their right (dominant) arm 2–3 cm above the table so that the tip of the index finger (the arm endpoint) was above the initial target and the forearm-shoulder plane was approximately parallel to the surface of the table. In response to an auditory ‘go’ signal from a computer, subjects moved the hand from the initial position to one of two targets placed beyond the reach of the arm in either the ipsi- or contralateral workspace (Fig. 1, filled circles). They were required to bend the trunk and the head as a single unit, thus minimizing the relative head-on-trunk displacement. Lateral inclinations of both hand and trunk were permitted in the limits determined by the cut-out section of the table.

Figure 1 Schematic diagram showing the trunk arrest paradigm for pointing to targets placed beyond the reach of the arm

The final targets were placed at a distance exceeding the full length of the arm by 30 %, at the angles of about 45 deg and 30 deg to the sagittal plane, for ipsi- and contralateral targets, respectively. The length of the arm was measured from the acromion to the tip of the outstretched index finger. To reach the target, subjects were forced to combine arm movements with a forward trunk motion of about 18–28 cm at the shoulder level produced by a hip flexion, and, when the arm moved backward, to return the trunk to the initial, vertical position.

Subjects received some prior training with full vision (three to five trials) but without trunk perturbations. Subjects wore liquid crystal glasses (Translucent Technologies, Inc., Plato S2 Spectacles) that became opaque about 100 ms before the movement onset and thus blocked vision of the target and the arm. After a holding period of 200–500 ms at the final position, the subject moved the arm back to the initial position, where vision was restored. Movements were thus produced to remembered targets, without knowledge of results (Poizner et al. 1998; Adamovich et al. 2001).

Subjects wore a harness with an electromagnetic plate fastened posteriorly. Before the ‘go’ signal, the plate was locked to an electromagnet attached to the wall behind the stool on which the subject sat. In 70 % of 60 trials, the electromagnet was unlocked 100 ms after the ‘go’ signal, i.e. before the movement onset so that the trunk movement was unobstructed. In 30 % of randomly selected trials, the electromagnet remained locked before and after the ‘go’ signal and thus the trunk motion was mechanically prevented, which resulted in an isometric pressure on the harness (the residual trunk motion was less than 3 cm at the level of the shoulder). Movements to the ipsilateral and contralateral targets were made in two separate experiments.

Subjects were allowed to touch the surface of the table only after the arm returned to the initial position, when the glasses became transparent. They were instructed to make movements in a stereotypical way (mean peak velocity of the hand was 114 cm s⁻¹, range 80–210 cm s⁻¹). They were informed that the trunk arrests would be made in an unpredictable manner and they should not anticipate the experimental condition in each trial, nor make corrections of the final hand position in the event of trunk arrest.

We anticipated that since the trunk moved predominantly in the sagittal plane, the most substantial effect of the trunk arrest would be a change in the sagittal components of the hand trajectory and velocity profiles. Therefore, we computed and compared these components for non-perturbed and trunk-blocked trials.

For data averaging, movements were aligned with respect to their onsets. Movement onsets and offsets for the endpoint and trunk were determined for each trial using the time at which hand tangential velocity rose above and fell below 3 % of its peak value, respectively. The mean traces (± 1 s.d.) for all measured variables were computed for each target in non-perturbed and trunk-blocked movements. For each variable, the onset of divergence of the traces from the two types of trials was identified as the point at which the mean trace from the trunk-blocked trials first left the ± s.d. zone for the mean trace from the non-perturbed trials.

The analysis of inter-joint co-ordination focused on the relationship between elbow flexion/extension and shoulder horizontal adduction/abduction angles. The changes in these angles during arm movements were the most substantial compared to other arm DFs such as shoulder protraction/retraction (mean ± s.d. value 4.1 ± 2.0 deg; measured in combined movements as the rotation of the vector defined by the two shoulder markers; cf. Pigeon & Feldman, 1998). Elbow and shoulder angles were computed based on the dot product of vectors defined by the co-ordinates of appropriate markers. The shoulder horizontal adduction/abduction angle was measured as the horizontal projection of the angle between two vectors, one defined by the right and left shoulder markers and the other parallel to the humerus between the right shoulder and elbow markers. The latency of divergences in the angle-angle diagrams in response to perturbation was measured relative to the onset of the divergence of the trunk velocities in the trunk-free and trunk-blocked trials.

