1. Introduction

Ionic polymer-metal composites (IPMCs) has attracted a lot of interest for soft and flexible structure, light weight, low driving voltage and large bending deflection in wet environment[1-3]. IPMC actuator is applied for biomimetic robotics and biomedical engineering as artificial muscles, robotic end-effectors and active catheters [2-11].

Typically the IPMC actuator fabricated by using a single flat actuator has bending motion. For applications like biomimetic robots, restricted motion is drawback. In cases, for underwater swimming robot has good performance with undulatory motion and multi-legged robot needs swing motion of leg with multi degree of freedom. To overcome these drawbacks, various methods was suggested.

There are two method to make multi-degree of freedom(DOF). The first method is to make pattern on each electrode of whole IPMC actuator. It is same as connections of single IPMC actuator [8-14]. To make patterned electrode, MEMS fabrication method, laser cutting and micro cutting method are widely used. Generally, the rotation axis of each IPMC actuator is parallel. Simple structure and easy wiring are advantage. The cylindrical IPMC actuator was developed for multi-DOF motion^(15,16). The manu- facturing process is complicated.

The second method is to assemble single IPMC actuators [17-20]. The rotation axis of each IPMC is various. To make multi-DOF, each IPMC is conjoined with plastic shims. It is useful for swimming robot⁽¹⁷⁾, bio-application system^(18,19) and multi-legged robot⁽²⁰⁾.

In this work, we focus on simply connection method of each IPMC actuator without plastic shim to make multi-DOF motion. This design can be advantageous in mobile robotic applications, particularly in legged robot to need 2-DOF swing motion. The main advantage of this connection method of IPMC is simple structure and accurate control of the end tip. There are three section, design 2-DOF IPMC actuator module, kinematic analysis and experiments.

2. Design of the 2-DOF IPMC actuator module

The electroless plating method with platinum as an electrode is used to prepare the IPMC actuator⁽¹³⁾. Generally, the IPMC actuator can bend in water easily whereas it is stiff in air. To make motion in air, H+ ion is changed to Li+ ion and conduct Ionic liquid replacement. The Platinum electrode cover the both side of Nafion NE-1110 through the electroless plating method. The thickness of the platinum electrode is 20μm through the 4 times of electroless plating.

The 2-DOF IPMC actuator module is consisted of the single IPMC actuator. The single IPMC actuator whose length is 15 mm and width is 10 mm is shown in Fig. 1(a) . The end of IPMC actuator has narrow slot to fit others. The narrow slot is about 0.5 mm as thickness of Nafion polymer. Assembled 2-DOF actuator is shown in Fig. 1(b) . They are connected to each other vertically through the slot. The instant adhesive prevents the separation each other. The copper wires are attached on the electrode of IPMC actuator using conductive epoxy adhesive.

Fig. 1. Connecting method (a) Single IPMC actuator samples, (b)2-DOF IPMC actuator module

3. Kinematic Analysis

For trajectory of end tip position kinematic analysis of 2-DOF IPMC actuator module is calculated. Single IPMC actuator is considered as rigid body because the bending displacement is quite small compared to the length ⁽¹⁷⁾. Connection of IPMC actuators is considered as rotating joint. Each initial joint axis and coordinate is shown in Fig. 2.

The origin q of the first rotating joint coordinate is located on origin O of the fixed coordinate. The first rotating joint axis is the +Z direction of the first rotating joint coordinate. Initially the first rotating join coordinate is same as the fixed coordinate. The origin q of the second rotating joint coordinate is located on l departed from the origin q along +Y direction of first rotating coordinate. The second rotating joint axis is the +Z direction of the second rotating joint coordinate. Initially the second rotating joint axis is the -X direction of the fixed rotating coordinate. The origin P of the end tip coordinate is located on l2departed from the origin q along +X direction of second rotating coordinate. Initial posture of the end tip coordinate is same as the fixed coordinate.

Fig. 2. Kinematic analysis of 2-DOF IPMC actuator module

Kinematic analysis can be expressed using P.O.E method⁽²¹⁾. The transformation of the first rotating coordinate about the fixed coordinate is below.

here,

$\omega_{1}=\left[\begin{array}{l}{0} \\ {0} \\ {1}\end{array}\right] q_{1}=\left[\begin{array}{l}{0} \\ {0} \\ {0}\end{array}\right] v_{1}=-\omega_{1} \times q_{1}=\left[\begin{array}{l}{0} \\ {0} \\ {0}\end{array}\right]$

$A_{1}=\left[\begin{array}{cc}{\left[\hat{\omega}_{1}\right] v_{1}} \\ {0} & {0}\end{array}\right]$

$\left[\hat{\omega}_{1}\right]=$ skew $-$ symetric matrix

In the same way, the transformation of the second rotating coordinate is below.

here,

$\omega_{2}=\left[\begin{array}{c}{-1} \\ {0} \\ {0}\end{array}\right] q_{2}=\left[\begin{array}{l}{0} \\ {l_{1}} \\ {0}\end{array}\right] \quad v_{2}=-\omega_{2} \times q_{2}=\left[\begin{array}{l}{0} \\ {0} \\ {l_{1}}\end{array}\right]$

$A_{2}=\left[\begin{array} {cc}{\left[\hat{\omega}_{2}\right]} & {v_{2}} \\ {0} & {0} \end{array}\right]$

The Initial position of the end tip coordinate is below.

