A Preliminary Study on a Twisted Strings-based Elbow Exoskeleton Dmitry Popov∗
Igor Gaponov†
Jee-Hwan Ryu‡
School of Mechanical Engineering Korea University of Technology and Education
A BSTRACT This paper presents a new concept of a 1-DOF elbow exoskeleton driven by a twisted strings-based actuator. A novel joint actuation mechanism is proposed and its kinematic model is presented along with its experimental evaluation, and guidelines on how to choose the strings suitable for such an exoskeleton are given. We also proposed and experimentally verified a human intention detection method which takes advantage of intrinsic compliance of the mechanism. The study showed that the developed twisted stringsdriven elbow exoskeleton is light, compact and have a high payloadto-weight ratio, which suggests that the device can be effectively used in a variety of haptics, teleoperation, and rehabilitation applications.
X1
X0
DX
q
DX m
Index Terms: I.2.9 [Artificial Intelligence]: Robotics— Kinematics and dynamics; H.5.2 [Information Interfaces and Presentation]: User Interfaces—Haptic I/O 1 I NTRODUCTION Exoskeletons are robotic systems worn by a person in such a way that the physical interface leads to a direct transfer of mechanical power between the human and environment. Their applications include rehabilitation and physiotherapy, human assistance, power amplification, haptic interaction with virtual environments, and teleoperation. In recent years, a significant progress in the field has been made, with the development of the exoskeletons for lower-limb support [2, 16], upper-limb support [3, 4, 6, 7, 11], and hand support applications [1, 5, 9]. However, such systems are not widely used due to several fundamental challenges in actual implementation, such as their big weight which causes operator’s fatigue, large size, low mobility, and mechanical complexity due to the use of many sensors. Another challenge is that a certain level of device compliance is required when working in uncertain environments, since collision with an obstacle or an abrupt change in a load force may effectively destroy the transmission mechanisms composing the drives of the exoskeleton. Therefore, there is a need in a power-effective, lightweight, and compliant actuators which can serve as drives for exoskeleton systems. The main goal of this research is to develop a light and compliant elbow exoskeleton with high payload-to-weight ratio. In order to build such an exoskeleton, a new type of actuators should be applied. In recent years, several promising technologies which can potentially help to increase the power density of the drives and the mobility of the exoskeletons were introduced. One of such technologies, twisted string actuation (TSA), has been shown to be effective in the design of robotic fingers, hands and arms, mobile robots, and linear actuators [10, 12, 13, 14, 15], and therefore is employed in the design of the proposed exoskeleton system. ∗ e-mail:
[email protected] [email protected] ‡ e-mail:
[email protected] † e-mail:
IEEE World Haptics Conference 2013 14-18 April, Daejeon, Korea 978-1-4799-0088-6/13/$31.00 ©2013 IEEE
DC Motor
String
Load
Figure 1: Work principle of a twisting string actuator
2 2.1
P ROPOSED E LBOW E XOSKELETON S TRUCTURE Linear Twisted String Actuators
People started using ropes to transmit power over a distance and to translate rotational motion into linear thousands of years ago, with ropes and strings used in military applications (ballistae and catapults), construction (windlasses), and other applications. Such twisted string actuators (TSA) operated on a well-known principle: When being twisted by a relatively low torque, the string (or several strings connected in parallel) contracts producing high linear force (Fig. 1). Thus, the string acts as a gear with a nonlinear gear ratio. Such actuators can employ single or multiple strings, with the single-string TSAs being more precise and the multiple-strings TSAs being faster and more durable due to their higher stiffness as a result of multiple strings used in parallel. Actuators employing twisted string actuation principle can be very light, quiet, compliant and powerful which makes them very attractive for the use in the exoskeleton systems. The mathematical model for both single and multiple strings TSAs is the same since it considers a single string or a batch of strings to be a cylinder of a uniform radius. 2.2