Repeated measures ANOVAs for the two conditions (combined, arrested) and the two target locations (ipsi- and contralateral) were performed to assess the effect of trunk arrest on the measured variables in each experiment. The level of significance of P < 0.05 was used in all tests.

The term ‘hand trajectory’ will refer to the trajectory of the tip of the index finger. The terms ‘endpoint trajectory’ and ‘hand trajectory’ will be used as synonyms.

The trunk trajectory did not deviate more than 7 deg from the sagittal plane. Trunk motion was thus basically produced by hip rotation with possible sagittal contributions from other degrees of freedom (DFs) along the spinal column. The mean peak value of the hand tangential velocity in the combined movements to either of the two targets was about two times higher than the trunk peak velocity (Fig. 2E, F). In trunk-blocked trials, the trunk displacement was reduced to about 3 cm and the peak velocity to about 16 cm s⁻¹. The trunk velocity profiles in the combined and arrested movements started to diverge after some delay (typically < 60 ms), depending on the subject and target.

Figure 2 Typical kinematic effects of the trunk arrest in movements to targets located beyond the reach of the arm

The trunk began to move and ceased moving practically simultaneously with the hand but the hand and trunk peak velocities were not synchronized (Fig. 2E, F); peak velocity of the trunk occurred significantly later than that of the endpoint, by 75 ± 44 ms (mean ± s.d.) for the ipsilateral and by 50 ± 37 ms for the contralateral target (P < 0.05).

When the trunk was arrested, the hand could not cover the whole pointing distance (Fig. 2A–D). However, the hand trajectory and velocity profiles initially matched those from the trials in which the trunk motion was unobstructed and began to diverge comparatively late in the movement, about 420 ± 50 ms for the group, for ipsilateral and 460 ± 80 ms for contralateral target, measured from the beginning of the arm movement (Fig. 2E, F). The divergence occurred near the peak velocity of the hand movement. Depending on the target and subject, the divergence point could occur simultaneously, after or before the hand peak velocity (Fig. 2E, F). The time from the peak velocity to the divergence point for the group was 40 ± 100 ms for the ipsilateral and 10 ± 120 ms for the contralateral target.

The effect of the trunk arrest became noticeable only after the hand had covered a substantial part of the movement distance in non-perturbed movements (56 ± 13 % for the ipsilateral and 63 ± 13 % for the contralateral target).

Although trials were randomized and subjects were instructed not to anticipate conditions in the forthcoming trial, this may have been insufficient to prevent changes in the control strategy in subsequent, blocked-trunk trials. Such changes also may have been masked by the averaging of kinematic curves. Velocity profiles in the sequential blocked-trunk trials were variable but the variability did not exceed that in free-trunk trials (Fig. 3A). We hypothesized that, if present, an adaptive control strategy would be associated with changes in the instance at which the hand reached peak velocity in sequential trunk-blocked trials. In Fig. 3B, these instances are shown as a function of the trial number for blocked-trunk trials (the mean time at which the hand reached its peak velocity in free-trunk trials was subtracted from these instances). The consistency of the response to the trunk block was estimated by computing Pearson correlation coefficients between the trial number and the time difference between the velocity peak for a given trunk-blocked trial and the averaged peak velocity for the free-trunk movements. Only one subject in each condition (S5 for the ipsi-lateral and S2 for the contralateral target) showed a regular change in the time difference between velocity peaks. Of these two, only in one subject (S5) was there a tendency to decrease the time difference in sequential blocked-trunk trials and thus improve the matching of hand movements in the two types of trials. In the majority of cases, the correlation coefficients were insignificantly different from zero (P < 0.05), implying that there were no systematic changes in the sequential responses to the trunk arrest.

