Speich Shao and Goldfarb 2005.pdf - Vanderbilt University

Mechatronics 15 (2005) 1127–1142
Modeling the human hand as it interacts with
a telemanipulation system
John E. Speich a, *, Liang Shao b , Michael Goldfarb b
a Mechanical Engineering, Virginia Commonwealth University, Richmond, VA, 23284-3015, United States
b Mechanical Engineering, Vanderbilt University, Nashville, TN 37235-1592, United States
Received 10 November 2004; returned to author for revision 15 April 2005
Abstract
This paper describes the development of a linear lumped-parameter hand/arm model for
the operator of a telemanipulation system. The authors previously developed a control
architecture that implements frequency-domain loop-shaping compensators to improve the
transparency or ‘‘feel’’ of a telemanipulation system, and a human model is used when simulating
this architecture. Typically, the human is modeled as a second order mass–spring–damper
system. The five-parameter model presented in this paper, however, includes an additional
spring and damper to better approximate the dynamics within the specific frequency range for
which compensators will be designed, typically below 20–30 Hz. The model form and parameters
were determined from experimental data taken from a telemanipulation system with
a single translational degree-of-freedom. Additional data was taken from a system with three
actuated degrees-of-freedom, and a set of model parameters was determined for each direction
of motion. Each set of model parameters presented in this paper is for the specific grip type
and hand/arm orientation used during interaction with each particular telemanipulation
system, however similar sets of parameters using this human model could be obtained for
interaction with other telemanipulation systems and haptic interfaces. A comparison of the
five-parameter model with a two-parameter spring–damper model suggests that in some cases
the use of additional model parameters may not offer a significant improvement.
Ó 2005 Elsevier Ltd. All rights reserved.
* Corresponding author. Tel.: +1 804 827 7036; fax: +1 804 828 4269.
E-mail address: jespeich@vcu.edu (J.E. Speich).
0957-4158/$ - see front matter Ó 2005 Elsevier Ltd. All rights reserved.
doi:10.1016/j.mechatronics.2005.06.001

1128 J.E. Speich et al. / Mechatronics 15 (2005) 1127–1142
Keywords: Telemanipulation; Human–robot interaction; Human modeling; Hand model; Finger model
1. Introduction
A general bilateral telemanipulation system, in which a human operator interacts
with an environment through a master–slave telemanipulator pair, is depicted in
Fig. 1. In the figure, V h and F h are the velocity and force, respectively, associated
with the port of interaction between the operator and the telemanipulator, and V e
and F e are the velocity and force, respectively, associated with the port of interaction
between the telemanipulator and environment. In a two-channel position-force
architecture, the operator can be modeled as an admittance and the environment
as an impedance. The human is modeled as an admittance because he or she commands
motion to and receives force from the master manipulator. As such, the operator
imposes motion on a motion-controlled slave manipulator, which imposes its
endpoint motion on the environment impedance. Motion imposed on the environment
impedance generates a force, which is imposed on a force-controlled master
manipulator, which in turn imposes that force on the admittance of the human.
When developing control architectures for telemanipulation systems, it is often
necessary to use a model of the human operator. The authors previously developed
a modified position-force control architecture that allows the use of frequency-domain
loop-shaping techniques to improve the transparency of a telemanipulation
system [1–4]. Transparency is the extent to which the manipulator system preserves
the ‘‘feel’’ of the environment. Using this architecture, compensators are implemented
to shape the magnitude of the impedance transmitted to the human operator
such that the telemanipulation system is more transparent. These compensators are
designed to address specific frequencies where the transparency improvement is desired.
In order to simulate this control architecture, a model for the human operator
block shown in Fig. 1 is required. Typically, the human is modeled as a three-parameter
mass–spring–damper system [5,6]. This paper presents a five-parameter model
that includes an additional spring and damper, which can better approximate the
dynamics of the operator within the specific frequency range for which compensators
are being designed. This frequency range is usually below 20–30 Hz and includes the
frequency range of human volitional motion.
This paper describes the development of both a two-parameter human hand/arm
model and a five-parameter model that characterize interaction with a telemanipulation
system. Experimentally determined model parameters are presented for interac-
Operator
V h
F h
Bilateral
Telemanipulator
System
V e
F e
Environment
Fig. 1. Block diagram representation of a telemanipulation system.

