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standing on leg movement time
International Journal of Industrial Ergonomics 47 (2015) 30e36
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International Journal of Industrial Ergonomics journal homepage: www.elsevier.com/locate/ergon
Effect of movement direction and sitting/standing on leg movement time Alan H.S. Chan*, Errol R. Hoffmann Department of Systems Engineering and Engineering Management, City University of Hong Kong, Kowloon Tong, Hong Kong
a r t i c l e i n f o
a b s t r a c t
Article history: Received 10 October 2014 Received in revised form 2 February 2015 Accepted 15 February 2015 Available online 9 March 2015
Data on leg movement times are summarised and it is noted that there is a need for more consistent data gathering. Experiments are reported for movements made either ballistically or with ongoing visual control, along with participants standing or sitting with leg movements made both in the sagittal and frontal planes. These conditions fulfil all commonly used foot-control situations. Regression equations are given for the movement times for each of these tasks. It is found that a modified form of Fitts' law is required to model the times for movements made with visual control, having an additional term in which movement time increases with increase of movement amplitude. Movements without ongoing visual control had movement times that increased linearly with movement amplitude. Relevance to industry: Many devices require control by the foot as well as the hands. We provide detailed information on the times for foot movements as dependent on the form of movement, posture of the operator and the direction of leg movement. © 2015 Elsevier B.V. All rights reserved.
Keywords: Leg movement times Fitts' law Movement direction Movement posture
1. Introduction Increasingly, the foot/leg system is being used in human/machine applications, particularly in applications where the hands are already heavily occupied (Chan and Chan, 2009, 2010; Bullinger et al., 1991; Pannetier and Wang, 2014). The use of leg often occurs when there is no possibility for ongoing visual control, such as when movements are made between the accelerator and brake pedal of an automobile (Hoffmann, 1991a). Under those circumstances, the movements are likely to be made in a ‘ballistic’ manner, where the movement is initiated and completed without correction to the path taken and final accuracy is not critical. Under other circumstances where final accuracy of a movement is required, as may occur in surgical applications (Van Veelen et al., 2003) or in foot mouse control (Springer and Siebes, 1996) it is necessary to use movements with ongoing visual control. There have been a number of studies of leg/foot movement times that have included movements made with ongoing visual control and movements that are pre-planned and are completed without modification (hereafter referred to as ballistic). These studies are listed in Table 1. Experiments are listed as ‘ballistic’ or
* Corresponding author. E-mail address: [email protected] (A.H.S. Chan). http://dx.doi.org/10.1016/j.ergon.2015.02.003 0169-8141/© 2015 Elsevier B.V. All rights reserved.
‘visually-controlled’ according to the criterion established by Gan and Hoffmann (1988) where it was shown that, below an Index of Difficulty of about three (Fitts, 1954; Fitts and Peterson, 1964) the movements may be made ballistically, whereas above this value, it is necessary to use ongoing visual control. Inspection of the experiments listed in Table 1 indicates a variety of forms of movement (discrete, sequential and reciprocal) along with movements made either ballistically or with ongoing visual control. As well, movements were made in the forward or lateral directions with seated or standing participants. The important feature is that there is not a single consistent set of data for the important industrial situations where the operator is either seated or standing, is making foot movements forward or laterally and the movements are made with and without ongoing visual control. As the data of Table 1 were gathered for different purposes (such as moving the foot from an accelerator to brake pedal and in walking) and by different methods (discrete and reciprocal movements), it was considered that a set of data using the same participants for all experiments and with better controlled conditions would be desirable. This is particularly the case as an attempt has recently been made to provide standardised foot movement times in a code for foot movement inputs (Park and Myung, 2012a). A modification of Fitts' Index of Difficulty (ID) may be necessary when correlating data of foot movement times due to the width of the shoe increasing the available target width. It has been shown
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Table 1 Summary of past experiments on foot/leg movement times. Mt ¼ movement time (ms); A ¼ amplitude of movement (mm); W ¼ target width (mm); ID ¼ Fitts' Index of Difficulty. Authors
Expt no. Posture
Drury (1975) Hoffmann (1991a) Hoffmann (1991b) Park and Myung (2012b) Chan and Ng 2008 Chan and Ng (2008) Hoffmann (1991b) Hoffmann (1991b) Chan et al. (2010) Drury and Woolley (1995) Drury and Woolley (1995)
3
1 2 2 3
Seated Seated Seated Seated Seated Standing Seated Seated Seated Standing Walking
Type of move
Movement Amplitudes direction (mm)
Target widths ID range mm
Ballistic Reciprocal Ballistic Discrete Ballistic Discrete Ballistic Discrete Ballistic Reciprocal Ballistic Reciprocal Visual Discrete Visual Discrete Visual Reciprocal Visual Reciprocal Visual Sequential
Lateral Lateral Lateral Angular Lateral Lateral Lateral Lateral Lateral Forward Forward
51,25 NA NA 40 NA 60, 80, 100 25 5, 10, 20 60 19, 38, 78 19, 38, 78
153, 230, 306 140, 190, 240,290 50, 119, 216, 344, 500 89,172,253 100, 300, 500 100, 300, 500 50, 100, 200, 400, 700 20 ¼> 640 60 ¼> 679 229, 457, 686 229, 457, 686
that the available ID is given in previous researches (Drury and Hoffmann, 1992; Hoffmann and Sheikh, 1991; Hoffmann, 1995),
IDavail ¼ log2 ½2A=ðW þ kFÞ
(1)
Here the available target width is given by (W þ k F); W is the set target width, F is the shoe width and k is a factor that may vary from about .6 to 1.0 (the proportion of shoe width adding to the available target width). When IDavail is greater than about three, Fitts law applies to the movements and the time for the moment is given by
MT ¼ a þ b IDavail
(2)
where MT is the movement time and a,b are empirically determined constants. When the IDavail value is small (less than about three), Gan and Hoffmann (1988) found that, for hand movements, the movement time was given by an expression in which MT was linear with the square-root of movement distance. However, the data of Table 1 indicate that several data sets (Chan and Ng, 2008) have a better fit when the MT is regressed with the amplitude of movement. In this work, both models will be evaluated.