Figure 3 Kinematic characteristics of hand movements to the ipsilateral target in individual blocked-trunk trials

Since the trunk moved in the sagittal plane, the most substantial deflection of the hand trajectory in blocked-trunk trials would also be in the sagittal plane, towards the body, if this deflection were not neutralized by appropriate changes in the arm joints. In this connection, we also computed sagittal components of the hand displacement and velocity profile. The effects of the trunk arrest on these (Fig. 4A–D) were similar to those of the tangential components (Fig. 2C–F). Like the tangential components, the sagittal components of hand displacement and velocity profiles began to diverge only when the hand approached or reached its peak velocity (Fig. 4C, D). At the divergence point, the mean sagittal distance between the hand trajectories in the non-perturbed and trunk-blocked trials was 1.5 ± 0.3 cm for the ipsilateral and 3.1 ± 1.0 cm for contralateral target. At the same time, the sagittal distance between the trunk trajectories from the two types of trials was significantly greater: 5.2 ± 2.1 and 7.8 ± 3.6 cm for movements to respective targets (Fig. 5). These findings suggest that the influence of the trunk displacement on the hand position was compensated by appropriate changes in the arm joint angles.

Figure 4 Sagittal components of the mean displacement and velocity of the hand and trunk for the subjects as in Fig. 2

Figure 5 The individual (A, B) and group mean sagittal trunk displacements (C, D) in non-perturbed trials during the time when the hand trajectory remained invariant despite the trunk arrest

In contrast to the endpoint trajectories and velocity profiles, the elbow and shoulder angles substantially changed in response to the trunk arrest, as could be seen from the comparison of individual kinematic characteristics for the blocked-trunk trials with the respective mean characteristics for free-trunk trials (Fig. 6) or from the comparison of the mean kinematic characteristics in the two types of trials (Fig. 7 and Fig. 8). While making non-perturbed movements to the ipsilateral target, subjects usually did not fully extend the elbow (Fig. 7A and Fig. 8A, dashed curves). In blocked-trunk trials, they increased the elbow extension (Fig. 7A and Fig. 8A, continuous curves). Simultaneously, they inverted the movement direction at the shoulder, from abduction in the non-perturbed trials to adduction in the trunk-blocked trials (Fig. 7C and Fig. 8C). These strategies were observed in four subjects. In the remaining three subjects, the elbow movements were not significantly different in the non-perturbed and trunk-blocked trials. At the same time, these subjects also inverted the direction of the shoulder horizontal adduction in response to the trunk arrest. While making movements to the contralateral target, subjects preserved the magnitude but changed the timing of the elbow extension and increased the magnitude of the shoulder horizontal adduction in response to the trunk arrest (Figs 7B, D and 8B, D).

Figure 6 Effects of trunk arrest on the elbow angle and shoulder horizontal adduction/abduction angle in hand movements to the ipsilateral target

Figure 7 Changes in averaged elbow angle and shoulder horizontal adduction/abduction angle in response to the trunk arrest

Figure 8 Effects of trunk arrest on the position/velocity curves (phase diagrams, averaged) for the elbow and shoulder horizontal adduction/abduction angles

A typical example of averaged elbow-shoulder diagrams is shown in Fig. 9, demonstrating substantial changes in the pattern of inter-joint co-ordination in response to the trunk arrest, especially for movement to the ipsilateral target (Fig. 9A). For this target, the co-ordination profiles for the non-perturbed and trunk-blocked trials in two subjects began to diverge with a minimal latency of 40 ms (for all subjects, the mean latency was 85 ± 35 ms). For movements to the contralateral target, the changes in the elbow-shoulder co-ordination in response to the trunk arrest were smaller but also evident (Fig. 9B). They occurred at a minimal latency of 62 ms (for the group, mean latency was 105 ± 43 ms; Fig. 10). In contrast, the hand trajectories in non-perturbed and trunk-blocked trials began to diverge significantly (P < 0.01) later: the mean latencies were 346 ± 79 ms for the ipsilateral target and 384 ± 118 ms for the contralateral target (computed from the onset of divergence in the trunk velocity profiles to the onset of divergence in the sagittal components of hand velocity profiles).

