32nd Annual International Conference of the IEEE EMBS

Buenos Aires, Argentina, August 31 - September 4, 2010

Biomechanical Conceptual Design of a Passive Transfemoral Prosthesis

R. Unal, R. Carloni, E.E.G. Hekman, S. Stramigioli and H.F.J.M. Koopman

Abstract— In this study, we present the conceptual design of

a fully-passive transfemoral prosthesis. The proposed design is
inspired by the analysis of the musculo-skeletal activity of the
healthy human leg. In order to realize an energy efficient device,
we introduce three storage elements, which are responsible of
the energetic coupling between the knee and the ankle joints.
Simulation results show that the power storage of the designed
conceptual prosthesis is comparable with the human gait.

I. INTRODUCTION
The main research challenges in the design of trans-
femoral prostheses are the efficiency with respect to the
metabolic/external energy consumption and the adaptability
to various walking conditions. In both literature and market,
different kinds of transfemoral prostheses are present and
they can be classified as follows:
• passive, i.e. not actuated - These prostheses can be
Fig. 1. The power flow of the healthy human gait normalized in body
considered efficient from the mechanical point of view weight in the knee (upper) and the ankle (lower) joints during one stride [15].
but the overall efficiency is hampered by the consider- The areas A1,2,3 indicate the energy absorption, whereas G indicates the
able amount of extra metabolic energy consumption [1]. energy generation. The cycle is divided into three phases (stance, pre-swing
and swing) with three main instants (heel-strike, push-off and toe-off).
Moreover, due to the constant mechanical characteris-
tics, these devices can not adapt to different conditions.
• controlled by means of internal, intrinsically passive,
In this paper, we propose a biomechanical conceptual de-
actuators - These prostheses use external power to adapt
sign of a fully-passive energy efficient transfemoral prosthe-
their dynamics to different gait pattern. For example,
sis. The concept is mainly based on mimicking the energetic
in [2] and [3], the dynamical behavior of the prosthesis
behavior of a human gait in terms of coupling the energy
during walking relies on the control of a magneto-
absorption and generation of the knee and ankle joints by
rheological damper, which produces the required break-
means of three energy storage elements. This study has been
ing torque for the knee joint.
introduced in our previous work [14], and here we intend to
• active (powered), i.e. actuated - These prostheses are
improve the working principle so to obtain a comparable
capable to inject power in order to provide active ankle
power storage capability between the human leg and the
push-off generation, so to reduce the extra metabolic
proposed prosthetic device. Promising results that promotes
energy consumption [4], [5], [6], [7].
the conceptual design, have been obtained by simulation.
Recently, some of the design studies have been focused on
the transfemoral prosthesis with energy storage capabilities II. ANALYSIS OF THE HUMAN GAIT
in order to reduce the power consumption. For example,
in [8], [9] and [10], energy storage and release are pro- In order to grasp the nature of walking, we analyze the
vided by using an adjustable spring. Electrically powered biomechanical data of the human gait, as been presented
transfemoral prostheses include a spring in parallel to the by Winter in [15]. In particular, Fig. 1 depicts the power
ankle motor unit and initial tests have been reported in [11]. flow at the knee (upper) and ankle (lower) joints during
Additionally, the design studies on soft actuators have shown one complete stride of a healthy human, normalized in body
that the energy efficiency of the system can be improved by weight. The figure highlights three instants, i.e. heel strike,
storing the energy during stance phase and by releasing it so push-off and toe-off, and three main phases:
to provide active ankle push-off generation [12], [13]. • Stance: the knee absorbs a certain amount of energy
during flexion and generates as much as the same
This work has been partially funded by the Dutch Technology Foundation
STW as part of the project REFLEX-LEG under the grant no. 08003. amount of energy for its extension. In the meantime,
{r.unal,r.carloni,s.stramigioli}@utwente.nl, Faculty of Electrical Engi- the ankle joint absorbs energy, represented by A3 in the
neering, Mathematics and Computer Science, University of Twente, The figure, due to the weight bearing.
