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The Development of a Nitinol Angular Actuator

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13 February 2025

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13 February 2025

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Abstract
Shape memory alloys are the key to sustainable technology and future industries. One of the most highlighted alloys around these times is Nitinol. It has special properties to work in extreme conditions and it can be specially projected for specific tasks. The Nickel-Titanium alloy is tested by NASA to build a new type of wheel to be used for future rovers which will be send to Mars. Other recently known devices to be built using this material are stents, root canal files, arches, bone implants used in medicine, aerospace gas turbines engines, thermal bimorph od dynamic actuators used in engineering, innovative SC brace or seismic retrofit applications in seismology and the list can continue. The purpose of this paper is to introduce the ungular actuator that has as a main component a Nitinol spring. In the theoretical part we identified the newest solutions in the sphere of Nitinol devices and presented them though the perspective of bibliometric maps obtained with the software VOSviewer. We focused on articles which analyze and improve the NiTi alloy in order to create a wider applicability range for it, studies over the already existing devices, testing models, novel applications and devices which utilize it and papers identifying new applications for actual NiTi devices/ equipment. Conclusions on the subject are that the industry is more and more interested in the shape memory materials and are open to investing in the research of the Nitinol. The presented device was physically developed and tested at the University Ștefan cel Mare of Suceava. Some results on the testing of the device are presented and discussed in this paper.
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1. Introduction

The latest trends express more and more the need to adapt, to reuse and to repair due to the huge impact human production and consuming has over our planet. Our ancestors were used to live modestly and respecting the limits of the nature, but in today`s market of offer and request the bigger the economy the bigger and more negative are the effects on land, water and air. This is the reason we selected Nitinol, a material that can be used for the same action multiple times.
In recent years the industry requests innovative solutions and materials to be used in actuators. One of the most researched branches nowadays are the shape memory alloy actuators. For example, the Nitinol actuators can be produced in multiple configurations and models depending on the alloy shape among other devices or equipment.
We focused on articles which analyze and improve the NiTi alloy in order to create a wider applicability range for it, studies over the already existing devices, testing models, novel applications and devices whom utilize it and papers identifying new applications for actual NiTi devices/ equipment.

2. State of the Art

In this paper we combined and analyzed 145 articles which include nitinol researches in its various shapes and forms. The purpose of this article is to highlight the new trends in the field of nitinol devices/ equipment/ forms/ applications through the bibliometric maps and to present a new actuator built with Nitinol.
Using the classification method, we highlighted the main forms of used NiTi and their main applications and domains. The article also brings up the innovative elements developed around the world by various institutes and laboratories over the last 6 years.
This article is structured in seven parts: the introduction places the theme of Nitinol, then in the state of the art the selected articles are represented with the purpose they have on the implemented system. In the third part the material and methods used are placed followed by the fourth part of the theoretical analysis of the articles. The fifth section is analyzing the resulting bibliometric maps from the network and temporal perspective. The following part presents the use of a Nitinol memorized spring to build an angular actuator. Finally, discussions and conclusions are identified in order to evolve to future directions of this research.

3. Materials and Methods

We selected the platform Web of Science and IEEE due to their wide variety of articles and its complexity. The selected articles are from the area of Nitinol devices and equipment, from two time periods and the wide category includes the other one. There have been made multiple analysis in this article and they involve a certain number of articles.
The included researches resulted through articles filtrations on Web of Science on the Nitinol published in the areas of Web of Science:
  • Materials Science Multidisciplinary;
  • Engineering Biomedical;
  • Engineering Electrical Electronic;
  • Engineering Manufacturing;
  • Engineering Multidisciplinary;
  • Orthopedics;
  • Robotics;
  • Engineering aerospace;
  • Engineering Industrial.
The extensions RIS (for the 145 articles) extensions were downloaded and used in the VOSviewer software [156] to generate network visualization bibliometric maps, density and the overlay visualization map.
The software VOSviewer [156] uses network data generates multiple types of bibliometric maps. The maps can be visualized and explored for more detailed perspectives providing access to every element identified in the map. The generated maps ca be recreated by anyone using the program with the condition to apply the same rules.
The advantages of such an analysis are:
  • to provide original content;
  • to observe connections and similitudes among the article;
  • to guide to specific content the researcher highlighting the novel path in the area;
  • to explore the evolution of a certain theme in time.