MT ¼ c þ d
pffiffiffi A
MT ¼ e þ f A
(3a) (3b)
As noted above, previous data sets do not provide a full consistent set of data for the various practical situations of operator posture (sitting/standing), direction of foot movement (forward or laterally) and form of movement (ballistic or with ongoing visual control). Thus experiments were designed to model foot/leg movement times for these eight combinations of conditions as a basis for a code for movement times, as attempted by Park and Myung (2012a,b). 2. Method Two experiments were performed by each participant: ballistic movements and movements requiring the use of ongoing visual control. The two experiments were done on different days, with half the participants performing the ballistic experiment first and the other half starting with the visually-controlled experiment. In each experiment, the targets were placed horizontally on the floor. In the case of ballistic movements, the target widths were designed so that the ID values (Equation (1)) were less than three and hence the effects of target width should be unimportant (Gan and
NA NA NA NA NA NA 2, 3, 4, 5, 5.8 3, 4, 5, 6 1, 1.5, 2, ¼> 4.5 2.6 ¼> 6.2 2.6 ¼> 6.2
Regression pffiffiffi MT ¼ 107 þ 11:2 A pffiffiffi MT ¼ 19:2 þ 12:13 pffiffiffi A MT ¼ 107:5 þ 6:5pffiffiffi A MT ¼ 252 þ 16:3 A MT ¼ 587 þ 1:14A MT ¼ 711 þ :78A 2:76W MT ¼ 81 þ 178ðIDÞ MT ¼ 58 þ 115ðIDÞ 35 log2 ðWÞ MT ¼ 105 þ 255ðIDÞ MT ¼ 74 þ 173ðIDÞ Toe:MT ¼ 192 þ 72:6ðIDÞ Heel: MT ¼ 91 þ 59:2ðIDÞ
Hoffmann, 1988). A copper probe attached to the shoe of the participant allowed measurement of movement time: loss of contact with the home plate started an electronic timer, while contact with the target stopped the timer. The same probe was used in both experiments and was taped to the participant's shoe, projecting a distance of approximately 25 mm from the front of the shoe, so that the participant had full visibility of the probe under all postures and movement directions. The contact plate was of width 10 mm, with a contact area at the front of one mm width. The plate was electrically insulated for all its length apart from the front section. This plate projected from the front of the shoe by a distance of 15 mm, so that the tip was clearly visible to the participant when making visuallycontrolled movements. The experimental setup is shown in Fig. 1a and b, illustrating the standing and sitting postures, the directions of movement and the target boards ballistic and visually-controlled movements. Because of the small electrical contact area at the front of the attached copper plate, the value of IDavail was effectively that related to the actual target width, that is, in Equation (1), the value of the added ‘F’ was close to zero. 2.1. Participants The same group of 32 students of City University of Hong Kong took part in each of the experiments on ballistic and visuallycontrolled movements; 23 males and 9 females, with an average age of 21.7 years. All were self-reported right-foot dominant and all used their right foot when making movements. Participants were fully informed of the purpose of the experiments and took part under the ethical guidelines of the University. 2.2. Procedure Participants performed the four amplitudes and conditions (forward/lateral and sitting/standing) in a balanced order, with 10 repetitions of each condition being performed sequentially. The sitting and standing conditions were carried out without external support e there were no armrests on the chair or supports while standing. In the seated condition, the chair height was adjusted so that the upper leg was approximately horizontal and the initial position of the lower leg was approximately vertical. When standing, with the movements being made by the right leg, the full body weight was supported on the left leg. The movements were made when the participant was ready and a break was given when requested; this was regularly required due to the full body weight being supported by the one leg. Prior to recording movement times, participants were allowed to practice movements for each condition until they felt confident that they were able to perform the task
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Fig. 1. The experimental arrangements for showing the (a) sitting posture with lateral ballistic movement and (b) standing posture with forward visually-controlled movement.
without error. When errors were made, the condition was repeated at the end of the section of trials.
Fig. 2. Experiment 1, ballistic foot movement times (ms).
lateral movement cases. The four movement cases were balanced across participants while the nine ID x A cases were randomised across participants, each with a different random order.
2.3. Statistical analysis In each case, repeated-measures Analysis of Variance was performed of movement time as the dependent variable with factors of movement direction (forward/lateral), posture (sitting/standing), amplitude of movement and Index of Difficulty in the case of visually-controlled movements. A repeated-measures model was applied and the Greenhouse-Geiser correction used for nonsphericity of the MT data. Tukey post-hoc tests were used to investigate locations of significant differences between levels of a factor. In each experimental condition, regression analysis followed in order to provide models for leg movement times. 2.4. Experimental design 2.4.1. Experiment 1: ballistic movements Four amplitudes of movement, 25, 100, 225 and 400 mm were used. Targets had a constant ID of 2.5 at each of these movement distances, yielding target widths of 8.8, 35.4, 79.5 and 141.4 mm. The amplitudes of movement were chosen so that they were equally spaced on a square-root scale, as movement times for the ballistic movements were expected, on the basis of hand movement experiments (Gan and Hoffmann, 1988) to be linearly related to the square-root of movement amplitude. Copper targets of these widths and of height 150 mm were attached to a target board. When the foot left a starting location, an electronic timer was started and stopped when the shoe hit the target. The target board was set up so that the initial position of the movement was, in each case, directly below the foot of the participant when the foreleg was in a vertical position. The target Index of Difficulty of 2.5 was based on past experiments (Hoffmann, 1991b; Chan et al., 2011) both of which indicated that there was a levelling out of movement time as ID decreased below a value of about three. 2.4.2. Experiment 2: visually-controlled movements There were nine experimental tasks: ID values were 4, 5 and 6, combined with amplitudes of movement of 200, 400 and 600 mm. Target widths were calculated to provide the corresponding values at each movement distance for the given ID values. The nine tasks were carried out for each of the four sitting/standing and forward/