Netherlands.
{r.unal,e.e.g.hekman,h.f.j.m.koopman}@utwente.nl, MIRA Institute, • Pre-swing: the knee starts absorbing energy, represented
Faculty of Engineering Technology, University of Twente, The Netherlands. by A1 in the figure, while the ankle generates the main
978-1-4244-4124-2/10/$25.00 ©2010 IEEE 515
 part of the energy for the push-off, represented by G,
which is about the 80% of the overall generation.
• Swing: the knee absorbs energy, represented by A2 in
the figure, during the late swing phase, while the energy
rate in the ankle joint is negligible.
Note that, in the healthy human gait, the knee joint is
mainly an energy absorber whereas the ankle joint is mainly
an energy generator. Moreover, there is almost a complete
balance between the generated and the absorbed energy, since
the energy for push-off generation, i.e. G, is almost the same
Fig. 2. Conceptual design of the proposed mechanism - The design consists
as the total energy absorbed in the three intervals A1,2,3 . of three storage elements, the torsional spring C1 at the knee joint, the linear
This means that, in order to design an energy efficient spring C2 between the upper leg and foot (via a lever arm) and the linear
transfemoral prosthesis, instead of providing all the energy spring C3 between the lower leg and the foot. Both C2 and C3 are subjected
to configuration change.
required for ankle push-off from the external actuators or
instead of dissipating the energy by using breaks, the design
should be such that the ankle directly exploits the energy
absorbed by both the knee and ankle joints during the gait. and, therefore, disengaged from the knee joint without energy
Therefore, we can state that the efficiency of the mechanism dissipation, since the knee joint has zero velocity at this
derives from an energetic coupling, i.e. an energetic transfer, instant. Simultaneously, the elastic element C3 is changing
between the knee and ankle joints. the attachment point from P4 to P5 , after it is unloaded for the
III. CONCEPTUAL DESIGN OF THE PROSTHESIS push-off (see Fig. 3a and 3b). After that, during the swing
phase, the state of the energy storage elements changes as
In the proposed concept, we introduce three storage
follows:
elements, which are responsible for the three absorption
intervals A1,2,3 and the transfer of the energies A1 and A2 • The attachment point of the spring C2 , which is un-
from the knee to the ankle joint. As summarized in Fig. 2, loaded, is changed from P1 (on the heel) to P2 (on
our design relies on: the upper foot) in order to store the energy A2 . At
• One torsional elastic element C1 at the knee joint, the beginning of the swing motion of the lower leg,
responsible for the absorption A1 and for its transfer the element C2 also provides the necessary ankle dorsi-
(during swing phase) to the elastic element C3 . flexion so to guarantee the ground clearance (see Fig. 4
• One linear elastic element C2 , which physically con- - left).
nects the upper leg, via a lever arm, and the foot. • Once the ankle joint is fixed for the ground clearance,
Therefore, it couples the knee and ankle joints. This the element C1 releases the energy A1 to the element
element is responsible for the absorption A2 during the C3 by changing the attachment point P6 of C3 upward
swing phase and for a part of the absorption A3 during along the lower leg (see Fig. 3c). This energy transfer is
stance phase. realized via pulley by aligning the arm for zero torque
• One linear elastic element C3 , which physically con- around the knee joint during swing phase. Therefore,
nects the lower leg and the foot and is responsible for this transfer will not interfere the natural swing motion.
the absorption A1 (received from C1 ) and a part of A3 Since the design detail of the mechanism is out of scope
during stance phase. in this work, Fig. 3 is representing just an illustration
It is assumed that the knee joint absorbs and generates the of the concept.
