FROM BENDING TO LINEAR MOVEMENT

A Linear Actuation Mechanism based on Conducting Polymer Actuators

Elise T. Burriss, Gursel Alici

University of Wollongong, School of Mechanical, Materials and Mechatronic Engineering, Australia

Geoffrey M. Spinks, Scott McGovern

University of Wollongong, School of Mechanical, Materials and Mechatronic Engineering, Australia

Keywords: Electroactive polymer actuators, Linear actuation, Kinematic design.

Abstract: The objects of this study are (i) to establish a linear actuation system based on the bending movement of

conducting polymer actuators, which operate in air, and (ii) to develop a model to predict the linear

displacement and force output of the actuation system, and employ the model to characterise the optimum

values of the system design parameters. The linear actuation system is based on a five bar parallel

mechanism with equal link lengths and a zero-length ground link, which is articulated through two bending

type polymer actuators. Kinematic and force analyses of the mechanism including numerical results are

presented, and its payload handling ability was experimentally evaluated. Experimental results presented

demonstrate that the linear actuation system can generate linear movement accurately and a rectilinear force

as a result of two bending type polymer actuators. This mechanism is offered as a lightweight, low power

consuming motion and force transmission system.

1 INTRODUCTION

Conducting polymers are favourable as actuators

due to their low actuation voltage, high force output

relative to their weight, good strain properties, light

weight, simple structure and silent motion. The

common materials used for actuators are Ionic

Polymer Metal Composite (IPMC), and electroactive

polymers (EAPs) such as Polypyrrole (PPy) and

Polyaniline (PANI) (Thompson, 2007).

Disadvantages of polymer actuators include low

speed of response, cyclic fatigue and non-linearity,

which increases difficulty in modelling and

controlling the actuator (Alici, Metz & Spinks 2005,

Eamex nd).

Bending actuators have been successfully used

in applications where a nonlinear motion is required,

such as a fin in an artificial fish (Alici et. al, 2007)

and robotic fingers (Alici & Huynh, 2007).

However, the bending motion may limit the control

of actuators along a linear path. Conducting

polymers have been used as actuators in applications

such as medical devices, toys, digital camera

accessories and artificial muscles for robots as

developed by Eamex 2008. Various PPy linear

actuator designs have been investigated, including

the PPy linear design by Otero, Cortes & Vazquez

Arenas (2007), in which two PPy films were

connected in parallel and immersed in a LiClO

aqueous solution, were able to produce a

displacement of 60% of the actuator length in the

longitudinal direction of the actuator. The use of

linear actuators in air may provide an alternative

when encapsulation of the electrolyte is not feasible.

Yamakita et. al (2004) have developed an IPMC

linear actuator for use in a biped walking robot. PPy

actuators are used in applications where the oxidised

or reduced position is maintained under a constant

voltage, for which IPMC is not suitable as it will

return to its original position. To overcome this

limitation of IPMC, Thompson (2007) adopted the

design by Yamakita et al. using polypyrrole film as

the active layers of a multi-layer actuator structure.

Two methods of connecting the PPy film together to

produce the linear design were employed by

Thompson: (i) masking part of the film during PPy

growth to create a flexible, electrically conductive

hinge; (ii) electrically connecting the film with Cu

T. Burriss E., Alici G., M. Spinks G. and McGovern S.

FROM BENDING TO LINEAR MOVEMENT - A Linear Actuation Mechanism based on Conducting Polymer Actuators.

DOI: 10.5220/0002166000130020

In Proceedings of the 6th International Conference on Informatics in Control, Automation and Robotics (ICINCO 2009), page

ISBN: 978-989-8111-99-9

tape, held in place with NdFeB magnets. This study

implements the design investigated by Thompson

using the second method of connecting the film

together, as the method of masking allows the

actuator to produce a clover-like shape under

actuation, which impedes control and stability of the

actuator. However, limitations arising through the

use of Cu tape may include oxidation of the Cu,

converting the tape to an insulator, thus limiting the

actuation of the PPy components connected by

copper tape. For optimisation of the PPy film in this

study, the geometry of PPy bending actuators is

limited to 50µm thickness and 4mm width as the

charge distribution has been found to be no longer

uniform at thicknesses greater than 50-60µm and

curling is prominent at widths greater than 4mm,

producing an increase in elastic stiffness of the

actuator (Alici, Metz & Spinks 2005, Metz, Alici &

Spinks 2006). These limitations are expected to be

also evident in PPy linear actuators.

A significant amount of work to determine the

performance of bending PPy actuators has been

previously conducted (Alici & Huynh 2007, Metz,

Alici & Spinks 2006, John, Alici & Cook 2008).