3. Results 3.1. Results of experiment 1 e ballistic movements 3.1.1. Movement time Mean data are shown in Fig. 2. ANOVA showed significant main effects of amplitude of movement [F(2.05,93) ¼ 61.97, p < .001], posture [F(1,31) ¼ 7.73, p < .01] and direction of movement [F(1,31) ¼ 29.3, p < .001]. There were no significant interactions between any factors. Tukey post-hoc tests showed that sitting movement time was greater than standing movement time (mean values of 453 and 438 ms; p < .001); lateral moves took longer than forward movements (470 vs 421 ms; p < .01); all comparisons of amplitude were significantly different (p < .001) apart from 25 to 100 mm. Mean values were 393, 405, 450 and 534 ms for the 25, 100, 225 and 400 mm amplitudes, respectively. Regressions of the data accounted for a greater proportion of variance in terms of the amplitude of movement, rather than the square-root of movement amplitude (Table 2). The average percent of variance accounted for in terms of amplitude of movement was 92.6%, while with square-root of amplitude the percent of variance accounted for by the regression was 80.1%. This is contrary to the usual model for ballistic movement (Gan and Hoffmann, 1988; Lin and Drury, 2013), but it is noted that the movement times for these ‘ballistic’ movements are much higher than those for hand/arm movements (Gan and Hoffmann, 1988; Hoffmann and Hui, 2010). 3.1.2. Standard deviation of movement times Analysis of Variance of the standard deviations of movement time for the ballistic movements showed only a significant main effect of the amplitude of movement [F(3,10) ¼ 5.43, p < .05]. Data are shown in Fig. 3. These SDs may be used, along with the mean values of movement time, to estimate the movement times for any given proportion of the population and would be useful for the establishment of a code for foot movement inputs such as that of Park and Myung (2012a,b). A purely empirical regression of SD with the experimental variables yields;
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SDballistic ¼ 43:6 þ ð3892=AmplitudeÞ 1469 ðDirection=AmplitudeÞ þ 13:5 ðDirectionÞ þ :051 ðAmplitudeÞ;
R2 ¼ :88
where Amplitude is in mm, Direction is a dummy variable with value ‘1’ for forward moves and ‘2’ for lateral moves. In this regression, the reciprocal of amplitude term accounts for 68% of variance, the Direction of movement x 1/amplitude interaction accounts for 12.1%, Direction 4% and amplitude 3.3%. The pattern of SDs is different to that illustrated in Lin and Drury (2013, Fig. 3), where it appears that SD increased almost linearly with the square-root of the movement amplitude. Note, however, that Lin and Drury did not actually give values for SD; the variation with amplitude is only apparent from inspection of the movement times for each of their 12 participants. The reason for the difference in pattern of SD with movement amplitude is difficult to determine due to the great differences in experimental methodology. Several of the possible factors are: direct movement with visual feedback vs touch screen movements with feedback via computer monitor; differences due to target impact vs sliding of the hand over a touchscreen; differences in levels of control capability due to differences in mass moment of inertia to muscle strength ratio. 3.2. Results of experiment 2 e visually controlled movements 3.2.1. Movement time Data for the four posture/direction cases are given in Fig. 4. Regressions in terms of a modified form of Fitts' law are given in Table 2, in which a term linear in the amplitude of movement is also added. ANOVA showed significant main effects of Index of Difficulty [F(1.31, 62) ¼ 121.9, p < .001], amplitude of movement [F(1.34, 62) ¼ 121.35, p < .001], posture [F(1,31) ¼ 29.89, p < .001 and direction of movement [F(1,31) ¼ 10.76, p < .005]. There were also significant interactions of ID x amplitude [F(3.1,62) ¼ 4.40, p < .01] and amplitude x posture [F(1.92, 62) ¼ 6.91, p < .005]. Tukey test showed that all IDs were significantly different (means: 605, 695 and 779 ms for ID ¼ 4, 5, 6; p's < .001), as were all amplitudes (means: 620, 688, 771 ms for A ¼ 200, 400, 600 mm) and postures (means: sitting 719 ms, standing 667 ms, p < .001). Lateral movements were faster than forward movements (671, 714 ms; p < .005). The posture amplitude interaction is shown in Fig. 5, where it is seen that movement times for the sitting posture are greater than those of the standing posture and increase at a greater rate with increase of movement amplitude. The ID Amplitude interaction is shown in Fig. 6. Post-hoc Tukey tests indicated that movement times for all amplitudes were significantly different at each value of ID, and all IDs were significantly different at each amplitude of movement (p < .01). As in the ballistic Experiment 1, regressions including a term of movement amplitude gave higher percent of variance accounted
Fig. 3. Experiment 1. Standard deviation of movement time (ms) for ballistic movements.
for than did that with a term in square-root of movement amplitude (average of 96.5% compared with 95.7%, respectively). The effects of movement amplitude were large compared to the usual results for arm movements and accounted for an average of 41.2% of the total variance accounted for by the regressions. 3.2.2. Standard deviation of movement times Analysis of Variance of the standard deviation of movement time showed main effects of ID [F(2,16) ¼ 32.42, p < .001], posture [F(1,16) ¼ 34.86, p < .001] and direction of movement [F(1,16) ¼ 17.52, p < .001]. There was also a significant interaction between amplitude of movement and posture [F(2,16) ¼ 3.93, p < .05]. Data are shown in Fig. 7. The data present a complex pattern which may be approximately modeled by a regression using dummy variables for posture (1 ¼ sitting; 2 ¼ standing) and direction of movement (1 ¼ forward; 2 ¼ lateral). The contributors to the regression are ID (40.5%), Posture (21.8%), Forward/lateral (10.9%) and amplitude (3.9%), giving a total of 77.1% variance accounted for by the regression.
SDvisual ¼ 78:3 þ 27:4 ðIDÞ 32:8 ðpostureÞ 23:3 ðDirectionÞ þ :042 ðamplitudeÞ; R2 ¼ :77
4. Discussion Models for leg movement times for many practical situations are provided by these experiments. By using the same participant group for all experiments, it was possible to obtain a consistent set of data that may overcome some of the inconsistencies shown in
Table 2 Conditions and results of present experiments. All movements were Discrete. MT ¼ movement time (ms); A ¼ amplitude of movement (mm); ID ¼ Fitts' Index of Difficulty. Posture
Type of movement
Movement direction
Amplitudes (mm)
Target widths mm
ID values
Regression
Seated Seated Standing Standing Seated Seated Standing Standing
Ballistic Ballistic Ballistic Ballistic Visual Visual Visual Visual
Lateral Forward Lateral Forward Lateral Forward Lateral Forward
25,100,225,400 25,100,225,400 25,100,225,400 25,100,225,400 200, 400, 600 200, 400, 600 200, 400, 600 200, 400, 600
8.8 ¼> 141.4 8.8 ¼> 141.4 8.8 ¼> 141.4 8.8 ¼> 141.4 6.25 ¼> 75 6.25 ¼> 75 6.25 ¼> 75 6.25 ¼> 75
2.5 2.5 2.5 2.5 4, 5, 4, 5, 4, 5, 4, 5,
MT MT MT MT MT MT MT MT
6 6 6 6
¼ 343 þ :463 A; r2 ¼ :99 ¼ 405 þ :382 A; r2 ¼ :93 ¼ 351 þ :328 A; r2 ¼ :94 ¼ 394 þ :370 A; r2 ¼ :84 ¼ 77 þ 85:9 ID þ :48 A; r 2 ¼ :96 ¼ 106 þ 94:8 ID þ :41 A; r 2 ¼ :98 ¼ 111 þ 81:6 ID þ :32 A; r 2 ¼ :99 ¼ 132 þ 85:8 ID þ :31 A; r 2 ¼ :93
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Fig. 4. Experiment 2, Visually econtrolled movements. (a) Participants sitting/forward leg movements (b) Sitting/lateral movements (c) Standing/forward movements (d) Standing/ Lateral movements.