same amount of energy during stance phase, therefore for
this phase, the knee joint is not considered as a contributor At the end of the swing phase, the attachment points of
to the ankle push-off generation. For this reason, an elastic the elements C2 and C3 are changed back to their initial
element to mimic this behavior is not included in the design. configuration at the heel, i.e. the attachment point of C2
moves back from P2 to P1 (see Fig. 4 - right) and the
A. Energy storage during swing phase attachment point of C3 moves back from P5 to P4 (see
The swing phase of the human gait is an energy absorption Fig. 3d). These changes guarantee that the total energy A1
phase for the knee joint and, therefore, the energy absorbed and A2 is stored in the elements C2 and C3 and, therefore,
at the knee joint has to be transferred to the ankle joint. it has been transferred to the ankle joint so to provide
For the storage purpose in the swing phase, all the three support to the ankle push-off generation. Note that to have
elastic elements are employed, and their working principle an energy efficient transfer, the change of the configuration
are depicted in Fig. 3 and Fig. 4. of the elements C2 and C3 should be realized ideally without
Due to ankle push-off, the lower leg has an amount of any dissipation. Therefore, at the heel strike, the attachment
kinetic energy equal to A1 , which is stored in the torsional points are changed along proper defined trajectories, which
spring C1 during the backward swing of the lower leg. Once keep the length of C2 and C3 constant (without elongation
the knee joint reaches full-flexion, the element C1 is locked or compression).
516
Fig. 3. Configuration change of the storage element C3 during swing phase
- (a) After push-off, the energy A1 is stored by loading the element C1 on Fig. 5. The working principle at stance phase - At the beginning of the
the knee joint. (b) At the full-flexion of knee joint, the energy storage is stance phase, both elements C2 and C3 are ready for the storage of the
completed and C1 is locked and disengaged from the knee joint. At this energy A3 (left). At the end of the stance phase, both springs are loaded
instant, the attachment point of the unloaded element C3 is changed from P4 (right).
to the P5 . (c) During swing motion the energy is transferred from C1 to C3
by changing upwards the position of the attachment point of C3 along the
lower leg (P6 ). (d) After the transfer has been completed, the position of P6
is fixed and the element C3 is brought back to stance configuration with the The elastic constants of the springs employed for the swing
heel-strike (change from P5 to P4 ). Note that the configuration changes of phase are derived from the energy values of the absorption
element C3 take place over a predefined trajectory which keeps the length
of the element constant.
intervals A1 and A2 . In particular, the elastic constant k1 of
the torsional spring C1 is determined from the absorption
interval A1 , i.e.:
1
A1 = k1 δ s1 2
2
where δ s1 is the radial deflection of the torsional spring C1
and is equal to the variation of the knee angle, which is about
0.84 rad during this interval (between 52% and 72% of the
stride). It follows that k1 = 20.88 Nm/rad.
The elastic constant k2 of the linear spring C2 is deter-
mined from the absorption interval A2 , i.e.:
Fig. 4. Configuration change of the storage element C2 during swing phase
- After pre-swing phase, the attachment point of the spring C2 is changed 1
from the heel (P1 ) to the upper part of the foot (P2 ) (left). At the end of the A2 = k2 δ s2 2
swing, the spring is loaded and its position changes back to the P1 (right).
2
The point P3 is the attachment point of the spring on the lever arm of the where δ s2 is the deflection of the spring C2 and is given by
upper leg. Note that the configuration changes of element C2 take place
over a predefined trajectory which keeps the length of the element constant. δ s2 =| PP3 P2 | −s20
where the magnitude of PP3 P2 is the length of the C2 element
B. Energy storage during stance phase when it is attached between P3 and P2 (see Fig. 4) and s20 is
its initial length, which is 0.43 m at the beginning of swing
During the stance phase, the state of the energy storage
(see Fig. 4 - left). It follows that k2 = 1925.6 N/m.
