fastest arm motions such as throwing a baseball, good pitchers release the ball at 37 m/s and accelerate their hands at more than 25 g. Motion bandwidths of normal arm movements are around 2 Hz (Neilson, 1972); the fastest hand motions including handwriting are at around 5-6 Hz (Brooks, 1990a, 1990b). In teleoperation, it is commonly presumed that 10 Hz is the maximum frequency of position commands from the human operator (Fischer et al., 1990).

If hand motion is being used to drive a telerobot or a dynamic simulation of an arm, then the general rule of thumb is that the sampling rate should be around 20 times the bandwidth (Franklin et al., 1990) in consideration of such factors as sensor noise. Taking 5 Hz as defining the frequency content of normal arm motion, then a sampling rate of roughly 100 Hz is called for. Andersson (1993) has proposed a virtual batting cage, in which a batter swings at virtual pitches shown through a head-mounted display (HMD). The bat must be tracked to simulate the hit (or miss). Andersson proposes that sampling rates of about 1 kHz are required to track such motions.

Latency requirements are determined by the psychophysical requirements of the application and are harder to define. For force feedback applications, the hand-tracking latencies must be very low, because the human arm is part of the control loop. For non-force-feedback applications, the hand-motion-to-visual-feedback lag can probably be much longer.

EYE TRACKING

Eye movements can be as fast as 600 deg/s. The smallest time constant for saccades is around 50 ms; the smallest saccades can be finished in 60 ms. The power spectral densities can have significant power up to 50 Hz for position and 74 Hz for velocity (Bahill et al., 1981). Given again the engineering rule of thumb that the sampling rate should be 20 times the bandwidth for noisy measurements, it has been recommended that eye movements be sampled at 1 kHz (Inchingolo and Spanio, 1985). This should allow sufficiently precise tracking of the eye trajectory to characterize the movement time and end-point. As mentioned in Durlach et al. (1992), the eye sees continuous images when display temporal frequency is 60 Hz and above. With 1 kHz sampling rates for eye movement, display targets can be well chosen every 1/60th of a second.

HEAD TRACKING

Head movements can be as fast as 1000 deg/s in yaw, although more usual peak velocities are about 600 deg/s for yaw and 300 deg/s for pitch and roll (Foxlin, 1993). The frequency content of volitional head motion



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