Modelling Movement Time for Haptic-enabled Virtual Assembly

Samir Garbaya

and Vincent Hugel

END-ICAP Laboratory - INSERM, Arts et Metiers Institute of Technology,

CNAM, LIFSE, HESAM University, F-75013, Paris, France

Laboratoire Cosmer, Université de Toulon, CS 60584 83041, Toulon Cedex 9, France

Keywords: Human Computer Interaction, Fitts' Law, Virtual Assembly, Haptic Feedback.

Abstract: Mechanical assembly consists of joining two or more components together. Manual assembly tasks include

different activities to obtain functional products. In order to estimate the assembly cost and elaborate the

assembly plan for a product, it is important to measure the duration of the assembly operations. The research

reported in this paper aims at investigating if Fitts’ law, which has been widely adopted in numerous research

areas including kinematics, human factors and human-computer interaction, can be adopted as a model to

estimate the movement time in assembling parts in virtual assembly environment with haptic feedback. The

results reported in this paper showed that Fitts’ law can be applied for modelling the movement time in

assembling cylindrical parts. However, the analysis of the experimental data showed that when changing the

diameter of the moved part, this could have an effect on the movement time. This is promising for the

formulation of an inverted Fitts’ law for cylindrical parts’ assembly.

1 INTRODUCTION

Global competition has forced manufacturers to

reduce production cycles and enable product design

agility. In general, a manufacturing process is divided

into product design, process design, manufacturing

and assembly. The attempts to accelerate the process

through the development of computer aided assembly

planning systems have not, in general, been

successful although the design has been carried out

using a modern CAD system (De Mello &

Sanderson). One of the main reasons for this lack of

success is that assembly is dependent on a great deal

of expert knowledge, which has proved to be very

difficult to formalize (Dewar, Carpenter, Ritchie, &

Simmons, 1997), (Nevins & Whitney, 1980). The

important advances made in the recent decades in

virtual reality technologies provided intuitive

approaches for virtual interaction, notably for the

virtualization of assembly operations and planning.

Instead of abstract algorithmic assembly planning, an

engineer could perform the assembly intuitively in

virtual environment (VE) using VR hardware and

software (Gupta, Whitney, & Zeltzer, 1997).

https://orcid.org/0000-0003-0676-8320

Assembling mechanical products by manipulating

virtual parts provides an information feedback to the

designer in order to refine the product design based

on the information obtained from the assembly trials

and the degree of feasibility of the assembly sequence

generated from the interaction with VE (Boothroyd,

Geoffrey. Dewhurst, Peter. Knight, 1994), (Santochi

and Dini, 1992). However, in order to obtain reliable

information from the interaction with the virtual

world, human behavior in the VE should be similar to

the behavior in real world. The virtual assembly

environment must provide the user with the illusion

of manipulating real parts. As such, the environment

must replicate the relevant characteristics of the real

assembly shop floor. Additionally, before using the

VE for complex interaction such as assembly

planning, it is important to show that the knowledge

obtained from the real world interaction, such as Fitts’

law, are also valid in VE. Then, quantitative and

qualitative information derived from the VE, such as

the assembly time of the vittual product and the

assembly plan, can be used for the design the

production system and for planning the activities in

the real world.

An assembly task can be divided into six basic

Garbaya, S. and Hugel, V.

Modelling Movement Time for Haptic-enabled Virtual Assembly.

DOI: 10.5220/0009038400530063

In Proceedings of the 15th International Joint Conference on Computer Vision, Imaging and Computer Graphics Theory and Applications (VISIGRAPP 2020) - Volume 2: HUCAPP, pages

53-63

ISBN: 978-989-758-402-2; ISSN: 2184-4321

activities such as reach, select, grasp, move, position,

and secure. Activities such as "reach" and "move" are

generated by biomechanics of body motions.

However, the activities such as “select”, “grasp”,

“position”, and “secure” require cognitive skills and

manual dexterity (Figure 1). For these reasons, the

estimation of the time necessary to assemble a

product is an important information for industry.

Figure 1: Segmentation of the manual assembly task.