elements C2 and C3 changes as follows:
During stance phase, the energy is stored in both C2 and
• The element C2 , which is already loaded with the
C3 . It should be noted that, this parallel structure leads to
energy A2 , elongates and absorbs part of the energy A3 . smaller elastic constant for the element C3 . During the stance
• While the ankle joint is in dorsi-flexion motion, a
phase, the deflection δ s2 of the storage element C2 is given
braking torque is applied to the ankle in order to bear the by
weight of the body. Instead of dissipating the energy by δ s2 =| PP3 P1 | −s20
using a brake system, the storage element C3 provides
the brake torque and, therefore, stores the corresponding in which the magnitude of PP3 P1 is the length of the element
energy A3 . C2 when it is attached between P3 and P1 (see Fig. 4) and
This working principle during the stance phase is depicted s20 is its initial length, which is 0.52 m at the end of swing
in Fig. 5. (see Fig. 4 - right). The deflection δ s3 of the stance storage
At the end of the stance phase, the storage elements C2 element is given by
and C3 are loaded and, therefore, are ready to release the δ s3 =| PP6 P4 | −s30
total energy of all absorption phases (A1 , A2 , A3 ) for the
ankle push-off. Note that, the first swing storage part C1 in which the magnitude of PP6 P4 is the length of the element
is only active during the swing phase. Therefore, there is no C3 , attached between P6 and P4 (see Fig. 5), and s30 is
undesirable interference of the storage parts during walking. its initial length, which is 0.16 m at the beginning of roll-
over (see Fig. 5 - left). The elastic constant k3 of the stance
IV. DESIGN PARAMETERS storage element C3 can be found from the energy value of
In this Section, we identify the storage element values by the absorption interval A3 , i.e.
using the biomechanical data for a human of 1.8 m height 1 1
and 80 kg weight [16]. A3 = k2 δ s2 2 + k3 δ s3 2
2 2
517
where k2 is the elastic constant of the storage element C2 .
It follows that k3 = 82500 N/m.
V. SIMULATION AND RESULTS
In this Section, we simulate the conceptual prosthesis
in Matlab/Simulink environment. The dynamic model has
been derived by using Kane’s method [17]. To demonstrate
the power absorption performance of the mechanism, the
simulation has been done for the swing and stance phases
separately. Note that, since the model has been built to see
the feasibility of the conceptual design, all the mechanical
losses and mass of the elastic elements are neglected.
For the simulation of the swing phase, we apply the
hip torque of a healthy human [15] to the device as an
external input, while for the simulation of the stance phase,
Fig. 6. The power flow of the healthy human gait [15] (dashed line) and
in addition to the hip torque, we apply the forces of the sound the power flow for the conceptual mechanism (continuous lines for the three
leg [15] to the torso as an external input. storage elements) during one stride (for a human of 1.8 m height and 80 kg
Fig. 6 illustrates the power storage profile of the concep- weight [16]).
tual mechanism (continuous lines) compared to the healthy
human gait (dashed line) [15]. The figure shows that the
R EFERENCES
profile of the power storage of the mechanism matches quite
well with the healthy human gait. The power analysis shows [1] R. Waters, J. Perry, D. Antonelli and H. Hislop, ”Energy Cost of
Walking Amputees: The Influence of Level of Amputation”, Jour. Bone
that the 66% of the absorption interval A1 , the 70% of the and Joint Surgery, vol. 58A, pp. 42-46, 1976.
absorption interval A2 and the 88% of the absorption interval [2] J.H. Kim and J.H. Oh, ”Development of an Above Knee Prosthesis
A3 can be stored with the proposed conceptual mechanism Using MR Damper and Leg Simulator”, IEEE Int. Conf. on Robotics
and Automation, 2001.
during natural gait. Therefore, overall the 76% of the possible [3] H. Herr and A. Wilkenfeld, ”User-adaptive Control of a Magneto
amount of energy can be harvested from walking in order Rheological Prosthetic Knee”, Industrial Robot: An Int. Jour., vol.
to realize ankle push-off generation. On top of this energy, 30, pp. 42-55, 2003.
