- Email: [email protected]
Stiffness characteristics of soft finger with embedded SMA fibers
Accepted Manuscript Stiffness char acter istics of soft finger with embedded SM A fiber s Junfeng Li, Lei Zu, Guoliang Zhong, Mingchang He, Haibin Yin, Yuegang Tan PII: DOI: Reference:
S0263-8223(16)31988-2 http://dx.doi.org/10.1016/j.compstruct.2016.10.045 COST 7871
To appear in:
Composite Structures
Received Date: Accepted Date:
28 September 2016 16 October 2016
Please cite this article as: Li, J., Zu, L., Zhong, G., He, M., Yin, H., Tan, Y., Stiffness char acter istics of soft finger with embedded SM A fiber s, Composite Structures (2016), doi: http://dx.doi.org/10.1016/j.compstruct. 2016.10.045
This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Stiffness characteristics of soft finger with embedded SMA fibers
Junfeng Li, Lei Zu, Guoliang Zhong, Mingchang He, Haibin Yin and Yuegang Tan First author: Junfeng Li, School of Mechanical and Electronic Engineering, Wuhan University of Technology, 430070, Wuhan, Hubei, China, [email protected] Second author: Lei Zu, School of Materials Science and Engineering, Wuhan University of Technology, 430070, Wuhan, Hubei, China, [email protected] Third author: Guoliang Zhong, School of Mechanical and Electrical Engineering, Central South University, Changsha, 410083, Hunan, China, [email protected] Fourth author: Mingchang He, School of Mechanical and Electronic Engineering, Wuhan University of Technology, 430070, Wuhan, Hubei, China, [email protected] Corresponding author: Haibin Yin, School of Mechanical and Electronic Engineering, Wuhan University of Technology, 430070, Wuhan, Hubei, China, [email protected] Tel.: +8615926461392; fax: +8602787651793
Last author: Yuegang Tan, School of Mechanical and Electronic Engineering, Wuhan University of Technology, 430070, Wuhan, Hubei, China, [email protected]
Abstract: In this paper, a novel variable stiffness finger actuated by heating the embedded SMA fibers is proposed. First, the concept of the variable stiffness mechanism and fabrication of the finger which can demonstrate continuous deformation are presented. Then, the parameters of the SMA used for variable stiffness are identified, which are used to model the phase transformation processes of its Young's modulus. In addition, experimental results show that the bending stiffness of the soft finger can be changed by heating the embedded SMA-3 fibers, resulting in a range of increase 49%. And, the model of the input current for SMA-3 wires and pulling force used to bend the soft finger is established. At last, the reaction force of the soft finger’s tip for different displacement is discussed with finite element analysis model, which is in qualitative agreement with the experimental results. The maximum range of increase for is 45.3% when the stiffness changed. Keywords: Variable stiffness; SMA; Soft finger
1. Introduction Continuum robots inspired by animals, such as elephant trunks, octopus arms, and squid tentacles, in contrast to traditional rigid-link robots, feature a continuous backbone with no joints, which have motivated a recent surge of research activity [1]. In recent years, three general continuum robot design types: tendon-based [2], concentric tubes [3], and the locally actuated backbone [4] are developed. These continuum robots provide a good solution which is suitable for navigation and inspection in congested spaces. However, unlike the biological muscular systems with enough flexibility such as the trunk of elephant, these continuum robots cannot switch from a low-stiffness to a high-stiffness when interacting with external environment and manipulating objects of different weight [5-6]. A robot with low-stiffness can effectively absorb shocks resulting from contact with the environment and can keep the contact situation stable. In addition, a robot with high-stiffness can manipulate a heavy object or support a human body firmly. These advantages have encouraged researchers to develop a number of variable stiffness mechanisms for continuum robots [7]. Traditionally, many different mechanisms are designed to achieve variable stiffness actuation for continuum robots. A hyper-redundant tubular manipulator with a variable neutral line mechanisms and adjustable stiffness is presented. The asymmetric arrangement of the tendons and the links achieves continuous stiffness modulation of continuum robots [8]. Particle jamming technology using granular media has recently been used to change the stiffness of continuum robot, which is achieved by applying a vacuum to enclosed grains-causes the grains to transition between solid-like states and liquid-like ones [9]. In addition, a continuum robot using “layer jamming” mechanism can achieve variable stiffness for minimally invasive surgery by MIT Labs. The mechanical concept of layer jamming mechanism was the
utilization of friction created between two flexible materials in the geometry of overlapping flaps, which can be controlled by a confining pressure [10]. However, these mechanical structures comprised of components, such as motors, air compressor and air valves, increases the system's complexity and weight, resulting in difficulty for these continuum robots to be built into an independent system at small scales. In order to reduce system's complexity, weight and size, thermally activated materials, such as wax or solder, can also be used as tunable stiffness elements in continuum robot [11]. In addition, structure embedded fusible alloy (Ni-Cr wires) is used in continuum robot, and the results shows that the highest stiffness of the actuator is more than eight times that of its lowest stiffness[12]. However, Comparison with shape memory alloys (SMAs), most thermally activated materials (e.g., Ni-Cr wires) have long activation timescales that are not ideal for practical manipulation applications. SMA falls into the category of smart materials and is capable of “remembering” and recovering an original shape after being deformed. Among the SMA materials, NiTi alloy has been widely used for actuator design due to its high strain (up to 8%) [13-14]. Compared with electric, hydraulic, and pneumatic actuators, SMA actuators have the advantages of high power-to-weight ratio, low driving voltages, biocompatibility, low production cost, small size, simple mechanical design, and silence operation, which make them suitable for a wide variety of applications, such as soft robotics, robotic surgical systems, and grippers[15]. In addition, SMA can also be used to change the stiffness of structure [16-17]. However, this kind of structure is not capable of producing large, complex and continuous deformations which is required in the continuum robots. To overcome the drawbacks of previous methods, we propose a new elephant trunks or octopus arms-like mechanism, which can obtain large continuous deformations as well as variable stiffness with embedded SMA.
(a)
(b)
Fig.1 Developed finger with variable stiffness mechanism. (a) hand with variable stiffness finger; (b) finger
In this work, as shown in Fig.1, a soft finger that is able to generate a continuous deformation and achieve variable stiffness mechanism is presented, which can be used to grasp different objects to improve the safety. The transformation from a low stiffness structure to a high stiffness one was accomplished by heating the embedded
SMA. The rest of this paper is organized as follows. Section 2 describes the design of the structure, materials and fabrication of variable stiffness finger. Section 3 presents the results of models and experiments for the soft finger with variable stiffness. Section 4 discusses the potential application of this actuator and concluding comments.
2. Design of the finger 2.1 Finger design As shown in Fig. 2, three types of SMA wires, referred to as SMA-1(red), SMA-2(blue) and SMA-3(green), are embedded in the structure of the finger. Fig. 2(a) shows that SMA-1 is used as the bone structure to support the finger. The continuous deformation mechanism is actuated by SMA-2. The pulley and the brackets are used to guide the SMA-2 to shrink along the shape of the actuator during the bending process. In order to measure the bending deformation of the soft finger, a sensor is fixed on surface of the finger. Fig. 2(b) shows that the basic mechanism of variable stiffness for this actuator relies on the six SMA-3 wires, which are placed in parallel to the SMA-1 wire in the brackets. In this research, the length of the finger will be referred as being the dimension parallel to x-axis, the thickness being parallel to z-axis, and the width being parallel to y-axis, where the deformation of the actuator occurs in the x-z plane. The relative position of all the components is shown in the schematic of cross section A-A of the actuator in Fig. 2(c).