4. Theoretical Analysis

In this section we are presenting three classifications, respectively first one is the classification after the generalized main objective, one after the form of the used Nitinol and after the main domain of application.

4.1. Classification after the Generalized Main Objective

Every studied article contains one or multiple types of Nitinol in different structures and compositions projected to have certain characteristics and to respond in electrical or thermal field. In Figure 1 are presented 19 forms of Nitinol with the articles they were found in.
We conceived this classification in order to provide a clear orientation for all the researchers who want to easily identify specific information regarding a certain type of nitinol. Firstly, we identified the main objective of every analyzed article and then simplified them and integrated them in one of the 7 categories presented in Table 1.
From a total of 147 articles 38% are focused on studying and testing the Nitinol alloy on different levels: dynamic fracture performances, evolution during cooling and heating on molecular level, martensite variant reorientation process, torsion and bending deformation modes, to capture the shear strain field, etc. A percentage of 21% from the researchers are studying/ testing the device/ equipment/ applications such as the micro-lattices/stents, MEMS applications, welding, actuators, biomedical devices, electrochemical micromachining, chips, power laser actuation, cement mortar beams and so on.
Another 19% of them work to improve the characteristics of already existing devices/ equipment/ applications/ model/ process on medical robots, reduction of the surface defects, reversible bending on electrical actuators, effectiveness of Auricchio model, minimize hysteresis, lower prices, obtain useful transformation temperatures, rise spring actuation performance, wastewater recovery, adhesion increase, etc. Also 10% build a new device/ equipment/ applications/ model like: ankle rehabilitation robot, applications on the material behavior and lifespan, develop additive manufacturing, micropump diaphragm, form fit connection, 3D models and built numerical simulation.
A reduced percentage of articles, 6,13% of them are testing models/ strategies on devices based on Nitinol: The Auricchio model, numerical one, three-dimensional phenomenological constitutive model and diffraction computed tomography. The smallest percentage, 1,36% and 2,72 % of the papers work to develop a new formula of Nitinol, respectively to improve the fabrication of devices using Nitinol.

4.2. Classification After the Nitinol form

Every studied article contains one or multiple forms of Nitinol in different structures and compositions projected to have certain characteristics and to respond in electrical or thermal field.
We conceived this classification in order to provide a clear orientation for all the researchers who want to easily identify specific information regarding a certain type of Nitinol. In the following Figure 1 are listed 19 forms of Nitinol with the articles they were found in.
Figure 1. Forms of Nitinol.
Figure 1. Forms of Nitinol.
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4.3. Classification After the Application Domain

Nitinol has such a wide variety of applications due to its shape memory feature activated at temperature changes, superelasticity (pseudoelasticity), corrosion resistance, anti-toxicity, good shock absorption characteristics, large range of temperature response depending on the atomic percentages of the Nickel and Titan and so on.
The medical field takes the first place when it comes to researches in the area of Nitinol applications and studies. Then the engineering field with a wide variety of devices, then civil engineering, robotics and so on. Definitely the charts would be different if we would compile multiple publication platforms. The following classification lists some of the identified utilization fields and the main applications of the Nitinol:
  • Medical:
    Blood pressure sensors on the head of a pin;
    Root canal files;
    Arches, stents;
    Spinal and dental implants;
    Vascular stent;
    Eyeglass frame;
    Micro-stent;
    Bone implant;
    Orthodontic wires;
    Minimally invasive surgical devices;
    Robotic needle insertion;
    Stents;
    Valves;
    Muscles.
  • Engineering:
    Rotary actuator;
    Actuator;
    Aerospace gas turbine engines;
    Dynamic actuators
    Actuators used for helicopter active rotor blade control;
    Thermal bimorph actuators;
    Sensor-less actuator.
  • Civil Engineering Industry:
    High damping materials;
    Thin-wall structures;
    Grate;
    Micro-lattice;
    NiTi foil for welding.
  • Robotics:
    Artificial muscle;
    Micro-actuators;
    Bionic manipulator.
  • Automotives:
    Actuators;
    Motors;
    MEMS.
  • Seismology:
    Innovative SC brace;
    Seismic retrofit applications.
  • Constructions: Cement mortar beams.
  • Mechanical: Pressure sensors.

