Design and realization of a Flexible Finger Actuated by ... · PDF fileA flexible finger for robotic application composed by a ... One gripper hand will use different ... classical

International Journal of Applied Engineering Research ISSN 0973-4562 Volume 12, Number 24 (2017) pp. 15635-15643 © Research India Publications. http://www.ripublication.com

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Design and realization of a Flexible Finger Actuated by Shape Memory Alloy (SMA) Wires

Daniela Maffiodo1 and Terenziano Raparelli 2

1,2 Department of Mechanical and Aerospace Engineering, Politecnico di Torino c.so Duca degli Abruzzi 24 10129 Torino Italy.

1Orcid: 0000-0002-5831-8156; 2Orcid: 0000-0003-0063-7733 Abstract A flexible finger for robotic application composed by a variable number of autonomous modules was designed and realized. The motion of a single module is performed by SMA wires, capable of changes in their own length and causing the bending of the module. The heating of the wire, e.g. by means of Joule effect, causes the shortening of the wire itself, whereas the cooling, while a bias force is applied, causes the stretching of the wire to the original shape. The combination of different modules actuation could cause a complex deformation of the finger itself. A finite element model was studied and implemented in order to properly design the device. The preliminary tests on a first prototype demonstrate a good behaviour of the device. Keywords: Shape memory alloy, SMA wires, flexible actuator INTRODUCTION Within the unconventional actuators, there are variously actuated devices that exploit flexing principles of the finger structure itself to move. Since the sixties, some flexible actuators were investigated: pneumatic actuators for application in rehabilitation McKibben artificial muscle [1] and robotics Rubbertuator [2] are well known. Another fluid deformable actuator able to exert both tensile and compressive forces has three cylindrical coaxial nonisotropic membranes connected to two end plates, whose original shape allows the independent air supply of three internal chambers: supplying the different chambers, the device is able to bend [3]. Shape Memory Alloys applications are a promising area in which it seems possible to realize innovative robotic devices. Since the 80s, some researchers have shown that these materials have undoubted advantages when dimensions are decreasing. They are the high power/weight ratio [4], sensing ability, remotability, low driving voltage, simplicity, cleanliness and silent actuation. On the other hand, they present undoubted disadvantages, such as low efficiency, fatique problems and characteristics that depend on life cycle. Nevertheless many researchers in recent years tried to design devices with SMA actuators in various fields of engineering: robotics [5-8], biomedical [9-11], structural [12, 13]. Different controls were implemented in order to overcome the drawbacks and obtain stable and repeteable behavior [14-16]

Some researchers have therefore attempted to implement flexible actuators driven by SMA actuators. An example is the SMA springs driven device studied by Yang et al. [17], which consists of a flexible rod with three embedded SMA springs, having a similar behaviour than the pneumatic actuator [3]. Nothing is said on the cooling of the device that seems to be a drawback of the device, due to the material that surrounds the SMA springs. In order to have the possibility to operate with devices having more degrees of freedom and therefore a larger working space, some researchers designed modular type actuators, in which a single unit is replicated and, by means of an appropriate arrangement, usually in series, a complex actuator is made. A brilliant example is the compliant modular actuator [18]. This structure consists of a series of light and small modules operating as linear, rotational o surface actuators. Each one is based different arrays of the same simple unit based on a folded sheet of SMA. The idea presented in this work is the combination of the previous concepts. A flexible module, implemented by means of SMA wires, which can be assembled in series with other identical modules to constitute a complete and versatile device. Starting from this idea, a flexible actuator was designed: the device will be modular and each finger will be made up of 2 or 3 modules. Each module will consist of a flexible central beam and SMA wires externally arranged at 120°. The actuation of one or more wires sma will generate the deflection of the beam in the corresponding direction. The wires are not embedded in the structure so to have a fast cooling. A rigid support will constitute the base on which the electric power cables, switches and drives for the control of the structure are arranged. The modularity of the gripping fingers, which are the most important object of this prototype, guarantees a great versatility of the device. One gripper hand will use different number of fingers, depending on the task. In the mechanical field, the actuator could be used as a gripping hand or positioner: in the first case it is important to take into account the forces exerted by the device while in the second case greater importance must be given to the precision of movement, the working space and the controllability of the structure. In the biomedical field, one finger could be used as an endoscope. In this case it must be very flexible, precise in the movements and each module must be very thin and long.


