1 Introduction

The human elbow joint rotation mechanism is actuated by four major parts: muscles, cartilage, ligaments, and tendons. When the muscle shrink in length by 20–40% of its original length, the tendon pulls up the lower bones. Then, the rotation occurs along the cartilage while the ligaments hold the upper bone and lower bone not to be detached when rotating. The contraction length of the muscles is important for the rotation of this entire mechanism. Fortunately, human muscles can shrink in length from 20 to 40%, so that arms can bend 90° (Fig. 1).

Fig. 1
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Human elbow joint and lift-up motion

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However, many researchers have studied artificial muscles using ionic polymer-metal composites (IPMCs), piezoelectric polymers (PZTs), and shape memory alloys (SMAs). IPMCs are active actuators that show large deformation when low voltage is applied and low impedance is exhibited [1,2,3,4]. They can be modeled as capacitive and resistive actuators that behave like biological muscles and are useful in actuation as artificial muscles for biomechanics and biomimetics applications [1, 3].

In this paper, the shape memory alloy wire was used for the actuating material and has the largest actuation stress in company with large strain among smart materials.

Shape memory alloys are a group of metal alloys that exhibit the characteristics of either large recoverable strains or large force due to temperature and/or load changes widely used in softrobotics for the continuous surface actuation [5,6,7,8,9,10,11,12,13,14]. In this research, the SMA wire is used for the longitudinal actuation.

The unique thermomechanical property of SMAs is due to the phase transformation from the austenite phase to martensite phase and vice versa. These transformations take place due to changes in the temperature, stress or a combination of both [15, 16].

When the SMA wire is heated beyond the activation temperature, it contracts due to the phase transformation from martensite to austenite as the temperature is raised using the resistive electrical (Joule) heating [17]. Thus, the shape memory effect, which is originated from the phase transformation, makes the actuation motion [15, 16].

When the SMA wire is in stress-induced martensite, high temperature and compete shape recovery transformations are observed on the material upon loading to austenite [15]. This property is called superelasticity and used to actuate the artificial muscle. Superelasticity, sometimes called pseudoelasticity, is an elastic (reversible) response to an applied stress caused by a phase transformation between the austenitic and martensitic phases of a crystal [15, 18]. As shown in Fig. 2, the graph starts from Point A. When stress is induced to the SMA, it moves along from B to C and D. At Point D, with the loading, stressed martensite phase is dominant until it recovers to the original point through Points E and F.

Fig. 2
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Loop of superelasticity property of shape memory alloy

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The material properties of SMA wire is shown in Table 1, which is referenced from DYNALLOY, Inc and ref. 25 Table 1.

Table 1 Material properties of the shape memory alloy (SMA) [19]
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2 Design of Artificial Muscle Elbow Joint

2.1 Linear Actuator

An artificial muscle elbow joint design is proposed for precise actuation. The SMA wire is coiled up in a diamond shaped structure with 12 cm length sides that contract along the longitudinal direction when actuated. The actuator’s links generate net force in the diagonal direction. Furthermore, slider lubricants are sprayed on the slider to make the motion smooth.

Unlike linear SMA wire arrangements, as shown in Fig. 3, the actuator can get the required displacement by the extra side length. Therefore, the actuator can get 2–3 times more linear displacement than linear longitudinal connection in addition to easily stopping the actuator when the target displacement is achieved.

Fig. 3
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Single diamond shaped actuator displacement

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This structure facilitates actuators in multiplying the force by stacking up the coiled wire perpendicularly. In this design, the SMA wire is coiled up to 3 times for the larger force.

Deformation schematic diagram is shown in Fig. 4. As SMA wires contract and find their minimal length along the four sides, the actuator moves on the slider. As the actuator pulls the tendon attached to the end of the links, it moves along the longitudinal direction of the diamond shape.

Fig. 4
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Schematic diagram of the single diamond actuator’s actuation deformation

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2.2 Overall Design

The overall design is represented in Fig. 5. The lower arm consists of a single diamond shaped actuator for the higher force while the upper arm uses double diamonds for reducing the actuator width. The tendon wire connects the actuator with the elbow part located between two muscle actuators that fix the tendon from both sides.

Fig. 5
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Overall design and Tendon driven rotating motion

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When the actuator pulls the tendon, it finds its minimal length between the bolt and hole as in Fig. 5. These mechanisms generate the rotating motion.

However, the rotation angle can be adjusted by parameters like bolt and hole distance, distance between bolt and slider’s neutral surface, and tendon wire stiffness. In this paper, the elbow joints are designed to achieve 45° angle each (Fig. 6).

Fig. 6
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Illustration of human elbow joint and robotic elbow joint

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2.3 Fabrication

All parts were fabricated with a 3D-printer. Stratasys F270 was used to prototype with ABS material.

While actuating, the SMA wire exerts up to 150 MPa and heat reaches 70 °C. The holes where the SMA wires pass through were reinforced by metallic materials to prevent heat fracture by the SMA wires.

The ball bearing was inserted for smooth movement in each joint.

3 Analysis of Elbow Joint

3.1 Actuation Force Measurement

Actuator force was measured by a 3-axis force sensor with a sensor accuracy of 1% (0.1 N) and maximum measuring force set at 250 N. The actuator’s end is fixed on the surface plate and the other side is fixed to pull the sensor. If the linear actuator pulls the tendon wire, the bolt fixed to the sensor head is followed by the wire (Fig. 7).

