1. Introduction
The design and construction of a mini-snake-like robot (SLR), particularly for endoscopy, is challenging because of the narrow space available and the total length of the gastrointestinal tract. If the design includes a hollow centre, traditional instruments for biopsy or intervention can be used, which represents an important requirement for the clinical user. Several designs have been reported for SLR devices, most rely on cable-transmission with remote motors controlling each joint, using various control strategies [
1,
2,
3,
4]. Clinically, a few SLR have been developed for Minimal Access Surgery (MAS). Choi et al. [
5] designed an 8 mm mini-endoscope, 104 mm in length, composed of 7 passive segments, and attached to a spring backbone. The system is equipped with three cables used for actuating the endoscope. The SLR for colonoscope reported by Hu et al. [
6], which measures 12 × 600 mm, consists of sections, each actuated remotely by two cables driven by two DC (Direct Current) servomotors.
The design of a SLR using external motors and cables for actuation has certain advantages, including low weight and inertial moment. However, on the downside, each cable has to extend the entire length of the robot for effective control. Additionally, each DOF requires two cables (or a cable/spring combination), which would increase cable friction and the external diameter [
7,
8,
9,
10]. For medical applications, the ideal design can be obtained by an actuation system embedded inside the robot [
11]. The key issues then concern size and performance of the actuator, which has to meet three requirements: (i) high torque-force-to-weight ratio; (ii) articulated actuation to allow the robot to adapt readily to its surrounding environment; (iii) back-drivability and flexibility allowing passive adaptation of robot shape to that of the surrounding environment without any active control.
A traditional DC or a piezoelectric motor [
12,
13,
14,
15,
16,
17,
18], would not be the ideal if the design involves embedding each motor within the robot because of weight and size issues. In contrast, SMA wires, widely used to design joints with multiple DOFs provide a better solution [
19]. They can be used in various configurations, including: (i) antagonistic [
20,
21,
22], (ii) with elastic joint [
23] and (iii) mixed antagonistic-elastic joint [
24,
25]. For neurosurgical applications, Ho et al. [
26] proposed an SMA actuator based on an active link consisting of two segments: 9 × 13 mm and 10 × 12 mm with a pulley to amplify the SMA movement. In this system, the slow response time (12 to 20 s) required to bend the joint from
to
limits the mechanical bandwidth performance. In the antagonistic configuration, SMA wires can be used with a spring in series for each SMA [
27,
28]. A recent study [
29] proposed to use SMA wires in antagonist configuration serializing two springs, one for each SMA in order to improve SMA reliability by reducing stress. The joint has 2 DOFs with intersecting axes and the SMA wires are in a straight configuration. However, the time to reach a designated configuration is increased because the springs are directly connected to the SMA wires. Additionally, it impacts on the total length of the actuator. Manfredi et al. [
30] reported a mini rotary actuator by using SMA wires in antagonistic configuration with on-board position and torque sensors. This study described the use of SMA wires for mini robotics applications requiring a high mechanical bandwidth, up to 10 Hz, with a low power consumption.
The present study concerns a novel patented [
31] mechanical design of a hollow joint for the construction of a SLR-endoscope based on use of SMA wires in an antagonistic configuration and intersecting axis. Its design consists of a primary and secondary transmission decoupled by a symmetrical torsional spring to improve the performance in terms of energy efficiency and heat reduction. The frame is a simple and compact homo-kinetic hollow joint with a light but stiff structure. The output torque varies with the diameter of the SMA wires used, although to ensure a high mechanical bandwidth this should not exceed 100
m. The joint was constructed by using a 3D printer and open-loop step response experiments are reported.
The described design offers three advantages compared with the previous reported studies of rotary actuators by using SMA in antagonistic configuration: (i) internal cavity for cabling or instruments channels, (ii) compact design by using pulleys to reduce the overall length and provision of 2 DOFs; (iii) inclusion of a torsional spring to confer a compliant behaviour with a low power consumption.
2. The Mini Compliant Joint Design
The joint design is symmetric with 2 DOFs using 2 SMA wires in an antagonistic configuration with a torsional spring for each DOF; thus, comprised of 4 wires and 2 springs in total as it is shown in
Figure 1. The torsional spring decouples the SMA wires from external forces, thereby providing a flexible and passive compliant behaviour, with reduced energy consumption, diminished heat generation and a safe stable mechanism [
32]. Additionally, the spring reduces the impact of any external torque on the system increasing the SMA life [
29]. With the SMA wire in antagonistic configuration, the operative range of each joint is related to the length of the wire, which can be
= 5–7% of its total length [
33]. To reduce the length of the joint, the SMA wire is coiled inside the frame using pulleys (accommodating the wire around the shape of the frame) in order to decrease the friction, hence increase overall efficiency.