Table 1. It should be emphasised, however, that the sources of data shown in Table 1 range from movements from an accelerator to a brake pedal (when in the same horizontal plane; Hoffmann, 1991a) to movements on a touch pad (Chan et al., 2010) and movements made with and without vision of the target area (Chan and Ng, 2008; Hoffmann, 1991a). Thus it is not surprising that there are fairly large variations in some of the data sets. A review of most of these data sets has been given by Ng and Chan (2009), where detailed information is given of the experimental conditions for each reference.
In the ballistic test there was not a highly significant interaction between posture and movement amplitude, as found in the movements made with visual control (Fig. 4), where sitting movement times were always greater than standing movement times and the difference increased with increasing movement amplitude. Movements in the lateral direction were faster than those in the forward direction. This pattern of mean movement times also occurred for ballistic movements, with standing lateral movements being the fastest. It is noted that, for both the ballistic and visually-controlled movements, the use of amplitude, rather than square-root of
Fig. 5. Experiment 2. The interaction between posture (sitting/standing) and amplitude of movement with visually-controlled movements.
Fig. 6. Interaction of Index of Difficulty and Amplitude of movement in the visuallycontrolled movements of Experiment 2.
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method used by Hoffmann and Hui (2010) who correlated the effect of the different arm components (full arm, lower arm, wrist, finger) in terms of the mass moment of inertia of the limb and its corresponding muscle strength, yielding a relationship that, for ballistic movements, required the square-root of amplitude to be multiplied by the one-tenth root of the mass moment of inertia. That model was obtained by means of a scaling argument, but attempts to apply the method to the present data were not successful due to the lack of data for mass moments of inertia and muscle strength for the different postures. Standard deviations of ballistic movement time for the forward movements of both standing and sitting postures show a rapid decrease up to an amplitude of movement of about 200 mm and then remain relatively constant (Fig. 2). Lateral movements showed an approximately constant level of variability of movement time. For the visually-controlled movements there was no clear pattern of the variation of SD with ID (Fig. 6). At this time, there is no theory or model available that might explain these data: regressions have been obtained that may be useful for prediction purposes. Fig. 7. Experiment 2. Standard deviation of movement time (ms) for visuallycontrolled movements.
4.1. Practical use of the models amplitude, accounts for a higher proportion of the variance. This is particularly the case for the ballistic movements where the average increase in percent of variance accounted for is 12.5%, compared to .8% in the case of visually controlled movements. In all cases, however, the regression in amplitude was better than that in square-root of amplitude. This was contrary to expectations since much data on arm/hand movements has shown the strength of the square-root relationship for ballistic movements (Gan and Hoffmann, 1988; Lin and Drury, 2013; Hoffmann and Hui, 2010). This is an area that requires further investigation, as it is also contrary to the data of Hoffmann (1991b), although the current data are much more detailed. This data raises questions whether, with the long movement times, participants in the ‘ballistic’ conditions may have been using some kinaesthetic or visual feedback to modify their movement response during the course of the movement. As velocity profiles were not measured in the experiment, this cannot be determined, particularly as all the ballistic experiments were carried out at a constant ID value. The times used by participants in the ‘ballistic’ movements would have allowed several visual corrections to be made during the movement (Lin and Hsu 2014). It is noted that two of the five ‘ballistic’ movement regressions in Table 1 were best in terms of amplitude of movement (Chan and Ng, 2008). Other research (Lin and Drury, 2013) has shown that ballistic movements may occur to high movement times when the target area is not visible or no path corrections are made. However, whether the corrective reaction times are similar for hand and leg movements is not known; it may be that such corrective reaction times are longer for the leg system than for the arm system. This is a research area needing further investigation. Note that the regressions for visually-controlled movements in Table 2 include significant effects of movement amplitude as seen also in Fig. 4. This is a deviation from Fitts' law that is generally not seen in studies of arm movements, although similar deviations have been noted by Welford et al. (1969) in older persons and by Hoffmann and Chan (2012) for underwater movements. The proportion of variance accounted for by the Index of Difficulty was 57% and 44% for the sitting tasks with forward and lateral movements, respectively, and 62% for each of the standing tasks. Thus, the effect of the amplitude of movement is strong in leg movements, an effect that does not generally occur with arm/hand movements. An attempt was made to account for the difference in movement times for the sitting and standing postures, based on the scaling
When applying the data of these experiments, it is first necessary to determine conditions of the task being considered. In particular, it is necessary to determine an ‘available ID’, taking into account the effect of the shoe width when moving to the target. When there is a finite width of the probe that is moving to the target, the available target width is greater than the set target width, as expressed by Equation (1). An ‘available ID’ can then be calculated by Equation (1) in order to estimate movement times. When IDavail < 3, the ballistic equations (Table 2) should be used and when IDavail > 3, the equations for visually-controlled movements (Table 2) are relevant. To obtain a prediction of the movement time to accommodate a particular proportion of the population, the regressions of Table 2, along with the standard deviations of Figs. 3 and 7 may be used. For example, consider a ballistic movement of amplitude 200 mm, with the leg of a seated operator moving laterally. The relevant equation from Table 2 gives a movement time of 436 ms. Fig. 2 gives an SD of MT of about 88 ms. If we wish to accommodate 85% of the population (1.4 SD above the mean MT), then the allowed movement time is 436 þ (1.4 88) ¼ 559 ms. It is envisaged that the models developed here will provide a useful update to the ACT-R cognitive architecture (Park and Myung 2012a,b). Acknowledgements The authors acknowledge the assistance of Chu Yuen Lap in data collection. The work was fully supported by a grant from City University of Hong Kong (SRG7004250). References Bullinger, H.-J., Bandera, J.E., Muntzinger, W.F., 1991. Design, selection and location of foot controls. Int. J. Ind. Ergon. 8 (4), 303e311. Chan, K.W.L., Chan, A.H.S., 2009. Spatial stimulus-response (S-R) compatibility for foot controls with visual, displays. Int. J. Ind. Ergon. 39 (2), 396e402. Chan, K.W.L., Chan, A.H.S., 2010. Three-dimensional spatial stimulus-response (S-R_ compatibility for visual signals with hand and foot controls. Appl. Ergon. 41 (6), 840e848. Chan, A.O.K., Chan, A.H.S., Ng, A.W.Y., Luk, B.L., 2010. A preliminary analysis of movement times and subjective evaluations for a visually-controlled foot-tapping tasks on touch pad device. In: Proceedings of the International MultiConference of Engineers and Computer Scientists 2010, vol. III, pp. 1968e1970. ISBN 978-988-18210-5-8, March 17-19, Hong Kong. Chan, A.H.S., Ng, A.W.Y., 2008. Lateral foot-movement times in sitting and standing postures. Percept. Mot. Ski. 106 (1), 215e224.
