Movement Time and Subjective Rating of Difﬁculty in Real and Virtual Pipe Transferring Tasks

: An experiment was performed to investigate the movement time (MT) and subjective rating of difﬁculty for real and virtual pipe transferring tasks. Thirty adults joined as human participants. The HoloPipes app in a Microsoft ® Hololens 2 augmented reality (AR) device was adopted to generate virtual pipes. The participants performed pipe transferring trials, from one location to another on a workbench, in both lateral and anterior–posterior directions. For the lateral transferring tasks, pipes in three diameters with three transferring distances and two origins were tested. For the anterior–posterior transferring tasks, pipes with a diameter of 2.2 cm with three transferring distances and two origins were tested. It was found that the MT of transferring a virtual pipe was signiﬁcantly ( p < 0.0001) shorter than that of transferring a real pipe. Moreover, male participants transferred the pipe signiﬁcantly ( p < 0.0001) faster than their female counterparts. Thus, the hypothesis that transferring a virtual pipe is less efﬁcient than transferring a real pipe was rejected. It was also found that the MT of transferring both a real and a virtual object was dependent upon gender, handedness, and the transferring direction. In addition, the subjective rating of difﬁculty in pipe transferring is positively correlated ( r = 0.48, p < 0.0001) with the MT. Based on Fitts’ law, additive MT models were proposed. These models could be used to predict the MT between handling real and virtual pipes under gender, handedness, and transferring direction conditions.


Introduction
Movement time (MT) is one of the major terms in assessing the performance of humanmachine systems and the motor skills of body segments.It is the time required for a user to complete a movement using one of their body segments.Examples of such movements include finger movements in small amplitude tapping tasks [1], hand/arm movements with an object to transfer the location of the object or tap a target with/without a stylus [2][3][4][5][6][7][8][9], foot movements to push a pedal or tap a target [10][11][12][13][14], head movements to give a command to a computer or other device [15][16][17][18][19], trunk movements to support the upper extremity movements or to indicate the functional capability of the body [20,21], and so on.Fitts' law [2,3] is probably the most commonly adopted scientific basis for explaining the MT of a body segment.This law claims that the MT of a body segment from one location to a target is dependent on the distance of the movement and the size of the target.The difficulty of the movement is defined using an index of difficulty (ID), which is a function of the ratio of movement distance (D) and target size (W): The following equation explains the original Fitts' law: Appl.Sci.2023, 13, 10043 2 of 14 where a and b are constants which may be determined by experimental data.Mathematically, the ID in Equation ( 2) has no units and a "bit" is given to this term as the unit to indicate the quantity of information involved in the movement [22].In Fitts' study, it was defined as log 2 (2D/W) and ranged from 1 to 7 bit for the tapping tasks using a stylus, 4 to 10 bit for disc transfer tasks, and 3 to 10 bit for pin transfer tasks [2,3].The a and b in Equation ( 2) are the intercept and slope of the linear equation, respectively.They have been adopted to assess the interface of human-machine systems where movements of body segments are required.To determine these regression coefficients, tasks and scenarios with levels of ID were manipulated and the MT data under each ID level were collected to fit the regression formula [23].
Since the inception of the Fitts' law in 1954 [2], numerous studies discussing the fitness of this law in explaining MT have been reported.Some earlier studies have proposed revisions of the ID to remedy the negative ID problem since negative ID does not exist and is not allowed [24,25].The literature has proposed more than a dozen alternative ID definitions, including log 2 (D/W), log 2 ((D/W) + 0.5), log 2 ((D/W) + 1), and so on [26][27][28].Instead of logarithm functions, power functions have also been proposed to estimate the difficulty of the tasks [29,30].Some of the studies have shown that ID may be estimated simply using D or D 1/2 when it is less than three [31,32].This implies that target size may be neglected in determining ID under such circumstances.Hoffmann [33] has considered the width of the finger and adopted a pad size of the finger index in the ID equation.
McGuffin and Balakrishnan [34] indicated that the ID in a pointing task could be decreased by expanding the target size, even at the final stage of hand movement.This implies that the ID, instead of a constant, might be changed before a body segment has reached the target in a Fitts' task.Even with so many ID variants proposed, the original definition of ID has still been widely adopted [35,36].
In addition to the revisions of the ID, additive MT models based on the original Fitts' equation have also been proposed.For example, Murata and Iwase [37] found that the original ID was poor in predicting the MT of positioning 2D targets vertically in a coronal plane.They suggested adding a sinϕ, the sine of the azimuth angle of the target location measured from the positive x-axis, which is included as a term in Equation (2) to remedy the underestimation of the MT under such circumstances.Cha and Myung [38] have extended the MT model of Murata and Iwase [36] by adding a θ term, which represents the inclination angle of the target in a spherical coordinate system in the MT equation.Alternatively, Machuca and Stuerzlinger [39] proposed to add a term representing the target depth change between the target and the previously selected one to compensate for the MT in the pointing tasks in their virtual environments.Furthermore, Clark et al. [40] suggested adding two terms, including the inclination angle and the interaction of the target size and inclination angle, in their MT equation for users using a virtual reality (VR) device.In addition to an incline angle term, Zhao et al. [5] proposed to add a tactile factor in their MT model to improve the fitness of their MT model for pointing virtual keypads in an augmented reality (AR) environment.
In addition to the revisions of the ID definition and additive MT models, Deng et al. [41] provided an MT model combining both revised ID and additive terms.They have requested their participants to move a virtual ball from a starting spot to a spherical end area using either a head-tracking or a handheld controller with a ray-casting technique.They split the movement of the virtual ball into phases of acceleration, deceleration, and correction, and claimed that the MT in each of these phases should be calculated using different equations.Their equations included both revisions of the ID and additional terms considering the size and depth of the virtual ball and the tolerance of the destination.
Both VR and AR devices have become popular both for entertainment purposes and in the industry [42][43][44][45][46]. The literature [47] has shown that AR is one of the techniques that may facilitate the performance of workers in adaptive automation assembly systems (A3Ss).Such systems form core components in one of the proposed frameworks of Industry 4.0.Therefore, studying the performance of humans in AR environments is significant in promoting the performance and productivity of the A3Ss.Comparisons of body segment movements interacting with virtual and real objects are helpful in improving the designs of VR/AR systems [5].Deng et al. [41] discussed the MT under virtual environments but did not compare the difference of the MT between handling real and virtual objects because their ray-casting technique is not applicable to real objects.Zhao et al. [5] compared the MT of pointing tasks between real and virtual calculator panels.Their participants pointed at buttons on both real and virtual keypads using the same hand/arm movements.However, they found that the MT of pointing virtual buttons when using an AR device was significantly (p < 0.0001) longer than that of pointing solid buttons in the real world.They explained that such a phenomenon was due to the lack of tactile feedback when using a virtual keypad.Indeed, lacking tactile feedback could affect the participants' capability in tapping the virtual buttons rapidly because the participants could not judge whether the pointing was successful or not at the moment when their fingertips were touching the virtual buttons.Instead of tactile feedback, their participants needed both auditory and visual feedback to confirm the success of the tapping.In addition to the lack of tactile feedback, the researchers also attributed the inefficiency of pointing virtual targets to the less accurate visual positioning of the targets due to the deviation of visual depth in the virtual environment.
The lack of efficiency in pointing virtual targets, such as in Zhao et al. [5], could also occur in virtual object grasping and transferring processes.This, however, has not been reported in the literature.This study was designed to fill this research gap.We aimed to investigate the difference of the MT between transferring an object in the real and virtual environment.Our first hypothesis was that transferring a virtual object from one location to another is less efficient than transferring a real object of the same size under the same transferring distance.Another hypothesis of this study was that the MT of transferring both a real and a virtual object is dependent upon factors such as gender, handedness, and transfer direction.The third hypothesis was that the participants need a longer time to transfer an object when they feel the transfer is difficult.In other words, the subjective rating of difficulty in object transferring is positively correlated with the MT.Our objective was to test these hypotheses.In addition, additive models, based on Equation (2), to predict the MT of transferring both real and virtual objects, considering the gender and handedness, were developed.The difference in the MT between transferring real and virtual objects was discussed.