Brackets SMA wire
Pulley SMA wire SMA-3 A SMA-1 S
Sensor
A S
SMA-2
x z (a)
(b)
y
Soft tube
A-A (c) SM
Fig.2 The configuration of soft finger: (a) the finger without variable stiffness mechanism; (b) the finger with variable stiffness mechanism; (c) cross-sections of the actuator
2.2. Materials and fabrication First, the SMA-1 (super elastic shape memory alloy) can make sure to obtain a constant curvature curves during the bending process of the finger. Then, the diameter of SMA-2 wire is 0.15mm which can make sure small hysteresis and quick response when actuated by heating current (ISMA-2), and it can be obtained from a company in Japan [18]. The SMA-3 wires will return to the memorized shape in straight line without change in length when heated with current (ISMA-3), which can change the stiffness of the finger since the Young’s Modulus constants corresponding to
martensite and austenite phases of SMA-3 wires will be different during the heating and cooling processes. The material used for the brackets of the soft finger is ULTEM9085 [19]. This material was selected due to its high melting point and high hardness, which can be used to prevent softening the finger when SMA-3 heated to high temperature. As shown in Fig.3, the brackets of the soft finger are manufactured by 3D printer. The SMA-1 and SMA-3(without applied stress) wires are clamped with soft tube to the brackets, which can prevent relative sliding along the x-axis direction (shown in Fig.2) between the SMA wires and the brackets during the bending process. Detailed parameters are summarized in Table 1. Table 1 Parameters for the finger and models Parameter Value Tensile modulus 2,270 MPa ULTEM9085 Tensile Strength, Yield 33 MPa Tensile Strength, Ultimate 42 MPa Melting points 120-140 ℃ Heat deflection 153℃ Diameter 0.6 mm Young's modulus 56 GPa SMA-1 Length 60 mm 6.359 × 10 m4 Wire diameter 0.15× 10m SMA-2 Resistance per meter 66.7 Ω Length 600× 10m Martensitic Young's modulus EM 23 GPa Austenitic Young's modulus EA 44 GPa Martensitic start temperature Ms 39℃ Martensitic finish temperature Mf 20℃ Austenite start temperature As 22℃ Austenite finish temperature Af 45℃ Wire diameter 0.5× 10m Initial strain 0m SMA-3 Length L 60× 10m Density ρ 5000 (Kg/m3) Resistance R(, ) 3.33 Ω The diameter of SMA d 0.5 ×10-3m 3.066 × 10 m4 Specific heat c 1400(J/Kg℃) Heat convection parameter h 165 (W/m ℃) Ambient temperature Tamb 25.5 ℃
SMA-3
SMA-2 SMA-1 (a)
(b)
Fig.3 The configuration of soft finger. (a) one side of the finger; (b) the other side of the finger;
3. Actuator modeling and stiffness test In order to assess the validity of variable stiffness mechanism for the soft finger, four sets of experiments are designed in this section to compare the performance of the actuator against the values obtained from the developed models. In this section, the parameters used in calculations and the results obtained from the model are listed in Table 1. 3.1 Young's modulus model SMA has inherent hysteresis during the transformation between martensite phase and austenite phase. The martensite fraction is a parameter given by (T, σ), which is modeled by SMA temperature and stress [20]. When (T, σ)=0, it means that SMA is completely in the martensite phase, and when (T, σ)=1, the SMA is completely in the austenite phase. The finger has hysteresis behavior in transition phases between heating and cooling. Therefore, two different equations which are approximated with cosine functions are defined for each transition phase. During the heating transformation (martensite phase to austenite phase), the martensite fraction (T, σ)is given by (T, σ)= cos a" (T $ A& ) ' b" σ* '
For A& '
+
,-
. T . A/ '
+
(1)
,-
During the cooling process, the martensite fraction (T, σ) is given by
For 6< '
=
>?
(T, σ)=
01
. . 67 '
=
>?
cos234 5 $ 67 8 ' 94 : '
;01
(2)
where Ms, Mf, As, Af are the start and finish transition temperatures associated with martensite and austenite phase transformations. 3@ , 9@ , 34 and 94 are constants which can be derived from four transition temperatures and given by
3@ = B/5D7 $ D< 8, 9@ = $3@/E@ , 34 = B/56< $ 67 8 and 94 = $34 /E4 , where CA and CM are material coefficients; 4 and @ are the initial martensite fractions for each transformation. The Young’s modulus F((, ))is the function of martensite fraction, given by F((, )) = (, )F4 ' (1 $ (, ))F@
(3)
where EM and EA are the Young's modulus constants corresponding to martensite and austenite phases, respectively.
During the heating transformation (martensite phase to austenite phase), F((, )) is given by 4 4 F((, )) = { cos 3@ ( $ D< ) ' 9@ * ' } F4 ' 2 2 {1 $
0?
cos 3@ ( $ D< ) ' 9@ * '
0?
}F@ (4)
During the cooling transformation (austenite phase to martensite phase), F((, )) is given by F5(, )8={
01
cos234 5 $ 67 8 ' 94 : ' J
01
;01
} F4 '
cos234 5 $ 67 8 ' 94 : '
;01
K F@ (5)
Since there is no load applied to SMA-3 and martensite and austenite phase transformations are fully completed during the heating and cooling processed, then = 0, 4 = 1 and @ = 0. In order to obtain the Young's modulus constants corresponding to martensite and austenite phases, the SMA-3 is tested by the tensile testing machine, as shown in Fig. 4. The ends of the SMA-3 wire covered with insulating material are fixed to the clamps of the machine. The current and the temperature sensor are used to heat the SMA and measure the temperature, respectively. Fig.5 shows that the minimum and maximum Young's modulus are 22GPa and 48GPa for the experimental data, respectively. However, in order to minimize the differences between the model and experiment data, the minimum and maximum Young's modulus of the SMA-3 which are corresponding to martensite and austenite phase are 23GPa and 44GPa for the model, respectively. Then, it clearly shows that the simulation results of the Young's modulus derived from the proposed model (Eq.(4) and Eq.(5)) are in qualitative agreement with the experimental results during the heating and cooling processes in the temperature section from 20℃ to 45℃, while there is small difference in the temperature section from 45℃ to 90℃.
Tensile testing machine Input current
SMA-3
Temperature sensor
Fig.4 The experiment setup for the modulus of elasticity test 50
Young's modulus E (Gpa)
45
40
Cooling Heating
35
30
Dashed lines: Simulation Solid lines: Experiment
25
20 0
20
Temperature ( ℃)
40
60
80
100
Fig.5 The variation of Young's modulus corresponding to heating and cooling processes 3.2 Variable Stiffness test 1 As shown in Fig.6(a) and Fig.6(b), the bending stiffness of soft finger can be changed when SMA-3 wires are heated by current (ISMA-3=0A, 1.2A), which is clearly shown with the length of the spring (L = 9.2 mm, L =11.5 mm). This variation of the bending stiffness configuration can be expressed by a simple beam system as shown in Fig 7(a). The concentrated load of the bending soft finger (without heating SMA-2) at the end point is given by [21] =
MNO PQ
The bending stiffness EI of the finger is given by [17]
EI = 5E1 I1 ' 6F3 5(, )8I3 8 =
(6) 1L3 3ω
(7)
where F is the modulus of elasticity constants of SMA-1; F 5 (, )8 is the
Young's modulus of SMA-3, which can be calculated by Eq.(3); and are the moment of inertia constants corresponding to SMA-1 and SMA-3, respectively; L is the length from the of the beam; ω is the deflection at end point of the beam. Fig.7 (b) shows the experiment setup to test the concentrated load modeled in Eq. (6) in the ambient temperature 25.5℃. Therefore, the SMA-3 wires can not complete the martensite phase during the cooling process. Then, 4 =0.81 and @ = 0.19 are the initial martensite fractions for heating and cooling transformation, which are used as parameters for the following experiment. The force sensor and temperature sensor are used to measure and temperature when the stiffness is changed by heating SMA-3. Detailed parameters are summarized in Table 1.
