Fig 1.
The illustration of multiple sampled points in the current frame and the next frame.
The grey ball with the radius r0[i] denotes the search neighborhood of k-th marker for frame [i + 1] and the figure illustrates the case when the k-th marker in the next frame is within a given search neighborhood. The distance example dj,k[i + 1] is given for the two markers in frame [i + 1] where subscripts j and k denote the corresponding markers. The point O represents the coordinate origin for the camera system.
Fig 2.
Optical marker placement for tracking the rotating motor.
Multiple 7 mm light-weight passive markers were attached on the measurement plane (motor wheel) and rotating motions were tracked with 4 Qualisys 300 cameras. The reference marker on the rod was used to identify the reference marker R0 manually. Three marker spacing setups (A, B, C in the dotted squares) were used to give different marker spacing cases.
Fig 3.
Tangential speeds of R0 marker for setup A with increasing frame rates.
Frame rates were: (a) 20 Hz, (b) 40 Hz, (c) 60 Hz, (d) 78 Hz. Since 78 Hz is above the required frame rate for setup A, the full speed rotation was tracked throughout the whole 10 seconds recording in (d), but others showed termination during the recordings.
Fig 4.
Comparison of trajectories for the successful tracking sessions and failing sessions.
From the top, the measurement conditions were (a) 77 Hz, setup A, (b) 78 Hz, setup A, (c) 99 Hz, setup B, (d) 100 Hz, setup B, (e) 162 Hz, setup C, and (f) 163 Hz, setup C. For the frame rates below the selected fN values, trajectories were truncated before reaching the full speed rotation.
Table 1.
Observation results for Experiment 1 and Experiment 2.
Fig 5.
Relation of the minimum frame rate with minimum marker spacing.
A paired data (dmin/vmax, fN) is plotted for each marker spacing case and fitted to the inverse proportional curve: y = 1 / Kx. The dotted curve shows the least squared fit curve and K is 0.41. The region above the curve means the successful tracking region (fN > vmax/Kdmin) and region below denotes the tracking failure.
Fig 6.
Relation of the minimum frame rate and the maximum speed of markers.
Paired data set of frame rate to failing speed (fS, vfail) is plotted for each spacing case and fitted with linear least square curve. Lines show the least squared fit for three marker spacings and the ratio between slopes are close to the minimum marker spacings.