J.E. Speich et al. / Mechatronics 15 (2005) 1127–1142 1129
tion with a telemanipulation system with a single translational degree-of-freedom
(DOF) and a knob-type grip interface. Additional data and model parameters are
presented for a telemanipulation system with three-DOF and a pencil-type grip
interface.
2. Previous work
The human arm, hand, and fingers are an amazingly complex system of muscles,
bones, nerves and other tissues, which are capable of grasping and manipulating objects
with great dexterity. Many researchers in the fields of biology and robotics have
paid considerable attention to understanding and developing models of the impedance
characteristics of the human arm and hand [5,7–12]. In the field of robotics,
this research is usually not as concerned with the complex neuromuscular interactions
within the human arm/hand, but rather the development of a simple model that
represents the arm/hand dynamics as an input/output relationship [7].
Several researchers have experimentally determined values for the human hand
impedance as a function of the direction of motion in the horizontal plane and as
a function of arm configuration [8–11]. Mussa-Ivaldi et al. [8] delivered small displacements
to the hand while a test subject maintained a particular posture. The
force on the hand was measured and the stiffness was calculated from the force
and displacement data. They concluded that the neuromuscular behavior of the
arm is predominately spring-like. Flash and Mussa-Ivaldi [9] investigated the interactions
between the geometrical, mechanical, and neural factors that determine arm
behavior. They found that the hand stiffness is strongly dependent on the arm configuration.
Gomi et al. [12] concluded that experimentally determined human-arm
stiffness values vary greatly between subjects, tasks, experimental apparatuses, and
perturbation patterns.
Ikeura et al. [13] investigated human-arm characteristics in the context of a
human and a robot cooperatively moving an object along a single degree-of-freedom.
In this same context, Rahman et al. [14] developed a second order model in
which the stiffness and damping coefficients vary with time and the model is updated
in real time. Chou and Hannaford [15] built a physical elbow system with the goal of
obtaining mechanical properties as close as possible to those of the human arm.
In the context of teleoperation, Kosuge et al. [5] modeled the human as an impedance
for the purposes of designing a teleoperation control architecture. They
experimentally determined the mass, damping and stiffness values for single
degree-of-freedom linear model. Lawrence [6] also suggested modeling the human
as an impedance for the purposes of illustrating a telemanipulation architecture. This
human impedance, z h , is given by the equation:
z h ¼ F h
x h s ¼ m hs 2 þ b h s þ k h
s
ð1Þ
where m h , b h ,andk h are the mass, damping and stiffness of the human operator; F h
is the force acting on the human; x h is the displacement of the human. Eq. (1)

1130 J.E. Speich et al. / Mechatronics 15 (2005) 1127–1142
corresponds to the mass–spring–damper model shown in Fig. 2. Kuchenbecker et al.
[16], used a mass–spring–damper model to characterize the human wrist during haptic
interaction with various grasp forces, and Hajian and Howe [17] studied the
mechanical impedance of the human finger.
In previous work, the authors [1–3] have used the human model suggested by
Lawrence. The models used by Kosuge et al. [4] and Lawrence [5] assumed that
the human has a perfectly rigid grasp on the end-effector of the manipulator, i.e.
the position of the end-effector is the same as the position of the operatorÕs hand.
The human interface on the manipulator used by Kosuge et al. was a round handle,
which the human probably grasped with the thumb, at least two fingers and part of
the palm. Using this type of grasp, the operator can maintain a very firm grip on the
handle, and thus the assumption that the grasp is perfectly rigid is valid for the purpose
of developing a simple model. The single degree-of-freedom manipulator used
in this study has a similar round handle, as shown in Fig. 3; however, the three degree-of-freedom
manipulator used in this research uses a stylus as the human interface,
as shown in Fig. 4. The operator of the three degree-of-freedom system grasps
the stylus as if it were a pencil, using only his or her fingertips. This type of grasp is
x h
F h
M h
k h
b h
Fig. 2. A mass–spring–damper model.
Fig. 3. The single DOF manipulator with the operator grasping the handle overlaid with a five-parameter
hand/arm model.