Concept of Elbow Exoskeleton
There are several possible kinematic designs for an elbow exoskeleton system, and they all differ in terms of size, weight, power, the possibility to adjust the mechanism for various arms sizes, actuator location, and others. In this research, we focused on designing a compact and light-weight mechanism which would be still able to carry a workload times heavier than its own weight. A simple anthropomorphic design was chosen, with the twisted string actuator located at the shoulder, as shown in Fig. 2. The prototype elbow exoskeleton system is composed of two mechanically connected links corresponding to the upper arm and the forearm of the human body. The links are connected by a rotational joint, coaxial with the human elbow joint. In addition, a pulley
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Flexion/extension
B
B Upper arm link
q
Motor String
Elbow joint
DX
Lower arm link
A
A A'
Flexion
Extension
To motor
Separator
b
Pulley
Figure 2: Proposed exoskeleton configuration
Separator coaxial with a rotational joint was rigidly attached to the forearm link (Fig. 2). The flexing and extending motions of the exoskeleton are realized by rotation of the pulley. Since the TSA system described above can only provide translational motion, it needs to be modified in order to convert the linear motion into rotational. One possible design is to connect the free end of the string to a pulley, as shown in Fig. 2, bottom. Such design was used in the first prototype of the exoskeleton. A string, connected to a motor shaft at one end and to the pulley at the other, contracts as a result of motor rotation. As it contracts, the string unwinds a part of itself wrapped around the pulley, which results in the rotational motion of the latter (the point A moves to position B, as shown in Fig. 3, upper-left). However, such design has an important flaw: When the motor starts to untwist the string, the latter goes over the pulley and wraps around it in the twisted state. This prohibits the pulley from returning to its initial position (Fig. 3, upper-right), since the effective length of the string is now reduced because some part of it is twisted and wrapped around the pulley. In order to overcome this drawback, an additional part of a twisted string actuation system, hereinafter referred to as the separator, was introduced (Fig. 3, center). The separator allows for the twisting of only the part of the string which is located between the motor and the separator itself. Thus, the string wraps around the pulley in the untwisted state, which allows the pulley to return to its initial position (Fig. 3, bottom). However, the separator does not work in case when a single string is used, which means that we can only use a multiple strings TSA in the proposed elbow exoskeleton. The exoskeleton in its current configuration can only exert flexion forces, and the extension motion is achieved due to gravity. If the bidirectional actuation is required, antagonistic TSAs can be used, which will also make it possible to control the stiffness of the exoskeleton. 3
K INEMATICS
In this section, the kinematics of a rotational TSA (hereinafter referred to as RTSA) is presented. An accurate mathematical model is very important as it can be used to find the maximum required motor torque, based on which an appropriate motor can be selected. In order to develop its mathematical model, we consider a set of strings to be a cylinder (Fig. 4, bottom-left) with the initial radius r and initial length L + L pul with a stiffness constant K. The stiffness K was measured experimentally as follows: workload of a known mass was attached at one end of the strings, while the other end was rigidly fixed. The resulting extension of the strings was measured using a linear displacement sensor, and the stiffness constant was found according to Hooke’s law as a ratio between the load force
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To pulley
B
B A Flexion
A A Extension
Figure 3: Rotation of a pulley by means of a twisted string (top), a schematic representation of a separator (center), and behavior of a rotational twisted string actuator after the separator is introduced (bottom)