Fitts' popular model has been proven one of the

most robust, highly cited and widely adopted models

to emerge from experimental psychology (Fitts,

1954), (Fitts & Peterson, 1964). It was applied in

numerous research areas; including kinematics,

human factors, and human-computer interaction

(Kerr & Langolf, 1977), (Hand, 1997). Psychomotor

studies in diverse settings have consistently shown

high correlation between Fitts’ index of difficulty and

the time to complete a movement task. Kinematics

and human factors are two fields particularly rich in

investigations of human performance using Fitts’

analogy (Fitts & Radford, 1966). Virtual reality offers

the potential to improve techniques over existing

computer interfaces, therefore offering benefits to

applications requiring human-computer interaction.

However, to obtain reliable results from VR, high

perceptual capabilities must be achieved and human

related factors should be taken into account in

designing 3D interfaces for the interaction with VE.

The literature review showed that most of the

reported studies used task completion time (TCT) and

error rates for the evaluation of the human

performance in VE. However, well-known paradigms

such as Fitts’ law were not used as a tool to validate

virtual environments before their adoption in the

product development (Chryssolouris, Mavrikios,

Fragos, & Karabatsou, 2000). For example, the

extrapolation of performance data obtained in VE to

the real world could only provide good results if the

characteristics of the VE allow the same interactive

conditions as in the real world.

In Fitts' experiment, the subject had to move a pointed

stylus as quickly as possible between two fixed

targets of width (W) set at a distance (A). The task

requires also hitting the two targets alternatively

(Figure 2.I). The analysis of the original Fitts’ law

experiment and the assembly of cylindrical parts

shows an analogy in the movement of the operator’s

hand in executing the task (Figure 2.II). Paul Fitts

suggested that the difficulty of a task could be

measured using the information metric bits, and he

introduced the idea that, the information is

transmitted through a human sensory channel when

carrying out a movement task (Fitts, 1954), (Langolf,

Chaffin, & Foulke, 1976). Fitts' equation for the

movement time (MT) is given by:

 =  + 

(1)

 = 









 in bits per response (2)

 =  + 









 in seconds (3)

Where ID is the Index of Difficulty and a, b are

constants.

The task index of performance (IP) is defined as

 =





in bits/second.

Sturges and Kilani applied Fitts' law index of

difficulty (ID) to quantify the dexterity and time

required to assemble a product (Sturges & Kilani,

1992). They formulated the task index of difficulty

as  = 2 (





) where W is the target width and S

the distance between the two parts to be assembled.

The manual assembly time is then obtained by

multiplying the ID by the human motor capacity.

However, this method did not investigate if the shapes

of the manipulated parts have any effect on the index

of difficulty, hence on the operator’s performance in

the execution of the assembly task.

(Gupta et al., 1997) reported on a 'peg in hole' task

performed using a PHANTOM device as a force

feedback system to manipulate a virtual peg in a hole.

The task index of difficulty was measured using Fitts'

law and by substituting the target width W for the

peg/hole clearance. Their formulation for the index of

difficulty was  = 2





 where h is the

handling distance; D is the diameter of the hole and d

is the diameter of the peg. The results indicated that

despite the provision of force feedback, a

significantly longer total assembly time was obtained

compared with the stable performance in the real task.

The increase of the assembly time might be originated

Position and

Secure

Grasp

Move

HUCAPP 2020 - 4th International Conference on Human Computer Interaction Theory and Applications

from the 3D interaction technique they used or the

lack of physical behavior of parts not included in the

virtual environment they developed.

Figure 2: The analogy between the original Fitts’ law (I)

and the assembly of cylindrical parts in virtual environment

(II).

(Deng, Geng, Hu, & Kuai, 2019) studied the

factors determining the movement time (MT) of

positioning an object in an immersive 3D virtual

environment where they varied three factors: the

object size, the movement amplitude and the target

tolerance. They identified three phases: the

acceleration phase, the deceleration phase and the

correction phase. They found that in the acceleration

phase, the movement time (MT) was inversely related

to object size and positively proportional to

movement amplitude but in the deceleration phase,

the (MT) was mainly determined by the movement

amplitude. In the correction phase, the (MT) was

affected by all three factors. Hence, they proposed a

three-phase model with different formulae at each

phase.

(Liu & Liere, 2011) introduced a 3D introduced a

model for the interaction with moving objects in

virtual environment. They divided the movement task

into two phases: the tacking phase and the connection

phase. According to their experiments, they found

that the time for the tracking phase is fixed once a task

has been established, However, the time for the

correction phase is dependent on the path length, the

velocity of the moving target and its width. The

authors considered that the movement time of an

object pursuit task can be minimized by determining

the optimum target velocity and that their model can

be used for the evaluation of the user interfaces

designed for the interaction with moving objects.

