For the sake of its function in communication, handwriting should proceed efficiently, that is to say, at a reasonable speed and with a minimum of effort. Experimentation as well as the development of handwriting in most cultures have shown that these requirements are fulfilled best by keeping the writing instrument down on the writing surface as much as possible, so as to produce connected, ‘cursive’ script. The additional task constraints on the legible production of any particular cursive script, however, are more specific. For our Latin script these may be summarised as follows. The writer is expected to produce letters of approximately constant shape, slant and size, and to join these to form connected words progressing from left to right, following a straight horizontal baseline. After years of practice, a proficient writer can meet these requirements, although his or her effector system is built up of segments that can only produce curvilinear trajectories. Indeed, the biomechanical arm–hand–finger system has many degrees of freedom, and the skilled writer readily exploits its redundancy to achieve the demanding graphic task. The present paper addresses the question of how the degrees of freedom problem is solved, i.e., how the effector segments are coordinated, especially as a function of the left-to-right progression within words.

An illustration of the coordination problem is the following. When the wrist joint is adducted, the hand’s orientation in work space is different from when the joint is abducted. The fingers making the same movement with respect to the hand to which they are attached, will thus describe trajectories in different directions depending on the rotation of the wrist. Since handwriting requires invariant slant, the coordination of the wrist–finger system must be adapted somehow, either continuously or intermittently. And because the letters are expected to be on a straight baseline (instead of following the curved hand sector centred around the wrist joint), the coordination problem becomes even more complex.

Earlier studies concerning progressive handwriting have shown that the requirement of progression indeed adds considerable complexity to the task, especially for inexperienced writers, and that the trace and kinematics of handwriting are substantially altered when progression is introduced, manipulated visually, or controlled externally. Moreover, modelling handwriting in a relatively parsimonious manner has shown that certain common phenomena, like subtle slant and size changes with progression, may be due to the geometry of the hand rotating in the wrist.

In our recent research, we studied the co-activated involvement of wrist and fingers in terms of their joint-angle amplitudes per stroke when writing progresses rightward, within and between words, across the page. We found that stepwise adaptations – in the form of well defined discontinuities in the co-activation pattern – occur not only between words, where they are a universal pen-up phenomenon, but also frequently within words, while the pen point continues to move in the writing plane. The latter adaptations generally implied the adoption, later in the word, of a wider range of movement directions by the fingers, leading to increased wrist–finger co-activation. Another important finding was that, early in the word, the subjects tended to adopt a specific coordination pattern as a function of word length and word position.

When closely inspecting the spatial trace and the kinematics of long, cursively written long words, a striking feature in most cases is that there are several instances of imperfect constancy of the size, slope and width of the word’s loops, and even of shape distortions and jerks, and of jumps in the baseline. Furthermore, it appears that these irregularities do not occur completely at random, but tend to fluctuate at intervals of about 3 to 4 letters. It might be that these fluctuations somehow reflect the adaptation events that were observed in the previous study. The primary goal of the present research is to detect and analyse any such fluctuations in the coordination of hand and finger excursions by studying the phase relations between the involved joint excursions. As a secondary goal, our study attempts to contribute to the assessment of the suitability of the phase-relation approach to graphic tasks like handwriting. In order to establish the utility of our measures, and to gain further insight into the implied mechanisms, we chose to investigate the two independent variables that proved to be co-determinants of coordination in our previous study, namely word length and word position on the writing line.