J.E. Speich et al. / Mechatronics 15 (2005) 1127–1142 1131
Fig. 4. Photographs of the three-DOF manipulator. In the lower photograph, the operator is holding the
stylus with a pencil-type grasp.
generally much softer than the grasp used on a handle, and therefore, a human
model that accounts for this softer interaction is necessary. The hand/arm model
developed in this paper does not assume that human has a rigid grasp on the robot,
but rather explicitly models the contact between the human and the robot as a soft
contact by including an additional spring and damper. This soft-contact model better
approximates the interaction between the human and the robotic interface when
the human uses a pencil-type grasp. The model developed in this paper is more general
than the model used by Kosuge and Lawrence and the model form is suitable for
both for both rigid and soft-contact grasps.
3. Hardware
Two different telemanipulation systems were used in this study, a single DOF system
and a three-DOF system. The single DOF telemanipulator interface shown in

1132 J.E. Speich et al. / Mechatronics 15 (2005) 1127–1142
Fig. 3 was used to collect the data used to develop the hand/arm model. This device
uses a N12M4T Kollmorgen DC servomotor, with an internal tachometer to measure
velocity and an aligned potentiometer to measure position. A gear-rack with linear
ball slide is used to transform the revolute motion of the servomotor into a linear
translation. The human interface is a handle mounted on the end of a cantilever
beam, which is fixed to the translating rack. The knob similar is to those used on levers
found on some types of industrial equipment. The cantilever is equipped with
strain gages to measure the force acting on the handle. The range of motion of
the telemanipulator interface is approximately 10 cm.
The master manipulator shown in Fig. 4 has three actuated DOF. It has an
approximately cubic workspace with 20 cm sides, and its end-effector is a stylus,
which is controlled by the human operator. The stylus is connected to the manipulator
using a universal joint, which provides an additional non-actuated three-DOF.
A six-axis ATI Mini-40 force–torque sensor (ATI Industrial Automation, Inc.) (not
shown) is used to measure forces near the end-effector of the master manipulator.
4. Experimental methods
To develop the human hand/arm model, a series of tests was conducted with the
single DOF manipulator. In each test, the operator grasped the end-effector of the
manipulator as shown in Fig. 3, as if he or she wanted to use it to manipulate an
object. Meanwhile, the manipulator was used to apply a time-varying force to the
operatorÕs hand for a duration of 50 s. The test subjects were asked to not resist
the motion of the handle and to maintain a consistent grasp. The applied force
was commanded as a band-limited white noise signal with a magnitude that spanned
the force range of the manipulator. Fig. 5 shows a typical power spectrum magnitude
of the force input to the single DOF device, which falls below 0 dB between 20 and
30
20
Magnitude (dB)
10
0
-10
-20
-30
10 -1 10 0 10 1 10 2
Frequency (Hz)
Fig. 5. Typical power spectrum (dB) of the force input to the single DOF device.