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DESIGN OF THE DEVICE On the basis of previous experiences on SMA applications [19, 20] and on design of robotic systems [21, 22], a SMA wires driven flexible actuator was designed. The grasping device actuated by shape memory wires studied in this research is basically a hand with mobile fingers solidly connected to a rigid basement hosting cables, switches and all things related to the device control. Fingers are an important part of the device and they are composed by modules, in order to obtain a versatile device, able to perform different tasks. The number of fingers can be different depending on the task,

usually 2 or 3. Each finger is composed by a number of modules, usually 2 or 3. The motion of a single module is performed by SMA wires, capable of changes in their own length and causing the bending of the module. The heating of the wire, e.g. by means of Joule effect, causes the shortening of the wire itself, whereas the cooling, while a bias force is applied, causes the stretching of the wire to the original shape.

Figure 1: a) module: 1) central rod, 2) base, 3) disks, 4) SMA wire; b) module bending, heated wire in red

Figure 2: A finger bended in a complex way

Figure 1a) shows a module, composed by:

1. Central rod, a thin cylinder which is the flexible core of each modulus;

2. Bases, having a greater diameter than the central rod; there are two bases (lower and upper end) placed at the rod ends;

3. Disks, having the same diameter of the base, but lower thickness, they have holes representing sliding constraints for the wires;

4. SMA wires, fixed to one base and in polar array

configuration, each couple of wires placed 120 degrees from the other, in order to allow to the module to bend in any direction.

Figure 1b) shows an inactive module on the left and an active module on the right. The bending is caused by a Joule heating of a wire (in red), that shortens due to the heating. The bias force, necessary to the stretching of the wire to the original length is exerted both by the central rod and by the inactive wires.


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Each modulus will be independently electrically driven so that the finger, composed by two or more moduli, will bend in only one direction or assume a more complex shape (Figure 2). This can be useful when using it to grasp complex shaped objects. MODULE MATHEMATICAL MODEL To design properly the finger, the behaviour of a single module was studied with a mathematical model. In particular, it is necessary to relate the central rod strain to the force applied on the module by the SMA wire. This cannot be done using the

classical Saint Venant or the Euler-Bernoulli beam theory because strains have same order of magnitude of the rod length, moreover normal stress and shear stress cannot be neglected. For these reasons, a finite element model was studied and implemented in Matlab. Central rod is modelled as a set of rigid rods, having length L, connected by torsional springs, having stiffness K (Figure 3a). Connection points between two rods are nodes, numbered from 0 (at the joint) to n.

Figure 3: Central rod modellization: a) a set of rigid elements L connected by torsional springs K; connections between rods are nodes (0÷n); b) Incremental model scheme

Torsional springs models the central rod elasticity, generating a moment:

ϕΔ⋅=Δ KM (4.1)

where : ΔM = spring reaction moment Δφ = angular displacement K = torsional spring stiffness The value of the stiffness K is depending on the rod material characteristics (particularly the elastic modulus E), on its length L and mass moment of inertia I:

LIEK ⋅

= (4.2)

An incremental model was implemented, considering infinitesimal changes on the applied forces, causing infinitesimal rods displacements (Figure 3b), so that the torsional displacement Δφi of the i-th rod can be written as:

ii MIE

LΔ⋅

⋅=Δϕ (4.4)

And considering all the rods:

2

3

10

KKL L

L

Δϕ1

Δϕ2

23

2'

3'

10

β+Δβ

ΔF

KK

K


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Δφ j =L

E ⋅Ij=1

i−1

∑ ⋅ ΔMij=1

i−1

∑ (4.5)

Moreover it is necessary to consider the moment applied to the node E, generated by a force ΔF applied in point F (Figure 4a), which represents the SMA wire force (applied at a distance R2 due to the disks, see Figure 1):

( ) ( )[ ]TOTNTOTNE ϕββϕββ sinsincoscosRFM 2 ⋅Δ+−⋅Δ+−⋅⋅Δ=Δ (4.6)

where (see figure 4a): ΔF = variation of the force applied in point F by the SMA wire ϕNTOT = angular position of rod N at time t R2 = distance between central rod and hole on the disk, where the SMA wire applies the force β = force direction at time t Δβ = variation of the force direction