Figure 9 Changes in the inter-joint co-ordination in response to the trunk arrest

Figure 10 Latencies of changes in the inter-joint co-ordination in response to the trunk arrest () compared to the time when hand trajectories in the non-perturbed and trunk-blocked trials began to diverge (□)

The finding that the trajectory and hand velocity profiles remained invariant during the initial half of the hand movement despite the trunk arrest can be explained in the following way. In non-perturbed trials, the influence of the trunk motion on the hand trajectory was actively neutralized by appropriate compensatory rotations in the arm joints linked to the trunk motion. These compensatory rotations could be cancelled with the trunk arrest by a short-latency reflex mechanism, leaving the hand trajectory unchanged. According to this hypothesis, the trunk arrest would result in substantial short-latency changes in the arm inter-joint co-ordination, which was the case in our study (Fig. 9 and Fig. 10). Changes in the arm inter-joint co-ordination in response to the trunk arrest could be detected kinematically at a minimal latency of 40 ms. This finding suggests a rapid reflex compensatory mechanism driven by vestibular or/and proprioceptive afferent signals. Similar behaviour has been observed during reaching towards targets placed within the reach of the arm, except that in this case the whole hand trajectory remained invariant whether or not the trunk motion was prevented (Adamovich et al. 2001). In these experiments, the influence of the trunk movement on the hand position was also neutralized by appropriate compensatory rotations of the elbow and shoulder joints (Pigeon et al. 2000; Adamovich et al. 2001). In contrast, when arm movements were made towards a target moving with the trunk, the arm inter-joint co-ordination did not change in response to the trunk arrest but the hand trajectory rapidly deviated from that in the free-trunk trials (Adamovich et al. 2001). It is likely that, in the free-trunk trials of the first task, subjects actively modified arm joint angles to prevent the influence of the trunk motion on the hand displacement. In contrast, in the second task, the trunk-related compensatory modifications of the arm-joint angles were cancelled in order to allow the full expression of the trunk contribution to the hand displacement. In other words, by regulating the gain of the compensatory synergy, the nervous system could transform reaching from a frame of reference associated with the laboratory to one associated with the trunk.

Some possible mechanisms involved in the active compensation of the trunk influence on the hand trajectory in a reaching movement within the reach of the arm (Adamovich et al. 2001) or during the early phase of movement beyond the arm's reach, in the present study, include proprioceptive feedback or vestibulo-spinal pathways targeting motoneurons of arm muscles (Brodal, 1974). The involvement of proprioceptive feedback could result, in particular, from motion at the hip joint. The involvement of vestibulo-spinal pathways could result from the trunk motion and associated motion of the head. These systems could induce short-latency changes in on-going, whole body movements, as has been shown by galvanic stimulation for the vestibular system (Fitzpatrick et al. 1994) and neck muscle vibration for proprioception (Lackner, 1988; Ivanenko et al. 2000).

Taken together, the results of our study show that although the hand and trunk moved in parallel, the trunk began to contribute to the hand transport only at a later phase of movement, starting at about the time when the hand reached peak velocity. Indeed, the arm-trunk system is not the only one in which task-specific compensations may come into play. The best-known example is the vestibulo-ocular reflex compensating for the influence of head rotation on gaze shift (Guitton, 1992; Johnson & Sharpe, 1994). Another example is the compensatory change in the vocal tract configuration that preserves a sound despite mechanical perturbations of the jaw (Kelso et al. 1984). Spinal frogs, while preparing to wipe a stimulus from the skin, may broadly vary the limb configuration to attack the stimulus in the appropriate direction. Thereby the position of the wiping point of the limb before the attack remains unchanged, implying a compensatory mechanism (Fukson et al. 1980; Berkinblit et al. 1986). In humans, the arm configuration usually remains the same when subjects produce coactivation of antagonist muscles, implying the existence of some compensatory mechanism balancing the muscle torques when coactivation is made. Finally, compensatory changes in the joint configurations that leave the values of essential task variables unchanged have been reported during sit-to-stand and pistol shooting tasks (Sholtz & Schöner 1999; Sholtz et al. 2000).

Movements considered in the present study represented a transition from an initial to a final equilibrium configuration (posture) of the arm-trunk system and, therefore, our data are relevant to the classical problem in motor control regarding the relationship between posture and movement (Von Holst, 1936; Von Holst & Mittelstaedt, 1950/1973). Different motor control approaches offer different solutions to this problem. In this connection, we will compare three of these - the reafference principle (Von Holst & Mittelstaedt, 1950/1973), an advanced version of the equilibrium-point (EP) hypothesis (the λ model; Feldman & Levin, 1995), and force control (FC) models. The latter are the models that, although varying in specific details, are united by the idea that the nervous system plans the desired movement trajectories and then, based on some internal representation of the motor apparatus, computes and specifies appropriate electromyographic (EMG) activity, muscle torques and forces to actualize the movement plan (Hollerbach 1982; Shadmehr & Mussa-Ivaldi, 1994; Wolpert et al. 1995).