Finger
L
L
Fig. 6 Variable stiffness test. (a) ISMA-3=0 A , L1 =9 mm; (b) ISMA-3=1.2 A, L2 =11.5 mm (a)
(b)
\
Force sensor Finger
X
F1 (a) (b) Temperature Fig.7 Variable Stiffness experiment. (a) the cantilever beam system; sensor (b) experiment setup
Fig. 8 shows the results of comparison between the model expressed in Eq. (7) and experimental data for different X. It can be seen that the proposed model is able to predict the bending stiffness of the soft finger during the heating and cooling processes accurately when ω is equal to 12 mm. The maximum EIYZ[ and
minimum EIY]^ stiffness are 1.215× 10 and 0.815× 10 Nm2, respectively. The range of increase is (EIYZ[ $ EIY]^ )/EIY]^=49%. As the ω is equal to 17 mm and 23 mm, the differences between the experimental data and the modeling data become bigger, because the Eq. (7) is only suitable for small ω. But the experiment data can still testify that the stiffness of the soft finger can be changed by heating the SMA-3 wires. 1.8
x 10
-3
X =23mm
1.7 1.6
X =17mm
Cooling
F (Nm2)
1.5 1.4
Heating
X =12mm
1.3 1.2 1.1
Simulation
1 0.9 0.8 20
Dashed lines: Heating Solid lines: Cooling Temperature ( ℃)
40
60
80
100
Fig. 8 The bending stiffness variation for different X
3.3 Variable Stiffness test 2 The constant curvature has often been viewed as a desirable characteristic in continuum robots due to the simplifications it enables in kinematic modeling, which has been successfully applied to many continuum robots [22]. Fig. 9(a) and 9(b) show the experiment setup when SMA-2 heated with current (ISMA-2=0.21A) and the bending configuration of the finger, respectively. Here, the relationship between the pulling force and the input current (ISMA-3) is investigated. First, the relationship between the pulling force and the bending angle _ of finger is presented. It is assumed that Euler-Bernoulli assumptions are valid and bending does not change the length of the finer. Hence, the curvature k at any point of the finer is proportional to the bending moment at that point. We can get `
a
=
bc d
g=
ef P h
i
0 . θ . 2π
(8)
where _ is the bending angle; g is the constant curvature; r is the distance between the SMA-2 wire and the geometrical neutral plane of the finger (4.3×10-3m), which is assumed to remain constant throughout the bending deformation; the Eq. (8) can be
simplified as = dP _ = ef
5el fl ;meQ 50(n,=)8fQ 8 do
_
\ r
(a)
(9)
g
_
(b) Fig.9 The bending configuration of the finger. (a) experiment setup;(b)analysis of the finger
The heat for phase transformation is generated by applying a current to the SMA wire, and the balance of the heat energy governs the temperature of the SMA wire. The heat transfer model is formulated to describe the rate of temperature change due to a change in current of the wire and the convective heat loss to the environment, which can be given by the first-order dynamic equation [20]. pqr
sn st
= u v(, ) $ wD( $ ZYx )
(10)
where p is mass density of SMA wire; c is specific heat of SMA wire; v is the volume of SMA wire; u is the current across SMA wire; R(, ) is the resistance of SMA wire, which is assumed constant in this paper; h is convection heat transfer coefficient; A is circumferential area of SMA wire; ZYx is the ambient temperature. Detailed information is listed in Table 1. Fig.10 shows the simulation results for SMA heat dynamics and their comparison with experimental results when the temperature is steady with enough heating time. It clearly shows that the model can predict the performance of input current (ISMA-3) and output temperature accurately.
160 simulation Experiment
140
Temperature (℃))
120
100
80
60
40
20
0
0.5
1
1.5
2
2.5
3
Input current ISMA-3 (A)
Fig.10 Input voltage and output temperature for SMA-3 By substituting Eq. (10) into Eq. (4) and Eq.(5), the following equation can be obtained F3 5(, )8 = 0 0 { ? cos23@ 5 u v(, ) ' wDZYx $ pqr} ~ */wD $ D< 8 ' 9@ : ' ? } F4 | Heating 0? 0? z ~ ( ) z ' J1 $ cos23@ 5 u v , ' wDZYx $ pqr} */wD $ D< 8 ' 9@ : ' K F@ i (11) { 01 ;0 1 ~ z { cos234 5 u v (, ) ' wDZYx $ pqr} */wD $ 67 8 ' 94 : ' } F4 z 01 Cooing ;01 y' J cos234 5 u v (, ) ' wDZYx $ pqr} ~ */wD $ 67 8 ' 94 : ' K F@
Then, Combining Eq.(9) and Eq.(11), the simulation results of relationship between and ISMA-3 can be derived. Fig. 11 shows the simulation results from the proposed model (Eq.(9) and Eq.(11)) are in qualitative agreement with the experimental results during the cooling and heating processes for different heating current in the bending angles _ , _ and _ . Since the bending stiffness of the finger increases when the applied current increases, the pulling force increases as well. It can be seen that as the SMA-3 wires complete the transformation from martensite to austenite when input current increases from 0 A to 1 A during the heating process, the reaches to the maximum value according to the model even though the experimental data increases slightly when the current increases from 1 A to 1.8 A. The maximum YZ[ and minimum Y]^ of the pulling force for bending angles 34°, 56°and 64°are 2.031N and 2.854 N, 3.082N and 4.203N, 3.735 N and 5.354 N, and the ranges of increase(YZ[ $ Y]^ )/Y]^ are 40.5%, 36.3.2% and 43.1%, respectively.
6 5
_ =64°
(N)
4
_ =56°
3 Cooling
_ =34°
2 Heating
1 0
Dashed lines: Simulation Solid lines: Experiment
0.5
1
1.5
Input current ISMA-3 (A)
2
Fig.11 Pulling force-input voltage curves for different bending angle 3.3 Variable Stiffness test 3 This set of experiments are conducted to test the reaction force of the finger’s tip for different bending shapes when the bending stiffness changed. Fig.12 (a) shows the 3D model of the soft finger to obtain the for different Young's modulus of SMA-3 with ANASYS. Fig.12 (b) shows the bending finger 3D model and the prototype actuated by heating SMA-2 (0.14 A) with a displacement x=20mm (from the finger’s tip to the central panel of the finger without bending) and there is no contact between the force sensor and the finger’s tip ( =0). Fig.12 (c), Fig.12 (d) and Fig.12 (e) show the simulation model and experimental setup for test by heating SMA-2 (0.14 A) with displacement x=15mm, x=10mm, x=5mm, respectively. Fig.13 shows the experimental results of (shown in Fig. 12) when the stiffness changed by heating SMA-3. Since the relationship between the Young's modulus and input current can be calculated by Eq. (10) and Eq. (11) (only for heating process), the black lines show the simulation results between and ISMA-3. The red lines show the force values of during heating and cooling processes when ISMA-3 changed, which are in qualitative agreement with the simulation results. It is clearly shows that the increases when the current increases from 0 A to 1.8 A since the stiffness of the finger increases. The maximum YZ[ and minimum Y]^ of the reaction force for the finger’s tip with displacement x=15mm, x=10mm, x=5mm are 0.175 N and 0.127 N, 0.212N and 0.295 N, 0.329 N and 0.478 N, and the ranges of increase (YZ[ $ Y]^ )/Y]^ are 37.8%, 39.2% and 45.3%, respectively.