Materials and Methods
A pipe transferring experiment was performed in the laboratory.

Human Participants
Thirty adult participants (15 males and 15 females) joined.All of them were healthy and had a corrected visual acuity of 0.8 or higher for both the left and right eyes and had normal color vision.The mean (±std) age, stature, functional arm reach (right), and body weight for female participants were 22.47 (±3.16) yrs, 159.80 (±6.95) cm, 58.27 (±3.84) cm, and 55.20 (±1.66) kg, respectively.The mean (±std) age, stature, functional arm reach (right), and body weight for male participants were 22.86 (±6.84) yrs, 172.93 (±3.15) cm, 62.93 (±3.09) cm, and 57.43 (±1.92) kg, respectively.The dominant hand of five female and two male participants was the left hand.All the other participants were right-handed.All the participants read and signed an informed consent before joining the study.

Pipes and AR Device
There were two types of pipes in the experiment: real and virtual.Three plastic pipes purchased from a local hardware store were prepared for the real pipe trials.The outer diameters (W) of these pipes were 2.2, 4.7, and 6 cm, and the lengths of these pipes were 12.5, 23.5, and 32 cm, respectively.The weights of these pipes were 30, 85, and 175 g, respectively.
A Microsoft ® Hololens 2 AR device (Microsoft ® , Redmond, WA, USA) was adopted.The weight of this device is 566 g.This device adopts built-in cameras, which allow tracking the hand gesture of the user.The app HoloPipes in Hololens 2 was adopted for the trials in the virtual conditions.In this app, there are pieces of pipes in different shapes (straight, arc, and U-shaped).A user may grasp or pinch a piece of pipe and place it in another location.When the hand of the user is approaching the pipe, a cubic frame surrounding the pipe appears (see Figure 1).The cubic frame disappears when the hand is away from the pipe.This frame was designed so that the user may change the dimension of the pipe by pulling or pushing on two diagonal corners of the frame using two hands or rotating the pipe by pinching and pulling a bar attached to one of the edges.Straight virtual pipes of the same dimensions as those of the real pipes were prepared.
purchased from a local hardware store were prepared for the real pipe trials.T diameters (W) of these pipes were 2.2, 4.7, and 6 cm, and the lengths of these pip 12.5, 23.5, and 32 cm, respectively.The weights of these pipes were 30, 85, an respectively.
A Microsoft ® Hololens 2 AR device (Microsoft ® , Redmond, WA, USA) was a The weight of this device is 566 g.This device adopts built-in cameras, whic tracking the hand gesture of the user.The app HoloPipes in Hololens 2 was ado the trials in the virtual conditions.In this app, there are pieces of pipes in differen (straight, arc, and U-shaped).A user may grasp or pinch a piece of pipe and pl another location.When the hand of the user is approaching the pipe, a cub surrounding the pipe appears (see Figure 1).The cubic frame disappears when t is away from the pipe.This frame was designed so that the user may change the di of the pipe by pulling or pushing on two diagonal corners of the frame using tw or rotating the pipe by pinching and pulling a bar attached to one of the edges.virtual pipes of the same dimensions as those of the real pipes were prepared.