J.E. Speich et al. / Mechatronics 15 (2005) 1127–1142 1133
Displacement (mm)
20
15
10
5
0
-5
-10
-15
-20
-25
-30
0 1 2 3 4 5 6 7 8 9 10
Time (s)
Fig. 6. Typical output displacement of the single DOF device.
30 Hz. Data for frequencies above 30 Hz was not considered, and may be unreliable
because the input force bandwidth may have been insufficient to excite the hand
dynamics at these frequencies. The applied force and position of the manipulator
were measured at the endpoint using a sampling frequency of 1000 Hz. The rootmean-square
(RMS) amplitude of the force input was selected to be on the order
of a Newton, which resulted in motion perturbations with RMS amplitudes on
the order of a few millimeters. A typical data set indicating the amplitude of movement
during the experimental characterization of arm dynamics is shown in Fig. 6.
The linear modeling techniques used in this paper are largely justified by the relatively
small motions used to characterize arm dynamics. The fairly small motions utilized
in the dynamic characterization are appropriate for the intended application
(i.e., stability analysis within a haptic or teleoperative feedback loop), but clearly
the accuracy of the model will be decreased as the amplitude of arm motion becomes
larger. Five test subjects completed five tests each, which yielded a total of 25 data
sets. MATLAB Real-Time Windows Target (The MathWorks, Inc.) was used to
implement the control algorithm for these experiments.
5. Data processing
The frequency response of the human-arm dynamics from force output to motion
input was obtained through the following relationship:
HðjxÞ ¼ X ðjxÞ
F ðjxÞ ¼ U fxðjxÞ
ð2Þ
U ff ðjxÞ
where U fx (jx) is the cross-power spectral density between the force input and the displacement
output, and U ff (jx) is the power spectral density of the force input. This
relationship can be derived by combining the convolution theorem with the

1134 J.E. Speich et al. / Mechatronics 15 (2005) 1127–1142
Fig. 7. The spring–damper model of Eq. (3) (dashed lines) and the five-parameter hand/arm model of Eq.
(10) (solid lines) fit to the average force-position data from the single DOF manipulator.
mathematical definitions of convolution and correlation. This approach to frequency-based
identification of the human-arm dynamics was implemented through
the spectrum function in MATLAB (The MathWorks, Inc.).
The processed data from the tests is presented in Fig. 7, which shows the average
magnitude and phase for all 25 tests. The fact that the magnitude rolls off at an average
slope of 20 dB/decade within the 1–10 Hz bandwidth indicates that an appropriate
human-arm model would have a relative order of one. Further, in the same
frequency range of interest, the phase appears to drop to about 90° before higher
order dynamics appear to generate additional influence. This would also suggest
using a model with a relative order of one. Based on these observations, the following
mathematical models were developed for human hand and arm.
6. A two-parameter human model
The dynamics of the human arm and hand can be represented by the spring and
damper model shown in Fig. 8. In this model, the upper body of the human operator
is considered to be fixed. The interaction force between the master manipulator and
F h
x m
b a
k a
Fig. 8. The spring–damper human arm model.

the human is labeled F h , and the motion of the endpoint of the manipulator is labeled
x m . The stiffness of the human is represented by k a and the damping of the
human is represented by b a . The transfer function between the applied force, F h ,
and the resulting motion, x m , can be written:
x h 1
¼
ð3Þ
F h b a s þ k a
This model has a relative order of one, which correlates with the data presented in
Fig. 7. Parameters for the model were determined by fitting Eq. (3) to the experimental
data as shown in Fig. 7. The fit was performed using the least-squares curve fitting
function lsqcurvefit in MATLAB. The resulting parameters were:
b a ¼ 3.6 N s=m
k a ¼ 40 N=m
J.E. Speich et al. / Mechatronics 15 (2005) 1127–1142 1135
This model captures the overall trend of the experimental data, however, the distinct
change in the slope of the magnitude plot between 2 and 3 Hz and the dip
between 2 and 6 Hz in the phase plot of the experimental data suggest the development
of a more representative model.
7. A five-parameter human hand/arm model
The dynamics of the human arm and hand can also be represented by the lumpedparameter
model shown in Fig. 9. The same five-parameter model is overlaid on the
photograph of the single DOF manipulator and the human operator in Fig. 3. Asin
the previous model, the upper body of the human operator is considered to be fixed.
The motion of the human is represented by x h , and its mass is represented by and m h .
The interaction force between the master manipulator and the human is labeled F h ,
and the motion of the endpoint of the manipulator is labeled x m . The stiffness of the
human is represented by k 1 and k 2 , and the damping of the human is represented by
b 1 and b 2 .
The equation of motion for the mass of the human, m h , can be written:
m h €x h ¼ k 2 x h b 2 _x h s þ k 1 ðx m x h Þþb 1 ð_x m _x h Þ ð4Þ
x m x h
k k
F 1
2
h
M h
b 1
b 2
Fig. 9. The five-parameter human hand/arm model.