(Cha & Myung, 2013) developed an extended

Fitts’ model for pointing task in 3D environment. The

authors added to the formulation of the original Fitts’

law the inclination and azimuth angles of the

spherical coordinate system. The extended model

showed better adequacy with the data collected from

the experiments in terms statistical values of the

correlation coefficient and the standard error of the

residuals for the measured and predicted movement

time. These results were considered by the authors

important for the design of pointing tasks in 3D

environment and for accurate prediction of human

performance.

(Raghu Prasad, Purswani, & Manivannan, 2013)

developed and experiment to predict the minimum

movement time for a task involving the right index

finger carried out in virtual environment. The analysis

of the collected data for the movement time and the

index of difficulty showed that Fitts’ law is applicable

for a force based virtual movement task with visual

guidance.

(Lin, Caesaron, & Woldegiorgis, 2019) studied

the accuracy the accuracy of egocentric distance

estimation in stereoscopic virtual environment. They

investigated different interaction methods with 3D

objects by designing an acquisition task involving

direct pointing and indirect cursor techniques. They

found that indirect interaction mode allowed more

accuracy than direct mode and higher accuracy was

obtained for pointing task located at greatest distance

from the user. They also reported that high task

difficulty led to low accuracy level compared to the

accuracy obtained for medium and low task diculty.

The authors consider their work useful for the design

of effective interaction techniques where the accuracy

is an important factor.

(Schwind, Leusmann, & Henze, 2019) studied

investigated the effect the changes of model and

texture of a users' avatar on input performance in a

two-dimensional Fitts' law target selection task. Their

research showed that task completion time was not

affected neither by model nor texture changes, which

supports that body ownership and spatial localization

are independent the mechanism in visual-haptic

integration.

(Gallegos-Nieto, Medellín-Castillo, González-

Badillo, Lim, & Ritchie, 2017)studied the transfer of

Modelling Movement Time for Haptic-enabled Virtual Assembly

knowledge and skills from haptic-enabled virtual

assembly environment to real-world. They used a

system called Haptic Assembly and Manufacturing

System (HAMS) developed by (Gonzalez-Badillo,

Medellin-Castillo, Lim, Ritchie, & Garbaya, 2014).

The authors conducted an experiment involving three

groups of subjects and three training modes: Virtual

assembly including haptic feedback, virtual assembly

without haptic and training by watching a video.

Compared to training by video, virtual assembly

allowed up to 80% improvement in the performance

of the real assembly task. Additionaly, training with

haptic-enabled virtual assembly led to greater levels

of effectiveness than without haptics. It was also

noticed that training with virtual assembly showed

more effectiveness for more complex assembly task.

(Sagardia & Hulin, 2017) developed a platform

for bimanual haptic feedback for the assembly of

complex virtual objects. The haptic device was made

of two DLR/KUKA robot arms that include an

additional force-torque sensor at each robot wrist and

it displays six-DoF force feedback. The objective of

their research was to solve the virtual assembly

problems such as assembling objects with complex

geometries, bimanual six-DoF haptic interaction for

hands and arms, and intuitive navigation in large

workspaces. The authors conducted an experiment of

assemblig a car control box to test their system. The

results showed that it was able to handle complex

geometries and it allowed large upper body

movements with providing force and tactile feedback

to the hand and the forearm of the user.

(Wang, Huang, Li, & Liu, 2017) proposed a new

model for simulating forces for virtual assembly tasks

of mechanical parts with a clearance fit. They

decomposed the assembly operation into free

navigation state, positioning state and assembly state.

Upon the contact between parts, a collision force is

simulated and the assembly process enters the

positioning state. For enhancing the user perception,

they developed a model for the force rendered during

the assembly state. The system was evaluated for the

assembly of four sets of shaft-bushing with clearance

fits and the results showed that force rendering was

appreciated by the user eventhough shoter task

completion time was obtained without providing

force rendering.

(Lubos, Bruder, & Steinicke, 2015) analyzed the

impact of comfort on 3D selection tasks in an

immersive desktop setup. They investigated the

importance of comfort for the performance in 3D user

interfaces by analysing a set of most comfortable

body poses for the interaction. They studied the

influence of a comfortable arm rest on performance

in immersive desktop setups to allow users to

experience the immersive interaction without the

negative aspects and to increase the user comfort. The

authors conducted Fitts’ Law experiment in

immersive desktop setups. The results showed that

comfort has a significant effect on effective

throughput according to Fitts’ Law in IVEs.