5. Bibliometric Simulation Analysis

5.1. Network Visualization

Thousands of elements are presented under multiple perspectives and environments, which slowly evolve under the name of development and evolution in science. The following Figure 2 highlights 480 items which have been present in our 110 analyzed articles at least for 5 times.
In order to clarify the presentation new increased the number of appearances per item to at least 10 appearances and now the map in Figure 3 is presenting the 74 most used items in the selected articles.
Shape memory alloy (Figure 4) as an item is identified in cluster 4 and it occurs 374 (adding up the SMA) times. The shape memory alloy we selected, Nitinol, has the property to change its shape to the memorated form when activated in electrical and thermal fields and then return to the initial one.
As examples of smart materials, we can name NiTi (Nickel-Titanium), Fe-Mn-Si (Iron- Manganese- Silicon), Cu-Al-Ni (Copper-Aluminium-Nickel), and so on. The item Nitinol (NiTi alloy, NiTi) (Figure 5) occurs 176 times in among the selected papers. Nitinol is an alloy that depending on the report of Nickel and Titanium rewinds to its memorized shape at a certain temperature. Nitinol can be identified as elastic or superelastic, in shapes such as: wires (ultra-fine, round or flat), plates (flat or waved), springs (helical, micro, flat or torsion) or rods. Nitinol has wide applications in automotives, aerospace, medical industries, electric field and so on.
Actuators are known to be present in science and industry for a very long time. From soft ones, electric, hydraulic, pneumatic, magnetic, mechanic or 3D printed ones they have various applications in the fields of energy, medicine, automotives, robotics and so on with the purpose of improving the mobility and the functionality of a certain device or system. The performance metrics that characterize an actuator are force, speed, energy efficiency, acceleration, followed by durability, operating conditions, volume and mass. Considering its robustness, weight and other details we may select a specific actuator for a certain task.
Actuators are worldwide used to convert energy into mechanical force. In actuators a wide variety of materials may be identified, from classic metals to polymers and even memory form materials. In this article we highlight, among a variety of devices and equipment, the type of actuators developed using Nitinol.

5.2. Temporal Analysis

We are always discussing evolution and development and analyzing then through the filter of past. All the subjects have a starting point, and our study identified a focused starting point on the theme of Nitinol in 2018 with 6 articles appropriate for our research which focus on the following elements: force variation [102], laser welding [103], numerical simulation [105], NiTi joints [106], micromechanical modeling [107]. In the purple dots we can observe the items: actuator, spacer, electrostatic flapping wing ac, soft robotic gripper, frequency jump and so on in completion to the preview mentioned elements.
In 2019 we identified 20 papers on the Nitinol and they compile subjects such as: actuators performance increase [82], nanomechanical testing [83], biomedical applications [84], Voronoi-based reconstruction [85], uniaxial loading [86], SMA/Kapton composites [87], thermal-mechanical cycling training [88], anisotropic compressive strength [89], actuation systems [90], adhesion work [91] and so on.
From the year 2020, the 24 identified articles highlight self-centering energy-dissipation braces [58], micromechanical strain partitioning [61], two-step PT [62], novel NiTi smart structures [65], post heat treatment methods [67], machining accuracy [68], critical loading conditions [71], graded materials [73], non-recoverable strain [76], Bionic manipulator [78], e-mobility [81], etc. With the dark green we can observe more specific items like fiber, actuator, application, voltage, martensitic transformation, layer, etc. to help sustain the developed system.
In 2021 a number of 28 papers decay of Ni4Ti3 and Ni3Ti precipitates [31], Micro Electro Mechanical System [33], Cyclic shear loading [34], Torsional loading [35], interfacial shear strength [38], welding [40], the elastocaloric effect [42], lath martensites and dislocations [46], biocompatibility [47].
From 2022, we selected 30 researches WEDM machining [3], Ni4Ti3 precipitates [4], reversible SMA-FRP soft actuators [7], MEMS [10], X-ray diffraction [12], high accuracy [16], vacuum environment [19], micro-lattices/stents [22], elastocaloric air cooler [23], Scanning and light beam deflection [25], critical energy release rate [26], Low speed drive system [28], super-elasticity of NiTi SMA [29], yield surface [30]. Last year focuses (with yellow) on more precise things like soft robotics, viscosity, thermo, mode controller.
In 2023 were identified 20 articles that are focused on: actuators [116,117,118,120], vibration dampers [119], microactuators [121,123], lightweight actuators [122], Nitinol experimenting stands [124,125], temperature reglation to increase performance [120,126,128], hight load SMA actuators [127], haptic wearable devices [133], independent actuation [130] and so on.
Last year, 2024, helped us to identify soft robotics, actuators and origami structures [137], structural elements [138], deep-sea manipulation [139], heat engine [140], Nitinol texturing in single or two layers [141], twisting wrist actuator [143], actuators for payloads displacement [145], servomechanism of a rotator-type joint [147], Flapping Wing Micro Aerial Vehicles [152], photoactuator [153], etc.
Figure 7. Overlay visualization 2018 - 2024.
Figure 7. Overlay visualization 2018 - 2024.
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6. Practical Application. Nitinol Spring Angular Actuator