(a)
Force sensor
x (b)
(c)
(d)
(e)
Fig.12 Output force analysis of the finger tip for different x. (a) 3D model of the finger for finite element analysis; (b) x=20mm; (c) x=15mm; (d) x=10mm; (e) x=5mm
0.5 0.45
x=5mm
0.4
Black lines: Simulation Red lines: Experiment
(N)
0.35 0.3
x=15mm
Cooling
0.25
Heating
0.2
x=20mm 0.15 0.1
0
0.5
1
1.5
Input current ISMA-3 (A)
2
Fig.13 The output force of the finger tip for different
4. Conclusions This paper has introduced a novel soft finger to achieve tunable stiffness by heating the embedded SMA-3 wires. The parameters of the SMA-3 wires are identified first. Then, design, modeling, analysis, and experimental results of the variable stiffness soft finger for three different sets of experiments are presented and the experimental results demonstrate that the proposed mechanism has the capability of obvious stiffness change (shown in Fig. 8), which results in a variation of . In addition, the decrease of the displacement enlarges the range of increase of (shown in Fig. 13). The ongoing work will focus on improving the performance of the presented soft finger. In addition, tests will be conducted to show that hands with variable stiffness’s fingers have better performance than those without ones to achieve enough flexibility and enable safe motion while grasping different weight of objects or interacting with humans. In addition, the advantage of this variable stiffness finger is that the properties of this structure can be used in medicine science or mechanical structures by modifying its size, weight, geometry and material.
Acknowledgment The research work was supported by the National Natural Science Fundament of china under Grant No. 51575409 and 11202153.
References 1. Bryan A. Jones, and Ian D. Walker, Kinematics for Multisection Continuum Robots, IEEE transactions on robotics, 2006; 22(1): 43-55. 2. David B. Camarillo, Christopher F. Milne, Christopher R. Carlson, Michael R. Zinn and J. Kenneth Salisbury, Mechanics Modeling of Tendon-Driven Continuum Manipulators, IEEE Transactions on Robotics, 2008; 24(6): 1262-1273. 3. R. S. Penning, J. Jung, N. J. Ferrier, and M. R. Zinn, An evaluation of closed-loop
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
control options for continuum manipulators, in Proceedings of the IEEE International Conference on Robotics and Automation, St. Paul, Minn, USA, 2012; 5392-5397. E. Guglielmino, N. Tsagarakis, and D. G. Caldwell, An octopus anatomy-inspired robotic arm, in Proceedings of the 23rd IEEE/RSJ 2010 International Conference on Intelligent Robots and Systems (IROS’10), Taipei, Taiwan, October 2010; 3091-3096. Wei Wang, Hugo Rodrigue & Sung-Hoon Ahn. Smart soft composite actuator with shape retention capability using embedded fusible alloy structures. Composites Part B. 2015; 78: 507-514. R. V. Ham, T. G. Sugar, B. Vanderborght, K. W. Hollander, and D. Lefeber, Compliant actuator designs: Review of actuators with passive adjustable compliance/controllable stiffness for robotic applications, IEEE Robotics and Automation Magazine, 2009; 16(3):81-94. Nadia G. Cheng, Maxim B. Lobovsky, Steven J. Keating, Adam M. Setapen, Katy I. Gero,Anette E. Hosoi, and Karl D. Iagnemma, Design and Analysis of a Robust, Low-cost, Highly Articulated Manipulator Enabled by Jamming of Granular Media, 2012 IEEE International Conference on Robotics and Automation RiverCentre, Saint Paul, Minnesota, USA May 14-18, 2012;4328-4333. Yong-Jae Kim, Shanbao Cheng, Sangbae Kim, and Karl Iagnemma, A stiffness-adjustable hyperredundant manipulator using a variable neutral-line mechanism for minimally invasive surgery, IEEE transactions on robotics, 2014; 30(2):382-395. E. Brown, N. Rodenberg, J Amend, A. Mozeika, E. Steltz, M. Zakin, H. Lipson, and H. Jaeger, Universal robotic gripper based on the jamming of granular material, in Proc. Nat. Acad. Sci. USA, 2010;107:18809-18814,. Y. J. Kim, S. Cheng, S. Kim, and K. Iagnemma, A novel layer jamming mechanism with tunable stiffness capability for minimally invasive surgery, IEEE Transactions on Robotics, 2013; 29(4):1031–1042. N. Cheng, G. Ishigami, S. Hawthorne, C. Hao, M. Hansen, M. Telleria, R. Playter, and K. Iagnemma, Design and analysis of a soft mobile robot composed of multiple thermally activated joints driven by a single actuator, IEEE International Conference on Robotics and Automation (ICRA), Anchorage, AK, USA, May 2010; 5207-5212. Wei Wang, Hugo Rodrigue & Sung-Hoon Ahn. Smart soft composite actuator with shape retention capability using embedded fusible alloy structures. Composites Part B. 2015;78:507-514. Junfeng Li, Hiroyuki Harada, Phase resistance with displacement feedback control for thick SMA actuators, International Journal of Precision Engineering and Manufacturing, 2015;16(1): 81-90. Junfeng Li, HaibinYin, Guoliang Zhong and Mingpeng Wang, Improved tracking control for an SMA actuator using controller based on error and inverse segmented model, International Journal of Applied Electromagnetics and Mechanics, 2015; 48(4):437-446.
15. Min-Woo Han, Hugo Rodrigue, Hyung-Il Kim, Sung-Hyuk Song, Sung-Hoon
16. 17.
18. 19. 20.
21. 22.
Ahn, Shape memory alloy/glass fiber woven composite for soft morphing winglets of unmanned aerial vehicles, Composite Structures, 2016;140: 202-212. C. Liang, C. Rogers, Design of shape memory alloy actuators, J. Intell. Mater. Syst. Struct. 1997; 8 (4):303-313. Qing-Qing Ni, Run-xin Zhang, Toshiaki Natsuki, Masaharu Iwamoto, Stiffness and vibration characteristics of SMA/ER3 composites with shape memory alloy short fibers, Composite structures, 2007; 79(4):501-507. http://www.stratasys.com/materials/fdm/ultem-9085 https://www.toki.co.jp/biometal/bmonlineshop/?cat=304 S.M.Dutta; F.H.Ghorbel, Differential hysteresis modeling of a shape memory alloy wire actuator IEEE/ASME transactions on mechatronics, 2005;10(2):189-197. J.M. Gere, S.P.Timoshenko, Mechanics of MATERIALS, Fourth SI Edition. Chapmam Hill, 1999. Hannan, M. W. and Walker, I. D., Kinematics and the implementation of an elephant’s trunk manipulator and other continuum style robots. Journal of robotic systems, 2003; 20(2): 45-63.