(Sallnäs & Zhai, 2003) Investigated how handling

over objects can be supported in virtual environment.

They carried out an experiment in which subjects

passed a series of cubic objects to each other and

tapped them at target areas. The user performance

was evaluated for the conditions where haptic

feedback is provided and not provided in the

interaction. The authors considered their study in the

framework of Fitts’ law and hypothesized that object

hand off represented a collaboratively performed

Fitts’ law task. The results showed that task

completion time was increased with Fitts’ index of

difficulty, both with and without haptic feedback. The

time required for passing objects did not differ

significantly between the haptic and no haptic

conditions. However, the provision of haptic

feedback allowed to reduce significantly the error

rate.

In order to study the validity of Fitts’ law in VE,

we have developed a set of experiments in which a

human operator performs the task of assembling two

cylindrical parts. The objective is to investigate if

Fitts’ law could be applied for the estimation of the

movement time for the assembly of cylindrical parts.

Moreover, whether the human performance patterns

are similar to that obtained in the original experiments

of Paul Fitts. The task studied in this research is

inverted: instead of a pointed stylus, the probe is a

virtual mechanical part of finite width; it is moved to

a target location that is of smaller width than the

probe. These conditions represent the inverted Fitts'

law paradigm in which the moved object has a larger

width that the target object. These conditions are

common in assembly industry. The objective is to

investigate if the diameter of the moved part has an

effect on the movement time of the assembly task. In

these experiments, the sensation of the weight of the

manipulated parts and the contact forces are provided

to the operator using six degrees of freedom (DOF)

force feedback system (figure 3).

In order to study the movement time, an

experiment of assembling cylidrical parts was

designed in virtual environment. The task execution

was observed and the performance of the operator

was measured in terms of the task completion time

(Cochran & Cox, 1950).

HUCAPP 2020 - 4th International Conference on Human Computer Interaction Theory and Applications

2 ARCHITECTURE OF THE

VIRTUAL REALITY SYSTEM

The VE software runs on a laptop PC equipped with

a 2.20 GHZ Intel Dual Core processor and an ATI

Mobility Radeon graphics card. The virtual scene was

created in C++, using OpenGL library, and visualized

on the computer screen of 15.6 inches. The frame rate

of the image display was maintained at 35 frames per

second (Figure 3).

Figure 3: Hardware platform used in the experiments.

Figure 4: Principle of the generation of force feedback with

the VIRTUOSE haptic device.

In order to provide the operator with force

feedback during the manipulation of parts, the

VIRTUOSE™ 6D haptic interface was used. This

haptic interface system has 6 DOF (3 translations and

3 rotations) and renders 3D force and torque (Figures

4 and 5). Although the weight of the pointed stylus

was not taken into consideration in the original study

carried out by Paul Fitts’, it was decided to include

force feedback in the research described in this paper

to represent the physical conditions of the real

assembly task.

Figure 5: Virtual Reality System Architecture.

The virtual parts are created in Solidworks

CAD system, then exported to the VR software using

file format conversion process (Figure 6). The virtual

assembly environment incorporates virtual

representations of the components used in the

experiments and the table on which the parts are

located. The start and end positions are marked on the

top surface of the table by two spots (Figure 8). In

order to create physical behavior of the manipulated

objects Open Dynamic Engine (ODE) was used. This

physical engine has its proper collision detection

system, which handles convex and non-convex

shapes of objects.

Figure 6: Polygonal mesh of 3D models of two parts used

in the experiments.

3 METHOD AND EXPERIMENT

DESIGN

Industrial engineers have consistently advocated that

small-amplitude movements are used whenever

possible in assembly work, on the ground that the

time required to complete a unit of work increases as

a function of its amplitude as well as a function of the

precision demanded by the task. In the experiments

carried out by Paul Fitts, the manipulated objects

were a pointed stylus, pins and washers, these objects

SIMULATION

FORCE

COMPUTATION

Feedbacks :

- Forces

- Positions

Informations :

- Positions

- Speed

Haptic

Device

Modelling Movement Time for Haptic-enabled Virtual Assembly

were considered weightless in the study of movement

time he carried out.