and strings’ extension. The length between the separator and the pulley Lsep does not contribute to the twisting process and should be kept as small as possible in order to minimize the size of the mechanism. The twisting length of the strings L is limited by the separator and remains constant throughout the twisting process. The mathematical model of the RTSA is based on a geometrical model of a cross-section of the strings during twisting, as depicted in Fig. 4. After the strings are twisted at an angle θ , they contract and, as the result of the contraction, unwind an additional length L∗pul from the pulley. When there is no load force applied, the relation between the motor angle and the length of the strings L∗pul can be found as follows: p L2 + θ 2 r 2 − L (1) L∗pul = The unwound string of length L∗pul is a part of the string wrapped around the pulley, with its total length denoted by L pul in Fig. 4. Therefore, the length X of a helix formed by the part of the strings between the motor and the separator is given by L + L∗pul , and in the case when the maximum available length of the strings is unwound from the pulley, X = L + L pul . A conventional mathematical model of a TSA [10, 13] considers the radius of the cylinder formed by twisted strings to remain constant throughout the twisting process. However, given that each string can not be infinitely compressed by its neighbors and that there are no air gaps inside the cylinder after a sufficient number of rotations, it can be assumed that the volume of the cylinder during twisting should remain constant [12]. Therefore, the radius of the cylinder must continuously increase if its length decreases. Knowing that the volume of a cylinder is V = πr2 h, the radius of the
Untwisted state L Lsep
DC Motor
Lpul
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Thrust Bearing Upper arm
A rpul
A
Twisted state
q
Separator String (untwisted part)
Pulley
B
Separator
Forearm Larm
A τL
L X
α
X
Fz
Figure 4: Kinematics of a twisted string.
cylinder after contraction can be found as follows: s rvar
=
r·
L + L∗pul L
(2)
where rvar and r correspond to the radii in twisted and untwisted states of the cylinder, respectively. The biggest difference between proposed and conventional mathematical models is that the proposed model takes into account the assumption about the constant volume of the cylinder. As it will be shown later in the paper, this assumption helped to increase the correlation between the theoretical model and experimental data significantly. When the work load is applied at the end of the twisted strings, the latter extend. This extension is caused by two forces, Fz and Fτ , where the former is the force generated by the applied work load and the latter represents the self-untwisting force of the strings (Fig. 4, bottom-center). A part of the strings with length Lsep + (L pul − L∗pul ) can not be twisted and therefore is only affected by the load force Fz , while the rest of the strings’ length L is affected by both forces. Thus, assuming that the separator partially prevents the extension of the twisted part of the strings L and that a total stiffness coefficient of several strings in parallel is several orders of magnitude higher than the self-untwisting force, we can simplify the mathematical model by neglecting the self-untwisting force Fτ . As a result, we assume that strings are extended by the applied load force Fz only. Taking into account the constant volume assumption (2) and the applied load force, the relation between the motor angle θ and the length of the string L∗pul can be found as follows: L∗pul
=
mg
It is possible to design an elbow exoskeleton system employing the RTSA, as shown in Fig. 5. The mechanism operates as follows. Firstly, let us assume that a work load is attached to the end of the forearm, as shown in Fig. 5, and it generates a moment Ml . Once the motor starts twisting the strings, they contract and generate a linear force Fz applied along their axis of rotation. This generated force will produce a moment Mr acting on the pulley, and once this moment becomes greater than the load moment Ml , the forearm starts to rotate around the elbow axis. Using equation (3), the relation between the elbow angle β and the motor angle θ can be found as follows: q 2 −L L2 + θi2 rvar mgLarm sin(βi + γ) − (4) βi+1 = r pul Kr2pul
rvar Fz
b
Figure 5: A schematic view of the proposed twisted string-driven elbow exoskeleton in its extended (left) and flexed (right) states. A close-up view of the separator with four strings is shown in the right.