The actuator is composed of three main parts as shown in
Figure 1: an upper frame (Frame 1), a lower frame (Frame 2) and a central frame (Joint frame), which functions as a link between the upper and the lower frames. As the configuration is symmetric, only the upper frame is described. Each frame has a pulley actuated by means of the 2 SMA wires in antagonist configuration. The pulley is linked to the central frame by a torsional spring resulting in a passive compliant joint as shown in
Figure 2b and described in detail in
Section 2.1. The joint design was optimised by Finite Element Analysis (FEA) to define the thickness and shape to reduce the weight of the joint, before its initial production by a 3D printer. In the final version, the external diameter and length are equal and measure 20 mm. The weight of the frame without the electronic system is 2 g.
Both SMA wires can be independently controlled to achieve the desired angle and to change the stiffness of the system by regulating the temperature of each wire. The stiffness can be adjusted by pulling simultaneously the two SMA wires in an antagonistic configuration, adjusting the force applied by each wire, although this requires precise control of the current provided to each SMA wire. The choice of the spring properties defines the stiffness of the system of the compliant joint.
The torsional spring located between the two pulleys decouples the primary from the secondary pulley. The torsional pulley can provide a maximal torque of 3 Nmm.
2.1. Working Principle
The joint has 2 DOFs with 2 intersecting axes, X and Y as shown in
Figure 2a. A pair of SMA wires in antagonistic configuration is required to control each axis; 4 SMA wires in total to assemble the joint. The working principle of each axes is showed in
Figure 2b and Equation (
1) describes the statics when
:
where
and
are the forces produced by each SMA wire,
is the output torque,
is the resultant torque produced by the SMA wires antagonist configuration,
K the torsional spring elastic constant (considering the Hooke’s law for a linear spring),
and
are the radius (6 mm) and the angle of the torsional pulley,
is half of the joint length (10 mm),
the angle of the torsional spring,
the maximal compliance angle. Equation (
2) defines K of the torsional spring to achieve the maximal compliance angle
.
When the power supply is off, an SMA wire provides a residual force of about
[
24,
34], where
is the maximal contracting force, which equates to a residual torque of
. This residual force has been experimentally investigated in
Section 3.3.
This allows the joint to have a residual compliance of
with no need for external power and a consequent reduction of energy consumption. Each joint can provide an output torque
as described by the equation:
which is reduced by circa
due to a residual strain of the opposite antagonistic SMA wire when it is not powered. The residual torque can be adjusted by controlling the temperature of the SMA to increase joint stiffness.
The performance of the system is determined by a balanced interaction of three parameters: diameter of the SMA wire , diameter of the pulley , and the joint length , which in turn determine the output torque , the output force , the angular motion range , the arc range of motion , the mechanical bandwidth of the system, the angular velocity and the radial velocity .
Increase in decreases , and the radial velocity . Additionally will be reduced because the thicker wire increases the response time. Both the and the will not be altered.
Increase of the pulley diameter , reduces the output parameters , , , ; will be reduced but the will increase because of the higher cantilever configuration.
increases directly both
and
without any effect on the other parameters.
Table 1 shows the correlation between the system design parameters and the system output performances.
2.2. Design of SMA Wires
The length of the wire is crucial to the overall design since this impacts on the range of motion of the joint
. If a reasonable range of joint motion needed is of
, the extension of the SMA wire is described by the equation:
where
is the SMA elongation,
is the joint range, and
is the radius of the SMA pulley. Assuming
radians, and
mm,
is described by:
and elongation described by Equation (
6):
Hence 35 mm is the required minimum SMA wire length, with
being considered as a precautionary limit. The reason for this consideration is also related to the mechanical stability of SMA wires. This mechanical behaviour has not been addressed in this study although this is related to the strain that can be recovered when the SMA is activated therefore the range of motion of the actuator. Several studies on SMA fatigue have shown limited degradation with a maximal strain of
after 5 × 10
cycles [
35,
36].
To achieve a compromise between a low power consumption but a good mechanical bandwidth, SMA wires used in this design have a low temperature profile of
C (Flexinol
produced by Dynalloy
Inc., Irvine, CA, USA) with a mechanical performance, heating and cooling time, reported in
Table 2. SMA wires with higher temperature profile have a higher mechanical bandwidth although they require a higher activation current. This phenomenon is related to the higher difference in temperature between the SMA wires and the environment, which increases the heat dissipation and therefore it reduces the deactivation time,
in
Figure 3a. The robust nature of the frame, permits use of different wire gauges. To achieve a high bandwidth, the SMA wires selected have a diameter of 50, 76, 100
m because the switch on-off time varies according to diameter of wire, i.e., 1.0–0.3 to 1.0–0.5, and 1.0–0.8 s. Thicker SMA wires can be employed but would incur increased energy consumption and reduction of mechanical bandwidth [
30].
An SMA wire of length L and diameter d, will have a volume proportional to and a surface to , therefore unit surface per volume is proportional to . A narrow wire is desirable because the heat generated is proportional to the surface area of the wire.
