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Cable-driven Parallel Manipulator for Lower Limb Rehabilitation
ROGÉRIO Sales Gonçalvesa, JOÃO CARLOS Mendes Carvalhob, LUCAS Antonio Oliveira Rodriguesc, ANDRÉ Marques Barbosad
School of Mechanical Engineering – FEMEC, Federal University of Uberlândia – UFU, Uberlândia, Brazil
[email protected], [email protected], [email protected] [email protected]
Keywords: Cable-driven parallel manipulator, Lower limb, Rehabilitation, Robots.
Abstract. The development of robotic devices to apply in the rehabilitation process of human lower
limbs is justified by the large number of people with lower limb problems due to stroke and/or
accidents. Thus, this paper presents a cable-driven parallel manipulator for lower limb rehabilitation
which is composed by a fixed base and a mobile platform that can be connected to one cable at most
six and can performing the movement of human gait and the individual movements of the hip, the
knee and the ankle. This paper starts with a study of the basic movements of the lower limb. Then the
kinetostatic and force analysis were presented. The graphical simulation and experimental tests of the
cable-driven parallel structure for lower limb rehabilitation movements are presented showing the
viability of the proposed structure.
Introduction
Stroke is the most common cause of disability in the developed world and can severely degrade lower
limb function. The use of robots in therapy can provide assistance to patients during training and
offers a number of advantages over other forms of therapy [1]. Movements’ recovery after stroke is
related to neural plasticity, which involves developing new neuronal interconnections, acquiring new
functions and compensating for impairment. Stroke rehabilitation programs should include
meaningful, repetitive, intensive and task-specific movement training in an enriched environment to
promote neural plasticity and movements’ recovery. Robotic training offer several potential
advantages in rehabilitation, including good repeatability, precisely controllable assistance or
resistance during movements and quantifiable measures of subject performance. Moreover, robot
training can provide the intensive and task-oriented type of training that has proven effective for
promoting movements learning [2-4].
Different mechanical systems have been developed and applied for rehabilitation. These
mechanical systems can be divided in: robots, exoskeletons, and cable-driven manipulators [5-6].
The most popular example of rehabilitation of the lower limb and the gait is Hocoma’s Lokomat
system (http://www.hocoma.com/). This system is a driven gait orthosis that automates locomotion
therapy on a treadmill and improves the efficiency of treadmill training. The Lokomat improves the
therapy outcome by providing highly intensive, individualized training in a motivational environment
of constant feedback.
Another example is the MoreGait system (Motorized orthosis for home rehabilitation of Gait) and
has been designed to be applied for home based gait training with a compact and transportable
structure base [7].
Another alternative that has been studied over the past few years are the cable-driven parallel
manipulator that consists on a base and a moving platform which are connected by multiple cables
that can be extended or retracted. Then, a cable-driven manipulator can move the end-effector by
changing the cables lengths while prevents any cable from becoming slack. Therefore, feasible tasks
are limited due to main static, or dynamic, characteristics of the cables because they can only pull the
end-effector but can not push it [8, 9].
Applied Mechanics and Materials Vol. 459 (2014) pp 535-542Online available since 2013/Oct/31 at www.scientific.net© (2014) Trans Tech Publications, Switzerlanddoi:10.4028/www.scientific.net/AMM.459.535
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These structures have characteristics that make them suitable for rehabilitation purposes. They
have large workspace which may be adapted to different patients and different training. The
mechanical structure is easy to assembly and disassembly which makes it easier to transport, and can
be reconfigured in order to perform different therapies. In the clinical point of view, the use of cables
instead of rigid links makes the patient fell less constrained which is important to help him/her to
accept the new technology. These characteristics make the cable-driven parallel manipulators ideal for
rehabilitation.
The drawbacks related to the use of cable-driven parallel structure are the physical nature of cables
that can only pull and not push and the workspace evaluation becomes forces dependent and can have
a complex and irregular shape [9].
Thus, this paper presents a cable-driven parallel manipulator for rehabilitation of the lower limb
human movements. The structure can be assembled from one to six cables that allow the individual
movements of the hip, the knee, the ankle and the human gait simulation with different limits and
speeds.
The development of this robotic device is justified by the large number of people with lower limb
problems.
One note that the aim of the proposed structure/device is to assist health professionals and not to
replace them.
Firstly the paper presents the lower limb movements. Secondly, the kinematic model of
cable-driven parallel robots and the device proposed in this paper were presented. Then, the static
force analysis is made by using the Jacobian matrix. Finally, the graphical simulation and
experimental tests of the cable-driven parallel structure for lower limb rehabilitation movements are
presented showing the viability of the proposed device.