Pipe Transferring Tasks
A workbench with a height of 75 cm was prepared.On this bench, each of circles consistent with the diameters of the pipes being tested were marked on the of a plastic board (3 mm thick) and the board was attached to the bench.One of th was the origin and the other was the end.The pipe transferring tasks, both trans virtual and a real pipe, were performed on this bench.On the bench, a pipe wa vertically in the origin of the circle by an experimenter.The participant sat approx 25 cm in front of the workbench.He or she was then instructed to grasp or pinch in the origin and transfer it to the other circle.
The pipe transferring tasks included lateral and anterior-posterior moveme Figures 2 and 3).For lateral movements, the pipes of all three diameters were teste distances (D: d1, d2, and d3) between the origin and end were tested for each pipe d These distances and the corresponding ID, calculated using the original Fitts' d [2,3], are shown in Table 1.When adjusting the diameter of the virtual pipe, the di of the virtual cubic frame also changed.The virtual pipe can be placed only in un frame size.This was why d1, d2, and d3 were different for different diameters of th

Pipe Transferring Tasks
A workbench with a height of 75 cm was prepared.On this bench, each of the two circles consistent with the diameters of the pipes being tested were marked on the middle of a plastic board (3 mm thick) and the board was attached to the bench.One of the circles was the origin and the other was the end.The pipe transferring tasks, both transferring a virtual and a real pipe, were performed on this bench.On the bench, a pipe was placed vertically in the origin of the circle by an experimenter.The participant sat approximately 25 cm in front of the workbench.He or she was then instructed to grasp or pinch the pipe in the origin and transfer it to the other circle.
The pipe transferring tasks included lateral and anterior-posterior movements (see Figures 2 and 3).For lateral movements, the pipes of all three diameters were tested.Three distances (D: d 1 , d 2 , and d 3 ) between the origin and end were tested for each pipe diameter.These distances and the corresponding ID, calculated using the original Fitts' definition [2,3], are shown in Table 1.When adjusting the diameter of the virtual pipe, the dimension of the virtual cubic frame also changed.The virtual pipe can be placed only in units of the frame size.This was why d 1 , d 2 , and d 3 were different for different diameters of the pipes.
For anterior-posterior movements, only the ø2.2 cm pipe was utilized for both real and virtual conditions.The d 1 , d 2 , and d 3 were 12.5 cm, 25 cm, and 37.5 cm, respectively.The pipes of the other two diameters were not tested due to the limitation of arm reach of the participants.The ID for these three distances were 3.51, 4.51, and 5.1 bit, respectively.For anterior-posterior movements, only the ø2.2 cm pipe was utilized for both real and virtual conditions.The d1, d2, and d3 were 12.5 cm, 25 cm, and 37.5 cm, respectively.The pipes of the other two diameters were not tested due to the limitation of arm reach of the participants.The ID for these three distances were 3.51, 4.51, and 5.1 bit, respectively.

Data Collection and Analysis
The order of the pipe transferring tasks for each participant was randomly arranged.For virtual pipe transfers, the participants practiced grasping and pinching the virtual pipe, transferring it to another location, and releasing it before performing the first trial.The participants could practice until they were confident that they could complete the pipe transfer.For each of the pipe diameter and distance conditions, the participants performed the transfer twice by reversing the origin and end circles using each of the dominant and non-dominant hands.These trials were not performed consecutively.For anterior-posterior movements, only the ø2.2 cm pipe was utilized for both real and virtual conditions.The d1, d2, and d3 were 12.5 cm, 25 cm, and 37.5 cm, respectively.The pipes of the other two diameters were not tested due to the limitation of arm reach of the participants.The ID for these three distances were 3.51, 4.51, and 5.1 bit, respectively.

Data Collection and Analysis
The order of the pipe transferring tasks for each participant was randomly arranged.For virtual pipe transfers, the participants practiced grasping and pinching the virtual pipe, transferring it to another location, and releasing it before performing the first trial.The participants could practice until they were confident that they could complete the pipe transfer.For each of the pipe diameter and distance conditions, the participants performed the transfer twice by reversing the origin and end circles using each of the dominant and non-dominant hands.These trials were not performed consecutively.