S0263-8223(16)31988-2 http://dx.doi.org/10.1016/j.compstruct.2016.10.045 COST 7871
To appear in:
Composite Structures
Received Date: Accepted Date:
28 September 2016 16 October 2016
Please cite this article as: Li, J., Zu, L., Zhong, G., He, M., Yin, H., Tan, Y., Stiffness char acter istics of soft finger with embedded SM A fiber s, Composite Structures (2016), doi: http://dx.doi.org/10.1016/j.compstruct. 2016.10.045
This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Stiffness characteristics of soft finger with embedded SMA fibers
Junfeng Li, Lei Zu, Guoliang Zhong, Mingchang He, Haibin Yin and Yuegang Tan First author: Junfeng Li, School of Mechanical and Electronic Engineering, Wuhan University of Technology, 430070, Wuhan, Hubei, China, [email protected] Second author: Lei Zu, School of Materials Science and Engineering, Wuhan University of Technology, 430070, Wuhan, Hubei, China, [email protected] Third author: Guoliang Zhong, School of Mechanical and Electrical Engineering, Central South University, Changsha, 410083, Hunan, China, [email protected] Fourth author: Mingchang He, School of Mechanical and Electronic Engineering, Wuhan University of Technology, 430070, Wuhan, Hubei, China, [email protected] Corresponding author: Haibin Yin, School of Mechanical and Electronic Engineering, Wuhan University of Technology, 430070, Wuhan, Hubei, China, [email protected] Tel.: +8615926461392; fax: +8602787651793
Last author: Yuegang Tan, School of Mechanical and Electronic Engineering, Wuhan University of Technology, 430070, Wuhan, Hubei, China, [email protected]
Abstract: In this paper, a novel variable stiffness finger actuated by heating the embedded SMA fibers is proposed. First, the concept of the variable stiffness mechanism and fabrication of the finger which can demonstrate continuous deformation are presented. Then, the parameters of the SMA used for variable stiffness are identified, which are used to model the phase transformation processes of its Young's modulus. In addition, experimental results show that the bending stiffness of the soft finger can be changed by heating the embedded SMA-3 fibers, resulting in a range of increase 49%. And, the model of the input current for SMA-3 wires and pulling force used to bend the soft finger is established. At last, the reaction force of the soft finger’s tip for different displacement is discussed with finite element analysis model, which is in qualitative agreement with the experimental results. The maximum range of increase for is 45.3% when the stiffness changed. Keywords: Variable stiffness; SMA; Soft finger
1. Introduction Continuum robots inspired by animals, such as elephant trunks, octopus arms, and squid tentacles, in contrast to traditional rigid-link robots, feature a continuous backbone with no joints, which have motivated a recent surge of research activity [1]. In recent years, three general continuum robot design types: tendon-based [2], concentric tubes [3], and the locally actuated backbone [4] are developed. These continuum robots provide a good solution which is suitable for navigation and inspection in congested spaces. However, unlike the biological muscular systems with enough flexibility such as the trunk of elephant, these continuum robots cannot switch from a low-stiffness to a high-stiffness when interacting with external environment and manipulating objects of different weight [5-6]. A robot with low-stiffness can effectively absorb shocks resulting from contact with the environment and can keep the contact situation stable. In addition, a robot with high-stiffness can manipulate a heavy object or support a human body firmly. These advantages have encouraged researchers to develop a number of variable stiffness mechanisms for continuum robots [7]. Traditionally, many different mechanisms are designed to achieve variable stiffness actuation for continuum robots. A hyper-redundant tubular manipulator with a variable neutral line mechanisms and adjustable stiffness is presented. The asymmetric arrangement of the tendons and the links achieves continuous stiffness modulation of continuum robots [8]. Particle jamming technology using granular media has recently been used to change the stiffness of continuum robot, which is achieved by applying a vacuum to enclosed grains-causes the grains to transition between solid-like states and liquid-like ones [9]. In addition, a continuum robot using “layer jamming” mechanism can achieve variable stiffness for minimally invasive surgery by MIT Labs. The mechanical concept of layer jamming mechanism was the
utilization of friction created between two flexible materials in the geometry of overlapping flaps, which can be controlled by a confining pressure [10]. However, these mechanical structures comprised of components, such as motors, air compressor and air valves, increases the system's complexity and weight, resulting in difficulty for these continuum robots to be built into an independent system at small scales. In order to reduce system's complexity, weight and size, thermally activated materials, such as wax or solder, can also be used as tunable stiffness elements in continuum robot [11]. In addition, structure embedded fusible alloy (Ni-Cr wires) is used in continuum robot, and the results shows that the highest stiffness of the actuator is more than eight times that of its lowest stiffness[12]. However, Comparison with shape memory alloys (SMAs), most thermally activated materials (e.g., Ni-Cr wires) have long activation timescales that are not ideal for practical manipulation applications. SMA falls into the category of smart materials and is capable of “remembering” and recovering an original shape after being deformed. Among the SMA materials, NiTi alloy has been widely used for actuator design due to its high strain (up to 8%) [13-14]. Compared with electric, hydraulic, and pneumatic actuators, SMA actuators have the advantages of high power-to-weight ratio, low driving voltages, biocompatibility, low production cost, small size, simple mechanical design, and silence operation, which make them suitable for a wide variety of applications, such as soft robotics, robotic surgical systems, and grippers[15]. In addition, SMA can also be used to change the stiffness of structure [16-17]. However, this kind of structure is not capable of producing large, complex and continuous deformations which is required in the continuum robots. To overcome the drawbacks of previous methods, we propose a new elephant trunks or octopus arms-like mechanism, which can obtain large continuous deformations as well as variable stiffness with embedded SMA.
(a)
(b)
Fig.1 Developed finger with variable stiffness mechanism. (a) hand with variable stiffness finger; (b) finger
In this work, as shown in Fig.1, a soft finger that is able to generate a continuous deformation and achieve variable stiffness mechanism is presented, which can be used to grasp different objects to improve the safety. The transformation from a low stiffness structure to a high stiffness one was accomplished by heating the embedded
SMA. The rest of this paper is organized as follows. Section 2 describes the design of the structure, materials and fabrication of variable stiffness finger. Section 3 presents the results of models and experiments for the soft finger with variable stiffness. Section 4 discusses the potential application of this actuator and concluding comments.
2. Design of the finger 2.1 Finger design As shown in Fig. 2, three types of SMA wires, referred to as SMA-1(red), SMA-2(blue) and SMA-3(green), are embedded in the structure of the finger. Fig. 2(a) shows that SMA-1 is used as the bone structure to support the finger. The continuous deformation mechanism is actuated by SMA-2. The pulley and the brackets are used to guide the SMA-2 to shrink along the shape of the actuator during the bending process. In order to measure the bending deformation of the soft finger, a sensor is fixed on surface of the finger. Fig. 2(b) shows that the basic mechanism of variable stiffness for this actuator relies on the six SMA-3 wires, which are placed in parallel to the SMA-1 wire in the brackets. In this research, the length of the finger will be referred as being the dimension parallel to x-axis, the thickness being parallel to z-axis, and the width being parallel to y-axis, where the deformation of the actuator occurs in the x-z plane. The relative position of all the components is shown in the schematic of cross section A-A of the actuator in Fig. 2(c).
