336 Motor Control
Figure 12.13 Equal-outcome curve for a particular dart-throwing task.
When the target is an area rather than a point, deviations from the curve are
permitted, so that it becomes an area in which initial velocity and flight angle
of successful throws must be located (after Müller, 2001).
deviates from 45°, provided that the height at which the ball
is released is also the height at which the target is located.
Conforming to these task constraints, Stimpel (1933) ob-
served positive correlations across series of throws to a cer-
tain target position between initial velocity and the absolute
deviation of the initial flight angle from 45°. It is not fully
clear how the particular covariation is established, but there
is the possibility that subjects produce equifinal trajectories
of the hand such that across time initial flight angle and ve-
locity covary in the proper way; thereby the proper relation is
established independent of the precise time at which the ball
is released (Müller & Loosch, 1999).
The plot of the relation between initial velocities and ini-
tial flight angles required for a certain outcome of the throws
can be thought of as an equal-outcome curve (Heuer, 1989).
Figure 12.13 gives an example for a particular dart-throwing
task, which also shows that with a target of a certain width,
deviations from the bull’s-eye-outcome curve have different
consequences for accuracy depending on where on the curve
subjects operate. In principle, equal-outcome curves can be
determined for all sorts of tasks and for various sets of com-
ponent variables. They specify how components of a skill
must be related to each other in the service of satisfying the
task constraints. In fact, this kind of analysis can become
considerably more complex than what can be represented in
terms of equal-outcome curves (or perhaps areas). An exam-
ple is the analysis of juggling by Beek (1989).
The very fact that components of a motor pattern covary in
the service of achieving particular outcomes has been taken as
evidence for the existence ofmovement Gestalts (Bewegungs-
gestalten)by Stimpel (1933) and his advisor Klemm (1938),
a notion that is analogous to perceptual Gestalts (see the chap-
ter by Palmer in this volume). The core of the notion of a
Bewegungsgestaltis the idea that the whole dominates its
components and is more precise than expected from the com-
ponents’ variabilities. Although these notions appear fairly
outdated now, it cannot be overlooked that they anticipate
synergetic concepts (Haken, 1982) that currently play an im-
portant role in the study of motor coordination (cf. Kelso,
1994; Schöner, 1994). One of the core concepts is that of an
order parameter (or collective variable) that enslaves the com-
ponent variables, so that higher level variables are not simply
the result of lower level variables, but dominate the lower
level variables instead. This general idea is captured by mod-
els like the task-dynamic model of Saltzman and Kelso (1987)
and the knowledge model of Rosenbaum, Loukopoulos,
Meulenbroek, Vaughan, and Engelbrecht (1995).
Coordination in the service of satisfying task constraints is
flexible: That is, patterns of covariation between certain ef-
fectors that can be observed when one task is performed may
be absent when a different task is performed (e.g., Kelso
et al., 1984). Nevertheless, for biologically important tasks
like standing, locomotion, eating, and so on, there may be
more rigid coordination patterns that not only support these
tasks, but may also impede performance of sufficiently dif-
ferent tasks. Although it is not certain that such more rigid
coordination patterns for biologically important tasks are in-
deed the origin of structural constraints on coordination, it is
certain that structural constraints do exist. Basically, they
limit the range of task-specific coordination patterns; while
they support the production of certain patterns, they tend to
impede the production of deviating patterns.
Structural constraints support symmetrical movements of
the two arms. Thus, mirror writing with the left hand be-
comes a fairly simple task when it is performed concurrently
with normal writing of the right hand (Jung & Fach, 1984).
The other side of the coin is the difficulty we encounter
when we attempt to produce different spatiotemporal patterns
concurrently with the two hands. Although it is certainly not
true that both hands are constrained to act as a unit in the
sense of having a common timing (Kelso, Southard, & Good-
man, 1979; Schmidt et al., 1979), bimanual movements tend
toward identical durations, and only with strictly required
different target durations can this tendency be overcome
(Spijkers, Tachmatzidis, Debus, Fischer, & Kausche, 1994).
Other deviations from strict symmetry are easier to achieve,
but nevertheless there is a widespread tendency for dif-
ferent movements with the two hands not to be as different
as they should be; the systematic errors here point to the
symmetric patterns that are the ones supported by structural
constraints.