318 Motor Control
FEMF 1 F 2(b)(a)Figure 12.1 (a) A joint with two opposing muscles, flexor (F) and extensor
(E); (b) mechanical analogue of two damped springs acting on a single mass
(M); the mass is stationary when the two opposing forces F 1 and F 2 cancel
each other. Reprinted with permission.
initially the knee is flexed, followed by extension. This for-
ward rotation of the shank results largely from passive forces
of different origins. The deceleration of the knee extension,
however, is largely a result of active muscular forces, with only
a small contribution of passive ones (Winter & Robertson,
1978). Thus, with the exception of a few very simple tasks, the
production of movement requires not only the generation of
appropriate active forces, but in addition passive forces have to
be taken into account.
Figure 12.1 illustrates a joint with two opposing muscles,
a kind of minimal movement device. Muscles are designated
as agonist and antagonist with respect to their function in a
particular movement. For example, when the movement is a
flexion of the joint, the flexor is the agonist and the extensor
is the antagonist; for an extension, the functional roles of
flexors and extensors are reversed. Of course, Figure 12.1 is
extremely simplified, both with respect to the mechanical
characteristics and with respect to the number of muscles act-
ing on the joint.
Muscles are complicated force generators. They contract
when they are activated via the motor nerves. Each axon of a
motor nerve innervates a smaller or larger bundle of muscle
fibers; the axon together with its muscle fibers is called a
motor unit. The activation can be recorded. Needle elec-
trodes, which are inserted in the muscle tissue, allow one to
record from single motor units, while surface electrodes pick
up averaged and filtered electrical activity of motor units
within a certain area below the electrodes. For isometric con-
tractions, there is a systematic relation between electromyo-
graphically recorded muscle activity (EMG) and force. In
particular, the relation between the integrated EMG signal
and force is linear (Lippold, 1952). However, for movements
for which phasic bursts of muscle activity are typical (at
least when the movements are rapid), the relation is more
complex.
Complications arise, first, from the temporal relations be-
tween bursts of muscle activity and forces, which can be
fairly variable. In general, forces develop only with a delay
when a muscle is activated, and after the end of the burst
there is a gradual decay. Complications arise also from
fatigue-induced changes, with fatigue being developed in
the course of repeated or prolonged activity. In addition, for
a given activation level, muscle force depends on the length
of the muscle and on the rate of its contraction. In particular,
the length-tension relation of muscle is important for models
of motor control: Muscle force increases with increasing
muscle length, and the slope becomes steeper the stronger
the activation of the muscle is (e.g., Rack & Westbury,
1969). Although the length-tension relation is not really lin-
ear, a linear approximation is useful, at least for certain
ranges of muscle length. Thus, one can think of a muscle
as being mechanically similar to a damped spring (cf. Fig-
ure 12.1).
A muscle can actively contract, but not stretch. (A rubber
band would perhaps be a better analogue than a spring.)
Therefore at least two opposing muscles are needed for a
simple joint. From Figure 12.1 it is apparent that, as the one
muscle contracts, the other one will be stretched. This implies
that, with given activations of the opposing muscles, the
force of the contracting muscles declines while that of the
stretched muscles increases. At a certain joint angle, and at a
certain relation between the lengths of the opposing muscles,
the forces developed by them will be equal, but in opposite
directions, and thus cancel each other. The net force is zero,
and the joint position at which this is the case is called the
equilibrium position. There is considerable evidence that
equilibrium positions are important for motor control
(cf. Kelso & Holt, 1980; Polit & Bizzi, 1979). In the simplest
version of a mass-spring model, movements come about sim-
ply by the specification of a new equilibrium position (e.g.,
Cooke, 1980), but experiments have revealed that the equi-
librium position shifts continuously and not stepwise (Bizzi,
Accornero, Chapple, & Hogan, 1984).
Movement results from the net force of opposing muscles
(and, of course, from passive forces). Thus, at first glance
there seems not to be much sense in cocontractions, in which
opposing muscles are active simultaneously. Nevertheless,
cocontractions can be observed in particular early during