Brackets SMA wire
Pulley SMA wire SMA-3 A SMA-1 S
Sensor
A S
SMA-2
x z (a)
(b)
y
Soft tube
A-A (c) SM
Fig.2 The configuration of soft finger: (a) the finger without variable stiffness mechanism; (b) the finger with variable stiffness mechanism; (c) cross-sections of the actuator
2.2. Materials and fabrication First, the SMA-1 (super elastic shape memory alloy) can make sure to obtain a constant curvature curves during the bending process of the finger. Then, the diameter of SMA-2 wire is 0.15mm which can make sure small hysteresis and quick response when actuated by heating current (ISMA-2), and it can be obtained from a company in Japan [18]. The SMA-3 wires will return to the memorized shape in straight line without change in length when heated with current (ISMA-3), which can change the stiffness of the finger since the Young’s Modulus constants corresponding to
martensite and austenite phases of SMA-3 wires will be different during the heating and cooling processes. The material used for the brackets of the soft finger is ULTEM9085 [19]. This material was selected due to its high melting point and high hardness, which can be used to prevent softening the finger when SMA-3 heated to high temperature. As shown in Fig.3, the brackets of the soft finger are manufactured by 3D printer. The SMA-1 and SMA-3(without applied stress) wires are clamped with soft tube to the brackets, which can prevent relative sliding along the x-axis direction (shown in Fig.2) between the SMA wires and the brackets during the bending process. Detailed parameters are summarized in Table 1. Table 1 Parameters for the finger and models Parameter Value Tensile modulus 2,270 MPa ULTEM9085 Tensile Strength, Yield 33 MPa Tensile Strength, Ultimate 42 MPa Melting points 120-140 ℃ Heat deflection 153℃ Diameter 0.6 mm Young's modulus 56 GPa SMA-1 Length 60 mm 6.359 × 10 m4 Wire diameter 0.15× 10m SMA-2 Resistance per meter 66.7 Ω Length 600× 10m Martensitic Young's modulus EM 23 GPa Austenitic Young's modulus EA 44 GPa Martensitic start temperature Ms 39℃ Martensitic finish temperature Mf 20℃ Austenite start temperature As 22℃ Austenite finish temperature Af 45℃ Wire diameter 0.5× 10m Initial strain 0m SMA-3 Length L 60× 10m Density ρ 5000 (Kg/m3) Resistance R(, ) 3.33 Ω The diameter of SMA d 0.5 ×10-3m 3.066 × 10 m4 Specific heat c 1400(J/Kg℃) Heat convection parameter h 165 (W/m ℃) Ambient temperature Tamb 25.5 ℃
SMA-3
SMA-2 SMA-1 (a)
(b)
Fig.3 The configuration of soft finger. (a) one side of the finger; (b) the other side of the finger;
3. Actuator modeling and stiffness test In order to assess the validity of variable stiffness mechanism for the soft finger, four sets of experiments are designed in this section to compare the performance of the actuator against the values obtained from the developed models. In this section, the parameters used in calculations and the results obtained from the model are listed in Table 1. 3.1 Young's modulus model SMA has inherent hysteresis during the transformation between martensite phase and austenite phase. The martensite fraction is a parameter given by (T, σ), which is modeled by SMA temperature and stress [20]. When (T, σ)=0, it means that SMA is completely in the martensite phase, and when (T, σ)=1, the SMA is completely in the austenite phase. The finger has hysteresis behavior in transition phases between heating and cooling. Therefore, two different equations which are approximated with cosine functions are defined for each transition phase. During the heating transformation (martensite phase to austenite phase), the martensite fraction (T, σ)is given by (T, σ)= cos a" (T $ A& ) ' b" σ* '
For A& '
+
,-
. T . A/ '
+
(1)
,-
During the cooling process, the martensite fraction (T, σ) is given by
For 6< '
=
>?
(T, σ)=
01
. . 67 '
=
>?
cos234 5 $ 67 8 ' 94 : '
;01
(2)
where Ms, Mf, As, Af are the start and finish transition temperatures associated with martensite and austenite phase transformations. 3@ , 9@ , 34 and 94 are constants which can be derived from four transition temperatures and given by
3@ = B/5D7 $ D< 8, 9@ = $3@/E@ , 34 = B/56< $ 67 8 and 94 = $34 /E4 , where CA and CM are material coefficients; 4 and @ are the initial martensite fractions for each transformation. The Young’s modulus F((, ))is the function of martensite fraction, given by F((, )) = (, )F4 ' (1 $ (, ))F@
(3)
where EM and EA are the Young's modulus constants corresponding to martensite and austenite phases, respectively.
During the heating transformation (martensite phase to austenite phase), F((, )) is given by 4 4 F((, )) = { cos 3@ ( $ D< ) ' 9@ * ' } F4 ' 2 2 {1 $
0?
cos 3@ ( $ D< ) ' 9@ * '
0?
}F@ (4)
During the cooling transformation (austenite phase to martensite phase), F((, )) is given by F5(, )8={
01
cos234 5 $ 67 8 ' 94 : ' J
01
;01
} F4 '
cos234 5 $ 67 8 ' 94 : '
;01
K F@ (5)
Since there is no load applied to SMA-3 and martensite and austenite phase transformations are fully completed during the heating and cooling processed, then = 0, 4 = 1 and @ = 0. In order to obtain the Young's modulus constants corresponding to martensite and austenite phases, the SMA-3 is tested by the tensile testing machine, as shown in Fig. 4. The ends of the SMA-3 wire covered with insulating material are fixed to the clamps of the machine. The current and the temperature sensor are used to heat the SMA and measure the temperature, respectively. Fig.5 shows that the minimum and maximum Young's modulus are 22GPa and 48GPa for the experimental data, respectively. However, in order to minimize the differences between the model and experiment data, the minimum and maximum Young's modulus of the SMA-3 which are corresponding to martensite and austenite phase are 23GPa and 44GPa for the model, respectively. Then, it clearly shows that the simulation results of the Young's modulus derived from the proposed model (Eq.(4) and Eq.(5)) are in qualitative agreement with the experimental results during the heating and cooling processes in the temperature section from 20℃ to 45℃, while there is small difference in the temperature section from 45℃ to 90℃.
Tensile testing machine Input current
SMA-3
Temperature sensor
Fig.4 The experiment setup for the modulus of elasticity test 50
Young's modulus E (Gpa)
45
40
Cooling Heating
35
30
Dashed lines: Simulation Solid lines: Experiment
25
20 0
20
Temperature ( ℃)
40
60
80
100
Fig.5 The variation of Young's modulus corresponding to heating and cooling processes 3.2 Variable Stiffness test 1 As shown in Fig.6(a) and Fig.6(b), the bending stiffness of soft finger can be changed when SMA-3 wires are heated by current (ISMA-3=0A, 1.2A), which is clearly shown with the length of the spring (L = 9.2 mm, L =11.5 mm). This variation of the bending stiffness configuration can be expressed by a simple beam system as shown in Fig 7(a). The concentrated load of the bending soft finger (without heating SMA-2) at the end point is given by [21] =
MNO PQ
The bending stiffness EI of the finger is given by [17]
EI = 5E1 I1 ' 6F3 5(, )8I3 8 =
(6) 1L3 3ω
(7)
where F is the modulus of elasticity constants of SMA-1; F 5 (, )8 is the
Young's modulus of SMA-3, which can be calculated by Eq.(3); and are the moment of inertia constants corresponding to SMA-1 and SMA-3, respectively; L is the length from the of the beam; ω is the deflection at end point of the beam. Fig.7 (b) shows the experiment setup to test the concentrated load modeled in Eq. (6) in the ambient temperature 25.5℃. Therefore, the SMA-3 wires can not complete the martensite phase during the cooling process. Then, 4 =0.81 and @ = 0.19 are the initial martensite fractions for heating and cooling transformation, which are used as parameters for the following experiment. The force sensor and temperature sensor are used to measure and temperature when the stiffness is changed by heating SMA-3. Detailed parameters are summarized in Table 1.