Data Collection and Analysis
The order of the pipe transferring tasks for each participant was randomly arranged.For virtual pipe transfers, the participants practiced grasping and pinching the virtual pipe, transferring it to another location, and releasing it before performing the first trial.The participants could practice until they were confident that they could complete the pipe transfer.For each of the pipe diameter and distance conditions, the participants performed the transfer twice by reversing the origin and end circles using each of the dominant and non-dominant hands.These trials were not performed consecutively.Instead, they were randomly arranged.For both the real and virtual pipe transfer trials, the participants were instructed to transfer the pipe from the origin to the end.They could adjust their pace so as to put the pipe exactly within the circle of the end.
The videos of the virtual pipe transfer tasks, shared by the Hololens 2, on a laptop computer were saved for each trial.For the real pipe transfer tasks, videos were taken using a smart phone.The videos were also stored on a laptop computer.The pipe movement time (MT), from the hand touching the pipe at the beginning to the release of the pipe at the end, was captured via the timer of the videos.In addition to the MT, the participant gave a subjective rating on the difficulty of the task on a five-point scale: 1. easy, 2. somewhat difficult, 3. difficult, 4. very difficult, and 5. extremely difficult.
For the lateral pipe transfer tasks, a total of 2160 trials were performed.These were comprised of 2 genders, 15 participants for each gender, 2 hands (dominant and nondominant hands), 2 origins, 3 pipe diameters, 3 transfer distances, and 2 types of pipes (real and virtual).For the anterior-posterior transfer tasks, a total of 720 trials were performed.These were comprised of 2 genders, 15 participants for each gender, 2 hands, 2 origins, 3 transfer distances, and 2 types of pipes.
We conducted descriptive statistics and analysis of variance (ANOVA) on both MT and subjective rating of difficulty.A pair-wised t test was performed on the ø2.2 cm pipe to compare the difference of the MT and subjective rating of difficulty between the lateral and anterior-posterior transfers.Duncan's multiple range tests were performed for the posterior comparisons of the factors if they reached the α = 0.05 significance level.Regression analysis was performed to incorporate the gender, handedness, real/virtual, transferring direction, and the ID [2,3], which aided in establishing the predictive MT model: MT = f (gender, handedness, type of pipe, transferring direction, ID) The regression analyses of MT were performed using both all the data collectively compiled and separately for each of the lateral and anterior-posterior transfer, type of pipe, and pipe diameter conditions.The ID was calculated using the original Fitts' definition: log 2 (2D/W).

Movement Time
Figure 4 shows the MT results for the lateral pipe transfers.The ANOVA results on the MT of the lateral transfers indicated that the effects of gender (p < 0.0001), type of pipe (p < 0.0001), W (p < 0.0001), and D (p < 0.0001) were significant.The interaction effects of both gender × type of pipe (p < 0.0001) and type of pipe × W (p < 0.0001) were also statistically significant.On the contrary, handedness was not significant on the MT.Based on the results of Duncan's tests, the MT of female participants (1852.74ms) was significantly longer than that of males (1616.13ms) (p < 0.05).The MT of transferring to a distance of d 3 (1874.91ms) was also significantly longer than transferring to a distance of d 2 (1737.02ms) and d 1 (1591.37ms) (p < 0.05).Additionally, the MT of transferring to a distance of d 2 was significantly longer than that of d 1 (p < 0.05).The MT of transferring a real pipe (2161.08 ms) was also significantly longer than that of transferring a virtual pipe (1307.79ms) (p < 0.05).Moreover, the MT of transferring the ø6 cm pipe (1820.87ms) was significantly longer than those of the ø4.7 cm (1723.73ms) and the ø2.2 cm pipes (1658.70 ms) (p < 0.05).The MT between the ø4.7 cm and ø2.2 cm pipes was not significant.
Figure 5 shows the MT results of pipe transferring in the anterior-posterior direction.The ANOVA results indicated that gender (p < 0.0001), handedness (p < 0.05), type of pipe (p < 0.0001), D (p < 0.0001), and handedness × type of pipe (p < 0.05) were significant on the MT.The MT of female participants (1732.43ms) was also significantly longer than that (1515.17ms) of male participants (p < 0.05).The MT of the non-dominant hand (1670.64ms) was significantly longer than that (1576.96ms) of the dominant hand (p < 0.05).Moreover, the MT of transferring a real pipe (1908.91 ms) was significantly longer than that (1338.69ms) of transferring a virtual pipe (p < 0.05), and the MT of transferring the pipe to a distance of d 3 (1748.69ms) was significantly longer than to a distance of d 2 (1615.36ms) and d 1 (1507.35ms) (p < 0.05).Lastly, the MT of transferring the pipe to a distance of d 2 was significantly longer than that of a distance of d 1 (p < 0.05).Figure 5 shows the MT results of pipe transferring in the anterior-posterior direction.The ANOVA results indicated that gender (p < 0.0001), handedness (p < 0.05), type of pipe (p < 0.0001), D (p < 0.0001), and handedness × type of pipe (p < 0.05) were significant on the MT.The MT of female participants (1732.43ms) was also significantly longer than that (1515.17ms) of male participants (p < 0.05).The MT of the non-dominant hand (1670.64ms) was significantly longer than that (1576.96ms) of the dominant hand (p < 0.05).Moreover, the MT of transferring a real pipe (1908.91 ms) was significantly longer than that (1338.69ms) of transferring a virtual pipe (p < 0.05), and the MT of transferring the pipe to a distance of d3 (1748.69ms) was significantly longer than to a distance of d2 (1615.36ms) and d1 (1507.35ms) (p < 0.05).Lastly, the MT of transferring the pipe to a distance of d2 was significantly longer than that of a distance of d1 (p < 0.05).The results of the pair-wise t test on the ø2.2 cm pipe trials indicated that the MT between the lateral transfers and the anterior-posterior transfers were not significantly different at α = 0.05.