1136 J.E. Speich et al. / Mechatronics 15 (2005) 1127–1142
Eq. (4) can be rewritten in Laplace notation as
m h x h s 2 ¼ k 2 x h b 2 x h s þ k 1 ðx m x h Þþb 1 ðx m x h Þs ð5Þ
where s is the Laplace variable. Solving Eq. (5) for the displacement of the human,
x h , gives the equation:
ðk 1 þ b 1 sÞx m
x h ¼
ð6Þ
m h s 2 þðb 2 þ b 1 Þs þðk 2 þ k 1 Þ
The force acting between the manipulator and the hand, F h , is the sum of the
forces in stiffness element k 1 and damping element b 1 , which can be expressed as
F h ¼ k 1 ðx m x h Þþb 1 ð_x m _x h Þ ð7Þ
Eq. (7) can be rewritten in Laplacian notation and simplified to give the equation:
F h ¼ðk 1 þ b 1 sÞðx m x h Þ ð8Þ
Substituting the expression for x h in Eq. (6) into Eq. (8) gives the following expression
for F h :
ðk 1 þ b 1 sÞx m
F h ¼ðk 1 þ b 1 sÞ x m
ð9Þ
m h s 2 þðb 2 þ b 1 Þs þðk 2 þ k 1 Þ
Eq. (9) can be rearranged to give the following equation for the ratio of the position
of the manipulator/human contact point to the force acting on the human:
x m
m h s 2 þðb 2 þ b 1 Þs þðk 2 þ k 1 Þ
¼
ð10Þ
F h m h b 1 s 3 þðm h k 1 þ b 1 b 2 Þs 2 þðk 1 b 2 þ b 1 k 2 Þs þ k 2 k 1
This transfer function between the applied force and the resulting motion has a relative
order of one, which correlates with the data presented in Fig. 7.
The ratio of the velocity of the manipulator/human contact point, V m , to the force
on the human, F h , is the admittance of the human, which can be written as
Y h ¼ V m
½m h s 2 þðb 2 þ b 1 Þs þðk 2 þ k 1 ÞŠs
¼
ð11Þ
F h m h b 1 s 3 þðm h k 1 þ b 1 b 2 Þs 2 þðk 1 b 2 þ b 1 k 2 Þs þ k 2 k 1
The parameters b 1 , b 2 , k 1 , k 2 , and m h of the hand/arm model expressed in Eq. (10)
were determined by fitting this equation to the experimental data collected from the
manipulator. The fit was performed using the least-squares curve fitting function lsqcurvefit
in MATLAB.
The steady state gain, a, for the force-position transfer function in Eq. (10) can be
written:
a ¼ k 1 þ k 2
k 1 k 2
ð12Þ
This equation can be rearranged to give the following expression for the stiffness k 2
in terms of the stiffness k 1 and the steady state gain:
k 2 ¼ k 1
ak 1 1
ð13Þ