Fig. 7
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Actuation force measurement by the 3-axis force sensor

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The actuator is fixed on the surface plate at three different positions, as shown in Fig. 8. With the positions, interior angles of the actuator are varied. This setting is intended for measuring the result pulling force with the interior angle of the actuator.

Fig. 8
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Actuator configuration position

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The pulling force is related to the actuator’s interior angle, shape, given electric current, SMA wire length and diameter. In this paper, the pulling force is measured with the interior angle, shape and given electric current (Fig. 9).

Fig. 9
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Interior angle of the single diamond actuator and double diamond actuator

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3.2 Determination of Maximum Force

The maximum force value from the data is not obvious due to the sensor drift and the actuator’s actuation characteristics.

The graphical method was used to solve this problem, which is similar to the yield strength determination (0.2% offset). The steepest gradient is calculated from the force data and used as a slope of the offset line, which starts at the offset time from the steepest gradient point of the force data. The actuation force data and offset line’s intersection point is selected as the maximum force value.

$$\begin{aligned} & Offset\, line y = a\left( {x - x_{1} } \right) + y_{1} \\ & a = Steepest\, gradient\, from\, the\, force\, data;\,\,x_{1} = Origin\, x\, coordinate\, ofthe offset line;\,\,y_{1} = Origin \,y\, coordinate\, of\, the\, offset\, line \\ \end{aligned}$$

The \(x_{1}\) and \(y_{1}\) points are determined arbitrarily considering the total actuation time and the peak force. In determining the \(x_{1}\) and \(y_{1}\) points, the peak force of the actuator was considered due to the phase transformation time on high stress, which is related with the phase transformation propagation. If the peak force is high, the offset line moves to the + x direction. On the contrary, if the peak force is low, the offset line moves to the − x direction.

As shown in Figs. 10 and 11, the maximum force is determined by the intersection point from the force data and offset line.

Fig. 10
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Actuation force and offset line graph [from the left (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12)]

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Fig. 11
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Actuation force with the position and current

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The measured force data is summarized in Table 2 where the single strand of coiled actuator can exert a linear force with maximum 44.4 N when 2.0 A current is given. If the double strands of the SMA wire with the same diameter were used, the force would be measured as 56.3 N at maximum. However, the double diamond shape actuator can exert 50.0 N, although it is coiled up with a single strand of SMA wire since the double diamond actuator has more efficient SMA wire paths than a single diamond.

Table 2 Actuation force measurements of the linear actuator
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The SMA wire shows special properties when large stress is induced at the hinge joint, such as superelasticity and phase transformation propagation. In this regard, the double diamond actuator has a more efficient design than a single diamond actuator.

4 Test of Arm with Joint and Gripper

4.1 Experiment System

The experimental setup of the robotic elbow joint is represented in Fig. 12. The single diamond shaped actuator and double diamond shaped actuator were assembled for the pulling actuation of the tendons in each direction. When the actuators pull the tendon, the elbow part makes the rotate motion according to the design parameters. And the DC motor was installed for the yaw rotation.

Fig. 12
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Experimental setup of the robotic elbow joint

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4.2 Experiment Process

The experiment process consists of four parts, as shown in Fig. 13.

Fig. 13
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200 g ball moving by the robotic elbow joint a initial configuration, b gripping the ball, c lifting up the ball, d moving the ball to the opposite side

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At the initial configuration in (a), each of the parts is arranged in horizontal direction. In (b), gripping the 200 g ball, the Smart Soft Composite (SSC) gripper forms a continuous curvature surface. In (c) the single diamond and double diamond actuators pull the tendon in each direction and the elbow part makes the rotating motion by the tendon driven mechanism. In (d) the DC motor attached to the surface plate rotates the robotic elbow joint to the opposite side.

5 Conclusions

The main purpose of this paper is to design and analyze the robotic elbow joint actuator.

  • Design was focused on efficiency and precision.

  • Analysis was focused on the actuation force.

The robotic elbow joint actuator design was newly introduced in this paper. The design aims to rotate 90°. Furthermore, the rotation angle can be modified by the design parameters.

The actuation forces were measured through the 3-axis force sensor. Although maximum force was not clear on the experiment, a graphical method for determining the maximum force of the actuator is suggested.

This actuator has many advantages compared to other actuators.

  1. 1.

    Light and simple:

    • 199 g, with no electric motor.

  2. 2.

    Large force:

    • The actuator can exert 56.3 N with a single diamond double strands of SMA wire.

  3. 3.

    Flexible and silent:

    • As the actuators connected by tendon, connections between elbow joint links are flexible and silent.

From the experiment results, this actuator can exert 56.3 N whose magnitude of the force is greater comparing to other smart actuators. And compared to electric motors, this actuator has better properties, such as actuation force, weight and energy consumption. But actuation speed remains a problem to be solved. It takes 3–5 s to lift up and 8–12 s to lay down. To achieve faster lift up and lay down motion, it is needed to boost cooling SMA wire.

A robotic elbow joint using the SMA actuator is designed and analyzed in this research. Because the connections between links are flexible and silent while actuating, the environment will be more comfortable. In addition, the robotic elbow joint can be applied to robotic arms, electric vehicles and wearable robots.