2015 IEEE World Haptics Conference (WHC)
Northwestern University
June 22–26, 2015. Evanston, Il, USA
Effects
of Body-powered Prosthesis Prehensor Stiffness on Performance
in an Object Stiffness Discrimination Task
Anton Filatov, Ozkan Celik, Member, IEEE
Abstract— In this paper, we present results from two human
subject experiments focusing on effect of prehensor stiffness
on object stiffness discrimination task performance in a bodypowered prosthesis. Humans have the ability to alter the directional endpoint stiffness of their arms through co-contraction
of agonist/antagonist muscle pairs. In the area of prosthesis
design, while the need for position and force control has long
been recognized, the concept of end effector stiffness modulation
has been mostly ignored. In this study we attempt to broaden
the existing knowledge base by (1) using an experimental setup
which mimics the control inputs of a shoulder-driven bodypowered prosthesis operated in voluntary closing (VC) mode,
and (2) exploring the impact of end effector stiffness modulation
on the quality of haptic feedback the user receives about the
environment. Results of the first experiment indicated that
tuning of prehensor stiffness in a body-powered prosthesis can
increase the performance of the user in correctly and more
easily identifying objects with varying stiffness.
Index Terms— Hand prosthesis, body-powered prosthesis,
stiffness modulation, stiffness discrimination.
I. I NTRODUCTION
Humans have the ability to alter the directional endpoint stiffness of their arms through co-contraction of agonist/antagonist muscle pairs [1], [2], and do so to match the
requirements of a particular task [3]–[5]. Although end point
force generation can also contribute to limb stiffness [6], [7],
humans can change the stiffness of their arms independently
of net joint torque [3], [8]. This ability is useful when
attempting to adjust to unstable environments [3], [4], [9]
or performing a constrained task [10]. It should be noted
that while stiffness is only a part of the overall end effector
impedance, evidence for damping modulation by humans is
less conclusive [7], [11].
In the area of prosthesis design, while the need for position
and force control has long been recognized, the concept of
end effector stiffness modulation has been mostly ignored.
Current commercially available upper-extremity prosthetic
devices make virtually no provisions for modulating the
stiffness of the end effector. In the case of body-powered
prostheses, the end effector stiffness is a function of the
stiffness of the spring in the prehensor, and the stiffness of
the body joint driving the actuator. However, the prehensor
spring (and therefore stiffness) cannot be modified on the
fly, and the body joint can control stiffness in only one
direction, a function of the cabled actuation system. In
EMG-controlled, robotic devices, joint stiffness is completely
The authors are with the Biomechatronics Research Laboratory, Department of Mechanical Engineering, Colorado School of Mines, Golden, CO,
80401 (e-mails: afilatov@mines.edu, ocelik@mines.edu)
978-1-4799-6624-0/15/$31.00 ©2015 IEEE
independent of user intention, and is secondary to velocity,
and in some cases, force control.
Recently several groups have begun to focus on this issue
[12]–[15]. Both Ajoudani et. al. [12], as well as Hocaoglu
and Patoglu [14] demonstrated tele-impedance control of
a robotic system as a stand in for a prosthetic device.
Blank et. al. [15] demonstrated the utility of impedance
modulation in two tasks (contact force minimization and
trajectory tracking) using both virtual and robotic systems.
However, these previous studies have been subject to several
limitations. In general, they either used idealized modes
of control [15], or were focused on EMG-driven systems,
which while extremely promising, are less commonly used
than the body powered prostheses [16]. Additionally, all
of them focused on the role stiffness modulation plays in
enabling either precise motion, or stability against external
disturbance.
In this study we attempt to broaden the existing knowledge
base by (1) using an experimental setup which mimics the
control inputs of a shoulder-driven body-powered prosthesis
operated in voluntary closing (VC) mode, and (2) exploring
the impact of end effector stiffness modulation on the quality
of haptic feedback the user receives about the environment.
The force feedback that a body powered prosthesis displays to a user during interaction with an object is proportional to the sum of KD , the device (prehensor) stiffness and
KO , the object stiffness, i.e.
F ∝ KD + KO
(1)
KD > KO
(2)
Thus, if
the majority of the feedback force, F, is dedicated to
providing the user feedback about the internal workings
of the gripper rather than to informing the user about the
response of the object. We therefore hypothesize that a
condition in which KD is minimized will result in optimal
user performance in an object stiffness discrimination task.
This paper presents the results of two related experiments.