ϕΝ−1Tot

ϕΝTotN

E

F

N-1

β+ΔβΔF

ϕΝTot

R2

ΔF

Figure 4: Point of application of the force Generalizing, for the i-th node, moment is:

( ) ( ) ⎥⎦

⎤⎢⎣

⎡⎟⎠⎞

⎜⎝⎛ Δ+⋅Δ+−⎟

⎠⎞

⎜⎝⎛ Δ+⋅Δ+⋅⋅Δ+Δ=Δ ∑∑

−

=−

−

=−−

1

11

1

111 sinccossinLFMM

i

jji

i

jjiii TOTTOT

os ϕϕββϕϕββ

(4.8)

And the total moment is the sum of the contribution of each node:

∑=

Δ=Δn

1jjTOT MM (4.9)

Equations (4.5), (4.6) and (4.8) represent the resolutive system. This system does not allow an algebrical solution and the linearization is not possible due to the great amount of the rod bending. Therefore, the equations were implemented in a Matlab model and numerically solved. RESULTS OF THE MODEL Starting from some basic assumptions, the implemented model was used for a parametric evaluation of different characteristics of the modulus. The length of a modulus was fixed to 40 mm and central rod, bases and disks were made of one piece only of nylon (density equal to 1.13 g/cm3, Young modulus of about 800 MPa, melting temperature is 120°C). A finger made of three modules in series, see figure 2) with two disks each, (see figure 1) was hypothesised.

Figure 5 shows, as an example, the simulated bending of a three modules finger with a rod diameter of 2.6 mm, caused by one SMA wire 5% shortening , with different values of the distance R2 (see figure 4) between central rod and SMA wire.


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Figure 5: Simulated bending of a three modules finger, caused by one SMA wire 5% shortening , with distance

between rod axis and SMA wire R2=3 mm÷8 mm (a to f). Decreasing the distance between SMA wire and rod axis, the

structure bends more and the workspace (the mobility) increases, but the output force and the system controllability decrease. The chosen compromise is a distance of 3.5 mm with a rod diameter of 2.6 mm. Observing the trend of the moment along the central rod, it is noted that this is, with a good approximation, constant, so that the geometric dimensions obtained previously allow to obtain a good distribution of the tensions during the progressive bending of the structure The simulated torque along the central rod is, with a good approximation, constant so that there is a good distribution of the tensions during the progressive bending of the structure. The force at maximum bending (when the SMA wire is 5% shortened) is 4N; that means that the device is able to exert significant force to grip an object. In particular, the mathematical model provides interesting results concerning the gripping force. Fig 6 shows the simulation of the presence of an obstacle at 20 mm or 40 mm respectively, and the resulting interaction force is about 0.7N e 0.3N respectively.

a)

b)

Figure 6: Simulated interaction with obstacle: (a) initial distance between finger and obstacle 4 cm;

(b) initial distance between finger and obstacle 2 cm


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a)

b)

Figure 7: a) three calibration screws allow the correct tensioning of the SMA wire,

b) the same screws allow the connection of two modules Prototype realisation The mathematical model gives some optimized modulus dimensions, and the final design determines all the other ones, with a particular eye to tricks for a simple assembly, to tensioning devices for the SMA wires and to connecting devices for one module to the other. A single module has two end bases having different diameter, such as to embed one to the other of the following module. These end bases lodge three calibration screws and three slots which allow fixing one module to another. Within the end basis there are countersinks able to lodge the SMA wires, the tensioning device (see figure 7), a metallic plate for the electrical continuity and a plastic plate for the electric insulation between modules.

Two intermediate disks guide the SMA wires with the aim of reducing the overall dimensions of the actuator during bending operations and to increase the bending amount under the same wire shortening. The intermediate disks have the same diameter of the largest end base to allow eventual application of coating and little thickness in order to have no structural functions. The design criteria was the reduction of the number of components in order to simplify assembly and functioning. As an example the three calibration screws (see figure 7) have 4 different tasks: the tensioning adjustment of the SMA wires; the stable connection between two modules; the electric conduction between electric and SMA wires; the hooking device for the electric wires. Table 1 shows the main SMA wire characteristics, given by the manufacturer. The wire heating is obtained by Joule effect, the cooling is on still air.