Lower Limb Movements
For a specific rehabilitation system to be developed, one should use appropriate characteristics of
motions and loads for each application. In published papers there is a lot of information about
movement limits, forces and torques at joints, but in general they do not explain how and in such
conditions these data were obtained. Therefore, these data must be used with prudence [6].
The lower limb includes the hip, knee and ankle joints [10]. The rehabilitation of the human foot is
not the purpose of this work.
The hip is the proximal joint of the lower limb that allows the limb to assume any position in space
and it has three axes and three degree of freedom (DOF). The movements of the hip occur at a
ball-and-socket joint with a marker degree of interlocking. The hip joint has two basic functions for
the lower limb: supporting the body weight and locomotion.
The hip motions are: the flexion and extension motions which occur about the transverse axis
(forward and backward movements), adduction and abduction which occur about the anteroposterior
axis (lateral movements), and movements of medial and lateral rotation which occur about the vertical
axis, which coincides to the longitudinal axis of the limb when the hip joint is in the straight position.
The range movement allowed by the hip joint in general depends on the knee, as it’s shown in several
anatomy books, such as in [10].
The knee is the intermediate joint of the lower limb which allows the end of the limb to be moved
towards or away from its root or, in other words, allows the distance between the trunk and the ground
to be varied. The knee works essentially by axial compression under gravity and has two DOF. This
movement is essential for running and optimal orientation of the foot relative to the irregularities of
the ground. The first degree of freedom is related to the transverse axis, around which movements of
flexion and extension occur along the sagittal plane. The second degree of freedom is related to
rotation around the horizontal axis of the leg, directed forward, with the knee flexed. The structure of
the knee makes axial rotation impossible when the knee is fully extended. The movements of flexion
and extension are the main movements of the knee.
536 Applied Mechanics and Mechanical Engineering IV
The ankle is the distal joint of the lower limb. It is a hinge joint and therefore it has only one degree
of freedom. It controls the movements of the leg relative to the foot, which occur along the sagittal
plane. These movements are essential for walking on flat or rough ground. It is a joint exposed to
extreme mechanical conditions during single limb support. It is then subjected to the entire body
weight and to the force generated by the dissipation of kinetic energy when the foot rapidly makes
contact with the ground during walking, running or jumping.
The ankle associated to hip, knee and foot motion allows the foot to take up any position in space
and to adapt to any irregularities of the ground [10].
Kinetostatic Modeling and Proposed Device
The cable-driven parallel manipulator, proposed in this paper, can be assembled from one to six
cables arranged in a rigid structure (fixed platform) having a moving platform (splint), Fig. 1(a).
Figure 1(b) shows the prototype built at the Laboratory of Robotics and Automation at Federal
University of Uberlândia. Figure 1(a) shows the elements of the cable-driven parallel manipulator,
consisting of sets formed by 24 volts x 45 Nm DC motor, encoder with 500 pulses per revolution and
pulley. In this first step toward the implementation of numerical simulations and experimental tests, a
1.80 m tall anthropometric wooden puppet was used to simulate a human body, Fig. 1(b).
The kinematic model of cable-driven parallel robots is obtained similarly to the model obtained
from traditional parallel structures [11]. The inverse kinematic problem consists in finding the cables
lengths, ρi, as function of the end-effector pose. The forward kinematic problem consists on finding
the end-effector poses for a given set of cables lengths ρi. For the kinematic model, the used
parameters are shown in Fig. 2. The kinematic variables are the cables length ρ i.
(a) (b)
Fig. 1 (a) Scheme of the proposed device; (b) Prototype build.
The inverse kinematic model of the proposed parallel structure can be found by Eq. 1 and Eq. 2.
Applied Mechanics and Materials Vol. 459 537
Fig. 2 Kinematic parameters.
iii pvQc −+=ρ (1)
++−
−+−+
−
=
βθγθγβθγθγβθβθγθγβθγθγβθ
βγβγβ
coscoscossinsinsincossinsincossincos
cossincoscossinsinsinsincoscossinsin
sinsincoscoscos
Q (2)
Considering i varying from 1 to n (number of cables), where: pi is the position vector of point Pi
with components ai, bi and ci in relation to a fixed reference frame, vi is the position vector of point Vi
with components xi, yi and zi related to the moving frame, C (cx, cy, cz) is the position vector of the
center of gravity of the moving platform, Q is the rotation matrix between fixed and moving frames
obtained by a rotation of θ about x-axis followed by a second rotation β about the new y-axis and a
third rotation γ about the new z-axis and, ρi is the distance between points Pi and Vi (length of cable i).
