3.1.1 A Preliminary Analysis
This chapter explores the differences between a 6 DOF elastic
rate controller and a 6 DOF isometric rate controller. Since both
isometric and elastic devices are self-centred, they both should
be compatible with rate control, in light of the analysis and
experimental results in the preceding chapter. The difference
between the two is that the elastic device allows a certain extent
of movement. Is the movement in an elastic device an advantage
comparing to pure isometric (stiff) device? Do isometric and elastic
devices afford a different "control feel" (Burrows,
1965) ? It is clear (by definition) that the only control feel
the human gets from an isometric device is force resistance. Also
by definition, the user feels both force resistance and the displacement
proportional to the force from an elastic device. The two variables
(force and displacement) in an elastic controller co-vary (or
even linearly co-vary if the springs used follow Hooke's law).
This could imply that an elastic device gives a richer control
feel than an isometric device, since the elastic device gives
the same information in more than one form (force and displacement).
3.1.2 The Controversy Surrounding Isometric Versus Elastic Devices
Researchers have not had much agreement on the preceding hypothesis. Poulton, for example, firmly believes in the advantage of elastic devices: "Spring centring is the best kind of control loading", "... the man feels a pressure which is proportional to the distance of the control from its centre. The pressure cue augments the usual position cue, and help the man track more accurately" (Poulton, 1974, page 306). In practice, most commercial 2 DOF joysticks are elastic, but we do not know whether they have been constructed that way due to human performance considerations or due to manufacturing cost considerations. For the purpose of developing 6 DOF hand controller for teleoperation, McKinnon, King, and Runnings (1987) suggested that the controller should involve some displacement. They stated that pure isometric controllers may cause instabilities and over control, but this was concluded solely from their anecdotal observations; no formal study was reported.
Other researchers, such as Gibbs and Notterman, strongly believe in the advantages of isometric devices over elastic devices. As discussed in section 2.2, Gibbs (1954) argued that "the discharge in some primary endings is considerably boosted in isometric conditions". Notterman further argued "When using the spring-loaded control, subjects had to learn to use feedback from the linearly related, theta-proportional reactive forces determined by Hooke's law, conjointly with movement cues and centrally stored information". In other words, Notterman considered the redundancy in elastic devices a burden to the human information processing system.
The literature review in the previous Chapter (section 2.2) has
examined many aspects of isometric devices in relation to isotonic
devices. Many of the studies reviewed there remain relevant to
the comparison of isometric and elastic devices. The following
subsections review issues related to isometric and elastic devices
in more depth, with emphasis on empirical studies on force versus
movement as proprioceptive cues.
3.1.3 Studies on Control Accuracy as a Function of Force and Movement and as a Function of Control Loading
Weiss (1954) reported a study on a positioning task without immediate visual feedback of cursor position (i.e. open-loop positioning). In one set of conditions, Weiss varied the maximum angular displacement of an elastic control stick from 3_ to 30_ while keeping the same pressure range from 1 to 30 lb. In another set of conditions the maximum pressure was varied from 0 to 30 lb while keeping the same movement range (30_). He found that the relative positioning error and its variability decreased with the extent of movement but pressure variation had no effect on accuracy. He thus concluded that movement was the more crucial dimension than force in proprioceptive feedback. Unfortunately Weiss' study did not include a pure isometric condition for comparison.
Results contrary to Weiss' (1954) were reported by Bahrick, Bennett, and Fitts (1955) . Bahrick and colleagues studied the accuracy of blindfolded subjects in positioning a 1 DOF horizontal rotary arm control as a function of spring loading. Subjects made rotary movements of 17.5_, 35_, and 70_ with various starting torque and terminal torque conditions. They found that subjects had smaller relative errors when (a) amplitude of movement was larger, (b) terminal torque was larger, and (c) relative torque change per unit movement was larger. The positioning errors were smallest when the ratio of relative torque change to displacement was largest. In conclusion, Bahrick et al found that force could provide useful cues in movement control. This was contrary to Weiss' finding.