The problem, as Von Holst characterized it, is that there are powerful neuromuscular mechanisms (‘postural reflexes’) that generate EMG activity and forces in order to resist perturbations that deflect the body from an initial posture. At the same time it is clear that the organism can intentionally adopt different postures. Each new posture adopted by the system might be considered as a deflection from the initial one. The deflection would result in resistance tending to return the system to its initial position. How then is an intentional movement from the initial posture and the achievement of a new posture of the body possible? We will refer to this problem as ‘Von Holst's posture-movement paradox’. Indeed, our everyday experiences show that the nervous system has no problem moving the body or its segments away from an initial posture and stabilizing different postures. However, the explanation of how the body can intentionally move away from the initial posture without triggering resistance might be a critical problem for some approaches to motor control.

The posture-movement paradox could be resolved if postural reflexes were completely or partially suppressed by a central pattern generator when the transition to a new posture is made. Von Holst & Mittelstaedt (1950/1973) rejected this suggestion as conflicting with experimental observations. Specifically, any posture of the body is maintained by resisting reactions similar to those seen in the restoration of the initial posture in response to perturbations. Deafferented patients point to the general importance of proprioceptive reflexes in the stability of any posture. Even after years of practice, these patients are unable to stand or walk without assistance, or maintain a steady-state position of the arm without vision (e.g. Levin et al. 1995).

Von Holst and Mittelstaedt suggested that, to produce movement, the nervous system influences afferent systems in some way to reset the initial ‘postural state’ so that the same postural mechanisms that stabilized the initial posture would act to stabilize a new one. This is a major idea underlying Von Holst's ‘reafference principle’. A similar idea is inherent in a version of the EP hypothesis, the λ model, with the addition that it explicitly indicates the parameters the control systems can reset to produce an unopposed movement to a new posture (Feldman & Levin, 1995). Specifically, the model is based on the experimental finding that the nervous system can reset the muscle activation thresholds (λs) and thus specify new spatial co-ordinates at which an equilibrium posture can be reached and maintained (Matthews, 1959; Asatryan & Feldman, 1965). With the resetting of activation thresholds, the initial posture appears to be a deflection from the newly specified posture. Therefore, the same neuromuscular mechanisms that produce EMG signals and forces in response to deflections from the initial position will produce, without any programming, EMG signals and forces tending to eliminate the deflection from the new posture and thus move the system to it (Feldman & Levin, 1995).

FC models cannot account for how the body or its segments (for example the arm) can actively change position without triggering resistance. The generation of muscle torques would result in the movement of body segments from an initial position. In response, mechanisms of postural stabilization would generate resistance that would tend to return the segments to their initial position. Control signals might attempt to reinforce the programmed action by generating additional torques that counteract this resistance. This strategy would clearly be non-optimal in terms of energy costs, requiring high EMG activity and forces not only for motion but for maintenance of final posture.

For example Schweighofer et al. (1998) simulated planar point-to-point arm movements using an FC strategy. Their equations 6 and 8 show that after the movement offset, muscles should generate tonic activity in proportion to the distance between the initial and the final muscle lengths. This implies that the final position is reached by overcoming the resistance to the deflection of the arm from the initial position. Thereby, at the final position, the muscle activity cannot be minimized without driving the limb back to the initial position. This prediction of the FC strategy (see also Bhushan & Shadmehr, 1999) obviously conflicts with the common observation that after transition of the arm to any new position, muscle activation can be minimized without arm motion.

This deficiency of FC models is related to the fact that they have no means for resetting the postural state of the system and thus do not solve Von Holst's posture-movement paradox in a physiologically feasible way. At present, FC models do not incorporate the empirically well-established physiological mechanism of EP shifts - changes in the activation muscle thresholds (Matthews, 1959; Asatryan & Feldman, 1965), a mechanism that, if deficient, results in dramatic movement problems in neurological patients (Levin et al. 2000). These models also do not take into account that practically all descending systems have the capacity to regulate the activation thresholds (Feldman & Orlovsky, 1972).