Experiment 1 had two goals: (1) to test the hypothesis that
prosthesis end effector stiffness impacts the ability of a user
to distinguish between two objects of different stiffness,
and (2) to examine whether this effect is present when
manipulating real and virtual objects. The subjects were
asked to use a prosthesis simulator (PS) system (shown in
Fig. 1, see [17] for details on an earlier version of the device)
to interact with an object and identify it as either a low or
339
Fig. 1.
Fig. 2.
Prosthesis simulator experimental setup.
a high stiffness spring. This task was performed with both
a low and a high device stiffness, and with real and virtual
objects. The second experiment was designed to explore the
trends suggested by Experiment 1 further, by increasing the
number of device stiffness settings from two to three, and
raising the difficulty of the task by expanding the object
set from two to four. Only virtual objects were used for
Experiment 2.
II. M ETHODS
A. Experiment 1: Real and Virtual Objects
1) Setup: The subject was seated to the left of the PS
device, which was held immobile in an adjustable vise on
a table. The subject’s elbow was resting on a support and
their right hand was holding the handle of the PS. The one
degree of freedom end effector gripper was mechanically
linked by a cable to a harness around the subject’s left
shoulder, mimicking the actuation system of a body-powered
upper limb prosthesis. Tension on the cable, provided by the
movement of the subject’s left shoulder actuated the gripper,
closing it. Interaction of the gripper with any object, real or
virtual, resulted in an increase of the torque on the griper
shaft, which was displayed as a proportional increase in
the force delivered through the mechanical linkage to the
subject’s shoulder. It should be noted that while many bodypowered prostheses operate in the voluntary opening mode,
only voluntary closing devices, such as the one used in this
study here, give the users direct sensory feedback about the
environment. Such devices are usually utilized for demanding
or delicate tasks.
The lever arm between the cable and the gripper shaft
was 28.1 mm, and the gripper had a range of motion of
90◦ . A Maxon RE 30 DC (24V, 3.81A) motor was also
mechanically linked to the gripper shaft, through a cable
drive with a gear ratio of 12:1 (Note: all torque measurements
and constants are reported at the gripper shaft). A picture of
this arrangement is shown in Fig. 2. Through all experiments,
this motor was used to simulate a linear torsional spring
340
Detail of prosthesis simulator end effector linkages.
with a constant of KD , acting to keep the gripper open,
approximating the behavior of a voluntary closing prosthetic
prehensor. For this experiment, the value of K alternated
between 41.4 mNm/◦ and 103 mNm/◦ , or KD− and KD+
respectively, representing the lowest and highest practical
stiffness settings for the device.
Two Slo-FoamTM hand exercise foam blocks with different spring constants were selected as experimental objects.
Both were fitted with a custom interface to enable quick
attachment and detachment to and from the gripper of
the PS. In order to create virtual representations of these
objects, their effective torsional spring constants, KO− and KO+
for the softer and harder of the two sponges respectively,
had to be experimentally determined. Repeated automated
compression of the sponges with the PS gripper showed that
KO− ∼
= 120 mNm/◦ and KO+ ∼
= 360 mNm/◦ (the nonlinear
stiffness behavior was approximated by a linear model, see
the Discussion section for a more detailed discussion of this
aspect). During virtual object trials, these values were used to
model the sponges as linear torsional springs, implemented
by the gripper motor once the subject closed the gripper
past the contact threshold. This threshold was also used to
measure trial time for all cases. For real objects, the threshold
was set to 20◦ , while for virtual objects the threshold was
shifted further, to 30◦ . This change was made in an attempt
to avoid saturation of the motor due to combined torques
required to represent the device stiffness and the virtual
spring. Thus, the total force, F, displayed to the subject
during any individual trial was
F = l(rKD + (r − t)KO )
(3)
where l is the lever arm of the harness, KD is the device
stiffness, r is the displacement of the gripper from its resting
position in degrees, t is the contact threshold, and
(
KO− , KO+ i f r ≥ t
KO =
(4)
0 if r < t
During all experiments, a screen was placed between the
subject and the PS, blocking their view of the gripper and
eliminating the effects of visual feedback. A keyboard used
for recording the subject’s responses was placed within reach
of the subject’s left hand.
2) Procedure: All subjects participated in two separate
data collection sessions, with each session comprised of two
trial blocks dedicated to a particular object type real or
virtual. For the duration of a trial block the device stiffness,
KD , was set to either KD− or KD+ . In order to minimize learning
effects, the order of the real and virtual sessions, as well
as of the high and low stiffness blocks was randomized
and counterbalanced across all subjects. Every block was
composed of 40 randomized trials, with 20 trials using soft
objects and 20 trials using hard objects. The first 10 trials
of each block were separately randomized and balanced,
forming a dedicated familiarization block within the data.