Briggs, Fitts, and Bahrick (1957) studied a compensatory tracking task of simulated aircraft dynamics (comprising simple integrators), with an elastic stick. Two levels of force and two levels of amplitude were tested in an experiment, with Time on Target (TOT) as performance measure. They found that "both force and amplitude (of movement) cues significantly affected performance, amplitude cues apparently exerting the greater influence". The best TOT measure was obtained with both sources at the largest extent. As with Weiss' study, a pure isometric condition was not tested by Briggs et al. (1957) .
Notterman and Tufano (1980) did include both isometric and elastic conditions in a tracking task in position control mode. They found that the elastic controller was better than the isometric device in tracking predictable target motion and that the isometric device was better than the elastic device in tracking unpredictable target motion but these findings were true only in early learning stages.
Howland and Noble (1953) comparatively studied controls with no
loading (isotonic), elastic loading, viscous loading, inertial
loading and various combinations of them. No isometric controls
were included in their study. Subjects were asked to track a horizontally
moving bar driven by a 15 cycle per minute harmonic signal in
position control mode. Ranked by percentage of time-on-target
(TOT), subjects' performance with various loadings in decreasing
order of TOT were: (1) elastic only, (2) elastic and viscous,
(3) viscous only, (4) no loading (isotonic), (5) inertial only,
viscous and inertial, elastic and viscous and inertial (not much
difference among these three), (6) elastic and inertial. Howland
and Noble attributed the superior performance with the elastic
loading to two factors. (a) The elastic loading aids the reversals
needed in harmonic movement. In other words, subjects may utilise
the device dynamics in generating movement that coincides with
the target signal (We return to this point in 3.1.5). (b) The
feel of control handle position is augmented with elastic loading
and therefore the "kinaesthetic stimulation" is enhanced.
This study is often cited in the literature on the effect of control
loading. It should be noted, however, that the control handle
in the study was rotary and the advantage of natural mapping in
isotonic controls might not be well taken in rotary controls.
However, the key conclusion that elastic controls augment position
sense is agreed upon by many other researchers.
3.1.4 Psychophysical Findings on Force and Movement JND
Some psychophysical experiments have been conducted recently on
human (finger) sensitivity in discriminating length and force.
Durlach, Delhorne, Wong, Ko, Ranbinowitz, and Hollerbach (1989)
and Tan, Pang, and Durlach (1992) found that human discrimination
of length did not follow Weber's law. The just noticeable difference
(JND) was 8.1% for a reference length of 10 mm, 4.6% for 40 mm
and 2.8% for 80 mm. In comparison, Pang, Tan, and Durlach (1991)
and Tan et al. (1992) found that force JND did follow Weber's
law. The average force JND was around 7-8%, independent of reference
force. It appeared that human sensitivity to force is lower than
sensitivity to length, particularly for large ranges of length
(>10 mm) or force (>2.5 Newton). For smaller ranges of force
(<2.5 Newton) or length ( <10 mm), the JNDs are about the
same (See Figure 3 and 4 in Tan, et al. (1992) ). One has to be
cautious in applying these psychophysical studies to input control
device design, however, since in these studies, the force JNDs
were not obtained with isometric force.
3.1.5 Time Related Effects of Control Loading
When performing manual control tasks, the process is not static. The dynamic aspects of the task can not be overlooked, especially in rate control. It has been found that control loading can also affect human judgement of dynamic properties of control tasks.
Adams and Creamer (1962) made the distinction between regulatory proprioceptive stimulation (RPS) and anticipatory proprioceptive stimulation (APS). RPS refers to the functions that proprioceptive feedback has on aiding users in judging their control actions (as reviewed in section 3.1.3). In addition to RPS, Adams and Creamer hypothesised that proprioceptive feedback might also have the properties of aiding users in anticipating the timing of their motor response (e.g. positioning a carriage along a trackway in 2.0 sec). Researchers found that control loading such as elastic springs indeed improve subjectsÌ accuracy in estimating elapsed time. (Adams and Creamer, 1962; Ellis, Schmidt, and Wade, 1968; and Ellis, 1969) . This is in agreement with TreismanÌs suggestion that subjects estimate time by ÏcountingÓ external stimuli (Treisman, 1963).
The notion that the human may dynamically make use of proprioceptive
cues provided by a control device is further demonstrated in Pew,
Duffendack, and Fensch (1967) . Pew and colleagues studied sine
wave tracking with elastic controls in position control mode at
various frequencies. With extended practice, subjects' performance
was disproportionately better at certain critical frequencies.