Finger
L
L
Fig. 6 Variable stiffness test. (a) ISMA-3=0 A , L1 =9 mm; (b) ISMA-3=1.2 A, L2 =11.5 mm (a)
(b)
\
Force sensor Finger
X
F1 (a) (b) Temperature Fig.7 Variable Stiffness experiment. (a) the cantilever beam system; sensor (b) experiment setup
Fig. 8 shows the results of comparison between the model expressed in Eq. (7) and experimental data for different X. It can be seen that the proposed model is able to predict the bending stiffness of the soft finger during the heating and cooling processes accurately when ω is equal to 12 mm. The maximum EIYZ[ and
minimum EIY]^ stiffness are 1.215× 10 and 0.815× 10 Nm2, respectively. The range of increase is (EIYZ[ $ EIY]^ )/EIY]^=49%. As the ω is equal to 17 mm and 23 mm, the differences between the experimental data and the modeling data become bigger, because the Eq. (7) is only suitable for small ω. But the experiment data can still testify that the stiffness of the soft finger can be changed by heating the SMA-3 wires. 1.8
x 10
-3
X =23mm
1.7 1.6
X =17mm
Cooling
F (Nm2)
1.5 1.4
Heating
X =12mm
1.3 1.2 1.1
Simulation
1 0.9 0.8 20
Dashed lines: Heating Solid lines: Cooling Temperature ( ℃)
40
60
80
100
Fig. 8 The bending stiffness variation for different X
3.3 Variable Stiffness test 2 The constant curvature has often been viewed as a desirable characteristic in continuum robots due to the simplifications it enables in kinematic modeling, which has been successfully applied to many continuum robots [22]. Fig. 9(a) and 9(b) show the experiment setup when SMA-2 heated with current (ISMA-2=0.21A) and the bending configuration of the finger, respectively. Here, the relationship between the pulling force and the input current (ISMA-3) is investigated. First, the relationship between the pulling force and the bending angle _ of finger is presented. It is assumed that Euler-Bernoulli assumptions are valid and bending does not change the length of the finer. Hence, the curvature k at any point of the finer is proportional to the bending moment at that point. We can get `
a
=
bc d
g=
ef P h
i
0 . θ . 2π
(8)
where _ is the bending angle; g is the constant curvature; r is the distance between the SMA-2 wire and the geometrical neutral plane of the finger (4.3×10-3m), which is assumed to remain constant throughout the bending deformation; the Eq. (8) can be
simplified as = dP _ = ef
5el fl ;meQ 50(n,=)8fQ 8 do
_
\ r
(a)
(9)
g
_
(b) Fig.9 The bending configuration of the finger. (a) experiment setup;(b)analysis of the finger
The heat for phase transformation is generated by applying a current to the SMA wire, and the balance of the heat energy governs the temperature of the SMA wire. The heat transfer model is formulated to describe the rate of temperature change due to a change in current of the wire and the convective heat loss to the environment, which can be given by the first-order dynamic equation [20]. pqr
sn st
= u v(, ) $ wD( $ ZYx )
(10)
where p is mass density of SMA wire; c is specific heat of SMA wire; v is the volume of SMA wire; u is the current across SMA wire; R(, ) is the resistance of SMA wire, which is assumed constant in this paper; h is convection heat transfer coefficient; A is circumferential area of SMA wire; ZYx is the ambient temperature. Detailed information is listed in Table 1. Fig.10 shows the simulation results for SMA heat dynamics and their comparison with experimental results when the temperature is steady with enough heating time. It clearly shows that the model can predict the performance of input current (ISMA-3) and output temperature accurately.
160 simulation Experiment
140
Temperature (℃))
120
100
80
60
40
20
0
0.5
1
1.5
2
2.5
3
Input current ISMA-3 (A)
Fig.10 Input voltage and output temperature for SMA-3 By substituting Eq. (10) into Eq. (4) and Eq.(5), the following equation can be obtained F3 5(, )8 = 0 0 { ? cos23@ 5 u v(, ) ' wDZYx $ pqr} ~ */wD $ D< 8 ' 9@ : ' ? } F4 | Heating 0? 0? z ~ ( ) z ' J1 $ cos23@ 5 u v , ' wDZYx $ pqr} */wD $ D< 8 ' 9@ : ' K F@ i (11) { 01 ;0 1 ~ z { cos234 5 u v (, ) ' wDZYx $ pqr} */wD $ 67 8 ' 94 : ' } F4 z 01 Cooing ;01 y' J cos234 5 u v (, ) ' wDZYx $ pqr} ~ */wD $ 67 8 ' 94 : ' K F@
Then, Combining Eq.(9) and Eq.(11), the simulation results of relationship between and ISMA-3 can be derived. Fig. 11 shows the simulation results from the proposed model (Eq.(9) and Eq.(11)) are in qualitative agreement with the experimental results during the cooling and heating processes for different heating current in the bending angles _ , _ and _ . Since the bending stiffness of the finger increases when the applied current increases, the pulling force increases as well. It can be seen that as the SMA-3 wires complete the transformation from martensite to austenite when input current increases from 0 A to 1 A during the heating process, the reaches to the maximum value according to the model even though the experimental data increases slightly when the current increases from 1 A to 1.8 A. The maximum YZ[ and minimum Y]^ of the pulling force for bending angles 34°, 56°and 64°are 2.031N and 2.854 N, 3.082N and 4.203N, 3.735 N and 5.354 N, and the ranges of increase(YZ[ $ Y]^ )/Y]^ are 40.5%, 36.3.2% and 43.1%, respectively.
6 5
_ =64°
(N)
4
_ =56°
3 Cooling
_ =34°
2 Heating
1 0
Dashed lines: Simulation Solid lines: Experiment
0.5
1
1.5
Input current ISMA-3 (A)
2
Fig.11 Pulling force-input voltage curves for different bending angle 3.3 Variable Stiffness test 3 This set of experiments are conducted to test the reaction force of the finger’s tip for different bending shapes when the bending stiffness changed. Fig.12 (a) shows the 3D model of the soft finger to obtain the for different Young's modulus of SMA-3 with ANASYS. Fig.12 (b) shows the bending finger 3D model and the prototype actuated by heating SMA-2 (0.14 A) with a displacement x=20mm (from the finger’s tip to the central panel of the finger without bending) and there is no contact between the force sensor and the finger’s tip ( =0). Fig.12 (c), Fig.12 (d) and Fig.12 (e) show the simulation model and experimental setup for test by heating SMA-2 (0.14 A) with displacement x=15mm, x=10mm, x=5mm, respectively. Fig.13 shows the experimental results of (shown in Fig. 12) when the stiffness changed by heating SMA-3. Since the relationship between the Young's modulus and input current can be calculated by Eq. (10) and Eq. (11) (only for heating process), the black lines show the simulation results between and ISMA-3. The red lines show the force values of during heating and cooling processes when ISMA-3 changed, which are in qualitative agreement with the simulation results. It is clearly shows that the increases when the current increases from 0 A to 1.8 A since the stiffness of the finger increases. The maximum YZ[ and minimum Y]^ of the reaction force for the finger’s tip with displacement x=15mm, x=10mm, x=5mm are 0.175 N and 0.127 N, 0.212N and 0.295 N, 0.329 N and 0.478 N, and the ranges of increase (YZ[ $ Y]^ )/Y]^ are 37.8%, 39.2% and 45.3%, respectively.