θr
L
Mr
θr
α L
Ml
Work Load
Fτ τL
Fz
g
r Fτ
q
String (twisted part)
q 2 − L − Fz L2 + θ 2 rvar K
(3)
where r pul is the radius of the pulley, Larm is the length of the forearm link, γ is the angle between the vertical line and the upper arm link, m is the weight of the applied load and g is the gravity constant. The subscripts ‘i’ and ‘i + 1’ denote the current and next data points, respectively. Angle β was considered to be zero when the forearm link was in the vertical-down position. Motor torque τL and angle θ required to lift the load of mass m at the angle β can be found as follows: τL
θ=
1 rvar
=
2 mg sin(β + γ) θ rvar · · Larm η · r pul · n L
s 2 mg sin(β + γ) · L + β · r pul − · Larm − L2 Kr pul
(5)
(6)
where η and n are the overall efficiency and transmission ratio of the mechanism, respectively. In order to design an efficient exoskeleton system, the proper electric motor should be chosen. Equation (5) can therefore be modified to find the maximum required motor torque as follows: τLmax
=
mg θ r2 · var · Larm η · r pul · n L
(7)
4 E XPERIMENTAL E VALUATION This section is dedicated to the experimental evaluation of the proposed kinematic model of the twisted string-driven elbow exoskeleton. The further subsections present a detailed description of the
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DC Motor Thrust Bearing Strings Separator
Motor torque (N⋅m)
τMmax
Figure 6: A picture of the prototype exoskeleton
experimental setup and an experimental study on the mathematical model of the exoskeleton under various load forces. 4.1 Experimental Setup A prototype twisted strings-driven exoskeleton was designed as described in the previous section and is shown in Fig. 6. The prototype was composed of two aluminum links, connected at a rotational joint, a pulley, plastic separator, a DC motor (Maxon RE-35 with a 2000-CPT encoder and a spur gearhead, gear ratio n = 18), an optical 1000-CPT encoder (Kwangwoo) measuring the elbow angle, and 6 Vectran strings (Kuraray Co., Ltd.) used in parallel. The shaft of the motor was aligned with the upper-arm link, and the strings were connected to the shaft of the gear at one end and to the pulley at the other. During experiments, the work load (various objects with known masses) was connected to the end of the forearm link, as shown in Fig. 6. The strings were aligned with the rotation axis of the motor. The total weight of the system including sensors was 2.2 kg, however, it can be significantly reduced by choosing a lighter motor and sensors and manufacturing the links using a lighter material, e.g. carbon. The lengths of the forearm and upper arm links were 0.41 m and 0.39 m, respectively. The radius of the pulley was chosen to be r pul = 0.04 m. The strings used in the prototype had the twisted length (distance between the motor and the separator) L = 0.25 m, and the initial radius of a single string was r = 0.36 · 10−3 m. Such a configuration is capable of carrying a workload of at least 10 kg and can be used in such applications as haptics, rehabilitation, power amplification, etc. The exoskeleton can be further customized depending on the design purpose, for instance, for rehabilitation applications the maximum power and weight can be reduced. 4.2 Kinematics Evaluation For all the experiments presented in this subsection, the upper arm of the exoskeleton was mounted on a fixed frame in order to eliminate any unmodeled disturbances during operation. The experiments were designed to verify the proposed kinematical model (4) and were conducted under different work load forces applied at the end of the forearm link. The experimental scenario was as follows. The strings were twisted until the elbow angle β became 90 degrees. After this, the strings were untwisted to their initial state (β = 0◦ ). The data of
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0.01 Experimental data Variable radius model
Pulley and Elbow Encoder
Work Load
0.02
0
5
10 Time (sec)
15
Figure 7: Torque generated by the motor while lifting a 5 kg-payload from β = 0◦ to 70◦ with γ = 20◦