Subjective Rating of Difficulty
Figure 6 shows the subjective rating of difficulty results for female and male participants for the lateral transfers.The ANOVA results indicated that the rating of difficulty was significantly affected by gender (p < 0.0001), handedness (p < 0.01), type of pipe (p < 0.0001), D (p < 0.0001), W (p < 0.001), gender × type of pipe (p < 0.0001), handedness × type of pipe (p < 0.01), D × W (p < 0.0001), and W × type of pipe (p < 0.05).Figure 5 shows the MT results of pipe transferring in the anterior-posterior dire The ANOVA results indicated that gender (p < 0.0001), handedness (p < 0.05), type o (p < 0.0001), D (p < 0.0001), and handedness × type of pipe (p < 0.05) were significant o MT.The MT of female participants (1732.43ms) was also significantly longer than (1515.17ms) of male participants (p < 0.05).The MT of the non-dominant hand (16 ms) was significantly longer than that (1576.96ms) of the dominant hand (p < Moreover, the MT of transferring a real pipe (1908.91 ms) was significantly longer that (1338.69ms) of transferring a virtual pipe (p < 0.05), and the MT of transferrin pipe to a distance of d3 (1748.69ms) was significantly longer than to a distance (1615.36ms) and d1 (1507.35ms) (p < 0.05).Lastly, the MT of transferring the pip distance of d2 was significantly longer than that of a distance of d1 (p < 0.05).The results of the pair-wise t test on the ø2.2 cm pipe trials indicated that th between the lateral transfers and the anterior-posterior transfers were not signific different at α = 0.05.The results of the pair-wise t test on the ø2.2 cm pipe trials indicated that the MT between the lateral transfers and the anterior-posterior transfers were not significantly different at α = 0.05.

Subjective Rating of Difficulty
Figure 6 shows the subjective rating of difficulty results for female and male participants for the lateral transfers.The ANOVA results indicated that the rating of difficulty was significantly affected by gender (p < 0.0001), handedness (p < 0.01), type of pipe (p < 0.0001), D (p < 0.0001), W (p < 0.001), gender × type of pipe (p < 0.0001), handedness × type of pipe (p < 0.01), D × W (p < 0.0001), and W × type of pipe (p < 0.05).The rating of difficulty for female participants (1.91) was significantly higher than that (1.54) of their male counterparts (p < 0.05).The rating of difficulty when transferring the real pipe (1.99) was also significantly higher than that (1.46) of the virtual pipe (p < 0.05).Furthermore, the rating of difficulty using the non-dominant hand (1.77) was significantly higher than that (1.68) of using the dominant hand (p < 0.05).The ratings of difficulty for both d 2 (1.69) and d 1 (1.64) transfers were significantly lower than that (1.85) of the d 3 transfer (p < 0.05).The difference between the d 2 and d 1 transfers was not significant.The ratings of difficulty for both the ø2.2 cm (1.79) and ø6 cm (1.73) pipes were significantly higher than that of the ø4.7 cm pipe (1.65) (p < 0.05).Finally, the difference between the ø2.2 cm and ø6 cm pipes was insignificant.
both d2 (1.69) and d1 (1.64) transfers were significantly lower than that (1.85) of the d3 transfer (p < 0.05).The difference between the d2 and d1 transfers was not significant.The ratings of difficulty for both the ø2.2 cm (1.79) and ø6 cm (1.73) pipes were significantly higher than that of the ø4.7 cm pipe (1.65) (p < 0.05).Finally, the difference between the ø2.2 cm and ø6 cm pipes was insignificant. Figure 7 shows the subjective rating of difficulty results for female and male participants for the anterior-posterior transfers.The rating of difficulty was significantly affected by gender, type of pipe, D, and gender × type of pipe.The p-values for all these terms were less than 0.0001.The effects of handedness were insignificant.Based on Duncan's test results, the rating of difficulty for female participants (1.80) was significantly higher than that (1.60) of their male counterparts (p < 0.05).The rating of difficulty when transferring the real pipe (1.83) was also significantly (p < 0.05) higher than that (1.58) of the virtual pipe.The ratings of difficulty for both the d2 (1.68) and d1 (1.59) cm pipes were significantly lower than that of d3 (1.84) pipe (p < 0.05).The difference between d1 and d2 transfers was also insignificant. Figure 7 shows the subjective rating of difficulty results for female and male participants for the anterior-posterior transfers.The rating of difficulty was significantly affected by gender, type of pipe, D, and gender × type of pipe.The p-values for all these terms were less than 0.0001.The effects of handedness were insignificant.Based on Duncan's test results, the rating of difficulty for female participants (1.80) was significantly higher than that (1.60) of their male counterparts (p < 0.05).The rating of difficulty when transferring the real pipe (1.83) was also significantly (p < 0.05) higher than that (1.58) of the virtual pipe.The ratings of difficulty for both the d 2 (1.68) and d 1 (1.59) cm pipes were significantly lower than that of d 3 (1.84)pipe (p < 0.05).The difference between d 1 and d 2 transfers was also insignificant.
ø2.2 cm and ø6 cm pipes was insignificant. Figure 7 shows the subjective rating of difficulty results for female and m participants for the anterior-posterior transfers.The rating of difficulty was significan affected by gender, type of pipe, D, and gender × type of pipe.The p-values for all th terms were less than 0.0001.The effects of handedness were insignificant.Based Duncan's test results, the rating of difficulty for female participants (1.80) was significan higher than that (1.60) of their male counterparts (p < 0.05).The rating of difficulty w transferring the real pipe (1.83) was also significantly (p < 0.05) higher than that (1.58 the virtual pipe.The ratings of difficulty for both the d2 (1.68) and d1 (1.59) cm pipes w significantly lower than that of d3 (1.84) pipe (p < 0.05).The difference between d1 and transfers was also insignificant.The results of the pair-wise t test on the ø2.2 cm pipe trials indicated that the subjective rating of difficulty of the lateral transfers (1.74) was significantly (p < 0.05) higher than that (1.65) of the anterior-posterior transfers.
The Pearson's correlation coefficient between the MT and subjective rating of difficulty for all the data in both lateral and anterior-posterior transfers was 0.48 (p < 0.0001).This indicates a positive correlation between the two variables.