Consequently, the transformation of the end tip coordinate about the fixed coordinate as product of each transformation matrix is below.

As a result, the position of the end tip is calculated according to each rotating joint angle.

The inverse kinematics is considered. The each rotating joint angle is calculated according to the given position of the end tip. The origin P of the end tip about the fixed coordinate is below.

Therefore,

Using equ. (6), (7), the each rotating joint angle is obtained.

4. Experimental Result

We experiment the motion of 2-DOF IPMC actuator module as shown in Fig. 3. The single IPMC actuator has 15 mm length and 7 mm width and 0.3 mm thickness. Two IPMC actuators are assembled perpendicular to the slot. The first IPMC actuator is clamped on clip. The IPMC actuators are wired on the electrodes using conductive epoxy adhesive.

The experimental setup shown in Fig. 4 includes a laser displacement sensor Keyence IL-65 to measure the bending displacement of the IPMC actuator. The voltages are sent through the power Op-amp L272 circuit connected to 2-DOF IPMC actuator.

Fig. 3. Prototype of 2-DOF IPMC actuator module

Fig. 4. Experimental setup

The single IPMC actuator of 15 mm length has 0.22 mm bending displacement at 2V input voltage as shown in Fig. 5. The reference signal is sine wave at 1 Hz, The input signal is made by signal function generator. The open-loop control is applied simply. The experimental result shows the IPMC actuator has followed the reference signal as well. The displacement of the IPMC actuator is proportional to the input voltage. The behavior of a short IPMC manipulator is linear and the single IPMC actuator is considered as rigid body. Our experimental results of the single IPMC actutor confirmed these assumptions. The bending speed is quit slow, so kinematic model is possible to apply without considering dynamic model.

The end tip trajectory of the 2-DOF IPMC actuator module is asked to follow a circle with 0.3 mm radius. The desired rotation angles are calculated from previous section. The experimental result of the 2-DOF IPMC is shown in Fig. 6. The sequential image of the captured video clip of the motion of the 2-DOF IPMC actuator module is shown in Fig. 7.

The novel 2-DOF module has been developed to successfully meet to high dexterity(DOF) and high compliance and soft touch. This proposed module design is the very simply and good example of utilizing standard IMPCs to archive an output in 2-DOF. The suggest assemble method is also very useful with the scalable IPMC model any number of configurations and sized IPMCs can be applied for any application.

This proposed actuator keeps the module simplt and robust with only two rotaty joints, make them easy to implement and minmal friction, backlash and other mechanical losses.

Fig. 5. Displacement of the single IPMC actuator, 15 mm length, 2V p-p input voltage, 1 Hz

This 2-DOF module has not any frame, so naturally soft and compliant through the IMPCs themselves, this adds some passive safety to the mechanism. It avoid to cause damage to objects or environment.

Compared previous results The design and manufacturing process is very easy. The suggested assembly method and wiring method is easy. The proposed module have good advantage in commercial product as low cost.

From the experimental tracking results it is clear the position control is good but errors is some significant. This can be explained by the imperfect fabrication of the prototype, the highly nonlinear and time-varying nature of the IPMCs. The accurate sensing(for example vision systems) as well as hardware and software technologies make to the improve the performance and remove electronic noise.

From the experimental results it is clear that the multi-DOF IPMC actuator is possible to link the 2-DOF IMPC actuator module with open-loop input very simply

Fig. 6. Experimental result of the circular motion at 1.25 V p-p at X axis, 2.5 V p-p at Y axis, 1 Hz

Fig. 7. Sequential image of the captured video during circular motion

5. Conclusion

In this work, the linked 2-DOF IPMC actuator module was developed. The main contribution is to show the very simple connection method, wiring method and open-loop control method. The link method with 2 IPMC actuator is assemble using a slot and conductive epoxy adhesive is used for wiring. And we considered the single IPMC actuator as rigid body to apply open-loop control. The inverse kinematics of the linked 2-DOF IPMC was established. The experimental results show 2-DOF motion of the IPMC actuator module. This 2-DOF IPMC actuator module can be improved or modified for example by adding more links to even more increase the workspace by adding an extra soft link to the tip of the manipulator for extra soft mani- pulation.

The presented linked 2-DOF IPMC actuator become productive towards making devices in practical applications, such as mobile robots and bio-applications.