[4] F. Sup, A. Bohara and M. Goldfarb, ”Design and Control of a Powered
extra energy should be injected to the system in order to Transfemoral Prosthesis”, Int. Jour. Robotics Research, vol. 27, pp.
realize the ankle push-off generation. Since the system is 263-273, 2008.
fully passive, this energy will be generated with extra torque [5] W.C. Flowers, ”A Man-Interactive Simulator System for Above-Knee
Prosthetics Studies”, PhD Thesis, MIT, 1973.
from the hip and the extra forces from the sound leg. The [6] D. Popovic and L. Schwirtlich, ”Belgrade Active A/K Prosthesis”,
application of the forces and torques to compensate this in de Vries, J. (Ed.), Electrophysiological Kinesiology, Int. Congress,
energy is dependent on the human adaptation. Even though Excerpta Medica, pp. 337-343, 1988.
[7] S. Bedard and P. Roy, ”Actuated Leg Prosthesis for Above-Knee
there will be mechanical losses in the mechanism, the total Amputees”, 7314490 US Patent, 2003.
amount of energy that can be stored in the system indicates [8] A. Rovetta, M. Canina, P. Allara, G. Campa and S.D. Santina,
significant support for the push-off, which will reduce the ”Biorobotic design criteria for innovative limb prosthesis”, Int. Conf.
on Advanced Robotics, 2001.
metabolic energy consumption of the amputee. [9] A. Rovetta, T. Chettibi and M. Canina, ”Development of a Simple
and Efficient Above Knee Prosthesis”, IMECE Int. Sym. Advances in
VI. CONCLUSIONS AND FUTURE WORKS Robot Dynamics and Control, 2003.
[10] M. Canina and A. Rovetta, ”Innovatory Bio-robotic System for the
In this study, we proposed a biomechanical conceptual Accumulation of the Energy of Step in a Limb prosthesis”, Int.
mechanism, inspired by the power flow in the human gait, for Workshop Robotics in Alpe-Adria-Danube Region, 2003.
a transfemoral prosthesis. The conceptual mechanism is build [11] F. Sup, H.A. Varol, J. Mitchell, T. Withrow and M. Goldfarb, ”Self-
Contained Powered Knee and Ankle Prosthesis: Initial Evaluation on a
up with three elastic storage elements, which properly create Transfemoral Amputee”, IEEE Int. Conf. on Rehabilitation Robotics,
a coupling between the knee and ankle joints so to obtain 2009.
an efficient energy transfer between the joints. The working [12] K. W. Hollander, T.G. Sugar and D. E. Herring, ”Adjustable robotic
tendon using a ’Jack Spring’TM ”, IEEE Int. Conf. on Rehabilitation
principle has been evaluated in simulation and the results Robotics, 2005.
show that the power storage capability of the mechanism [13] R. Bellman, A. Holgate and T.G. Sugar, ”SPARKy 3: Design of
is comparable with the healthy gait. Therefore, this study an Active Robotic Ankle Prosthesis with Two Actuated Degrees of
Freedom Using Regenerative Kinetics”, IEEE/RAS-EMBS Int. Conf.
shows the feasibility of the concept towards the realization on Biomedical Robotics and Biomechatronics, 2008.
of an energy efficient transfemoral prosthesis. [14] R. Unal, R. Carloni, E.E.G. Hekman, S. Stramigioli and H.F.J.M.
Future work will focus on the design of the concept, Koopman, ”Conceptual Design of an Energy Efficient Transfemoral
Prosthesis”, IEEE/RSJ International Conference on Intelligent Robots
which will be improved by optimizing the design parameters and Systems, 2010.
according the maximum power storage capabilities. Mini- [15] D.A. Winter, The Biomechanics and Motor Control of Human Gait:
mum mechanical losses and control of the release rate of the Normal, Elderly, and Pathological, University of Waterloo Press, 1991.
[16] J. Rose and J.G. Gamble, Human Walking, Williams & Wilkins, 2005.
elastic elements will also be taken into account during the [17] T.R. Kane, Dynamics, Theory and Applications, McGraw-Hill, 1985.
realization of the prosthetic device.
518