In addition, every block was preceded by a familiarization
session, in which the subjects were aware of which objects
they were interacting with, and allowed to explore them at
will. In between each block, every subject took a short break
of 3-5 minutes.
During each trial, a single object was placed or simulated
in the PS gripper and the subject was asked to compress it,
and determine its stiffness (low or high) based on the force
feedback received. Once the subject made the determination,
they pressed the corresponding input button on the keyboard,
and the trial ended. During real object sessions, the subject
was verbally instructed to sit back in a relaxed posture
and wait while the object was physically removed from
the gripper, and then either switched out or replaced back
into the gripper. The subject was then verbally instructed
to resume trials. During virtual object blocks, the objects
were automatically cycled through after the subject recorded
a response and moved back to a neutral posture, resetting
the gripper. Data collected during the trial included decision
time, defined as the time between the initial contact with the
object and the subject’s identification input, as well as the
accuracy of the subject’s response. Subjects were instructed
to prioritize accuracy over speed, and no limit was placed on
the duration of the trial, or the number of gripper contractions
within a trial.
B. Experiment 2: Four Virtual Objects
1) Setup: The mechanical setup described above remained
intact, with a few adjustments made to address issues that
were revealed by the initial data collection. Despite precautions, the gripper motor occasionally reached its torque limit
when simulating the hard virtual object at the high device
stiffness setting, resulting in an unnatural sensation for the
subjects. To eliminate this issue, the peak torques involved
were lowered by reducing the travel of the gripper to 50◦ ,
with a virtual contact threshold of 20◦ . The simulated object
set was also expanded to four, two soft and two hard, with
the following effective torsional stiffness coefficients: KO1 =
48 mNm/◦ , KO2 = 96 mNm/◦ , KO3 = 192 mNm/◦ , KO4 = 240
mNm/◦ . In order to partially compensate for the lower overall
torques, the lever arm of the cable, l was reduced to 18.7 mm.
The device stiffness set KD was expanded to include three
evenly spaced stiffness levels, KD = [KD1 KD2 KD3 ], with KD1
= 41.4 mNm/◦ , KD2 = 62.2 mNm/◦ , and KD3 = 82.9 mNm/◦ .
Thus, Eq. 3 above remained the same, while Eq. 4 became
(
KO1 , KO2 , KO3 , KO4 i f r ≥ t
(5)
KO =
0 if r < t
2) Procedure: All subjects completed a single session
made up of three trial blocks, each one dedicated to a
single value of KD . In order to combat learning effects,
the order of presentation of the blocks was randomized
and counterbalanced across all subjects. All blocks were
comprised of 60 randomized trials, with 15 trials reserved
for each of the four objects. The first 12 trials of every
block were independently randomized and counterbalanced,
providing a hidden familiarization buffer within the data. In
addition, as in Experiment 1, every block was preceded by a
familiarization session, in which the subjects cycled through
all of the objects in order of increasing stiffness at least twice.
The cycle was repeated as many times as necessary until the
subjects indicated confidence in their ability to distinguish
between the four objects.
Similar to the virtual blocks in Experiment 1, during each
trial a single object was simulated in the gripper of the PS
device. The subject actuated the gripper, compressing the
object which resulted in an increase in the force feedback
displayed to the subjects shoulder, proportional with the
stiffness of the object. Once the subject identified which of
the four objects they were interacting with, they pressed the
corresponding input button, and the trial ended. Similar to
Experiment 1, the accuracy of subject’s response and the
decision time were recorded. Subjects took a 3-5 minute rest
between every block.
C. Subjects
A total of 8 subjects participated in Experiment 1, 5
females and 3 males. All subjects were right hand dominant.
A total of 12 subjects participated in Experiment 2, 2 females
and 10 males. All subjects, except for one, were right hand
dominant. All experimental procedures were reviewed by
the Colorado School of Mines Internal Review Board, and
informed consent was given by all participants.