However, the complexity and greater degree of

variability in a linear actuator means that the

performance of a bending actuator may not directly

translate to linear actuators. The modelling of linear

actuators is necessary to accurately predict the force,

displacement and work outputs for control of the

actuator in practical applications. Modelling and

optimisation work on PPy bending actuators by

Alici, Metz & Spinks (2005), in which a

mathematical model to calculate the expected

bending behaviour of PPy bending actuators was

developed, and suggests that as the length of the

actuator decreases, force output increases. This

study has investigated the effect of the length of PPy

components in linear actuators to determine if length

has a similar effect on outputs in linear actuators.

Combinations of 2mm, 3mm, 4mm wide and 10mm,

15mm and 20mm long linear actuators, where the

length refers to the length of each component, were

experimentally evaluated for force and displacement

outputs. It was found that an increase in the length of

the PPy links in the linear actuators allowed a

greater range of motion, whilst shorter and wider

actuators lifted greater loads. The linear actuators

were also compared to bending actuators of

corresponding dimensions and it was found that the

bending actuators had a greater range of motion and

the linear actuators lifted heavier loads. As the

proposed linear actuation mechanism converts the

rotational work into the linear work, ideally they are

equal to each other, it is expected that while the

displacement is decreasing, the force is increasing,

and vice versa.

2 FUNCTIONING PRINCIPLE OF

LINEAR ACTUATION SYSTEM

As the polymer actuators considered in this study are

cantilevered from one end, they generate a rotary

(bending) type motion. This is analogous to a single

jointed crank motion. A single degree of freedom

mechanism such as a four-bar mechanism does not

allow control the output motion. With this in mind, a

five-bar mechanism which needs two inputs (two

bending type polymer actuators) is one of the multi

crank mechanisms having practical importance,

especially for following any arbitrary trajectory

precisely (Alici, 2000). This mechanism serves as a

bending to-linear motion converter; converting

bending angle into a linear movement, and bending

moments into linear forces.

2.1 Kinematic Analysis

The topology of the mechanism is depicted in Figure

1, where it is assumed that the mechanism links are

rigid for the sake of generating a pseudo-rigid-body-

model for the size and operation optimization of this

linear motion mechanism. The joints connected to

the frame are the active ones. The others are passive.

For the joint inputs

and

θ and the specified link

lengths

43210

L,L,L,L,L the analytical expressions

for the coordinates of the output point P are obtained

using the following algorithm (Alici, 2000):

()

,jsinLicosLLL

,jsinLicosLL

242405

11111





θ+θ+=

θ+θ=

(1)

,jDiCLBORAB



+=−== (2)

,DCR

,LBOD,LBOC

1x1

−=−=

(3)

LRL

−+

(4)

The coordinates

(

)

y,x of the output point P are;

ICINCO 2009 - 6th International Conference on Informatics in Control, Automation and Robotics

CDQyy

DCQxx

−++=

−−+=

(5)

Figure 1: Proposed linear actuation module based on a

parallel five-bar mechanism.

Depending on the link lengths, the expression in

the square-root can become negative, which suggest

that some kinematic design constraints are not

satisfied. For a linear motion output, the output point

can be constrained to move in a rectilinear fashion.

This requires that

=θ AND

LL = AND

LL = . Such a mechanism will convert all of its

rotary work into the linear work - an efficient motion

converter. The analytical expressions for the output

point of such a linear motion module are obtained as

()

[]

()

[]

coscosLL

sinsin

sinLy

sinsinL

coscosLL

cosLx

1210

11P

121

121011P

−θ+θ++

θ−θ+θ=

−θ−θ−

θ+θ++θ−=

(6)

where

()

[]

1210

cos1L2

coscosLL2LR

θ+θ++

θ+θ+=

(7)

Depending on the link length of the mechanism,

Eq.6 simplifies to

For

LL = and ⇒θ=θ

and

1110

11P

cos4L-cosL4L-L-4L

sinLy

θθ+

θ=

ii)

For 0L

and ⇒θ=θ

and

211P

cosLLsinLy θ−+θ=

iii)

For 0L

LL = and ⇒θ=θ

and

11P

sinL2y θ=

When choosing the link sizes, it is important for

effective force transmission to minimize the

variation of the transmission angle

from 90

; the

acceptable range is

4090 ∓ (Alici, 2004). It is

mathematically expressed as

1cos

⎟

⎠

⎞

⎜

⎝

⎛

−=ψ (8)

For

13050 ≤ψ≤ , 8126.1

845.0

≤

⎟

⎠

⎞

⎜

⎝

⎛

≤ . With

reference to Eq.8, for a given

L and

L , the range

L satisfying the effective transmission angles

can be calculated. It must be noted that

L should

be greater than

L to prevent any physical

interference among the mechanism links. A practical

ratios of

0.3

5.1

≤

⎟

⎠

⎞

⎜

⎝

⎛

≤ and 0.2

0.1

≤

⎟

⎠

⎞

⎜

⎝

⎛

≤

should result in proportionate link lengths and

transmission angles. For the data shown in Table 1,

the transmission angle and the vertical movement of

the linear actuation module are calculated and

presented in Figure 2.