Furthermore, it was found that these critical frequencies changed
with the elastic stiffness. This means that the subjects learned
to use the natural resonant frequency of the arm-stick combination
to match the frequency of the target movement being tracked.
3.1.6 The Neurophysiological Sources of Proprioception
Since proprioceptive feedback is one of the key issues in the debate on isometric versus elastic controllers, a brief review of the basic literature on the mechanism of proprioception (or kinaesthesia) is provided here. For details of the basic science of proprioception, the reader is suggested to consult McCloskey (1978) , Roland (1978) , Clark and Horch (1986) or Matthews (1981) .
Neurophysiological research has found that a multiplicity of somatosensory receptors (mechanoreceptors) can be involved in providing information to the central nervous system (CNS) (Sage, 1977; Schmidt, 1988; Gandevia and Burke, 1992) . Each type of receptor has its unique functions. The CNS integrates signals from these different types of receptors, producing an ensemble of somatosensory information.
Joint receptors In early research, joint receptors were considered the most important source of proprioception. It was hypothesised that different groups of receptors at the same joint were tuned to particular joint angles; as a joint moved from one angle to another, different populations of receptors on the joint would be fired, much like how a mechanical-optical encoder works. Today's view, however, is that joint receptors are sensitive only when a joint approaches one of the limits of its range (Clark and Horch 1986) . As Matthews (1988) put it "Thirty years ago things looked relatively simple. The joint receptors were in, and everything else was out. ...This simplicity has now vanished; joint receptors are largely out and muscle receptors are in".
Muscle spindles Muscle spindles are currently considered the major source of proprioception (Matthews, 1981, 1988) . They are believed to be sensitive to both tension and movement, but more so to movement. Many studies suggest that "The muscle spindle receptors appear quite capable of encoding muscle length" (Clark and Horch, 1986) .
Golgi tendon organs According to early thinking, Golgi tendon organs were considered inaccurate protective measures, that is, they would signal only whenever the muscles approach their safe operation limits (Schmidt, 1988) . Recent work, however, has found that they are actually very sensitive, but only to active tension, not passive tension (Jami, 1992) . In fact they are considered as the major sensors of tension, although muscle spindles are also sensitive to tension. "Tendon organs, by nature of their response properties, appear the most likely candidates to signal forces" (Clark and Horch, 1986, page 13-55).
Cutaneous receptors The bending of joints will stretch some regions of skin around the joints and relax others, causing the receptors in the skin to provide signals with regard to the position and movement. Experimental studies do not generally find an important role for cutaneous receptors in signalling positions, however, due to their slowly adapting nature. Anaesthesia of the skin around the knee joint had no effect on knee positioning, for example (Clark and Horch, 1986) . However, this was not true of finger joints. The skin of the fingers might play a special role in proprioception (Clark and Horch, 1986).
In light of above review, we can surmise what types of proprioceptors
are approximately involved with each type of control devices.
For example, when manipulating an isometric device, involving
no movement and only tension, Golgi tendon organs should be the
major source for proprioceptive feedback, although muscle spindles
may also contribute to a lesser extent. With an isotonic device,
where movement is involved but not tension, joint receptors, muscle
spindles and cutaneous receptors in the skin around the joints
might contribute to proprioception in varying degrees. When using
an elastic device, on the other hand, both movement and tension
are involved, and therefore joint receptors, muscle spindles and
cutaneous receptors in the skin around the joints and Golgi tendon
organs all may contribute to the proprioception of hand action.
Collectively these hypotheses suggest, therefore, that all other
factors being equal, an elastic controller should elicit response
from more proprioceptors than any other class of device, because
it allows movement while providing force feedback through the
elastic elements.
3.1.7 The Role of Proprioception in Motor Control
Thus far we have reviewed issues related to proprioception in order to understand the difference between isometric controls and elastic controls. However, we have not addressed the question of how important proprioception is in motor control tasks in general. That is, to what extent does motor control rely on peripheral feedback, or can most tasks be performed in an open-loop fashion with commands originating centrally only?