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International Journal of Industrial Ergonomics journal homepage: www.elsevier.com/locate/ergon
Effect of movement direction and sitting/standing on leg movement time Alan H.S. Chan*, Errol R. Hoffmann Department of Systems Engineering and Engineering Management, City University of Hong Kong, Kowloon Tong, Hong Kong
a r t i c l e i n f o
a b s t r a c t
Article history: Received 10 October 2014 Received in revised form 2 February 2015 Accepted 15 February 2015 Available online 9 March 2015
Data on leg movement times are summarised and it is noted that there is a need for more consistent data gathering. Experiments are reported for movements made either ballistically or with ongoing visual control, along with participants standing or sitting with leg movements made both in the sagittal and frontal planes. These conditions fulfil all commonly used foot-control situations. Regression equations are given for the movement times for each of these tasks. It is found that a modified form of Fitts' law is required to model the times for movements made with visual control, having an additional term in which movement time increases with increase of movement amplitude. Movements without ongoing visual control had movement times that increased linearly with movement amplitude. Relevance to industry: Many devices require control by the foot as well as the hands. We provide detailed information on the times for foot movements as dependent on the form of movement, posture of the operator and the direction of leg movement. © 2015 Elsevier B.V. All rights reserved.
Keywords: Leg movement times Fitts' law Movement direction Movement posture
1. Introduction Increasingly, the foot/leg system is being used in human/machine applications, particularly in applications where the hands are already heavily occupied (Chan and Chan, 2009, 2010; Bullinger et al., 1991; Pannetier and Wang, 2014). The use of leg often occurs when there is no possibility for ongoing visual control, such as when movements are made between the accelerator and brake pedal of an automobile (Hoffmann, 1991a). Under those circumstances, the movements are likely to be made in a ‘ballistic’ manner, where the movement is initiated and completed without correction to the path taken and final accuracy is not critical. Under other circumstances where final accuracy of a movement is required, as may occur in surgical applications (Van Veelen et al., 2003) or in foot mouse control (Springer and Siebes, 1996) it is necessary to use movements with ongoing visual control. There have been a number of studies of leg/foot movement times that have included movements made with ongoing visual control and movements that are pre-planned and are completed without modification (hereafter referred to as ballistic). These studies are listed in Table 1. Experiments are listed as ‘ballistic’ or
* Corresponding author. E-mail address: [email protected] (A.H.S. Chan). http://dx.doi.org/10.1016/j.ergon.2015.02.003 0169-8141/© 2015 Elsevier B.V. All rights reserved.
‘visually-controlled’ according to the criterion established by Gan and Hoffmann (1988) where it was shown that, below an Index of Difficulty of about three (Fitts, 1954; Fitts and Peterson, 1964) the movements may be made ballistically, whereas above this value, it is necessary to use ongoing visual control. Inspection of the experiments listed in Table 1 indicates a variety of forms of movement (discrete, sequential and reciprocal) along with movements made either ballistically or with ongoing visual control. As well, movements were made in the forward or lateral directions with seated or standing participants. The important feature is that there is not a single consistent set of data for the important industrial situations where the operator is either seated or standing, is making foot movements forward or laterally and the movements are made with and without ongoing visual control. As the data of Table 1 were gathered for different purposes (such as moving the foot from an accelerator to brake pedal and in walking) and by different methods (discrete and reciprocal movements), it was considered that a set of data using the same participants for all experiments and with better controlled conditions would be desirable. This is particularly the case as an attempt has recently been made to provide standardised foot movement times in a code for foot movement inputs (Park and Myung, 2012a). A modification of Fitts' Index of Difficulty (ID) may be necessary when correlating data of foot movement times due to the width of the shoe increasing the available target width. It has been shown
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Table 1 Summary of past experiments on foot/leg movement times. Mt ¼ movement time (ms); A ¼ amplitude of movement (mm); W ¼ target width (mm); ID ¼ Fitts' Index of Difficulty. Authors
Expt no. Posture
Drury (1975) Hoffmann (1991a) Hoffmann (1991b) Park and Myung (2012b) Chan and Ng 2008 Chan and Ng (2008) Hoffmann (1991b) Hoffmann (1991b) Chan et al. (2010) Drury and Woolley (1995) Drury and Woolley (1995)
3
1 2 2 3
Seated Seated Seated Seated Seated Standing Seated Seated Seated Standing Walking
Type of move
Movement Amplitudes direction (mm)
Target widths ID range mm
Ballistic Reciprocal Ballistic Discrete Ballistic Discrete Ballistic Discrete Ballistic Reciprocal Ballistic Reciprocal Visual Discrete Visual Discrete Visual Reciprocal Visual Reciprocal Visual Sequential
Lateral Lateral Lateral Angular Lateral Lateral Lateral Lateral Lateral Forward Forward
51,25 NA NA 40 NA 60, 80, 100 25 5, 10, 20 60 19, 38, 78 19, 38, 78
153, 230, 306 140, 190, 240,290 50, 119, 216, 344, 500 89,172,253 100, 300, 500 100, 300, 500 50, 100, 200, 400, 700 20 ¼> 640 60 ¼> 679 229, 457, 686 229, 457, 686
that the available ID is given in previous researches (Drury and Hoffmann, 1992; Hoffmann and Sheikh, 1991; Hoffmann, 1995),
IDavail ¼ log2 ½2A=ðW þ kFÞ
(1)
Here the available target width is given by (W þ k F); W is the set target width, F is the shoe width and k is a factor that may vary from about .6 to 1.0 (the proportion of shoe width adding to the available target width). When IDavail is greater than about three, Fitts law applies to the movements and the time for the moment is given by
MT ¼ a þ b IDavail
(2)
where MT is the movement time and a,b are empirically determined constants. When the IDavail value is small (less than about three), Gan and Hoffmann (1988) found that, for hand movements, the movement time was given by an expression in which MT was linear with the square-root of movement distance. However, the data of Table 1 indicate that several data sets (Chan and Ng, 2008) have a better fit when the MT is regressed with the amplitude of movement. In this work, both models will be evaluated.
