Small irregularities that often appear in the final portion of the smooth, bell-shaped velocity profile during arm movements to a target have been referred to as secondary submovements. Starting from a seminal study by Woodworth (1899)
, the role of secondary submovements during pointing and reaching movements has been a focus of many investigations (Abrams & Pratt, 1993
; Chua & Elliott, 1993
; Crossman & Goodeve, 1983
; Elliott et al., 2001
; Keele, 1968
; Khan & Franks, 2003
; Meyer et al., 1988
; Novak et al., 2002
; Pratt & Abrams, 1996
; Pratt et al., 1994
; Walker et al., 1997
; Woodworth, 1899
). The common assumption has been that the major portion of distance to the target is covered in a primary, ballistic submovement characterized by smooth acceleration and deceleration. If the primary submovement misses the target, secondary, corrective submovements are performed. The major support for this interpretation is provided by an observation that decreases in target size are usually accompanied with more frequent emergence of secondary submovements.
Dounskaia, Wisleder, and Johnson (2005)
questioned the traditional interpretation of submovements. They suggested that secondary submovements are not homogeneous and that they can be related to different subtasks included in the pointing task. In addition to the obvious subtask of accurate target achievement that may require corrective submovements, motion termination was considered as another possible source of velocity fluctuations, i.e. submovements. Motion termination is a movement component that is necessary to perform in addition to motion deceleration to stop at the target. Indeed, during deceleration, the limb approaches the target with negative, distinct from zero, acceleration. However, acceleration needs to be nullified as soon as the target has been achieved. In other words, the arm needs to be arrested and stabilized at the target, which requires specific component of control, i.e. motion termination. The existence of the stabilizing component of control has been recognized in electromyographic studies in which the third phase of the tri-phasic pattern of muscle activity has been interpreted as responsible for limb stabilization (Berardelli et al. 1996
). Apparently, the limb stabilization may be accompanied with small fluctuations, specifically during fast movements that require high negative acceleration while approaching the target and quick reduction of this acceleration to zero when the target has been achieved.
The influence of motion termination on submovement emergence was examined by Dounskaia et al. (2005)
with use of movement mode manipulations. Submovement incidence (that characterizes the probability of emergence of secondary submovements) was compared between discrete and reciprocal pointing movements. The discrete mode required termination of motion at the target and dwelling in this position for a period of time. In other words, it required arresting and stabilizing the arm at the target. The reciprocal mode included motion to the target and immediate reversal back to the home position without dwelling on the target. In this mode, the stabilization of the arm at the target was not performed (Guiard, 1993
; Meulenbroek & Thomassen, 1993
; Meulenbroek et al., 1998
). Quantitatively, the difference between the two modes was that both velocity and acceleration were nullified at the target during discrete movements, whereby reciprocal movements involved nullification of velocity only, while acceleration remained non-zero during the reversal.
It was found that submovement incidence was higher during the discrete than reciprocal mode, supporting the influence of motion termination. Also, manipulations of target size were performed that resulted in the traditional observation that submovements emerge more frequently during movements to small than to large targets, suggesting that the accuracy regulation subtask also contributed to the submovement production. Furthermore, it was found that the two manipulations were associated with distinct submovement types. Submovements representing gross changes in the velocity profile (revealed as zero-crossings of the first and second motion derivative, i.e. velocity and acceleration) were responsive to the movement mode manipulations and not to changes in target size. In contrast, fine submovements (revealed as zero-crossings of the third derivative of displacement, jerk) were more frequent with decreases in target size, and their incidence was independent of movement mode. These results suggested that if any corrective adjustments of pointing accuracy were performed, they were limited predominantly to the fine submovements.
The finding that gross submovements are associated with motion termination was supported by Wisleder & Dounskaia (2007)
who compared submovement incidence between discrete and cyclic movements. In addition, a hypothesis was tested that fine submovements are related to low movement speed rather than small target size, and that more frequent emergence of them with decreases in target size is a result of the speed-accuracy tradeoff (Fitts, 1954
). Support for this possibility was obtained by examining cyclic movements at two distinct frequency levels. It was found that incidence of fine submovements increased with decreases in movement frequency, and it was independent of target size. Nevertheless, when cyclic frequency was self-paced, correlation of incidence of fine submovements with movement duration was rather low. Thus, the validity of the traditional interpretation in application to fine submovements remained uncertain and requires additional investigations.
The purpose of the present study is to contribute to the revision of the traditional submovement interpretation by examining possible sources of submovements. This is achieved by testing three movement modes. In addition to the discrete mode that requires motion termination at the target and reciprocal mode during which motion is reversed at the target without a dwell period, and hence, without motion termination, a passing mode is included in the present experiment. The passing mode requires crossing the target and terminating motion after that. Thus, it includes both subtasks, motion termination and accuracy regulation. However, in contrast to the discrete mode during which the two subtasks are performed simultaneously while approaching the target, they are performed separately from each other during passing movements. Accuracy regulation is performed prior to the target passing, and the remaining movement portion includes only the motion termination subtask. To isolate submovements not related to accuracy regulation, submovements will be analyzed in the passing mode only after passing the target. The role of accuracy constraints will be further emphasized by using small and large targets. If the conclusion of the previous studies that gross submovements emerge due to motion termination is correct, these submovements will appear in the discrete and passing mode and not in the reciprocal mode, and there will be no increase in their incidence with decreases in target size. If fine submovements are corrective adjustments performed to accurately achieve the target, they will be observed during the discrete and reciprocal mode and not during the passing mode, and they will be more frequent during movements to small than large targets. However, if fine submovements are related to decreases in movement speed, they will be observed in all three modes but more frequently for small than large targets. Thus, the comparison of submovements among the three modes provides new means for examining the contribution of different factors to submovement production.