6.1. Methodology

The NiTi alloy was the emerging point in the experiments. Multiple samples were purchased such as classical Nitinol springs, superelestic springs and memorized plates. In the angular actuator was used a 50%Ni and 50%Ti spring (Figure 8).
Nitinol springs are resistant to damp environments or chemicals without degrading rapidly and are also corrosion resistant. They can be made from both classic and super-elastic Nitinol. Nitinol springs are used in various fields including medical devices (such as stents and guide wires), robotics and aerospace. Their ability to adapt and recover after deformation makes them valuable in complex systems.
Characteristics of the Nitinol:
Wire diameter: 1 mm;
Diameter of the coil: 6 mm;
Total length: 76,2 mm;
Stretching capacity: x 4
Transition temperature: 45 ⁰C.

6.2. Constructive Description

The actuator (Figure 9) consists of a Nitinol spring (15) with a coil diameter of 1.15 mm, a rest length of 30 mm, a coil circumference of 6 mm and a 30 mm reserve (12) from which the system can be tensioned or relieved, a compensating steel spring (6), a spring clamping system (11) and a spring tension and spring contraction monitoring system. The axis of rotation of the actuator (16), on which the adjusting rod (17) is installed, and the two supports for supporting the steel and Nitinol springs (14) are mounted perpendicular to the base plate (13).
In the construction of the angular actuator test stand, we used a heat-resistant vessel (1) in which we placed the actuator in liquid media (3). The liquid was heated by means of a thermocouple (2) mounted on the rim of the thermal vessel. The temperature variation was measured with a thermometer (5) attached to the holder (8), and the protractor (9) for visualizing the angle of displacement of the indicator needle (10) is mounted on the holder (7). The indicator needle is located on the end of its holder (4) which is clamped in the support plate (18).
The Nitinol spring is memorized so that at a temperature above 40⁰ C it expands, and at temperatures lower than the previous value it returns to its original shape.

6.3. Description of Actuator’s Operation

The data was acquired using the experimental stand presented in Figure 14. The actuator is positioned in the heat-resistant vessel (1) which creates the favorable operating environment by storing the fluid (water). Using the thermowell (2) the temperature of the fluid will be controlled to observe the behavior of the Nitinol (15) in stages, the expansion of the spring with increasing temperature and the contraction of the steel spring (6).
In the second part, the thermoplunger is taken out of the immersion (water) medium (3) for cooling and contraction of the Nitinol spring and detensioning of the steel spring, respectively.
The temperature of 30 ⁰C will be considered as the starting point of the Nitinol spring deflection, and after the temperature of 90 ⁰C the spring will not deflect. The liquid temperature was raised to 95 ⁰C, but there was no further reaction after this threshold. The ambient temperature at the time the experiment was started was 20 ⁰C.
Several displacement positions of the Nitinol spring-loaded actuator are shown in the following Figure 10, the initial position at 0, 10⁰, 20⁰, and 158⁰ displacements.

7. Experimental Data Collection

For data acquisition, the stand was submerged in water and, by varying the temperature, the Nitinol spring causes the actuator to contract and relax, or angular displacement.
The following Figure 11 shows the characteristic of actuator displacement as a function of heating temperature. The amount of displacement is relatively small between 20 ⁰C and 40 ⁰C, but the displacement visibly increases with temperature. A jump occurs between 50 ⁰C and 60 ⁰C when the displacement increases from 26⁰ to 40⁰. The characteristic emphasizes the sudden displacement that the actuator makes when the liquid medium reaches a temperature of 80 ⁰C and 150 ⁰, respectively. At 90 ⁰C the displacement reaches 158⁰. Even if the temperature was raised to 95 ⁰C the displacement angle remained the same.
The characteristic of the angular displacement of the actuator (Figure 12) as a function of cooling temperature shows the constant angular displacement of the actuator up to a temperature of 60 ⁰C at which the Nitinol spring contracts to an angle of 50o, followed by continuous cooling with small contact jumps until it returns completely to its initial position at 20 ⁰C.