Figure 4a reports two graphs taken from the Dynalloy
SMA wires datasheet,
d vs.
time, and
d vs.
. To achieve a mechanical bandwidth of 1 Hz, the SMA wire requires a diameter of
m (
Figure 4a-top graph; it can produce a force of
N (
Figure 4a-bottom graph), thus achieving a good mechanical bandwidth.
The mechanical property of the spring was selected to have a compliance range up to when the maximal torque is applied to the system.
The overall size of the joint is reduced by using pulleys although they can increase the fatigue stress of the SMA wires, with a consequent reduction of the life time of the joint. The bending stress produced by a pulley is described by the following equation:
where
represents the maximal normal strain.
2.3. Powering and Heating
One issue of SMA is its low energy efficiency, up to 5–7%, which has limited its use in actuator systems. The low efficiency induces heat generation which in turn alters the resistance of the SMA, described by:
where
is the resistance per cm,
L is the wire length, and
is the resistance of the whole wire. In the worst case scenario at full power up to 95% of this energy is lost as heat in the SMA wires.
Table 3 illustrates the resistance values of the wires used in the design. The power consumption of the actuator is not a constant value, because it depends on the heat dissipation, being higher initially and then reducing slightly [
37]. In the present experiments, the power reached 212–525–700 mW (
Table 4). Future R&D will be directed to optimization of the control to increase the efficiency of the SMA. In a robot design the compliant behaviour of the component actuators reduces the need for keeping the SMA wire active due to the passive mechanical behaviour of the springs, which reduces the energy required for locomotion (
Figure 3). In addition, previous studies reported by the authors have shown a low power consumption by a rotary actuator whilst maintaining a desired angular position [
30,
38,
39].
4. Discussion and Conclusions
A 2 DOFs joint (20 × 20 mm), with an internal diameter of 8 mm, and weighing 2 g is described. It is actuated by 4 SMA wires in antagonistic configuration with 2 torsional springs and a range of . The preliminary experiments have shown that the actuator design provide a good performance, including mechanical bandwidth, power supply, and light weight.
The experiments with different SMA wires confirmed generation of a wide range of forces needed to cope with different frame robustness. SMA has a low energy efficiency that can vary from 5% to 7%, therefore there is a requirement for an efficient system of heat dissipation. Several considerations were necessary to achieve the final design to minimise overheating. The MCj’s frame can be made of metal and can be used to dissipate the heat produced considering that the mass of the SMA wires is negligible compared to that of the joint. An advantage of this design in reducing the heat production is the use of a passive compliant system by means of a torsional pulley. This solution allows the SMA wires not always to be active, reducing overheating, without compromising its compliant behaviour. Even so, the overall temperature needs to be monitored. The low-level control can monitor the temperature and reduce the performance in the event of overheating. A flexible skin is also needed to protect the mechanism of the joint and to avoid any electrical leakage with an external material. Also, the pulleys where the SMA wire is in contact require to be constructed from non-electrically conductive material.
When more joints are connected, to form a tethered snake-like robot, the high-level locomotion control can reduce the overall heat using different strategies, by considering a residual torque of each joint when the power is off. Another strategy would be avoiding simultaneous activation of all the joints; instead it will ensure sequential activation or activation only of the advancing joints at the tip of endoscope. In essence, the environment will not be affected by overheat for the following reasons: (i) the SMA wires are not exposed and are not touching the external environment; (ii) the negligible mass of the SMA wires compared to the frame allows to dissipate the excessive temperature by using metal; (iii) the passive compliant mechanism reduces the need for keeping the SMA wires always active; (iv) we have proved in a previous study that the required energy to keep a desired angular position with SMA in antagonistic configuration is low [
30].
The frame was confirmed to be mechanically stable without any evidence of mechanical backlash. The system for coiling the SMA inside the frame requires improvement, possibly by using a different material for the pulleys together with improved manufacturing to reduce the friction and to ensure smooth rotational movements and durability, e.g., by using a miniaturised ball bearing inside each pulley. Other improvements are needed in relation to (i) manufacturing process and (ii) the electronics system including actuation control strategy.
The manufacturing process can be improved by using different materials (e.g., aluminium, titanium), which are lighter and stronger, to reduce the weight and increase heat dissipation. The current experiments have confirmed that the SMA wires can be coiled inside the frame by means of small pulleys to reduce the friction and the overall dimensions of the joint. In this context, the size and friction of the pulley is crucial to the smooth performance of the actuator.
Different control strategies can be implemented. This includes the use of a sensor-less position and torque joint control [
30,
37]. The efficiency and the system dynamics can also be improved by adjusting the current provided to each wire. This will however require cooperative control of the antagonist SMA wires to adjust the stiffness of the actuator. The efficiency and the system dynamics will benefit from improved control of the current provided to the wire. The energy consumption of each joint requires a tether to supply the power needed, which can also be used to stream video images captured by an on-board camera.