Most of the assembly tasks involve grasping,

moving and positioning parts in a fixed locating

position. However, mechanical parts could have

different geometric shapes and finite dimensions that

might affect the operator performance in the assembly

task execution. This study focuses on the

manipulation of cylindrical parts and investigates the

potential of applying Fitts’ law to obtain a model that

represents the time required to move a mechanical

part during the assembly operation. By analogy with

the experiments carried out by Paul Fitts (Fitts, 1954),

the VE represented in the Figure 7 was used to run 3

experiments for which different combinations of the

diameter of the manipulated part, the movement

distance and the hole diameter of the mating part were

used. The operator picks the primary part (the

manipulated part) with the VIRTUOSE™ haptic

device, then he/she moves the part towards the

secondary part (the receiving part) and finally he/she

drops it to the desired position and orientation. Then,

the primary part is moved back at the start position

and the task is repeated 10 times. Each subject had to

execute the task ten times for each combination of the

diameter of the manipulated part, the movement

distance and the diameter of the hole of the receiving

part. After the completion of the experiments, a

second session with the same task execution and

conditions took place after 3 days. An algorithm was

developed to automatically record the task

completion time (MT), the locating position and the

orientation of the part for further analysis.

3.1 Experiment 1: Moving a

Cylindrical Part with Insertion

Task

The subjects were asked to move a cylindrical part

having 5 cm of diameter (the primary part) from a

starting position to a target cylindrical part (called the

secondary part). The subject inserts the primary part

into the hole of the secondary part and then returns it

over the starting position, repetitively, for 10 cycles

(Figure 7 and Figure 8). The secondary part is a

cylindrical container for which the hole’s diameter

(W) is 8 or 16 cm, located at a distance (A) equal to

30, 60, or 90 cm from the starting position. The

combination of the two target diameters (W) and

three center-to-center movement amplitudes (A)

resulted in five possible indices of task difficulty (ID)

of 1,90; 2,90; 3,49; 3,90; and 4,49.

By considering the different values of the target

width and amplitude of movement, six combinations

representing the different experimental conditions

were obtained.

Figure 7: Task execution in experiment 1.

Ten subjects from the university community (1

female, 9 males) aged from 20 to 40 years old and all

right-handed. They were seated on the chair in front

of the computer screen and manipulates the virtual

part with the VIRTUOSE™ haptic device. For

ergonomic considerations, a calibration between the

VE and the 3D interaction device was made so that

the handle of the VIRTUOSE™ is manipulated at the

users’ elbow height. In order to be familiarized with

the haptic device and 3D interaction technique each

subject had to practice the assembly operation during

a training session of 15 minutes for which the user

performance was not recorded. A repeated-measures

design counter-balanced by conditions was carried

out. This included three experimental conditions

presented to the subjects in a random order.

During the execution of the virtual task, subjects

were instructed to work as accurately and rapidly as

possible.

Figure 8: The virtual environment used for the experiment

HUCAPP 2020 - 4th International Conference on Human Computer Interaction Theory and Applications

3.1.1 Data Analysis and Results

In order to perform the analysis of data collected from

the experiment the means of movement time for each

experimental condition was computed (Table 1).

The analysis of the data represented in the Table

1 showed that for each category of target diameter

(W), the movement time (MT) increased

progressively as movement amplitude (A) increased.

It is also important to notice that for each amplitude,

the movement time increased progressively as the

target diameter was decreased. These trends were

observed in the original Fitts’ experiments of the

reciprocal taping with the pointed stylus (Fitts, 1954).

The index of performance can be considered constant

(1,4 – 1,59) for the index of difficulty ranging from

2,9 to 4,49 but falls to 1,06 for ID = 1.9. In order to

confirm that Fitts’s law can be applied in the

assembly of cylindrical parts, a linear regression

analysis was performed on the assembly time and the

task index of difficulty for the data obtained for each

subject who participated in this experiment. The

result showed the linear relationship between MT and

ID as follows:

MT = a + b ID

With a correlation coefficient r = 0,742, this

confirms the existence of a statistically significant

correlation between the variables MT and ID of the

studied model. The linear regression analysis of MT

on ID yielded the following estimated model:

 = 0,94 + 0,411

The curve of the fitted model for the studied data

is presented in Figure 9.

Table 1: Mean movement time and index of performance

obtained in the experiment.