Motor behaviour accompanying our daily activities involves very
complex coordination and regulation of joints and muscles, with
a great number of degrees of freedom. Each hand alone has 17 active
joints and 23 degrees of freedom, excluding another 6 degrees
of freedom of the free motion of the palm. How such a complex
system is controlled has interested many psychologists, physiologists,
physical educators and human factors specialists. In general,
two opposing views have been taken towards issues in motor control
and have been the subject of a long-standing debate in the psychomotor
literature (See Schmidt, 1988; Stelmach, 1979; and Singer, 1980
for general overviews). The centralist view emphasises the dominance
of centrally stored motor programs and posits that human motor
control comprises mainly open-loop behaviours. In contrast, the
peripheralist theory stresses the importance of information feedback
and posits that human motor control comprises mainly closed-loop
behaviours. Both camps have found abundant evidence in support
of their theories. The centralists have found cases which show
that precise movement can be produced after deafferentation, either
surgically with animals or accidentally with humans. Centralists
also argue that proprioception is too slow for useful movement
control. The peripheralists, on the other hand, have found much
empirical counter-evidence to support their arguments against
the centralist view. Although the debate is likely to continue,
many other researchers suggest that the human motor control system
actually operates under both modes, and that the role of feedback
is a positive one in any case, even if central control is paramount.
3.1.8 Summary of the Reviews on Isometric and Elastic Devices
The foregoing reviews, as well as the related ones in section 2.2 on isometric and isotonic devices, are by no means complete and exhaustive. Two facts are nonetheless apparent: (1) The human performance differences between isometric and elastic devices are a function of multiple factors and to understand these is much more complicated than one might expect. (2) The literature is controversial and definitive conclusions can not easily be drawn. Nevertheless, the analysis of the literature reveals the following major points.
1. Both isometric and elastic devices are self-centring and therefore compatible with rate control, in light of the results in Chapter 2.
2. By definition, isometric devices operate on force alone while elastic devices involve both force and movement that are proportionally related.
3. Some researchers believe in the overall superiority of elastic devices (e.g. Poulton). Others (e.g. Gibbs, Notterman) consider isometric devices superior.
4. Human control accuracy increases with the amplitude of both movement and force, as evident in Bahrick et al (1955) and Briggs et al (1957) . Weiss (1954), however, found that only movement contributes to control accuracy .
5. Displacement JND is smaller than force JND, that is, we are better able to perceive relative changes in position than changes in force.
6. Proprioception, as introduced by different types of control loading (e.g. elastic), may not only improve static control performance (accuracy) but also may improve dynamic aspects of control performance.
7. There are multiple neurophysiological sources of proprioception, some of which respond to force stimuli and others to movement stimuli. Elastic devices may elicit activation of more sources of proprioception.
8. Points 4 - 7 collectively suggest that elastic devices might
be superior to isometric devices due to potentially richer proprioceptive
feedback, however, the general role of proprioception in motor
tasks is controversial. Different schools of thoughts put different
degrees of emphasis on its importance in motor control.
3.1.9 A Two-Factor Theory
Based on the above review, this section proposes a two-factor theory for understanding the difference between isometric rate control and elastic rate control. In contrast to isotonic or isometric devices which have fixed resistance (either zero or infinite), the resistance of elastic devices ranges between zero and infinity, depending on the stiffness of the elasticity. In light of the compatibility principle proposed in the previous chapter, a controller has to be self-centred in order to facilitate rate control processes. This self-centring effect decreases as the stiffness of the device decreases. When the elastic stiffness reaches zero, the elastic controller becomes a freely moving, isotonic controller without any self-centring effect. When the stiffness is infinite, on the other hand, the elastic controller becomes a non-moving, isometric device which has the strongest self-centring effect. In short, in order to maintain compatibility for rate control, the optimal stiffness for an elastic controller should be close to the infinite stiffness of an isometric device.
In light of the analysis of proprioceptive feedback, on the other hand, a greater extent of displacement may allow the human operator to have more accurate perception of her control actions. For this reason, an elastic device should have a relatively low elastic stiffness to allow a greater extent of movement with the same range of force.
Apparently, these two factors, compatibility and feedback, dictate
conflicting requirements for the magnitude of the elasticity.
An optimal design will thus be a result of a trade-off between
these two factors. It should be stiff enough so as to be compatible
with rate control but loose enough to allow accurate proprioceptive
feedback.