MT ¼ c þ d
pffiffiffi A
MT ¼ e þ f A
(3a) (3b)
As noted above, previous data sets do not provide a full consistent set of data for the various practical situations of operator posture (sitting/standing), direction of foot movement (forward or laterally) and form of movement (ballistic or with ongoing visual control). Thus experiments were designed to model foot/leg movement times for these eight combinations of conditions as a basis for a code for movement times, as attempted by Park and Myung (2012a,b). 2. Method Two experiments were performed by each participant: ballistic movements and movements requiring the use of ongoing visual control. The two experiments were done on different days, with half the participants performing the ballistic experiment first and the other half starting with the visually-controlled experiment. In each experiment, the targets were placed horizontally on the floor. In the case of ballistic movements, the target widths were designed so that the ID values (Equation (1)) were less than three and hence the effects of target width should be unimportant (Gan and
NA NA NA NA NA NA 2, 3, 4, 5, 5.8 3, 4, 5, 6 1, 1.5, 2, ¼> 4.5 2.6 ¼> 6.2 2.6 ¼> 6.2
Regression pffiffiffi MT ¼ 107 þ 11:2 A pffiffiffi MT ¼ 19:2 þ 12:13 pffiffiffi A MT ¼ 107:5 þ 6:5pffiffiffi A MT ¼ 252 þ 16:3 A MT ¼ 587 þ 1:14A MT ¼ 711 þ :78A 2:76W MT ¼ 81 þ 178ðIDÞ MT ¼ 58 þ 115ðIDÞ 35 log2 ðWÞ MT ¼ 105 þ 255ðIDÞ MT ¼ 74 þ 173ðIDÞ Toe:MT ¼ 192 þ 72:6ðIDÞ Heel: MT ¼ 91 þ 59:2ðIDÞ
Hoffmann, 1988). A copper probe attached to the shoe of the participant allowed measurement of movement time: loss of contact with the home plate started an electronic timer, while contact with the target stopped the timer. The same probe was used in both experiments and was taped to the participant's shoe, projecting a distance of approximately 25 mm from the front of the shoe, so that the participant had full visibility of the probe under all postures and movement directions. The contact plate was of width 10 mm, with a contact area at the front of one mm width. The plate was electrically insulated for all its length apart from the front section. This plate projected from the front of the shoe by a distance of 15 mm, so that the tip was clearly visible to the participant when making visuallycontrolled movements. The experimental setup is shown in Fig. 1a and b, illustrating the standing and sitting postures, the directions of movement and the target boards ballistic and visually-controlled movements. Because of the small electrical contact area at the front of the attached copper plate, the value of IDavail was effectively that related to the actual target width, that is, in Equation (1), the value of the added ‘F’ was close to zero. 2.1. Participants The same group of 32 students of City University of Hong Kong took part in each of the experiments on ballistic and visuallycontrolled movements; 23 males and 9 females, with an average age of 21.7 years. All were self-reported right-foot dominant and all used their right foot when making movements. Participants were fully informed of the purpose of the experiments and took part under the ethical guidelines of the University. 2.2. Procedure Participants performed the four amplitudes and conditions (forward/lateral and sitting/standing) in a balanced order, with 10 repetitions of each condition being performed sequentially. The sitting and standing conditions were carried out without external support e there were no armrests on the chair or supports while standing. In the seated condition, the chair height was adjusted so that the upper leg was approximately horizontal and the initial position of the lower leg was approximately vertical. When standing, with the movements being made by the right leg, the full body weight was supported on the left leg. The movements were made when the participant was ready and a break was given when requested; this was regularly required due to the full body weight being supported by the one leg. Prior to recording movement times, participants were allowed to practice movements for each condition until they felt confident that they were able to perform the task
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Fig. 1. The experimental arrangements for showing the (a) sitting posture with lateral ballistic movement and (b) standing posture with forward visually-controlled movement.
without error. When errors were made, the condition was repeated at the end of the section of trials.
Fig. 2. Experiment 1, ballistic foot movement times (ms).
lateral movement cases. The four movement cases were balanced across participants while the nine ID x A cases were randomised across participants, each with a different random order.
2.3. Statistical analysis In each case, repeated-measures Analysis of Variance was performed of movement time as the dependent variable with factors of movement direction (forward/lateral), posture (sitting/standing), amplitude of movement and Index of Difficulty in the case of visually-controlled movements. A repeated-measures model was applied and the Greenhouse-Geiser correction used for nonsphericity of the MT data. Tukey post-hoc tests were used to investigate locations of significant differences between levels of a factor. In each experimental condition, regression analysis followed in order to provide models for leg movement times. 2.4. Experimental design 2.4.1. Experiment 1: ballistic movements Four amplitudes of movement, 25, 100, 225 and 400 mm were used. Targets had a constant ID of 2.5 at each of these movement distances, yielding target widths of 8.8, 35.4, 79.5 and 141.4 mm. The amplitudes of movement were chosen so that they were equally spaced on a square-root scale, as movement times for the ballistic movements were expected, on the basis of hand movement experiments (Gan and Hoffmann, 1988) to be linearly related to the square-root of movement amplitude. Copper targets of these widths and of height 150 mm were attached to a target board. When the foot left a starting location, an electronic timer was started and stopped when the shoe hit the target. The target board was set up so that the initial position of the movement was, in each case, directly below the foot of the participant when the foreleg was in a vertical position. The target Index of Difficulty of 2.5 was based on past experiments (Hoffmann, 1991b; Chan et al., 2011) both of which indicated that there was a levelling out of movement time as ID decreased below a value of about three. 2.4.2. Experiment 2: visually-controlled movements There were nine experimental tasks: ID values were 4, 5 and 6, combined with amplitudes of movement of 200, 400 and 600 mm. Target widths were calculated to provide the corresponding values at each movement distance for the given ID values. The nine tasks were carried out for each of the four sitting/standing and forward/