J.E. Speich et al. / Mechatronics 15 (2005) 1127–1142 1137
The magnitude plot in Fig. 7 has a steady state gain, a, of approximately 32 dB,
which corresponds to a gain of 0.025 m/N. Using this value for a and Eq. (13),
the remaining parameters b 1 , b 2 , k 1 and m h were selected such that the plot for
Eq. (10) fit the data in Fig. 7. The resulting parameter for the human hand/arm
model were:
b 1 ¼ 4.5 N s=m
b 2 ¼ 7.9 N s=m
k 1 ¼ 48.8 N=m
k 2 ¼ 375 N=m
m h ¼ 1.46 kg
Notice in Fig. 7 that the five-parameter hand/arm model (solid lines) is a better
approximation of the experimental data than the two-parameter spring–
damper model (dashed lines) in both magnitude and phase, especially between 2
and 6 Hz.
8. A comparison with other models
This section presents a comparison of the five-parameter model developed in this
paper with the experimental models presented by Kosuge et al. [5] and Tsuji et al.
[10] and the model suggested by Lawrence [6]. The models used by Kosuge, Tsuji
and Lawrence can all be expressed using Eq. (1).
Kosuge et al. [1] experimentally found the following human-arm parameters:
b h ¼ 17 N s=m
k h ¼ 243 N=m
m h ¼ 11.6 kg
Tsuji et al. [10] found values for the stiffness and damping for a human hand
impedance model as a function of the direction of motion in the horizontal plane
and as a function of arm configuration. The following values for the stiffness, k h ,
and the damping, b h , are rough estimates taken from figures presented by Tsuji
for arm motion perpendicular to the operator in the distal arm position:
b h 20 N s=m
k h 300 N=m
m h ¼ 3.25 kg
Lawrence [6] suggested using the following human-arm parameters:
b h ¼ 175 N s=m
k h ¼ 175 N=m
m h ¼ 17.5 kg

1138 J.E. Speich et al. / Mechatronics 15 (2005) 1127–1142
which according to Lawrence, correspond to an operator with the manipulator
firmly in hand, but with very little arm tension.
The human impedance models of Kosuge, Tsuji and Lawrence can be expressed
using Eq. (1), which can be written as the ratio of the position of the human, x h ,
to the force acting on the human, F h , given by the equation:
x h 1
¼
ð14Þ
F h m h s 2 þ b h s þ k h
Using Eqs. (10) and (14), Fig. 10 presents a comparison of the models used by
Kosuge et al. (dash-dot lines), Tsuji et al. (dotted lines), Lawrence (dashed lines)
and the five-parameter hand/arm model developed in this paper (solid lines). At
low frequencies, the magnitude plots differ primarily by a scaling gain. At frequencies
above approximately 1 Hz, the magnitude plots of the models used by Kosuge,
Tsuji and Lawrence all drop off at 40 dB per decade, which indicates that these
models have a relative order of two. In contrast, the hand/arm model developed
in this paper has a relative order of one. The magnitude plot for the hand/arm model
drops off at 20 dB per decade, which better matches the experimental data for this
manipulator. The phase plots of the models used by Kosuge, Tsuji and Lawrence all
approach 180°, i.e., they have a relative order of two. In contrast, the phase plot of
the hand/arm model approaches 90° and has a relative order of one, which better
matches the experimental data from this manipulator. The human-arm models
which have relative orders of two consider the mass of the manipulator and the mass
of the human arm to be lumped together; however, the five-parameter model has a
relative order of one and considers the mass of the human separately. Considering
the human mass separately provides a model that better matches the data from this
manipulator and models the dynamics of the interaction between the mass of the
robot and the mass of the human.
Magnitude
0
-50
-100
-150
10 -2 10 0 10 2
0
Phase
-100
-200
10 -2 10 0 10 2
Frequency
Fig. 10. Comparison of the human admittance models of Kosuge (dash-dot lines), Tsuji (dotted lines),
Lawrence (dashed lines) and the five-parameter hand/arm model developed in this paper (solid lines).