III. R ESULTS AND D ISCUSION
A. Experiment 1 Results
For all subjects, the first 10 trials (training) of each
block were dropped from analysis as discussed above. The
statistical analysis of the decision time data set is complicated
by the presence of an anomaly in data for S7. During the
real object data collection session of this subject, the PS
device mechanically failed when attempting to collect data
at the KD+ device stiffness setting. The decision was made
to ask S7 to repeat the session, effectively doubling the
subject’s experience at that particular device setting. In the
final analysis, S7 was the only subject to demonstrate a faster
341
TABLE I
AVERAGE AND STANDARD DEVIATIONS OF DECISION TIMES IN SECONDS
FOR REAL AND VIRTUAL OBJECTS , ACROSS SEVEN SUBJECTS
TABLE II
AVERAGE AND STANDARD DEVIATION OF IDENTIFICATION ERROR
RATES
(%) FOR REAL AND VIRTUAL OBJECTS , ACROSS SEVEN SUBJECTS
K
Real Obj.
Virtual Obj.
K
Real Obj.
Virtual Obj.
KD+
KD−
5.5 (±2.4)
4.2 (±1.8)
4.6 (±2.7)
3.2 (±1.9)
KD+
KD−
23.8 (±14.5)
30.0 (±20.2)
16.2 (±12.2)
4.8 (±5.7)
decision time at the KD+ setting when compared to the KD−
setting, and only in the real object condition. It is reasonable
to conclude that the additional experience significantly improved the performance of S7 at the KD+ condition with real
objects. Therefore, data for S7 was excluded from statistical
analysis, based on objective circumstances. Table I below
summarizes the average decision times for the remaining
seven subjects in all conditions during the first experiment.
The decision time data were subjected to a two-way
repeated measures analysis of variance, with the factors being
the two device stiffness settings (KD− and KD+ ), and the two
object types (real and virtual). The significance threshold for
all statistical tests was set at p < 0.05. The main effect of
device stiffness on decision time resulted in an F ratio of
F(1, 6) = 8.39, p = 0.027, indicating a statistically significant
decrease in decision time when subjects were using a low
stiffness device. The main effect of object type on decision
times produced an F ratio of F(1, 6) = 5.33, p = 0.06, indicating that the difference in decision times for real and virtual
objects was not statistically significant. The interaction effect
was non-significant, F(1, 6) = 0.01, p = 0.91. Including the
data of S7 in the analysis results in a meaningful change only
in the main effect of device stiffness, with the intact eight
subject data set producing an F ratio of F(1, 7) = 4.34, p =
0.075. As discussed above, objective considerations point to
S7 as an outlier in the data set.
The impact of device stiffness on decision time was confirmed as significant by one-way repeated measures analysis
of variance applied to the reduced real and virtual object data
sets individually, with p = 0.027 and p = 0.031 respectively.
Similarly, when examined individually the subjects’ decision
time was not significantly affected by the type of object, real
or virtual, they were interacting with (p = 0.19 at the high
stiffness setting, and p = 0.058 at the low device stiffness
setting).
Table II summarizes the error rates for all conditions
during Experiment 1.
The error data trends are less clear, with real objects
showing a small increase in error rates at the low stiffness
setting, while the virtual object data indicate a marked
decrease in errors. To trace the source of this discrepancy,
the error rates were broken down by subject, and the results
are presented in Table III.
B. Experiment 1 Discussion
The initial experiment provides support for the hypothesis
that low end effector stiffness results in improved performance when attempting to distinguish between objects based
342
on their stiffness. At the low stiffness setting, the users
identified objects faster, and in the case of virtual objects,
demonstrated a significant decrease in error rate as well.
No significant difference was found between the subjects’
decision times when interacting with real and virtual objects,
indicating the potential to remove physical springs from
further experiments without compromising the applicability
of the results.
The error results are less uniform, with 4 out of 7 subjects
showing an increase in the error rate when using a low
stiffness device to interact with real objects. Conversely, 6
out 7 subjects demonstrate a noticeable decrease in error rate
when interacting with virtual objects using a low stiffness
device compared to a high stiffness device. This may be
explained by the fact that while the use of virtual objects
left the entire 90◦ travel arc of the gripper unobstructed,
the physical sponges inevitably took up some of that space.
This reduced the amount of information the subjects received
about the objects during a single contraction. In addition,
while the physical objects responded in a linear fashion
during initial compression, after a sufficient deflection, the
response becomes non-linear (demonstrating a hardening
spring behavior), as more and more sponge material is
squeezed into a smaller space. This effect occurs with both
the hard and the soft sponge, increasing the similarity of
their response at extreme gripper deflections, and may have
contributed to the error rate trends.
