It is difficult to compare the current study with previous ones in the literature, since earlier studies of this kind have all been done in 1 or 2 DOF, instead of for 6 DOF tasks. One also has to be cautious about the validity of generalising the results of experiments on input control, including the present one, since they are usually carried out with specific devices and for one specific task. Nonetheless, this section summarises the results from this experiment and relates them to the previous literature.
The experiment has largely confirmed the hypotheses laid out in
section 2.4. The strongest conclusion we can draw from the data
is the interaction between device resistance and transfer function.
The isotonic device performed better than the isometric device
in position control mode. This ranking of isometric and isotonic
devices was reversed in rate control. Hence, we draw the following
conclusion:
Conclusion 2.1. The compatibility principle in input technique design: for certain types of physical devices, the transfer function has to be designed accordingly. In particular, for isometric devices, rate control is more compatible. For isotonic devices, position control is more compatible.
Some of the controversy in the literature can be explained in part by the interaction pattern found in this study. Taking Gibbs' studies as an example, Gibbs (1954) strongly advocated the superiority of isometric control, which produced consistently smaller tracking errors than did isotonic control across tests spanning 6 days (15 minutes each day). In that study rate control was used as the transfer function in both isotonic and isometric conditions. Eleven years later, Burke and Gibbs (1965) repeated Gibbs' (1954) experiment in position control mode. They made the conclusion that the isometric device was still better than the isotonic device even in position control mode. However, this later conclusion was not as strong as the original conclusion with respect to rate control mode made in (Gibbs 1954) . As the authors claimed, "the relative superiority of pressure control was approximately 10 per cent in the present (position control ) study, as compared with values of approximately 25 per cent to 50 per cent established by Gibbs (1954) (rate control)".
In checking the details of Burke and Gibbs (1965) , it is questionable whether the conclusion of 10 per cent was reliable. Burke and Gibbs (1965) had a within-subjects design with two groups of 5 subjects. Group A tested with an isotonic stick in the first five days (15 to 30 trials per day) and Group B tested with an isometric stick in the first five days. Tracking errors with Group A (with isotonic position) were consistently smaller than Group B (with isometric position) in the five days. On day 6, the two groups switched devices and Group A (now with the isometric device) had better performance. On Day 10, the two groups once again switched devices and this time Group A (now with isotonic device again) had smaller tracking errors. Judging from their plot (Figure 3 in Burke and Gibbs, 1965), had the authors counted the performance difference only in last day, or the means of each device across all days, the isotonic device would have "won". However, the authors decided to draw their conclusion only from the data across Day 9 and Day 10, which supported their hypothesis of isometric superiority, even in position control mode.
Taking Lincoln (1953) as another example, the work is a classic study in demonstrating that position control is better than rate control, as cited in Poulton (1974) . But in reviewing the study with the interaction pattern in mind, it is found that Lincoln used only an isotonic controller in his experiment. With that controller, position control was substantially better than rate control. Clearly, these results might have been different had an isometric controller been used.
The interaction between device resistance and transfer function can also be found by examining the list of experiments reviewed in Poulton (1974, Table 15.3, page 308-309). Eight experiments on the list used rate control, and all supported isometric superiority. Of the two experiments that used position control, one made no conclusion, and one, which was Burke and Gibbs (1965) , questionably supported isometric superiority. Poulton also surmised that Burke and Gibbs (1965) should have supported isotonic superiority, but from his methodological asymmetrical skill transfer point of view, rather than from the present interaction point of view.
The interaction pattern can also be seen in the data from Kim et al. (1987) . In rate control mode, the isometric joystick performed much better than the isotonic joystick. In position control mode, the isometric joystick performed only slightly worse than the isotonic joystick. Unfortunately one can not draw a firm conclusion from their data, since only two subjects were tested.
There are also exceptions to the interaction pattern found in the current study. For example, Dunbar, et al. (1983) found that an isometric 3 DOF controller produced lower RMS errors than an isotonic controller, even when position control mode was used.
The differences between the two compatible modes in this study,
namely the isotonic position control and the isometric rate control,
can be summarised as follows.
Conclusion 2.2 Isotonic position control is more intuitive than isometric rate control
Isotonic position control is intuitive and therefore imposes lower
mental load on the user. The user can form control actions more
directly with position control than with rate control and therefore
it is easier to learn. However, the advantage of isotonic position
control due to intuitiveness, in comparison with isometric rate
control, decreases as practice progresses.
Conclusion 2.3. Isotonic position control is more fatiguing than isometric rate control
It is difficult to provide support to the usersÌ hand without
changing the characteristics of 6 DOF isotonic position control.
Prolonged (in tens of minutes) unsupported hand movement is bound
to causes some fatigue. In contrast, isometric rate control does
not move, so the user can rest her hand on a support stand (or
desktop).
Conclusion 2.4. Isometric rate control produces smoother control trajectories.
By definition, with rate control the user has control of the velocity of the controlled object. Since the integrator in the rate control transfer function has a low pass filtering effect, the trajectories generated by isometric rate control therefore tend to be smoother than trajectories generated by isotonic position control. In many applications, this is particularly important. For instance, when controlling the entire graphics world, or moving the virtual camera in 3D graphics, we need the control motion to be as smooth as possible. Many VR demos suffer from jerky motion on displays, as a result of the combination of low update rate, noise and position control. Smooth motion is also important in telerobotic tasks.
Another advantage related to rate control is the fact that control motions are not restricted by hand anatomy. The user can perform an unlimited range of 6 DOF motions with rate control. With position control, some motions are limited by the hand joint angles, even though this can be partially solved by indexing (clutching).
Given the desirability of rate control in many respects, it is
therefore important to look into ways of improving isometric rate
control. As discussed earlier, the key to rate control is the
self centring effect in isometric control. In the following chapter
we compare performance of the same isometric rate control device
with another device that is self-centring: a device which provides
elastic resistance feedback.