W (cm) A (cm) ID MT (sec) IP

8 30 2,90 2,049 1,41

8 60 3,90 2,530 1,54

8 90 4,49 2,815 1,59

16 30 1,90 1,796 1,06

16 60 2,90 2,070 1,40

16 90 3,49 2,481 1,40

Figure 9: Curve of the fitted model of the experiment 1.

3.2 Experiment 2: Locating a Part with

Finite Width in a Position without

Locating Tolerance

The subjects were asked to carry out a similar task,

but without inserting the primary part into the

secondary part. Rather, target acquisition required

subjects to perform a reciprocal taping at the start

position marked by a white spot and at the final

position, represented by a disk of 5 cm of diameter

and 5 mm of thickness, located on the table (Figure

10). However, in all combinations, the diameter of the

white spot, located at the start position, is equal to the

diameter of the moved part. The taping should be

carried out so that the axis of symmetry of the moved

part, the center of symmetry of the white spot at the

start position and the center of the disk at the final

position are superimposed.

Figure 10: The virtual environment used for the experiment

The task is repeated 10 times continuously without

releasing the primary part. The subjects were

requested to execute the task as accurately and

quickly as possible. The movement amplitudes were

20, 30, and 50 cm. In addition to the variation of the

movement amplitude, the diameter of the primary

Modelling Movement Time for Haptic-enabled Virtual Assembly

part was also varied across experimental conditions

(5, 7, and 9 cm). Of interest was whether the diameter

of the moved part contributed towards the overall task

difficulty as documented by (Boothroyd, Geoffrey.

Dewhurst, Peter. Knight, 1994).

3.2.1 Data Analysis and Results

This experiment aims at evaluating human

performance, in terms of the time required to move a

cylindrical part between two distant positions, during

the execution of a manual assembly task in VE. The

objective is to investigate whether Fitts’ law applies

when the locating tolerance (equivalent to the target

width in the original Fitts’ law experiment) is not

allowed. The different combinations between the

means of movement time MT, primary part diameters

(D) and movement amplitudes (A) for the two

sessions of the experiment 2 are presented in Table 2.

Table 2: Mean movement time and index of performance

obtained from the experiment 2.

W (cm) D (cm) A (cm) ID MT (sec) IP

5 5 20 3 1,310 2,29

5 5 30 3,58 1,552 2,30

5 5 50 4,32 1,787 2,41

5 7 20 3 1,276 2,35

5 7 30 3,58 1,420 2,52

5 7 50 4,32 1,694 2,55

5 9 20 3 1,261 2,37

5 9 30 3,58 1,420 2,52

5 9 50 4,32 1,736 2,48

It is noticed from the data of the Table 2 that for a

fixed target diameter (W=5 cm), the movement time

increased when the movement amplitude (A) was

increased. Moreover, the index of performance is

relatively constant (2,3– 2,5) for the index of

difficulty ranging from 3 to 4,32. These results

correspond to those obtained in the experiment 1. In

order to ascertain the relationship between the

movement amplitude and the movement time and to

investigate if the diameter of the moved part affects

the movement time, Two-way ANOVA analysis was

carried out using the movement time recorded for

each combination. The movement time is the

dependant variable and the factors for this test are: the

diameter (D) of the moved part and the movement

amplitude (A).

Since the P-values of these factors are less than 0,05,

this confirms that the movement amplitude and the

diameter of the moved part have a statistically

significant effect on the movement time (MT) at the

95% confidence level (Table 3).

Table 3: Results of the analysis of variance for the

movement time MT.

Source

Sum of

Squares

Df Mean

Square

F-Ratio P-Value

Main

Effects

0,0135 2 0,0067 7,31 0,046

0,317 2 0,158 171,45 0,0001

Residual

0,0036 4 0,0009

Total

0,334 8

Figure 11: The Curve of the fitted model for the experiment

The result of the regression analysis yielded a

correlation coefficient r = 0,972. The equation of the

fitted model is:

 = 0,2 + 0,347

The curve of the fitted model for the experiment 2 is

presented in the figure 11.

3.3 Experiment 3: Assembly Task with

Different Values of the Diameter of

Primary Part (D), Movement

Amplitude (a), and the Diameter of

the Secondary Part (W)

The subjects were asked to perform a similar task but

with the condition where the diameter of the hole of

the secondary part (named target width W) was

varied: 4 and 9 cm as was the movement amplitude

(A): 30 and 60 cm and the diameter of the primary

part (D): 5, 7 and 14 cm. The combination of targets

widths and movement amplitudes resulted in the

following values of the task index of difficulty: 3, 32;

3, 9; 4, 32; and 4, 9 (Figure 12).