Regression Analyses of Movement Time
The relationship between the MT and independent variables for all the data obtained in the experiment were determined using a regression analysis.We obtained the following equation: MT = −195.2x 1 + 61.0 x 2 + 176.8 x 3 + 819.1 where x 1 , x 2 , x 3, and x 4 are gender, handedness, transferring direction, and type of pipe, respectively, and are dummy variables, as follows: x 1 = 0 if female, = 1 otherwise, x 2 = 0 if dominant hand, = 1 otherwise, x 3 = 0 if anterior-posterior transfer, = 1 if lateral transfer, x 4 = 0 if transferring virtual pipe, = 1 if transferring real pipe, The R adj 2 of Equation ( 4) is 0.92.The regression coefficient of x 2 in Equation ( 4) was significant at p < 0.01.All the other regression coefficients in this equation were statistically significant at p < 0.0001.The ID values in Table 1 were adopted in establishing Equation ( 4).
Alternatively, we also conducted a regression analysis of the MT (ms) for each of the lateral-anterior/posterior, type of pipe, and diameter of pipe condition using the following equation: where x 1 and x 2 are dummy variables to represent gender and handedness and have been defined above; β 1 , β 2 , and β 3 are constants to be determined.The results of the regression analysis are shown in Table 2. Note: all the β 1 , β 2 , and β 3 were statistically significant at p < 0.0001 except those at † p < 0.05, † † p < 0.01, and * p > 0.05.The unit for MT, β 1 , and β 2 is ms; the unit of β 3 is ms/bit.The units of diameter and 1/β 3 are cm and bit/s, respectively.