One can assume that the FC model can be reconciled with the EP hypothesis by incorporating the physiologically well-established mechanisms of EP resetting. However, the problem of integration of the two hypotheses is not as simple as it may seem. In FC models, control levels directly programme and specify kinematic, EMG and force variables. In contrast, in the EP hypothesis, these variables are not programmed or computed but emerge dynamically in response to resetting of muscle activation thresholds produced by control levels. These thresholds are regulated, although not necessarily always, independently of muscle forces and kinematic variables. We would be concerned with the logical consistency of a theory integrating conflicting ideas of the two approaches to motor control.

One might think that the FC model is more advanced than the EP hypothesis since it postulates feed-forward commands for an efficient control of movements. Feed-forward control is actually inherent in the EP hypothesis, specifically the λ model. Parameters such as muscle activation thresholds predetermine, in a feed-forward manner, where, in spatial co-ordinates, the system may reach a balance of forces and thus re-establish an equilibrium state. In general, changes in control parameters and resulting shifts in the EP precede changes of EMG activity, muscle forces and kinematics. In fact, all intentional movements, according to the λ model, are guided in a feed-forward manner. This allows the system to effectively use reflexes in the production of even fast movements, ensure stability of posture and movement despite reflex delay, and generate, if necessary, anticipatory reactions preventing undesirable effects of perturbations if they are known in advance. For example in response to a sudden unloading, the arm position changes (Asatryan & Feldman, 1965). In contrast, the initial arm position remains the same if subjects themselves initiate unloading (Forget & Lamarre, 1995), an anticipatory reaction simulated in the λ model (Feldman & Levin, 1995).

Since point-to-point movements necessitate changes in parameters underlying postural resetting, the theoretical framework of the EP hypothesis (specifically, the λ model) appears to be preferable to that of FC models for discussion of our results.

According to the λ model, a hand movement from an initial to a final equilibrium position results from shifts in activation thresholds of arm and trunk muscles. Taken together, these thresholds represent a referent (R) configuration of the arm-trunk system described by appropriate, threshold joint angles (Feldman & Levin, 1995; Lestienne et al. 2000). The activation of each skeletal muscle depends on the difference between the actual and the referent configurations of the system. This difference thus represents a global factor that determines, together with local biomechanical and reflex factors, how muscles are activated and eventually bring the system to an equilibrium configuration. The difference between the equilibrium and the referent configurations represents a measure of the muscle activation and forces that balance the external forces, for example, gravity. In the model, the virtual hand trajectory determined by the shifts in the R configuration is called the referent hand trajectory. The trajectory, comprised of the initial, intermediate and final equilibrium positions of the hand associated with sequential changes in the R configuration, is called the equilibrium hand trajectory.

In the present study, we focused on horizontal components of the hand movements whereas external, gravitational forces acted vertically. Therefore, to a first approximation, we can consider the horizontal projections of the referent and equilibrium hand trajectories to be identical.

The response of the system to the shifts in the R configuration depends not only on external forces but also on the inertia of moving segments, muscle stiffness and damping (the latter two are regulated by specific central commands in the λ model). Therefore, the actual hand trajectory might differ from the equilibrium one. It has been shown by perturbation methods and modelling that for fast arm point-to-point movements not involving the trunk, the difference between these trajectories is small (for details see Won & Hogan, 1995; Gribble et al. 1998; Ghafouri & Feldman, 2001). In terms of the λ model, the basic empirical findings in the present study can be interpreted in the following way. At the initial phase of the free-trunk trials, the proprioceptive and/or vestibular afferent signals elicited by the trunk motion result in a modification of the referent configuration of the arm underlying the transport arm motion in the absence of trunk motion. At a later phase, starting approximately when the hand reaches its peak velocity, the effect of afferent signals is attenuated to allow a contribution of the trunk motion into the hand movement direction and extent. The same reflex mechanism arrests the changes in the referent configuration of the arm in response to the trunk block and temporarily provides the invariance of hand trajectory. This description can be extended, based on some additional data showing how the arm transport component is controlled.