3. Results 3.1. Results of experiment 1 e ballistic movements 3.1.1. Movement time Mean data are shown in Fig. 2. ANOVA showed significant main effects of amplitude of movement [F(2.05,93) ¼ 61.97, p < .001], posture [F(1,31) ¼ 7.73, p < .01] and direction of movement [F(1,31) ¼ 29.3, p < .001]. There were no significant interactions between any factors. Tukey post-hoc tests showed that sitting movement time was greater than standing movement time (mean values of 453 and 438 ms; p < .001); lateral moves took longer than forward movements (470 vs 421 ms; p < .01); all comparisons of amplitude were significantly different (p < .001) apart from 25 to 100 mm. Mean values were 393, 405, 450 and 534 ms for the 25, 100, 225 and 400 mm amplitudes, respectively. Regressions of the data accounted for a greater proportion of variance in terms of the amplitude of movement, rather than the square-root of movement amplitude (Table 2). The average percent of variance accounted for in terms of amplitude of movement was 92.6%, while with square-root of amplitude the percent of variance accounted for by the regression was 80.1%. This is contrary to the usual model for ballistic movement (Gan and Hoffmann, 1988; Lin and Drury, 2013), but it is noted that the movement times for these ‘ballistic’ movements are much higher than those for hand/arm movements (Gan and Hoffmann, 1988; Hoffmann and Hui, 2010). 3.1.2. Standard deviation of movement times Analysis of Variance of the standard deviations of movement time for the ballistic movements showed only a significant main effect of the amplitude of movement [F(3,10) ¼ 5.43, p < .05]. Data are shown in Fig. 3. These SDs may be used, along with the mean values of movement time, to estimate the movement times for any given proportion of the population and would be useful for the establishment of a code for foot movement inputs such as that of Park and Myung (2012a,b). A purely empirical regression of SD with the experimental variables yields;
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SDballistic ¼ 43:6 þ ð3892=AmplitudeÞ 1469 ðDirection=AmplitudeÞ þ 13:5 ðDirectionÞ þ :051 ðAmplitudeÞ;
R2 ¼ :88
where Amplitude is in mm, Direction is a dummy variable with value ‘1’ for forward moves and ‘2’ for lateral moves. In this regression, the reciprocal of amplitude term accounts for 68% of variance, the Direction of movement x 1/amplitude interaction accounts for 12.1%, Direction 4% and amplitude 3.3%. The pattern of SDs is different to that illustrated in Lin and Drury (2013, Fig. 3), where it appears that SD increased almost linearly with the square-root of the movement amplitude. Note, however, that Lin and Drury did not actually give values for SD; the variation with amplitude is only apparent from inspection of the movement times for each of their 12 participants. The reason for the difference in pattern of SD with movement amplitude is difficult to determine due to the great differences in experimental methodology. Several of the possible factors are: direct movement with visual feedback vs touch screen movements with feedback via computer monitor; differences due to target impact vs sliding of the hand over a touchscreen; differences in levels of control capability due to differences in mass moment of inertia to muscle strength ratio. 3.2. Results of experiment 2 e visually controlled movements 3.2.1. Movement time Data for the four posture/direction cases are given in Fig. 4. Regressions in terms of a modified form of Fitts' law are given in Table 2, in which a term linear in the amplitude of movement is also added. ANOVA showed significant main effects of Index of Difficulty [F(1.31, 62) ¼ 121.9, p < .001], amplitude of movement [F(1.34, 62) ¼ 121.35, p < .001], posture [F(1,31) ¼ 29.89, p < .001 and direction of movement [F(1,31) ¼ 10.76, p < .005]. There were also significant interactions of ID x amplitude [F(3.1,62) ¼ 4.40, p < .01] and amplitude x posture [F(1.92, 62) ¼ 6.91, p < .005]. Tukey test showed that all IDs were significantly different (means: 605, 695 and 779 ms for ID ¼ 4, 5, 6; p's < .001), as were all amplitudes (means: 620, 688, 771 ms for A ¼ 200, 400, 600 mm) and postures (means: sitting 719 ms, standing 667 ms, p < .001). Lateral movements were faster than forward movements (671, 714 ms; p < .005). The posture amplitude interaction is shown in Fig. 5, where it is seen that movement times for the sitting posture are greater than those of the standing posture and increase at a greater rate with increase of movement amplitude. The ID Amplitude interaction is shown in Fig. 6. Post-hoc Tukey tests indicated that movement times for all amplitudes were significantly different at each value of ID, and all IDs were significantly different at each amplitude of movement (p < .01). As in the ballistic Experiment 1, regressions including a term of movement amplitude gave higher percent of variance accounted
Fig. 3. Experiment 1. Standard deviation of movement time (ms) for ballistic movements.
for than did that with a term in square-root of movement amplitude (average of 96.5% compared with 95.7%, respectively). The effects of movement amplitude were large compared to the usual results for arm movements and accounted for an average of 41.2% of the total variance accounted for by the regressions. 3.2.2. Standard deviation of movement times Analysis of Variance of the standard deviation of movement time showed main effects of ID [F(2,16) ¼ 32.42, p < .001], posture [F(1,16) ¼ 34.86, p < .001] and direction of movement [F(1,16) ¼ 17.52, p < .001]. There was also a significant interaction between amplitude of movement and posture [F(2,16) ¼ 3.93, p < .05]. Data are shown in Fig. 7. The data present a complex pattern which may be approximately modeled by a regression using dummy variables for posture (1 ¼ sitting; 2 ¼ standing) and direction of movement (1 ¼ forward; 2 ¼ lateral). The contributors to the regression are ID (40.5%), Posture (21.8%), Forward/lateral (10.9%) and amplitude (3.9%), giving a total of 77.1% variance accounted for by the regression.
SDvisual ¼ 78:3 þ 27:4 ðIDÞ 32:8 ðpostureÞ 23:3 ðDirectionÞ þ :042 ðamplitudeÞ; R2 ¼ :77
4. Discussion Models for leg movement times for many practical situations are provided by these experiments. By using the same participant group for all experiments, it was possible to obtain a consistent set of data that may overcome some of the inconsistencies shown in
Table 2 Conditions and results of present experiments. All movements were Discrete. MT ¼ movement time (ms); A ¼ amplitude of movement (mm); ID ¼ Fitts' Index of Difficulty. Posture
Type of movement
Movement direction
Amplitudes (mm)
Target widths mm
ID values
Regression
Seated Seated Standing Standing Seated Seated Standing Standing
Ballistic Ballistic Ballistic Ballistic Visual Visual Visual Visual
Lateral Forward Lateral Forward Lateral Forward Lateral Forward
25,100,225,400 25,100,225,400 25,100,225,400 25,100,225,400 200, 400, 600 200, 400, 600 200, 400, 600 200, 400, 600
8.8 ¼> 141.4 8.8 ¼> 141.4 8.8 ¼> 141.4 8.8 ¼> 141.4 6.25 ¼> 75 6.25 ¼> 75 6.25 ¼> 75 6.25 ¼> 75
2.5 2.5 2.5 2.5 4, 5, 4, 5, 4, 5, 4, 5,
MT MT MT MT MT MT MT MT
6 6 6 6
¼ 343 þ :463 A; r2 ¼ :99 ¼ 405 þ :382 A; r2 ¼ :93 ¼ 351 þ :328 A; r2 ¼ :94 ¼ 394 þ :370 A; r2 ¼ :84 ¼ 77 þ 85:9 ID þ :48 A; r 2 ¼ :96 ¼ 106 þ 94:8 ID þ :41 A; r 2 ¼ :98 ¼ 111 þ 81:6 ID þ :32 A; r 2 ¼ :99 ¼ 132 þ 85:8 ID þ :31 A; r 2 ¼ :93
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Fig. 4. Experiment 2, Visually econtrolled movements. (a) Participants sitting/forward leg movements (b) Sitting/lateral movements (c) Standing/forward movements (d) Standing/ Lateral movements.
