Flexibility of Motor Control 345reversal, but it can be close to zero at the upper movement re-
versal. In this case the frequency ratio becomes 1 : 1. This dif-
ference between horizontal and vertical movements disap-
pears under conditions of microgravity because of the
absence of gravitational load, and subjects adapt rapidly (dur-
ing parabolic flights) to produce the appropriate 1 : 2 ratio
also with vertical movements (Hermsdörfer et al., 2000).
Force adjustments are both predictive and reactive. This
basic principle is evident already from the everyday observa-
tion that when someone hands an object to someone else, the
latter can normally hold it without difficulties; only when the
object is unexpectedly light or heavy, short-lived difficulties
arise. Without knowing about the change of the mass of a
moved object, the first movement is perturbed, but the next
movement is properly adjusted to the new load (Bock, 1993).
In fact, corrections for the unexpected mass set in as early as
during the first movement, which, in the case of an unexpect-
edly high load, results mainly in a prolonged movement du-
ration (Bock, 1993; Smeets, Erkelens, & Denier van der Gon,
1995). It seems that under conditions of microgravity, when
objects are weightless but nevertheless have normal mass and
thus inertial load, movements exhibit characteristics of
movements with an unexpectedly high mass even for weeks
(Sangals, Heuer, Manzey, & Lorenz, 1999).
Motor commands for active movements are most likely
among the information that is involved in predictive force ad-
justments, as can be evidenced from the grip-force adjust-
ments while moving a hand-held object. Of course, this kind
of prediction can work only when force adjustments are re-
quired as a consequence of self-generated activity. When
force adjustments are required to accommodate variations in
load, which are independent of self-generated activity, pre-
dictions must rely on other kinds of information. Obviously,
proper force adjustments depend on experience; the first
movement after an unnoticed change of the load is performed
with an initially maladjusted force, but not the second one. In
addition, seen object size plays a role, although force adjust-
ment is not necessarily related to estimates of weight.
Gordon, Forssberg, Johansson, and Westling (1991) exam-
ined the lifting of boxes of identical weight but different
sizes. Although subjects judged the smaller boxes to be heav-
ier than the larger ones, peak grip and load forces were
stronger for the larger ones. However, this difference was
present only during lifting and disappeared during subse-
quent holding of the object, when force adjustments were
perhaps related to the actual weight and no longer to the vi-
sually mediated predictive mechanisms.
Adjustments to objects of different masses seem to be
comparatively simple achievements, similar to adjustments
to different visuo-motor gains. When the external forces
which act on a moving limb are transformed in a more
complex way, similarities between adjustments to modified
visuo-motor transformations and modified external force
fields become more conspicuous. Shadmehr and Mussa-
Ivaldi (1994) introduced such forces while the participants
moved a robot arm. For example, forces were proportional to
hand velocity and nearly orthogonal to the direction of hand
movement, so that initially the paths of the hand were
strongly curved. With continued experience the paths became
again approximately straight lines, which—as an aside—can
be taken as additional evidence for the claim that motor plan-
ning refers to end-effector kinematics. After removal of the
external forces there were negative aftereffects: The paths of
the hand were curved again, but in the opposite direction. The
aftereffects indicate that the adjustments were based on a new
internal model of the dynamic transformation.
Similar to the findings with modified visuo-motor trans-
formations, multiple internal models of dynamic transforma-
tions can be acquired (Shadmehr & Brashers-Krug, 1997).
Again there seems to be a labile period after a new model has
been learned, during which it will be unlearned when another
dynamic transformation is experienced, but after a period of
consolidation this is no longer the case. Once an internal
model has survived the labile period, it can be put to efficient
use even months later.
Adjustments to new dynamic transformations generalize
across different types of movement (Condit, Gandolfo, &
Mussa-Ivaldi, 1997) and also across the work space
(Shadmehr & Mussa-Ivaldi, 1994). When movements are
performed in a different region of the workspace from during
the practice period, external forces can remain invariant
either with respect to the movement of the end-effector in
coordinates of extrinsic space or with respect to the joint
movements. Generalizations across the work space turned
out to be approximate in joint coordinates. This is consistent
with a particularly intriguing parallel between adaptation to
shifted visual directions and additional external forces.
Prism adaptation involves modified relations between pro-
prioceptive and/or visual signals and their meaning in terms
of egocentric directions. Adaptation to a modified external
force field seems to involve a modified relation between mus-
cle activations (or motor commands) and the directions of
consequent movements (Shadmehr & Moussavi, 2000). For
example, the EMG signal from an elbow flexor can be plotted
as a function of movement direction (more precisely, it is the
EMG signal integrated across a certain time interval around
the start of the movement); this results in a directional tuning
curve of a muscle. Of course, the peak of this curve is shifted
when the shoulder joint is moved. However, there is also a
shift induced by the adaptation to a new force field, and this