The low stiffness virtual object condition appears to have
been the easiest by far, with significantly shorter decision
times, and error rates significantly lower than all other
conditions. This is not unexpected, as the low stiffness of the
device means that a greater percentage of the force displayed
back to the subject is contributed by the object, and the
TABLE III
I DENTIFICATION ERROR RATES (%) BY SUBJECT
Real Objects
Virtual Objects
Subj.
KD+
KD−
KD+
KD−
1
33.3
13.3
13.3
6.7
2
26.7
20
13.3
0
3
6.7
16.7
3.3
3.3
4
46.7
30
33.3
16.7
5
30
73.3
33.3
3.3
6
10
26.7
6.7
0
8
13.3
30
10
3.3
TABLE IV
AVERAGE AND STANDARD DEVIATION OF DECISION TIME ( IN
SECONDS ), NEEDED TO IDENTIFY ONE OF FOUR VIRTUAL OBJECTS ,
TABLE V
AVERAGE AND STANDARD DEVIATION OF ERROR RATES (%) ACROSS
ALL SUBJECTS ATTEMPTING TO IDENTIFY ONE OF FOUR OBJECTS ,
SORTED BY DEVICE STIFFNESS SETTINGS
SORTED BY DEVICE STIFFNESS SETTINGS
K1
K2
K3
5.1 (±2.5)
4.6 (±2.2)
5.2 (±2.4)
virtual spring was a simplified linear approximation of the
more complex response of the physical sponges.
Anecdotally, a significant majority of the study participants
reported a preference for the lower end effector stiffness setting, without being aware of their relative performance. This
indicates that prosthesis users may be able to optimize the
stiffness settings of their devices to match the requirements
of a particular task, given the mechanical capability and an
intuitive interface.
Total error
Between group error
K1
K2
K3
47.0 (±19.0)
19.8 (±16.4)
49.3 (±18.4)
18.9 (±14.3)
51.0 (±16.4)
21.0 (±14.5)
the data. Nevertheless, the results of this experiment will
inform design of future studies, which will take into account
the issues uncovered. Particularly, object sets should be
kept small, with subjects ideally required to make a simple
binary choice. Also, familiarization procedures should also
be expanded and improved in accordance with the difficulty
level of the task.
IV. C ONCLUSION
C. Experiment 2 Results
Data from the first 12 (training) trials in every block for
all subjects were dropped from further analysis, as discussed
above. Table IV shows the average decision time during the
second experiment.
A one-way repeated measures analysis of variance revealed no significant difference in the subjects’ performance
at the three different device stiffness settings (p = 0.40)
Table V presents the error rates for all subjects in all
conditions. It also contains the adjusted between-group error
rates, obtained by ignoring errors within the soft and hard
groups, i.e. not counting the instances in which subjects
mistook the KO1 object for the KO2 object, or confused KO3
with KO4 .
This study reinforces the importance of prehensor stiffness
modulation in task performance by prosthesis users. It complements previous work in the area by (1) providing evidence
for the importance of stiffness modulation in body-powered
prostheses, and (2) demonstrating the impact of end effector
stiffness on task performance for stiffness discrimination.
Results of the first experiment indicated that performance
of prosthesis users in a stiffness discrimination task can be
improved by proper modulation of device stiffness.
V. ACKNOWLEDGEMENTS
We gratefully acknowledge the assistance of Jeremy F.
Guiley in developing code for both human subject experiments.
D. Experiment 2 Discussion
R EFERENCES
The results of Experiment 2 do not appear to follow or
extend those of Experiment 1, with various device stiffness
settings producing little to no impact on overall task performance. The results are profoundly undermined by the
extremely high error rates, which are close to 50% across
all conditions, indicating that subjects had great difficulty in
identifying the correct object stiffness. The error rate of subjects using the lowest device stiffness setting in Experiment
1 and Experiment 2 shows an increase of over 10x!
Anecdotally, many subjects reported difficulties in keeping
track of the relative stiffness of each of the four objects
throughout the trial. A further look into the data showed
that any potential effects from the stiffness settings were
shadowed by learning effects, with decision times nearly
uniformly high during each subjects first trial block, before
dropping off in later trials. This suggests that the familiarization protocol built into each block was insufficient, requiring
subjects to learn on the go, with no feedback or knowledge of
results, which could have significantly increased error rates.
In summary, we concluded that the difficulty level of
the task in Experiment 2 was not adjusted appropriately,
which made it difficult to draw meaningful conclusions from
[1] N. Hogan, “Adaptive control of mechanical impedance by coactivation
of antagonist muscles,” IEEE Transactions on Automatic Control,
vol. 29, no. 8, pp. 681–690, 1984.