Table 1. It should be emphasised, however, that the sources of data shown in Table 1 range from movements from an accelerator to a brake pedal (when in the same horizontal plane; Hoffmann, 1991a) to movements on a touch pad (Chan et al., 2010) and movements made with and without vision of the target area (Chan and Ng, 2008; Hoffmann, 1991a). Thus it is not surprising that there are fairly large variations in some of the data sets. A review of most of these data sets has been given by Ng and Chan (2009), where detailed information is given of the experimental conditions for each reference.
In the ballistic test there was not a highly significant interaction between posture and movement amplitude, as found in the movements made with visual control (Fig. 4), where sitting movement times were always greater than standing movement times and the difference increased with increasing movement amplitude. Movements in the lateral direction were faster than those in the forward direction. This pattern of mean movement times also occurred for ballistic movements, with standing lateral movements being the fastest. It is noted that, for both the ballistic and visually-controlled movements, the use of amplitude, rather than square-root of
Fig. 5. Experiment 2. The interaction between posture (sitting/standing) and amplitude of movement with visually-controlled movements.
Fig. 6. Interaction of Index of Difficulty and Amplitude of movement in the visuallycontrolled movements of Experiment 2.
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method used by Hoffmann and Hui (2010) who correlated the effect of the different arm components (full arm, lower arm, wrist, finger) in terms of the mass moment of inertia of the limb and its corresponding muscle strength, yielding a relationship that, for ballistic movements, required the square-root of amplitude to be multiplied by the one-tenth root of the mass moment of inertia. That model was obtained by means of a scaling argument, but attempts to apply the method to the present data were not successful due to the lack of data for mass moments of inertia and muscle strength for the different postures. Standard deviations of ballistic movement time for the forward movements of both standing and sitting postures show a rapid decrease up to an amplitude of movement of about 200 mm and then remain relatively constant (Fig. 2). Lateral movements showed an approximately constant level of variability of movement time. For the visually-controlled movements there was no clear pattern of the variation of SD with ID (Fig. 6). At this time, there is no theory or model available that might explain these data: regressions have been obtained that may be useful for prediction purposes. Fig. 7. Experiment 2. Standard deviation of movement time (ms) for visuallycontrolled movements.
4.1. Practical use of the models amplitude, accounts for a higher proportion of the variance. This is particularly the case for the ballistic movements where the average increase in percent of variance accounted for is 12.5%, compared to .8% in the case of visually controlled movements. In all cases, however, the regression in amplitude was better than that in square-root of amplitude. This was contrary to expectations since much data on arm/hand movements has shown the strength of the square-root relationship for ballistic movements (Gan and Hoffmann, 1988; Lin and Drury, 2013; Hoffmann and Hui, 2010). This is an area that requires further investigation, as it is also contrary to the data of Hoffmann (1991b), although the current data are much more detailed. This data raises questions whether, with the long movement times, participants in the ‘ballistic’ conditions may have been using some kinaesthetic or visual feedback to modify their movement response during the course of the movement. As velocity profiles were not measured in the experiment, this cannot be determined, particularly as all the ballistic experiments were carried out at a constant ID value. The times used by participants in the ‘ballistic’ movements would have allowed several visual corrections to be made during the movement (Lin and Hsu 2014). It is noted that two of the five ‘ballistic’ movement regressions in Table 1 were best in terms of amplitude of movement (Chan and Ng, 2008). Other research (Lin and Drury, 2013) has shown that ballistic movements may occur to high movement times when the target area is not visible or no path corrections are made. However, whether the corrective reaction times are similar for hand and leg movements is not known; it may be that such corrective reaction times are longer for the leg system than for the arm system. This is a research area needing further investigation. Note that the regressions for visually-controlled movements in Table 2 include significant effects of movement amplitude as seen also in Fig. 4. This is a deviation from Fitts' law that is generally not seen in studies of arm movements, although similar deviations have been noted by Welford et al. (1969) in older persons and by Hoffmann and Chan (2012) for underwater movements. The proportion of variance accounted for by the Index of Difficulty was 57% and 44% for the sitting tasks with forward and lateral movements, respectively, and 62% for each of the standing tasks. Thus, the effect of the amplitude of movement is strong in leg movements, an effect that does not generally occur with arm/hand movements. An attempt was made to account for the difference in movement times for the sitting and standing postures, based on the scaling
When applying the data of these experiments, it is first necessary to determine conditions of the task being considered. In particular, it is necessary to determine an ‘available ID’, taking into account the effect of the shoe width when moving to the target. When there is a finite width of the probe that is moving to the target, the available target width is greater than the set target width, as expressed by Equation (1). An ‘available ID’ can then be calculated by Equation (1) in order to estimate movement times. When IDavail < 3, the ballistic equations (Table 2) should be used and when IDavail > 3, the equations for visually-controlled movements (Table 2) are relevant. To obtain a prediction of the movement time to accommodate a particular proportion of the population, the regressions of Table 2, along with the standard deviations of Figs. 3 and 7 may be used. For example, consider a ballistic movement of amplitude 200 mm, with the leg of a seated operator moving laterally. The relevant equation from Table 2 gives a movement time of 436 ms. Fig. 2 gives an SD of MT of about 88 ms. If we wish to accommodate 85% of the population (1.4 SD above the mean MT), then the allowed movement time is 436 þ (1.4 88) ¼ 559 ms. It is envisaged that the models developed here will provide a useful update to the ACT-R cognitive architecture (Park and Myung 2012a,b). Acknowledgements The authors acknowledge the assistance of Chu Yuen Lap in data collection. The work was fully supported by a grant from City University of Hong Kong (SRG7004250). References Bullinger, H.-J., Bandera, J.E., Muntzinger, W.F., 1991. Design, selection and location of foot controls. Int. J. Ind. Ergon. 8 (4), 303e311. Chan, K.W.L., Chan, A.H.S., 2009. Spatial stimulus-response (S-R) compatibility for foot controls with visual, displays. Int. J. Ind. Ergon. 39 (2), 396e402. Chan, K.W.L., Chan, A.H.S., 2010. Three-dimensional spatial stimulus-response (S-R_ compatibility for visual signals with hand and foot controls. Appl. Ergon. 41 (6), 840e848. Chan, A.O.K., Chan, A.H.S., Ng, A.W.Y., Luk, B.L., 2010. A preliminary analysis of movement times and subjective evaluations for a visually-controlled foot-tapping tasks on touch pad device. In: Proceedings of the International MultiConference of Engineers and Computer Scientists 2010, vol. III, pp. 1968e1970. ISBN 978-988-18210-5-8, March 17-19, Hong Kong. Chan, A.H.S., Ng, A.W.Y., 2008. Lateral foot-movement times in sitting and standing postures. Percept. Mot. Ski. 106 (1), 215e224.
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