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Table 1. SMA wire characteristics

Diameter (μm) Recommended deformation ratio

250 3-5%

electrical Linear resistance (Ω/m) Recommended current (A) Recommended Power (W/m)

20 1 20

strength Maximum developed force at 600MPa (N) Recommended developed force at 190MPa (N) Recommended deformation force at 35MPa (N)

28.8 9 1.7

thermal Activation start temperature (°C) Activation finish temperature (°C) Relaxation start temperature (°C) Relaxation finish temperature (°C)

68 78 52 42

Density (g/cm3) Young Modulus (martenisite) (Gpa) Young Modulus (austenite) (Gpa)

6.45 28 75

To simplify the wire assembly, the module design foresee the use of a single wire for one module. Figure 8 shows the assembly of a single module and figure 9 shows the assembly of a three modules finger. Simple actuations of the three different modules of the prototype demonstrate the good working of the flexible actuator. Future tests for the displacement and force measurement are being defined.

Figure 8 : Actuator single module

Figure 9: Actuated prototype of a three module finger CONCLUSIONS A Model for the design of a flexible actuator was implemented and the results used to create a prototype of a modular device. The preliminary tests on the designed and realized actuator show stable and correct operation. The modular design of the actuator has proven to be very effective as it has made it


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possible to choose the size of the device as needed. The modules are made up of few elements for which the actuator is particularly economical to achieve and this advantage would be even more pronounced in the case of serial production. The small size of the device allows for a light and flexible structure, but at the same time manual assembly of the system is quite difficult. A possible improvement of the actuator may consist of making tools to facilitate its assembly. The compact design makes this actuator ideal for medical and mechanical applications, but it should be noted that required power supply of SMA wires is quite high. Ultimately, the preliminary results achieved with this prototype are encouraging, especially considering the novelty aspects brought by SMA wires. Although there are some issues that seem to limit possible applications, many possible solutions can be identified when the search in this field will be more consolidated. Future works will include test benches for the displacement and force measurement. Moreover a control system will be included to the device in order to avoid overheating of the wire and increase its life, this control could be a resistance feedback control [19] or another type of control, incuding to the mechatronic system also a position or force sensor [12-16, 23]. REFERENCES [1] Schulte, H.F.Jr, The characteristics of the McKibben

artificial muscle (1961) The Application of external power in prosthetics and orthotics. National Academy of Sciences-National Research Council, Washington D. C., Appendix H, pp. 94-115.

[2] Inoue, K., Rubbertuators and applications for robots (1988) Robotics Research: The 4th International Symposium, Bolles R, Roth B (eds). MIT Press, Cambridge, Mass. pp. 57-63.

[3] Ferraresi, C., Franco, W., Quaglia, G., A novel bi-directional deformable fluid actuator (2014) Proc. of the institution of Mechanical Engineers, Part C, vol. 228, n. 15, pp. 2799-2809.

[4] Ikuta, K., Micro/miniature shape memory alloy actuator (1990) Proceedings IEEE International Conference on Robotics and Automation, vol.3, pp. 2156-2161, doi: 10.1109/ROBOT.1990.126323.

[5] Raparelli, T., Beomonte Zobel, P., Durante, F., Mechanical design of a 3-dof parallel robot actuated by smart wires (2009) Proceedings of EUCOMES 2008 - The 2nd European Conference on Mechanism Science, pp. 271-278, DOI: 10.1007/978-1-4020-8915-2_33.

[6] Lee, K-T., Lee, G-Y., Choi, J-O., Wu, R., Ahn, S-H., Design and Fabrication of a Smart Flexible Structure using Shape Memory Alloy Wire (SMA) (2010) Proceedings of the 2010 3rd IEEE RAS & EMBS International Conference on Biomedical Robotics and Biomechatronics, pp. 599-603.

[7] Fukuda, T., Hosokai, H., Kikuchi, I., Distributed type of

actuators by shape memory alloy and its application to underwater mobile robotic mechanism (1990) Proceedings of IEEE International conference on Robotics and Automation, pp. 1316-1321, doi: 10.1109/ROBOT.1990.126182.

