The organization and control of goal-directed movements has been studied extensively using variations of the well known Fitts' task [1, 2]. Within this general paradigm, the width of the target (W) and distance (A) of the movement are systematically varied across trials and subjects are asked to point at targets as rapidly and as accurately as possible. Generally, these studies have allowed to conclude that there is a linear relationship between the index of difficulty (ID = Log2 [2A/W]) and movement time (MT) (see [3, 4] for reviews of this effect) with the MT increasing when the ID increases. It has been suggested the increase in MT corresponds to an increase of the amount of visual information that needs to be processed to generate a movement that would arrive at the target.
Rapid discrete goal-directed movements are characterized by a well known coordination pattern between the eye and the hand movement [5–7]. The gaze always starts prior to the hand movement and reaches the target at about the (i) hand movement onset [5, 7], (ii) hand peak acceleration [8, 9] or (iii) hand peak velocity [10–12]. Generally, the gaze is in the vicinity of the target during hand deceleration. Such a gaze-hand lead pattern is naturally assumed to allow (i) the early update of the initial hand motor plan on the basis of accurate target location encoding [13–15] and (ii) the control of the final phase of the movement on the basis of visual information about relative target and hand locations [9, 16, 17]. Surprisingly, the effect of the difficulty of the task (and hence of the target size) on the temporal gaze-hand coordination has not been directly investigated. It is certainly of interest (for instance, from a human factors perspective) to determine whether the reported gaze-hand organization, considered as optimal, is ID dependent.
Often, goal-directed movements are produced in a reciprocal rather than in a discrete manner. For instance, in the classical experiments of Paul Fitts, subjects pointed back and forth between two targets as fast and as accurately as possible for 20 sec. Despite the fact the linear relationship between the ID and movement time was first reported for reciprocal movements, there has been an ongoing debate about 1) whether the units of actions for discrete and reciprocal movements are similar [18–21], and 2) whether the relationship between the ID and movement time is linear . For example, Guiard [19, 23] showed that the deceleration phase of a reciprocal pointing completely overlaps the reacceleration phase of the following pointing movement, taking advantage of the stored elastic energy. Such a kinematic organization, governed by a cyclical unit, is qualified as harmonic (see  for details about harmonicity calculation) and Guiard  has argued this organization does not support the suggestion that reciprocal movements can be decomposed into discrete segments. This latter interpretation, often labeled the concatenation hypothesis, would imply a waste of this stored elastic energy once every half-cycle. Nevertheless, there are several examples where reciprocal pointings became inharmonic when the target size was decreased and the ID increased above a critical value included between 4.01 and 4.91 bits [23–25]. Recently, Huys et al.  also presented a demonstration that, for reciprocal movements, the relationship between ID and movement time is not continuous and that different control mechanisms correspond to low and high IDs with rhythmic movements implemented in easy tasks and discrete movements in difficult ones. This suggestion also has received support from neuro-imaging research [26, 27]. For instance, Schaal et al.  reported that discrete wrist flexion and extension movements activated more cortical areas than rhythmic wrist movements. Specifically, more prefrontal and parietal areas were involved in reaching and complex sequential actions than for rhythmic movements, suggesting that rhythmic movements are monitored by an automatic control whereas more cognitive functions are required to control discrete movements.
As recently underlined by Lazzari et al. , the investigation of gaze-hand coordination during reciprocal tasks has received little attention despite the fact that for reciprocal movements, visual information is required both to bring the movement in progress to a successful conclusion and to prepare the next movement . Hence, a trade-off has to be made between visual control of the final phase of the current movement and the magnitude of the gaze-hand lead pattern for the upcoming movement. Such a trade-off could potentially be influenced by the accuracy requirements (ID). According to Elliott et al. , when the accuracy requirements are relatively low, accurate movements may be concluded without visual information about relative target and hand locations during the terminal phase. Formally, larger targets could allow subjects to determine that the planned motor program (updated from accurate target location encoding) does not require terminal corrections. On the other hand, higher IDs would be associated with additional visual processing cost relative to the final phase of the preceding movement leading to a decrease of the gaze-hand lead pattern magnitude.
Two experiments were designed to analyze the effect of various IDs on the kinematics of the hand movement and the temporal coordination between the gaze and the hand. We examined the coordination of the gaze-hand lead pattern when fast discrete pointings and reciprocal pointings to four different target sizes were produced. Our results show a stable and fixed gaze-hand lead pattern for discrete pointings. For reciprocal pointings, the gaze-hand lead pattern was much smaller and decreased linearly with an increased target size. We discuss the role of this differential control mechanism for discrete and reciprocal movements.