HUCAPP 2020 - 4th International Conference on Human Computer Interaction Theory and Applications

Figure 12: Virtual environment for the experiment 3.

3.3.1 Data Analysis and Results

The means movement times (MT) calculated for the

combined trials of the experiment 3 are presented in

Table 4.

The index of performance (IP) can be considered

relatively constant within two intervals ([1.65 – 1.8]

and [2.3 – 2.5]) for the index of difficulty ranging

from 2.73 to 3.73 and 3.9 to 4.9, respectively.

Furthermore, the relationships among the data do not

correspond closely to those found in the two previous

experimental conditions.

Table 4: Mean movement time and index of performance

obtained in the experiment 3.

In fact, for each category of target width (W) the

movement times increased progressively as the

amplitude (A) was increased, however, for each

category of amplitude (A) the movement time did

note change significantly when the tolerance (W) was

decreased, this result did not match with the trends

found in the original experiments carried out by Paul

Fitts.

The correlation test of MT with ID gives a

correlation coefficient r = 0, 286. This confirms the

existence of statistically significant relationship

between MT and ID. The equation of the fitted model

represented in the figure 13 is the following:

 = 1,3 + 0,138

The result of this experiment showed that Fitts’

law model can be adopted to estimate the movement

time, in the case where the diameter of the primary

part (D) is greater than the diameter of the secondary

part (W). In practice, this case of manipulation occurs

in assembly without inserting the primary part in the

hole of the secondary part. However, further

investigations are necessary to determine why in the

conditions of experiment 3 (when the tolerance (W)

was decreased) the movement time did not follow the

trend of the original Fitts’ law. It is also important to

quantify the effect of the diameter of the moved part

in the formulation of the equation of the movement

time.

Figure 13: Curve of the fitted model for the experiment 3.

4 DISCUSSION

The experiments reported in this paper examined the

use of Fitts’s Law as a tool for evaluating cylindrical

parts assembly tasks in virtual environment. While

Fitts’ Law generally held under the three virtual

assembly conditions, further investigations are

necessary to explain why decreasing the target width

(W) in the experimental condition 3 did not increase

the movement time. In order to represent real world

interaction, the virtual assembly environment

designed in this research provided haptic sensation to

the user. However, in order to confirm the validity of

Fitts’s law for the assembly of cylindrical parts, it is

necessary to conduct the same experiments in real

world and compare the trends obtained in virtual and

in real world conditions. It is also important to

W (cm) A (cm) ID

(seconds)

4 30 3,90 1,651 2,36

4 60 4,90 1,953 2,51

4 30 3,90 1,601 2,43

4 60 4,90 1,941 2,52

4 30 3,90 1,644 2,37

4 60 4,90 2,107 2,32

9 30 2,73 1,657 1,65

9 60 3,73 2,067 1,80

9 30 2,73 1,618 1,69

9 60 3,73 2,073 1,80

9 30 2,73 1,728 1,58

9 60 3,73 1,953 1,91

Modelling Movement Time for Haptic-enabled Virtual Assembly

explore and qualify the effect of the diameter of the

manipulated part on movement time.

5 CONCLUSION AND

RESEARCH PERSPECTIVES

The research reported in this paper showed an

analogy between the results obtained in the original

Fitts’ law experiments and the task of moving

cylindrical parts in virtual assembly environment

including haptic feedback. The rate of movement

time recorded in three experiments increased

uniformly as movement amplitude was increased for

each category of target width, and increased

uniformly as tolerance was decreased for a category

of movement amplitude except for the experiment 3.

The index of performance is constant over a wide

range of the task index of difficulty. This confirms the

hypothesis of Fitts’s law stating that movement time

varies with task difficulty in such a way that the index

of performance is constant over a wide range of

movement amplitude and tolerances. However, the

results obtained in the experiment 3 require further

investigations in order to evaluate the effect of the

diameter of the moved part on movement time. This

could lead to a new formulation of Fitts’ law as a

model of the movement time in assembly task. It is

also worth noting that in order to ascertain the

statistical significance of the results, it is planned to

run the experiments with involving bigger number of

subjects.

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