A growing number of empirical and simulation studies support the notion that changes in the control variables responsible for the shifts in the equilibrium position of the arm in fast point-to-point movements finish substantially before the movement offset. Specifically, these shifts end approximately at the time of peak velocity of the hand (Flanagan et al. 1993; St-Onge et al. 1997; Gribble et al. 1998; Ghafouri & Feldman, 2001). There are alternative suggestions that the shifts in the equilibrium position underlying fast point-to-point arm movements end only with the movement offset (Latash & Gottlieb, 1991; Latash, 1993; Gomi & Kawato, 1996). Gribble et al. (1998) have shown, however, that these suggestions resulted from simplified assumptions reducing the highly non-linear neuromuscular system to a set of linear spring-like elements (for discussion see also Feldman et al. 1998). Gomi and Kawato's conclusions conflict with results of two empirical studies that do not depend on the assumption of linearity of the system: one showing that shifts in the equilibrium point end substantially before the end of the actual reaching movement, about the time when the hand reaches the peak velocity (Ghafouri & Feldman, 2001) and the other that the hand equilibrium and actual trajectories are spatially close to each other (Won & Hogan, 1995).

In combination with the results of the present study, the evidence that the shifts in the equilibrium position underlying fast point-to-point arm reaching terminate early in the movement (Ghafouri & Feldman, 2001), make it reasonable to describe the trunk-assisted reaching in the following way. The control signals underlying the hand transport and trunk leaning are produced in parallel but the influence of the trunk movement on the hand trajectory is initially compensated by appropriate rotations of the arm joints, until the shifts in the equilibrium position of the hand are completed. As has been argued above, this event occurs about the time when the hand reaches the peak velocity. After that, the gain of the compensation of the trunk is attenuated to allow the trunk to contribute to the hand movement extent and direction.

In conclusion, although the hand and the trunk moves in parallel, the arm and trunk contributions to the hand transport are probably determined by central commands that are generated sequentially.

Trunk-assisted reaching may not be the only task in which different segments move in parallel whereas central commands related to important functional components of the task are generated sequentially. In particular, central commands underlying speech production are probably generated sequentially but the motor responses overlap, resulting in an acoustic effect called co-articulation (Fowler & Saltzman, 1993). In addition, Adamovich et al. (1994) analysed fast discrete movements while subjects continuously generated rhythmical movements of the forearm. They also found that although kinematically the two movements overlap, they are evoked sequentially at a control level (see also Sternad et al. 2001).

The present study is thus relevant to the problem of ‘serial order in behaviour’ discussed by Lashley (1951). He noticed that components of different behaviours, including locomotion, prehension and language are generated sequentially and that such generation cannot result from moment-to-moment responses to a serially ordered environment. Rather, the serial order is a manifestation of a control principle guiding the behaviour of the organism. Lashley also suggested that different components of action could be prepared in advance, without specific ordering whereas an independent neural structure, an action scheme or engram (Bernstein, 1967; Latash, 1993) releases these components in a specific order and at a specific rate. The ordering and rate may be determined depending on mechanical and neural factors (Sternad et al. 1998). In particular, in the present study, the sequential control strategy may be necessary to account for the difference in the arm and trunk inertia; control systems might be forced to wait until the trunk acquires a speed comparable to that of the arm in order to smoothly integrate both movements and preserve the hand movement direction. Another possibility is that the trunk contribution to the hand displacement is not initiated until the control signals determining the virtual, equilibrium configuration of the arm approach some threshold values related to the biomechanical limits of arm joint rotations. When the extension limit of the arm has been reached, control levels allow other, trunk degrees of freedom to assist in the task completion. In reaching tasks involving grasping, peak velocities of the endpoint, trunk and hand aperture are reached sequentially (Wang & Stelmach, 2001). Indirectly, this may indicate that control signals underlying the grasp component are initiated when the two transport components have been completed, so that the control signals underlying the three components of reaching are also generated sequentially, a hypothesis that can be tested in future studies.

We wish to thank Drs Mindy Levin and Ramesh Balasubramaniam for helpful comments on the manuscript as well as Dr David Ostry for the discussions of different motor control theories, which is partly reflected in this paper. This work was supported by research grants from the CIHR and FCAR (Canada).