8. Discussions and Conclusions

The theoretical analysis conducted at point 4 in our research contains 3 classifications. The first one (section 4.1.) is the one after the main objective of the selected papers and we generalized it so it would fit in one of the 7 categories. This allows us to provide a more focused perspective over the Nitinol researches. The majority of authors are concentrating on the studying and testing of the alloy with the purpose to offer higher efficiency, better characteristics, improved rearmament and so on to make the Nitinol better known and more used on the market. The classification after the form (section 4.2.) of Nitinol used help the researchers that would consult our paper to easily identify the articles that addresses the use of a specific form of Nitinol.
The classification after the application domain (section 4.3.) we included a reduced part of the devices/ equipment/ applications that were developed in the selected articles. A large part of them is in the domain of the medical/ biomedical field such as: orthodontic wire, root canal files, valves, stents, micro stent, robotic needle, spinal and dental implants, etc. Another domain which highlights the deep research into the Nitinol area is engineering with actuators, aerospace gas turbines, thermal bimorph actuators and so on, then some civil engineering industry examples were identified: grates, micro-lattice, thin wall structures, etc.
The bibliometric simulation analysis from point 5 gives us the visual perspective using bibliometric maps and generating network visualizations, temporal and geographical analysis. On a broad approach the network visualization exhibits all the items most identified on the titles and abstracts of the selected articles. We highlighted some of the items we find more important: ”smart memory alloy”, ”NiTi”, ”application”, ”device”, ”actuator”, ”performance”. The temporal perspective includes all this elements and positions then in different moments of research. For example the element ”application” is predominantly identified around 2020, while the focus on the cooling process has been increased around 2022. Among the years the interest for the Nitinol has increased and its development is continuous providing new solutions to improve and discover novel devices and applications.
One of the most relevant maps that we inserted in this article is the overlay visualization map which contains the 147 selected articles from 1018 to 2024 from the platform Web of Science. This map is relevant because revels the evolution of Nitinol in the researches and highlights the main subjects that have been reached on this topic in each year.
The behavior of the angular actuator upon heating with a heat gun, i.e., natural cooling of the Nitinol spring in liquid medium is visible in Figure 20 which was obtained by polynomial interpolation of the points to order 3. It is concluded that at the temperature of 90 oC the maximum angle of displacement, i.e. 158o, is reached in a time of about 45 minutes and the return from the temperature of 95 oC to that of 20 oC, i.e. to the initial position is after 207 minutes, reaching the memorized shape.
Figure 13. Behavior of the angular actuator during natural heating and natural cooling of the nitinol spring in liquid medium. The red curve represents the displacement with increasing temperature and the blue curve represents the displacement with cooling.
Figure 13. Behavior of the angular actuator during natural heating and natural cooling of the nitinol spring in liquid medium. The red curve represents the displacement with increasing temperature and the blue curve represents the displacement with cooling.
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Analyzing the heating displacement curve, it can be observed that in the range 20 oC -30 oC, the displacement in relation to the temperature increase occurs slowly and at insignificant values. After the temperature of 30 oC the actuator changes its behavior, the displacement occurs linearly up to the temperature of 75o C, every 10o increase in temperature by 10o a displacement of 30o occurs. After a temperature of 70 oC the displacement stabilizes, its variation with temperature being very small.