Static Force Analysis
When the cable-driven manipulator performs a given task, the end-effector exerts force and moment
on the external environment, and the forces are transmitted by extending and retracting cables and
ensuring the condition of pulling cables. The static force analysis is important to determine the quality
of force transmission, which is a fundamental aspect of the energetic efficiency of the manipulator and
is necessary in order to obtain a feasible workspace. Therefore, the static analysis is done, taking into
consideration that all cables must remain in tension under any load. It should be noted that the
rehabilitation exercises are performed with low speeds.
The equilibrium equations for forces and moments acting on each cable can be given by Eq. 3 and
Eq. 4.
PFF i
n
i
i
n
i
i ==∑∑==
ρ̂11
(3)
MvQt i
n
i
i
n
i
i =×=∑∑== 11
ρ̂ (4)
538 Applied Mechanics and Mechanical Engineering IV
Written in matrix form:
[ ] [ ] [ ]WFJT = (5)
Where vector F represents the cable tension, which are forces that must be done by actuators, W is
the vector of external forces and moments applied to the system, which are the limb and the splint
weight and, J is the Jacobian matrix of the structure. ρ̂ is the unitary vector defining the cable
direction to the actuator.
The Jacobian matrix can be written as Eq. 6 for the structure with i cables.
×××=
ii
i
vQvQvQJ
ρρρρρρ
ˆˆˆ
ˆˆˆ
2211
21
…
…
(6)
Equation 5 is used to evaluate the cable tension for a given trajectory in respect to the kinematic of
the cable-driven parallel architecture [8-9, 12-13].
Graphical Simulations and Experimental System
In order to visualize the proposed structure it was realized a graphical simulation using the same
parameters values used to construct the prototype of the cable-driven parallel manipulator, Fig. 1. For
graphical simulation the software SolidWorks®
and VisualNastran Desketop 4D®
were used. These
programs permit kinematics and dynamic simulations through a constructed solid model and virtual
constraints.
Figure 3 shows the flexion hip. The patient’s leg should be immobilized for this movement. The
movement starts with the leg in horizontal position, Fig. 3(a), and the proposed device performing the
hip flexion, Figs. 3(b-c). The extension movement is the reverse sequence.
(a) (b) (c)
Fig. 3 Flexion hip.
Figure 4 shows the abduction and adduction hip. The abduction is showed in Figs. 4(a-c) and the
adduction in Figs. 4(d-f).
The extension and flexion knee can be performed with the patient supine, Fig. 5, or with the patient
seated, Fig. 6. In case the patient supine is necessary positioning his thigh, done by two cables that
keep their lengths constant, Fig. 5(a). The other two cables carry the extension movement, Figs. 5(a-c)
and flexion Figs. 5(d-f).
From the graphical simulation, the proposed structure can reproduce the lower limb movements.
Applied Mechanics and Materials Vol. 459 539
(a) (b) (c)
(d) (e) (f)
Fig. 4 Abduction and Adduction hip.
(a) (b) (c)
(d) (e) (f)
Fig. 5 Extension and flexion knee.
540 Applied Mechanics and Mechanical Engineering IV
The proposed structure is driven by sets of DC gear-motors, which are responsible for the
movement of the patient's splint by varying the cables length. The tensions on the cables are
maintained using load cells to control it, Fig. 1.
In order to verify that the device proposed in this paper is able to perform the movements
rehabilitation, experimental tests were conducted with different combinations. For this, was used an
anthropomorphic and anthropometric wooden puppet, e.g., shape and size proportional to the human
body and it is 1.80 m tall. Figure 6 shows the experimental test of knee extension.
The numerical simulation of the human gait is presented in [14].
(a) (b) (c)
(d) (e) (f)
Fig. 6 Knee extension experimental test with two cables.
Conclusions
In this paper a cable-driven parallel manipulator for rehabilitation of the lower limb movements has
been presented. The development of this robotic device is justified by the large number of people with
lower limb problems.
The developed cable-driven parallel manipulator structure can be assembled with at most six
cables that connect the fixed platform and mobile platform (splint), allowing the realization of the
lower limb movements. The kinetostatic and static force models were obtained for the proposed
structure.
The use of software for simulation of multibody systems allowed the verification of proposed
structure facilitating prototype construction.
Graphical simulations and experimental test had been carried through proving the validity of the
proposed cable-driven parallel manipulator that can reproduce the lower limb movements.
Thus, this device has the necessary requirements to be applied in physical therapy clinics, hospitals
and home, facilitating and optimizing the physiotherapist work, as well as provide information about
patient evolution.
Experimental tests will be carried out on humans.
Applied Mechanics and Materials Vol. 459 541
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Applied Mechanics and Mechanical Engineering IV 10.4028/www.scientific.net/AMM.459 Cable-Driven Parallel Manipulator for Lower Limb Rehabilitation 10.4028/www.scientific.net/AMM.459.535
