Understanding how handwriting and drawing movements are performed requires knowledge of the constraints that are posed by movement planning processes at different levels in the motor hierarchy, as well as understanding how these constraints interact. For example, the way in which one holds a tool or an instrument like a pen in the case of drawing or handwriting, imposes a geometric constraint on the selection of joint configurations. Such a constraint is likely to have evolved with increasing experience in using the tool, in such a way that the task can be performed as comfortably as possible. On the other hand, in the case of handwriting or drawing, the choice for a specific way of holding the pen may have led to the establishment of preferences to move in certain directions rather than in others. Such preferences may constrain higher order processes, e.g., the selection of starting points in planning sequences of strokes. Besides these long-term effects of the geometry of the writing system, temporary changes in a person’s normal pen grip, for example by extending the pen tip further from the tips of the fingers, are likely to change the spatial characteristics of produced graphic output. Therefore, tasks like handwriting and drawing, which involve complex processes dealing with cognitive, dynamic and kinematic aspects of the movements, cannot be understood fully without regarding these processes in combination. In this context, the purpose of the present study is to gain insight into the constraints that pen grip and writing posture pose to the kinematics of drawing tasks. It will be argued that such constraints may, at least in part, be related to known stroke direction preferences.

For the purpose of this study a computational model of the 3D kinematics of the human writing hand was built. It recognizes the fact that handwriting and drawing are essentially 2D tasks performed in a 3D space. Until now, the writing arm has been modeled primarily as a 2D effector system moving in the horizontal writing plane. This may suit the purpose of these studies, but it implies that kinematic aspects related to the third dimension are ignored. As outlined above, these kinematics may have their bearings on other aspects of graphic production. For example, a 3D effector system wielding a pen will not by definition keep the pen tip in contact with the writing surface, as is the case with the 2D systems typically used for modeling handwriting movements. Therefore a 3D writing system will have to take care explicitly of maintaining contact between pen tip and writing surface. The requirement for a 3D effector system to deal with such additional task demands, as compared to a 2D system acting in the writing plane is, in turn, likely to interact with the way in which the pen tip is moved within the 2D writing plane.

Our model does not involve any assumptions regarding trajectory planning, neither in workspace coordinates, nor in joint coordinates. Consequently, the model does not function as a motor control model of graphic task performance. Within realistic ranges of motion and using realistic limb segment sizes, the model assumes that joint angles can be adopted independently of each other, thereby ignoring factors such as the existence of joint synergies due to polyarticular muscles. Rather than as a model of motor control, the model was built as a tool to analyze the geometric mapping of the hand and fingers’ joint space onto the workspace. It enables researchers to study this mapping under a variety of kinematic constraints, like the type of pen grip used, the joints that are free to move, or the sizes of limb segments.

With the model we ran simulations that allowed analyses of functional characteristics of the graphic workspace. The particular question we addressed was to what extent the size and shape of the graphic workspace or the spatial distribution of a certain effort function relates to preferences for movement directions, as well as how they vary with changing pen grip and writing posture.

The excursion sum of a posture is zero when all joints are in the middle of their ranges of motion, while it reaches a maximum when all joints are at one of their range-of-motion end-points. Thus, the distribution of these excursion sums tells us something about the amount of effort required to reach each part of the graphic workspace. The ?_i’s might be used to express the idea that, for example, changing the angle of, say, a finger joint costs less effort than changing the angle of, say, a wrist joint. In the present study, however, we only used values of 0 and 1 for the ?_i’s. Thus, a subset of joints could be selected of which all joints contributed to the same extent to the excursion-sum (?_i=1), while the remaining joints did not contribute at all (?_i=0). In this way, we abstracted from biomechanical differences between joints and focused on effort in a geometric, rather than kinetic or dynamic sense.