Virtual and Real Pipe Transfers
The MT of transferring a real pipe was significantly (p < 0.0001) longer than that of transferring a virtual pipe for both lateral and anterior-posterior transferring.Our first hypothesis was rejected.The lack of efficiency in pointing virtual targets which occurred in Zhao et al. [5] did not occur in our pipe transferring tasks.This may be attributed to the fact that the movements of our pipe transferring were much more complicated than that pointing a target.The participants in Zhao et al. [5] needed only to move their fingertips to tap the button on a keypad, while our participants needed to grasp or pinch the pipe, transfer it to the end, and then release the pipe.
For real pipe transferring, the participants pinched the ø2.2 cm pipe and grasped the pipes of the other two dimensions to hold the pipe firmly.For virtual pipes, the participants could either pinch or grasp the pipe no matter how large the pipe was.The Holopipe app recognizes a catch of the pipe when the fingertip of the index finger is in touch with the thumb.We observed that most of our participants pinched the virtual pipes for all three dimensions.The virtual pipe did not "drop" unless the tips of the index finger and the thumb were not in contact with each other during the transfer of the pipe.Pinching was easier than grasping in both holding and releasing a pipe because the former involves only the index finger, while the latter involves all four fingers in addition to the thumb.Moreover, the participants needed to aim at the end circle before they could put the pipe in circle.It was also easier to aim at the end circle while pinching than while grasping.These were the main reasons why transferring a virtual pipe was perceived as easier and required less time to complete than transferring a real one.Our findings should be considered when implementing an AR device in training programs involving object transferring.The efficiency in transferring virtual objects could be significantly higher than that of transferring real objects of the same dimension for the same distance.Trainees who transfer virtual objects using an AR device in a training program might overestimate the efficiency of object transferring which will occur in the real world.
As we have mentioned earlier, when the hands of the participants reached the virtual pipe, a virtual cubic frame appeared.This provided a visual cue of hand positioning with respect to the pipe and was helpful for users to confirm hand-virtual pipe contact.This implies that using supplemental designs, such as the cubic frame in the HoloPipe app, to provide extra visual cues would improve the efficiency of human interaction with virtual objects.We also observed that the pinching or grasping of the pipe was successful even when the fingertips were not actually "in touch with" the pipe.This means that there was a tolerance between the fingertips and the virtual pipe for a pinch or grasp which did not exist in the real pipe transferring.The participants' hand must be in touch with the pipe and have control of the pipe before a real pipe transfer could be started.This also contributed to the MT difference between the real and virtual conditions.This implies that tolerance designs in the geometry of hand-virtual object contacts could make an AR app more friendly when this app is operated using hand gestures.More studies are required to confirm this.
The pair-wise t test results revealed that the difference in the MT of transferring the ø2.2 cm pipe between the lateral and anterior-posterior directions was insignificant.Handedness was significant on the MT of anterior-posterior pipe transfer but was insignificant on the lateral pipe transfer.Gender was significant on the MT in both transfer directions.Therefore, our second hypothesis was partially supported.The ANOVA results on both the MT and subjective rating of difficulty showed that gender, type of pipe, and transferring distance were all significant factors on the two dependent variables.The correlation analysis results also indicated a positive correlation between the MT and the rating of difficulty.These confirmed the acceptance of the third hypothesis of this study.

MT Modeling
The literature [31,32] has revealed that target size may be neglected in determining the ID when the ID is less than three.The ID in establishing Equation ( 4) was in the range of 3.3 to 5.1 bit, which was higher than three and the target size, i.e., the diameter of the pipe, should be considered.Equation ( 4) is an additive model considering gender, handedness, transferring direction, and real/virtual conditions.The R adj 2 of this equation was 0.92 indicating that 92% of the variation of the MT may be explained by this model.This model may be applied in predicting the MT in the corresponding pipe transferring conditions.
The regression coefficients indicate the change of MT when an independent variable has changed one unit.Among all the regression coefficients in Equation ( 4), the regression coefficient of x 2 (61.0) is the lowest, indicating that using either the dominant or nondominant hand, on average, only leads to an MT difference of 61 ms.This is consistent with the results in Table 2 where five regression coefficients of handedness were not significant at α = 0.05.Four of these five coefficients occurred in virtual pipe conditions, indicating that the insignificance of handedness occurred primarily when the participants were interacting with the virtual pipe.
The regression coefficient of x 4 (819.1) in Equation ( 4), on the other hand, was the highest among all regression coefficients.Transferring a real pipe, on average, needed 819.1 ms longer than transferring a virtual pipe.This implies that transferring a real pipe was less efficient than transferring a virtual pipe.This was consistent with the results in the ANOVA of the MT.The regression coefficient of x 1 in Equation ( 4) indicates that the MT of female participants, on average, was 195.2 ms longer than that of their male counterparts.The β 1 values in Table 2 show that the MT difference between the two genders occurred primarily in transferring the real pipe, especially in the lateral transfers.The hand sizes of female adults, in general, are smaller than those of male adults.Our female participants probably needed more time to grasp, move, position, and release the real pipe than their male counterparts due to their relatively smaller hand size even though we did not measure this size.While transferring a virtual pipe, hand size, on the other hand, played a minor role in the MT because both males and females pinched the pipe.
The inverse of the regression coefficient of the ID indicates the information processing rate, or the performance, of the object transfer [2,3,15].This inverse in Equation ( 4) is 3.5 bit/s (1/0.2823), which was the average of overall conditions.The 1/β 3 in Table 2 shows the information processing rate under each transferring condition.The values of transferring real pipe (1.7 to 2.3 bit/s) are lower than those of transferring virtual pipe (3.1 to 3.4 bit/s).This provides another piece of evidence, in addition to the ANOVA results, that transferring a real pipe was inefficient compared to transferring a virtual pipe.
The information processing rate of Fitts' disc and pin transfer tasks were 7.5 to 10.4 bit/s and 8.9 to 12.6 bit/s [2], respectively.This rate involves finger, wrist, and arm motions, which were reported by Langolf et al. [1] to be 38, 23, and 10 bits/s, respectively.Hancock et al. [48] revealed that movements using fingers and wrist only produced the performance of 20 bits/s.The movements involved preferred foot and head movements that were in the range of 18 bits/s [10] and 5 to 7 bit/s [15,18], respectively.All these information processing rates were higher than the values in our study.This could be attributed to the fact that the movements in the above-mentioned literature were rapid movements that the participants were requested to complete as fast as possible.Our participants were instructed to put the pipe exactly within the end circle at their self-selected pace.In other words, placement errors of the pipes in the end circle were not allowed.The participants could sacrifice their movement speed to fulfill the accuracy requirement.Murakami and Yamada [7] indicated that human motion was featured by a significantly reduced degree of trajectory variation and amplified movement time toward the target when tapping errors are not allowed.These could explain the low information rate of our data.