[2] F. A. Mussa-Ivaldi, N. Hogan, and E. Bizzi, “Neural, mechanical, and
geometric factors subserving arm posture in humans,” The Journal of
Neuroscience, vol. 5, no. 10, pp. 2732–2743, 1985.
[3] D. W. Franklin, E. Burdet, R. Osu, M. Kawato, and T. E. Milner,
“Functional significance of stiffness in adaptation of multijoint arm
movements to stable and unstable dynamics,” Experimental Brain
Research, vol. 151, no. 2, pp. 145–157, 2003.
[4] D. W. Franklin, G. Liaw, T. E. Milner, R. Osu, E. Burdet, and
M. Kawato, “Endpoint stiffness of the arm is directionally tuned to
instability in the environment,” The Journal of Neuroscience, vol. 27,
no. 29, pp. 7705–7716, 2007.
[5] A. Kadiallah, G. Liaw, M. Kawato, D. W. Franklin, and E. Burdet,
“Impedance control is selectively tuned to multiple directions of
movement,” Journal of Neurophysiology, vol. 106, no. 5, pp. 2737–
2748, 2011.
[6] E. J. Perreault, R. F. Kirsch, and P. E. Crago, “Effects of voluntary
force generation on the elastic components of endpoint stiffness,”
Experimental Brain Research, vol. 141, no. 3, pp. 312–323, 2001.
[7] E. J. Perreault, R. F. Krisch, and P. E. Crago, “Multijoint dynamics and
postural stability of the human arm,” Experimental Brain Research,
vol. 157, no. 4, pp. 507–517, 2004.
[8] R. Osu, D. W. Franklin, H. Kato, H. Gomi, K. Domen, T. Yoshioka,
and M. Kawato, “Short-and long-term changes in joint co-contraction
associated with motor learning as revealed from surface EMG,”
Journal of Neurophysiology, vol. 88, no. 2, pp. 991–1004, 2002.
343
[9] D. W. Franklin, E. Burdet, K. P. Tee, R. Osu, C.-M. Chew, T. E.
Milner, and M. Kawato, “CNS learns stable, accurate, and efficient
movements using a simple algorithm,” The Journal of Neuroscience,
vol. 28, no. 44, pp. 11 165–11 173, 2008.
[10] R. Osu, N. Kamimura, H. Iwasaki, E. Nakano, C. M. Harris, Y. Wada,
and M. Kawato, “Optimal impedance control for task achievement in
the presence of signal-dependent noise,” Journal of Neurophysiology,
vol. 92, no. 2, pp. 1199–1215, 2004.
[11] L. P. Selen, P. J. Beek, and J. H. van Dien, “Impedance is modulated
to meet accuracy demands during goal-directed arm movements,”
Experimental Brain Research, vol. 172, no. 1, pp. 129–138, 2006.
[12] A. Ajoudani, N. G. Tsagarakis, and A. Bicchi, “Tele-impedance: Preliminary results on measuring and replicating human arm impedance
in tele operated robots,” in IEEE International Conference on Robotics
and Biomimetics (ROBIO), 2011, pp. 216–222.
[13] A. Ajoudani, M. Gabiccini, N. Tsagarakis, A. Albu-Schaffer, and
A. Bicchi, “Teleimpedance: Exploring the role of common-mode and
configuration-dependant stiffness,” in 12th IEEE-RAS International
Conference on Humanoid Robots (Humanoids), 2012, pp. 363–369.
[14] E. Hocaoglu and V. Patoglu, “Tele-impedance control of a variable stiffness prosthetic hand,” in IEEE International Conference on
Robotics and Biomimetics (ROBIO), 2012, pp. 1576–1582.
[15] A. A. Blank, A. M. Okamura, and L. L. Whitcomb, “Task-dependent
impedance and implications for upper-limb prosthesis control,” The
International Journal of Robotics Research, vol. 33, no. 6, pp. 827–
846, 2014.
[16] R. F. Weir, “Design of artificial arms and hands for prosthetic applications,” Standard Handbook of Biomedical Engineering and Design,
pp. 32.1–32.61, 2003.
[17] L.-K. Chua, J. A. Martinez, and O. Celik, “Haptic body-powered
upper-extremity prosthesis simulator with tunable stiffness and sensitivity,” in IEEE Haptics Symposium (HAPTICS), 2014, pp. 545–549.
344