8. Future Directions

This research has its roots in older studies and researches from our laboratory, such as: devices with intelligent materials [108] used in energetics, special actuators [102], electro and thermomechanical actuators [109] linear heliothermic actuator [110], electromechanical micropump [111] and we used Nitinol to study its lifespan [18] and to develop special actuators and materials with shape memory [112], clutch type thermocouple [113], Nitinol operated Micropump [114], a locking system [115] and we hope it will result in the development of newer devices and equipment with applications in electrical engineering.
Shape memory alloys or smart materials are used in small and large scale structures in multiple fields such as robotics, engineering, medical devices, automotives, aeronautics, aerospace, mechanical engineering, power plants and biomedical fields (microsensors, stents, cement mortar beams, artificial muscle, micro-actuators, bionic manipulator, etc.).
In future research we can identify the form of Nitinol that is appropriate for each applicability domain. There are certain connections between the type of used Nitinol, related to its elasticity and durability, and the shapes it used in certain applications.
In the perspective of a more precise research there could be made a classification after the chemical composition/ formula of the Nitinol alloy, but this is out of our expertise area. This article can be also extended increasing the number of the analyzed articles, analyze a higher number of items or finding various classifications appropriate for a review.
The future of the research in this area is taking fast steps and the trends are always going to change. The industries are more and more interested to invest in researches that use smart materials as an alternative for the classic ones. Our future directions are leading to more deepen and precise research in the field of Nitinol devices.

Author Contributions

Conceptualization, L.D.M., O.V.G. and M.P.; methodology, L.D.M.; software, O.V.G. and M.P.; validation, L.D.M., O.V.G. and M.P.; formal analysis, L.D.M. and O.V.G.; investigation, L.D.M. and M.P.; resources, L.D.M., O.V.G. and M.P.; data curation, O.V.G.; writing—original draft preparation, L.D.M., O.V.G. and M.P.; writing—review and editing, O.V.G. and M.P.; visualization, O.V.G.; supervision, L.D.M.; project administration, L.D.M.; funding acquisition, M.P. All authors have read and agreed to the published version of the manuscript.

Funding

This paper has been financially supported within the project entitled “DECIDE – Development through entrepreneurial education and innovative doctoral and postdoctoral research, project code POCU/380/6/13/125031, project co-financed from the European Social Fund through the 2014-2020 Operational Program Human Capital”.

Institutional Review Board Statement

Not applicable.

Informed Consent Statement

Not applicable.

Data Availability Statement

Not applicable.

Conflicts of Interest

The authors declare no conflict of interest.

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Figure 2. Network visualization for items identified at least 5 times.
Figure 2. Network visualization for items identified at least 5 times.
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Figure 3. Network visualization of the items with at least 15 occurrences.
Figure 3. Network visualization of the items with at least 15 occurrences.
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Figure 4. Network visualization highlighting the item Smart Memory Alloy.
Figure 4. Network visualization highlighting the item Smart Memory Alloy.
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Figure 5. Network visualization highlighting the item NiTi.
Figure 5. Network visualization highlighting the item NiTi.
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Figure 6. Network visualization highlighting the item Actuator.
Figure 6. Network visualization highlighting the item Actuator.
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Figure 8. Nitinol spring.
Figure 8. Nitinol spring.
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Figure 9. Nitinol actuator.
Figure 9. Nitinol actuator.
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Figure 10. Angular displacement of the angular actuator on heating.
Figure 10. Angular displacement of the angular actuator on heating.
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Figure 11. Characteristics of the actuator displacement versus heating temperature.
Figure 11. Characteristics of the actuator displacement versus heating temperature.
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Figure 12. Actuator angular displacement versus cooling temperature characteristic.
Figure 12. Actuator angular displacement versus cooling temperature characteristic.
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Table 1. Classification after the generalized main objective.
Table 1. Classification after the generalized main objective.
Generalized main objective Reference
To improve the device fabrication [5,153]
To fabricate new NiTi alloys [4,23,150,154]
To test models/ strategies on a device based on Nitinol [9,21,27,44,143,144,148,149,155]
To build a new device/ equipment/ application/ model [17,18,32,33,70,81,82,85,105,131,136,139,140,147,151,152]
To improve the characteristics of an already existing device/ equipment/ application/ model/ process [1,2,3,7,8,10,15,20,28,31,38,59,63,72,80,104,106,107,121,127,130,132,134,135,137,141,142,146]
To study/ test device/ equipment/ applications [22,25,29,37,39,40,41,42,53,54,68,75,83,87,90,94,95,96,98,101,102,103,117,118,121,122,123,126,129,138,145]
To study/ test the NiTi alloy [6,11,12,13,14,16,19,24,26,30,34,35,36,43,45,46,47,48,49,50,51,52,55,56,57,58,60,61,62,64,65,66,67,69,71,73,74,76,77,78,79,84,86,88,89,91,92,93,97,99,100,116,119,120,125,128]
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