Limitations of the Study
The virtual pipe adopted in this study was generated by the HoloPipes app in the Hololens 2 device.The sensitivity of this app in sensing the hand-pipe contact in the transferring tasks could affect the MT and subjective rating of difficulty and was unknown.Our results, apparently, are not applicable in handling virtual pipes generated by other AR apps or software and using other AR devices.This is the first limitation of this study.In addition, only real and virtual pipes were tested.The shape of the object could be an important factor affecting the MT and subjective rating of difficulty.For example, the MT and perceived difficulty in transferring a ball or a rectangular bar could be different from those of transferring a pipe.Such a difference could even be obvious when the ball or the rectangular bar is virtual.Even Deng et al. [41] have studied the MT of transferring a virtual ball.Their participants, however, did not use their hands to grasp the virtual ball as we normally do in moving a real ball.Their results, therefore, are not comparable to the MT of transferring a real ball.Comparing the difference of the MT of transferring an object with a shape other than a pipe will provide interesting research topics in the future.
Another issue of the real and virtual objects relates to the weight.The MT of transferring an object from one location to another may be affected by the weight of the object when a significant amount of muscular contraction and exergy consumption are required.Transferring a heavy object may require more time than transferring a light object due to the activation of muscular contraction for the former.The weights of our real pipes were only 175 g or less.We believe that such a weight had no or little effect on the MT of pipe transferring, and the effects of pipe weight on the MT could be neglected.To the best of our knowledge, most of the object transferring studies using Fitts' law tested tiny, light-weight objects so that their participants could transfer the object as quickly as possible.The effects of the weight have not been considered.We believe that when the weight of the object reaches a certain threshold, the effects of the weight could play a role in the MT.Future research may be performed to verify if this is true and to investigate the effects of object weight on the MT under similar scenarios.

Conclusions
The hypothesis that transferring a virtual object is less efficient than transferring a real object was rejected.The participants could transfer a virtual pipe from one location to another on the same horizontal surface significantly faster than transferring a real pipe.This finding contradicted with the prior literature [5] that implicated the results reported in the past concerning the MT of pointing tasks to not be applicable to the tasks of virtual object transferring.This also indicates the complexity of hand-virtual object interactions and the need for more research in the future.The hypothesis that the MT of transferring both a real and a virtual object is dependent upon several factors was partially supported and the hypothesis that the subjective rating of difficulty in object transferring is positively correlated with the MT was supported by our data.This implies that AR designers may predict the performance of AR users based on their ratings of difficulty in using the app on the device.Finally, we have established additive Fitts' law-based MT models.These models could be adopted to predict the MT between handling real and virtual pipes under gender, handedness, and transferring direction conditions.There are many other unexplored issues concerning user behaviors in interacting with virtual objects when using an AR device.The effects of the weight and shape of the object being handled, as we have mentioned in Section 4.3, on the MT provide interesting future research topics.

Figure 1 .
Figure 1.A virtual pipe and the cubic frame surrounding the pipe: a view from the Holole

Figure 1 .
Figure 1.A virtual pipe and the cubic frame surrounding the pipe: a view from the Hololens 2 user.

Figure 2 .
Figure 2. Pinching a real ø2.2cm pipe (a) and grasping a virtual ø4.7 cm pipe (b) at the origin (photo taken by another Hololens 2 user).

Figure 3 .
Figure 3. Putting (a) a real and (b) a virtual pipe (photo taken by another Hololens 2 user) in the end circle in the anterior-posterior direction.

Figure 2 .
Figure 2. Pinching a real ø2.2cm pipe (a) and grasping a virtual ø4.7 cm pipe (b) at the origin (photo taken by another Hololens 2 user).

Figure 2 .
Figure 2. Pinching a real ø2.2cm pipe (a) and grasping a virtual ø4.7 cm pipe (b) at the origin (photo taken by another Hololens 2 user).

Figure 3 .
Figure 3. Putting (a) a real and (b) a virtual pipe (photo taken by another Hololens 2 user) in the end circle in the anterior-posterior direction.

Figure 3 .
Figure 3. Putting (a) a real and (b) a virtual pipe (photo taken by another Hololens 2 user) in the end circle in the anterior-posterior direction.

Figure 6 .
Figure 6.Subjective rating of difficulty in lateral pipe transfers.

Figure 6 .
Figure 6.Subjective rating of difficulty in lateral pipe transfers.

Table 1 .
Distance (D)and Index of Difficulty for lateral movements.Note: Unit for W and distance: cm; unit for ID: bit.

Table 1 .
Distance (D) and Index of Difficulty for lateral movements.
Note: Unit for W and distance: cm; unit for ID: bit.

Table 1 .
Distance (D) and Index of Difficulty for lateral movements.

Diameter (W) d 1 ID 1 d 2 ID 2 d 3 ID 3
Note: Unit for W and distance: cm; unit for ID: bit.

Table 2 .
Regression coefficients and R adj 2 of the MT models.