(a)
Force sensor
x (b)
(c)
(d)
(e)
Fig.12 Output force analysis of the finger tip for different x. (a) 3D model of the finger for finite element analysis; (b) x=20mm; (c) x=15mm; (d) x=10mm; (e) x=5mm
0.5 0.45
x=5mm
0.4
Black lines: Simulation Red lines: Experiment
(N)
0.35 0.3
x=15mm
Cooling
0.25
Heating
0.2
x=20mm 0.15 0.1
0
0.5
1
1.5
Input current ISMA-3 (A)
2
Fig.13 The output force of the finger tip for different
4. Conclusions This paper has introduced a novel soft finger to achieve tunable stiffness by heating the embedded SMA-3 wires. The parameters of the SMA-3 wires are identified first. Then, design, modeling, analysis, and experimental results of the variable stiffness soft finger for three different sets of experiments are presented and the experimental results demonstrate that the proposed mechanism has the capability of obvious stiffness change (shown in Fig. 8), which results in a variation of . In addition, the decrease of the displacement enlarges the range of increase of (shown in Fig. 13). The ongoing work will focus on improving the performance of the presented soft finger. In addition, tests will be conducted to show that hands with variable stiffness’s fingers have better performance than those without ones to achieve enough flexibility and enable safe motion while grasping different weight of objects or interacting with humans. In addition, the advantage of this variable stiffness finger is that the properties of this structure can be used in medicine science or mechanical structures by modifying its size, weight, geometry and material.
Acknowledgment The research work was supported by the National Natural Science Fundament of china under Grant No. 51575409 and 11202153.
References 1. Bryan A. Jones, and Ian D. Walker, Kinematics for Multisection Continuum Robots, IEEE transactions on robotics, 2006; 22(1): 43-55. 2. David B. Camarillo, Christopher F. Milne, Christopher R. Carlson, Michael R. Zinn and J. Kenneth Salisbury, Mechanics Modeling of Tendon-Driven Continuum Manipulators, IEEE Transactions on Robotics, 2008; 24(6): 1262-1273. 3. R. S. Penning, J. Jung, N. J. Ferrier, and M. R. Zinn, An evaluation of closed-loop
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
control options for continuum manipulators, in Proceedings of the IEEE International Conference on Robotics and Automation, St. Paul, Minn, USA, 2012; 5392-5397. E. Guglielmino, N. Tsagarakis, and D. G. Caldwell, An octopus anatomy-inspired robotic arm, in Proceedings of the 23rd IEEE/RSJ 2010 International Conference on Intelligent Robots and Systems (IROS’10), Taipei, Taiwan, October 2010; 3091-3096. Wei Wang, Hugo Rodrigue & Sung-Hoon Ahn. Smart soft composite actuator with shape retention capability using embedded fusible alloy structures. Composites Part B. 2015; 78: 507-514. R. V. Ham, T. G. Sugar, B. Vanderborght, K. W. Hollander, and D. Lefeber, Compliant actuator designs: Review of actuators with passive adjustable compliance/controllable stiffness for robotic applications, IEEE Robotics and Automation Magazine, 2009; 16(3):81-94. Nadia G. Cheng, Maxim B. Lobovsky, Steven J. Keating, Adam M. Setapen, Katy I. Gero,Anette E. Hosoi, and Karl D. Iagnemma, Design and Analysis of a Robust, Low-cost, Highly Articulated Manipulator Enabled by Jamming of Granular Media, 2012 IEEE International Conference on Robotics and Automation RiverCentre, Saint Paul, Minnesota, USA May 14-18, 2012;4328-4333. Yong-Jae Kim, Shanbao Cheng, Sangbae Kim, and Karl Iagnemma, A stiffness-adjustable hyperredundant manipulator using a variable neutral-line mechanism for minimally invasive surgery, IEEE transactions on robotics, 2014; 30(2):382-395. E. Brown, N. Rodenberg, J Amend, A. Mozeika, E. Steltz, M. Zakin, H. Lipson, and H. Jaeger, Universal robotic gripper based on the jamming of granular material, in Proc. Nat. Acad. Sci. USA, 2010;107:18809-18814,. Y. J. Kim, S. Cheng, S. Kim, and K. Iagnemma, A novel layer jamming mechanism with tunable stiffness capability for minimally invasive surgery, IEEE Transactions on Robotics, 2013; 29(4):1031–1042. N. Cheng, G. Ishigami, S. Hawthorne, C. Hao, M. Hansen, M. Telleria, R. Playter, and K. Iagnemma, Design and analysis of a soft mobile robot composed of multiple thermally activated joints driven by a single actuator, IEEE International Conference on Robotics and Automation (ICRA), Anchorage, AK, USA, May 2010; 5207-5212. Wei Wang, Hugo Rodrigue & Sung-Hoon Ahn. Smart soft composite actuator with shape retention capability using embedded fusible alloy structures. Composites Part B. 2015;78:507-514. Junfeng Li, Hiroyuki Harada, Phase resistance with displacement feedback control for thick SMA actuators, International Journal of Precision Engineering and Manufacturing, 2015;16(1): 81-90. Junfeng Li, HaibinYin, Guoliang Zhong and Mingpeng Wang, Improved tracking control for an SMA actuator using controller based on error and inverse segmented model, International Journal of Applied Electromagnetics and Mechanics, 2015; 48(4):437-446.
15. Min-Woo Han, Hugo Rodrigue, Hyung-Il Kim, Sung-Hyuk Song, Sung-Hoon
16. 17.
18. 19. 20.
21. 22.
Ahn, Shape memory alloy/glass fiber woven composite for soft morphing winglets of unmanned aerial vehicles, Composite Structures, 2016;140: 202-212. C. Liang, C. Rogers, Design of shape memory alloy actuators, J. Intell. Mater. Syst. Struct. 1997; 8 (4):303-313. Qing-Qing Ni, Run-xin Zhang, Toshiaki Natsuki, Masaharu Iwamoto, Stiffness and vibration characteristics of SMA/ER3 composites with shape memory alloy short fibers, Composite structures, 2007; 79(4):501-507. http://www.stratasys.com/materials/fdm/ultem-9085 https://www.toki.co.jp/biometal/bmonlineshop/?cat=304 S.M.Dutta; F.H.Ghorbel, Differential hysteresis modeling of a shape memory alloy wire actuator IEEE/ASME transactions on mechatronics, 2005;10(2):189-197. J.M. Gere, S.P.Timoshenko, Mechanics of MATERIALS, Fourth SI Edition. Chapmam Hill, 1999. Hannan, M. W. and Walker, I. D., Kinematics and the implementation of an elephant’s trunk manipulator and other continuum style robots. Journal of robotic systems, 2003; 20(2): 45-63.