[8] Wang, Z., Hang, G., Li, J., Wang Y., Xiao, K., A micro-robot fish with embedded SMA wire actuated flexible biomimetic fin (2008) Sensors and Actuators A, vol. 144, pp. 354-360.

[9] Giataganas, P., Evangeliou, N., Koveos, Y., Kelasidi, E., Tzes, A., Design and experimental evaluation of an innovative SMA-based tendon-driven redundant endoscopic robotic surgical tool (2011) 19th Mediterranean Conference on Control & Automation, pp. 1071-1075.

[10] Duerig, T., Pelton, A., Stöckel, D., An overview of nitinol medical applications (1999) Materials Science and Engineering A, vol. 273–275, pp. 149–160.

[11] Petrini L., Migliavacca F., Biomedical Applications of Shape Memory Alloys (2011) Journal of Metallurgy, doi:10.1155/2011/501483

[12] Song, G., Kelly, B., Agrawal, B.N., Active position control of a shape memory alloy wire actuated composite beam (2000) Smart Mater. Struct., 9, pp. 711–716.

[13] Lima, W. M., Araujo, C. J., Valenzuela W. A. V., Rocha Neto, J. S., Control of strain in a flexible beam using Ni-Ti-Cu shape memory alloy wire actuators (2012) J. Braz. Soc. Mech. Sci. & Eng., vol.34, n.spe, pp.413-422. ISSN 1678-5878. http://dx.doi.org/10.1590/S1678-587820 12000500010.

[14] Moallem, M., Deflection control of a flexible beam using shape memory alloy actuators (2003) Smart Mater. Struct., 12, pp. 1023–1027.

[15] Shameli, E., Alasty, A., Salaarieh H., Stability analysis and nonlinear control of a miniature shape memory alloy actuatorfor precise applications (2005) Mechatronics, vol. 15, pp. 471–486.

[16] Choi, S.B., Han, Y.M., Kim, J.H., Cheong, C.C., Force tracking control of a flexible gripper featuring shape memory alloy actuators (2001) Mechatronics, Vol. 11 (6), pp. 677-690, ISSN 0957-4158, https://doi.org/10.1016/S0957-4158(00)00034-9.

[17] Yang, K., Gu, C.L., A compact and flexible actuator based on shape memory alloy springs (2008) J Mech Eng Sci., vol. 222, pp. 1329–37.

[18] Torres-Jara, E., Gilpin, K., Karges, J., Wood, R.J., Russ, D. Compliant Modular Shape Memory Alloy Actuators (2010) IEEE Robotics and Automation Magazine. Vol.17, 4, pp. 78-87.

[19] Maffiodo, D., Raparelli, T., Resistance feedback of a shape memory alloy wire (2016) Advances in Intelligent Systems and Computing, vol. 371, pp. 97-104. DOI: 10.1007/978-3-319-21290-6_10.


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[20] Maffiodo, D., Raparelli, T., Three-fingered gripper with flexure hinges actuated by shape memory alloy wires (2017) International Journal of Automation Technology, vol. 11 (3), pp. 355-360. DOI: 10.20965/ijat.2017.p0355.

[21] Ferraresi, C., Maffiodo, D., Hajimirzaalian, H. A model-based method for the design of intermittent pneumatic compression systems acting on humans (2014) Proceedings of the Institution of Mechanical Engineers, Part H: Journal of Engineering in Medicine, vol. 228 (2), pp. 118-126. DOI: 10.1177/0954411913516307.

[22] Colombo, F., Maffiodo, D., Raparelli, T., Active Gas Thrust Bearing With Embedded Digital Valves and Backpressure Sensors (2017) Tribology Transactions, vol. 60 (5), pp. 807-813. DOI: 10.1080/10402004.2016.1213344.

[23] Ferraresi, C., Maffiodo, D., Hajimirzaalian, H., Simulation and control of a robotic device for cardio-circulatory rehabilitation (2016) Advances in Intelligent Systems and Computing, vol. 371, pp. 357-365. DOI:10.1007/978-3-319-21290-6_36.

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Design and realization of a Flexible Finger Actuated by ... · PDF fileA flexible finger for robotic application composed by a ... One gripper hand will use different ... classical