the motor angle θ and the elbow angle β was recorded, and the motor current was measured and later converted into the motor torque τl in order to verify equation (5). The steps were repeated for a different workload. A comparison between experimental and theoretical values of motor torque is presented in Fig. 7. Although there is a small discrepancy between the theoretical and practical data of motor torque, Equation (7) can be used to estimate the maximum required motor max in Fig. 7), so that a proper torque (dashed line denoted by τM motor can be chosen for the elbow exoskeleton system. The oscillation observed in Fig. 7 is caused by the flaws in the mechanics of the prototype exoskeleton, namely the fact that the strings were not mounted perfectly coaxially with the motor shaft. This caused the motor torque to oscillate, and the pattern repeated with each rotation. As can be inferred from Fig. 7, 18 rotations were performed in the experiment. The experimental relation between the motor angle θ and the elbow angle β from two experiments (Fz = 10 N and Fz = 60 N) is shown in Fig. 8, together with constant-radius and variable-radius models of the twisted strings. It can be observed that the proposed variable-radius mathematical model provides a better match with the experimental data in comparison to the conventional model in both cases. It is also noticeable that the experimental curve remains almost identical for both load forces, which confirms the assumption about high total stiffness coefficient of the strings. 4.3
Human Intention Experiments
As was mentioned above, exoskeletons can be used as an human interface device in haptics and teleoperation applications. Regardless of the task, it is practically attractive to develop a method to measure human intention in order to move the exoskeleton in the intended direction. With the help of the proposed twisted stringsbased actuation mechanism, we can detect human intention without the use of the dedicated force sensors, and the only required sensor is a rotational encoder installed at the elbow joint. Even though the selected strings have a high total stiffness and are almost inextensible in their initial state, they will act as a spring after being twisted for some angle. Such a feature of an RTSA allows the operator to flex and extend the elbow for some small angle, even when motor torque is applied, because the actuator itself is intrinsically compliant. As for the conventional geared actuators with the links rigidly attached to the gears, such flexion/extension would be impossible. In addition, the stiffness of the proposed twisted string-based actuator can be controlled by an antagonistic actuator. In our prototype elbow exoskeleton, the human intention detection was realized as
90
90 Experimental data Conventional model Variable radius model
60 45 30 15 0
Experimental data Conventional model Variable radius model
75 Elbow angle β (deg)
Elbow angle β (deg)
75
60 45 30 15
0
10
20 30 Twisting angle θ (rotations)
40
Load force = 10 N
0
0
10
20 30 Twisting angle θ (rotations)
40
Load force = 60 N
Elbow angle β (deg)
80
Motor torque τm (mN⋅m)
Figure 8: Comparison of constant- and variable-radius mathematical models with different load forces
20
The experimental results of human intention detection are shown in Fig. 9. The motor was controlled in torque mode, and the value of supplied motor torque was limited by control software. At first, the operator applied some force at the end of the forearm link in a positive direction, thus intending to move the forearm up. This led to a positive angle error, the corresponding command was sent to the motor and the forearm link was moved in the upward direction. During such motion the error remained positive, so when the operator wanted to slow down or reverse the direction of motion, he or she needed to apply force in the opposite direction. For instance, in the described experiment, the operator decided to slow down the motion for a short time after approximately 6 seconds and then reversed the direction of motion after 10 seconds by pushing the forearm link in the opposite direction. As the result, the proposed exoskeleton was controlled directly by the operator without the use of any additional force sensors.
Current angle Previous angle
60 40 20 0
10 0
−10 −20
0
5
10
15 Time (sec)
20
25
30
Figure 9: Elbow angle (top) and motor command (bottom) time plots of the human interaction experiment
follows: • After the operator flexes or extends his or her elbow, the difference between the previous and current values of the elbow angle β is measured. • This elbow angle error is translated into the motor command, and the exoskeleton moves in desired direction. In the conducted experiment, the motor command was calculated by simply multiplying the angle error by a proportional gain. • The work load force can be estimated using equation (5), where the torque of the motor τL is obtained from the measured motor current, motor angle θ and the angle β from encoder attached at the elbow joint. This approach can be used in the case when the operator can lift the payload all by himself, or when no payload is attached. The proposed algorithm can be utilized in haptics, teleoperation and rehabilitation applications. The developed method can be applicable in the case when two antagonistic RTSAs are used, since both actuators will act as springs. In case of power amplification, a different method to detect human intention should be developed.