J.E. Speich et al. / Mechatronics 15 (2005) 1127–1142 1139
9. Modeling human interaction with the three-DOF manipulator
Model parameters for human interaction with the three-DOF manipulator shown
in Fig. 4 were determined in a similar manner. Five test subjects who were familiar
with the device were used, and each subject completed five tests. To begin each test,
the subject grasped the stylus of the manipulator with a pencil-type grip, as if he or
she wanted to use it to manipulate an object by pushing it with a pencil. The test subject
was seated in front of the manipulator with their elbow bent at an angle of
approximately 90°. Next, the operator moved the stylus about the workspace of
the manipulator, as if he or she was using it to manipulate an object. Then, the operator
stopped near the center of the workspace, and the manipulator was used to apply
time-varying forces to the operatorÕs hand for 10 s. The test subject was asked to
not resist the motion of the stylus and to maintain a consistent grip on the stylus. The
forces were applied in each of the three-DOF simultaneously for 10 s, and were commanded
as band-limited white noise signals with magnitudes that spanned the force
range of the manipulator (10 N). The applied forces and position coordinates of the
manipulator were measured at the endpoint using a sampling frequency of 2000 Hz.
Data from the three-DOF manipulator were processed as described in Section 5.
This data is presented in Fig. 11, which shows separate magnitude plots for each of
the three-DOF. These plots show the average magnitude from the series of 25 tests.
Fig. 11. Eq. (10) fit to the average force-position data for the x (top), y (middle) and z (bottom) directions.

1140 J.E. Speich et al. / Mechatronics 15 (2005) 1127–1142
Table 1
Human model parameters for the three-DOF telemanipulation system
Direction Parameters
b 1 (N s/m) k 1 (N/m) m h (kg) b 2 (N s/m) k 2 (N/m)
X 12.9 122 0.85 12.9 330
Y 9.20 108 4.03 47.6 104
Z 17.6 81.4 0.68 13.5 13.0
The positive x direction is used to define motion toward the human operator, while
the positive y direction represents motion vertically upward, and the positive z direction
corresponds to motion to the operatorÕs left. Although movements along the
three translational DOF are presumably coupled to some extent, they were assumed
to be decoupled, and different model parameters were determined for each DOF.
Separate human interaction models were necessary because separate control loops
were designed for each DOF of the manipulator.
The magnitude plots in Fig. 11 roll off at slopes of approximately 20 dB/decade
within the 1–10 Hz bandwidth, which suggest that an appropriate human-arm model
would have a relative order of one, like the five-parameter mathematical model
developed in Section 7. This model was fit to the experimental data in Fig. 11 using
Eq. (10). Only the data below 30 Hz was used to determine the fit, and Eq. (13) was
used to constrain the low frequency (steady state) gain to match the data. Three distinct
sets of model parameters were determined, one for each direction of human motion,
as listed in Table 1.
Gomi et al. [12] concluded that experimentally determined human-arm stiffness
values vary greatly between subjects, tasks, experimental apparatuses, and perturbation
patterns. Flash and Mussa-Ivaldi [9] investigated the interactions between the
geometrical, mechanical, and neural factors that determine arm behavior. They found
that the hand stiffness is strongly dependent on the arm configuration. Thus, the model
parameters presented in this paper are for the specific grip type and human hand/
arm orientation used during interaction with each of these particular telemanipulation
systems, however similar sets of parameters for this human model could be obtained
for interaction with other telemanipulation systems and haptic interfaces.
The human model developed in this section is being used by the authors to examine
the stability robustness and transparency of a scaled telemanipulation system
that uses the three-DOF manipulator as the human interface [1–3,18]. For this
telemanipulation system, the frequency band between 0.5 Hz and 10 Hz is of primary
interest when assessing the system transparency. Therefore, the parameters for the
human model were selected to best fit the experimental data in the frequency range
between 0.5 and 10 Hz.
10. Conclusions
The authors have developed a model for the human arm and hand as they interact
with a telemanipulation system and experimentally determined the model parameters

J.E. Speich et al. / Mechatronics 15 (2005) 1127–1142 1141
for a single DOF and a three-DOF telemanipulation system. The model adds an
additional spring and damper to the mass–spring–damper model typically used to
represent a human and better approximates the dynamics of the human while interacting
with the manipulators used in this study. This model can be used to design
and analyze control architectures for telemanipulation systems and haptic interfaces
[1–4].
Acknowledgments
Support for this work was provided by NASA Grant No. NGT 852857. The
authors gratefully acknowledge this support. The human interaction model for the
single DOF manipulator was presented at the 2001 ASME International Mechanical
Engineering Congress and Exposition [18].
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