5 D ISCUSSION 5.1 How to Choose Pulley Size Every TSA has a limitation on maximum contraction of the string, since twisting it at a large angle will result in the rupture of the string after a number of cycles. The angle that one should not exceed during twisting so as not to cause an irreversible damage to the string is called permissible angle of twisting [12]. By introducing a pulley in a RTSA, we increase the length of the string available for twisting, since an additional length L∗pul can be unwound from the pulley, as shown in Fig. 4. Such configuration leads to the increased permissible angle of twisting. The radius of the pulley may vary, but the bigger it is, the smaller motor torque will be required in order to displace the same work load. On the other hand, in this case the required contraction of the string will increase, which will require a greater length L of the twisting string to be used. However, for a practical wearable elbow exoskeleton system the parameter L is naturally constrained by the physical dimensions of the human upper arm. Also it will require more rotations of the motor and high speed of it as a result. If the pulley radius is kept small, the required string contraction will decrease, but at the cost of higher required motor torque. This will create a necessity to use a more powerful motor, which generally leads to its increased size and weight and is also undesirable for a practical exoskeleton. 5.2 How to Choose the Strings An important issue for the proposed twisted string actuators-based elbow exoskeleton is how many strings and of what type should
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lifting the workload by himself or herself. Furthermore, we plan to introduce an antagonistic twisted string actuator analogous to that described in the paper in order to realize both extension and flexion motions and to control the stiffness of the exoskeleton. ACKNOWLEDGEMENTS This research is supported by Ministry of Knowledge and Economy of Korea grant as part of the Development of a Tele-Service Engine and Tele-Robot Systems with Multi-Lateral Feedback project. R EFERENCES
Figure 10: Simplified structure of several twisted strings composing three layers (left) and three strings corresponding to each layer (middle). The picture on the right shows two possible designs of separator.
be used. In general, the elbow exoskeleton should be capable of working with big load forces, and therefore the strings will be subjected to high tension forces, too. The strings used in the twisted string actuators should be manufactured using some high stiffness material, such as Vectran or Kevlar [8]. As it follows from equation (5), the smaller the radius of the formed cylinder, the smaller motor torque of the motor is required. Therefore, we need to find such a combination of the strings so that they will be capable of sustaining large load forces while providing the smallest possible radius of the cylinder formed by the twisted strings. From a practical point of view, it is not convenient to use many strings at the same time because of the difficulties with mounting and pre-tensioning. In addition, it is recommended to avoid the cases when the strings do not twist evenly around each other, since this will lead to the existence of the inner and outer layers of the strings, with the strings located in the outer layer twisted around the strings in the inner layer. In this case the outer strings will be under the bigger tension which may lead to their faster rupture, and as the result such combinations of the strings will not follow the described kinematic model (4). The separator should be designed in such a way that strings are threaded inside it symmetrically with respect to their axis of rotation (Fig. 10). In this case the cylinder will be uniform, and the strings will not twist in layers around each other. 6 C ONCLUSION AND F UTURE W ORKS This work presents a preliminary study on the elbow exoskeleton system which employs a novel revolute joint mechanism based on a twisted string actuator. The developed device is intrinsically compliant, has no inertia and zero backlash. In addition, the exoskeleton is light, cheap and mechanically simple due to the fact that no mechanical gears and force sensors are used. In its current design, the proposed mechanism has a payload-to-weight ratio of approximately 4. We developed and experimentally verified the kinematics and motor torque relationship of the exoskeleton and showed that the proposed mathematical model fits the practical data better than the conventional model. The derived kinematics allows to calculate maximum required motor torque, which can be used in the design of a practical exoskeleton system. Finally, we conducted a human interaction experiment in which we designed a control algorithm utilizing intrinsic compliance of the twisted string actuator, which suggests that the exoskeleton can be effectively used as a rehabilitation device, as well as applied in various haptics and teleoperation applications. As our future work, we are planning to develop a control algorithm for power amplification when the operator is not capable of
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