Table 1: Numerical values of the parameters for the

exemplary results shown in Figure 2.

Parameters

mm40L

mm20LL

mm22LL

115to90

The corresponding generalized relationship

between rate of change

θθ

⎡⎤

Θ=

⎣⎦





of the input

bending angles and the output velocity vector

FROM BENDING TO LINEAR MOVEMENT - A Linear Actuation Mechanism based on Conducting Polymer Actuators

[]

yxX





is given by (Alici & Shirinzadeh,

2005)

()()

Θ=Θ

⎥

⎦

⎤

⎢

⎣

⎡

θθ∂

∂

θθ∂

∂



(9)

where J is the mechanism Jacobian matrix.

90 95 100 105 110 115

Vertical Position y

(mm)

90 95 100 105 110 115

100

120

140

Input Bending Angles,

and

(degree)

Transmission Angle (degree)

Figure 2: Variation of the vertical position of the output

point P and the transmission angle with the input bending

angles. The net vertical distance is 7.6858 mm.

2.2 Force Analysis

Assuming that two active links AO

and BO

made of electroactive polymers generate bending

moments

M and

M , which act on the actuation

module in the opposite directions. Assume that the

output point P can apply a planar force vector of

jFiFF

yxp



+= to the environment to realise a

functional task. Please recall that the mechanism

converts the work in the bending coordinates

into

the work in linear coordinates X. These two works

are ideally equal to each other.

90 95 100 105 110 115

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

Input Bending Angles,

and

(degree)

Vertical Force F

(mN)

Figure 3: Variation of the vertical force component of the

output point P with the input bending angles. The net

vertical force is 0.6837 mN. The horizontal component of

the force is zero.

Using the duality between the generalized

relationships for motion and force transfer between

the actuation and output spaces, the following force

relationship is obtained (Alici &

Shirinzadeh, 2005);

MJFFJM

T −

=⇒= (10)

where

[

]

yxP

FFF = and

[]

MMM = and

(.)

denotes transposition. For the data in Table 1 and

[

]

11M =

Nmm, the force output at point P is

calculated using Eq.10 and is presented in Figure 3.

Because the mechanism link lengths are chosen such

that it can generate a vertical movement, the

mechanism will not create any horizontal force

component. These kinematic and force analyses

suggest that it is possible to optimize the topology of

the mechanism for an efficient motion and force

transmission.

3 CONDUCTING POLYMER

ACTUATORS: SYNTHESIS

AND ACTUATION PRINCIPLE

The PPy film was manufactured by combining a

solution of 0.1M pyrrole monomer with 0.1M

lithium triflouromethanesulfonimide (Li

TFSI

−

) in

propylene carbonate (PC) with 1 % H

O, degassed

with nitrogen gas and stirred for 15 minutes. This

solution was used to grow the PPy onto a gold

sputter coated, 0.45

μm Millipore Immobilon-P

porous poly(vinylidene fluoride) (PVDF) film by

electrodeposition over a period of 12 hours at -33

with a current density of 0.1mA.m

-2

. After

polymerization, the film was washed in acetone and

then resoaked in a 0.1M LiTFSI electrolyte and then

stored away from oxygen. Actuators were then cut

to desired size using a scalpel and were limited to

size by the area of the 40mm x 55mm film. The

resulting film consists of two PPy outer layers and

two gold layers separated by a PVDF core is shown

in Figure 4.

Figure 4: General structure of trilayer polymer actuator.

ICINCO 2009 - 6th International Conference on Informatics in Control, Automation and Robotics

After doping with electrolyte, both the PPy

layers of a bending actuator become partially

oxidised (Figure 5a) and upon application of a

positive voltage, one of the polymer layers is highly

oxidized and the other is reduced. In an attempt to

neutralise the charge imbalance, ions transfer from

the electrolyte into the polymer layers. In LiTFSI

doped actuators, TFSI

anions move into interstitial

spaces in the polymer backbone of the oxidized

layer, causing it to expand. Simultaneously, the

opposing polymer film is reduced and contracts by

removing TFSI

ions, overall creating a bending

motion (Figure 5b.) By applying a square wave

voltage, the actuator is allowed to return it to its

original position and continue to bend through the

neutral position so that the actuator may bend

alternately in both directions.

Figure 5: Schematic of PPy actuator doped in LiTFSI (a)

partially oxidised (b) under an applied voltage.

To produce the linear actuators, two pieces of PPy

film cut to equal dimensions were connected

together in parallel at their tips with copper tape and

two Ø 3mm × 0.5mm neodymium iron boron

(NdFeB) magnets one either side of each tip

(Figures 6-7.) Once placed between the electrodes,

the PPy configuration effectively produces four PPy

components, with the length referred to throughout

this paper as the length depicted in Figure 7b.

Figure 6: Configuration of the linear PPy actuator with Cu

tape and NdFeB magnets.

Under an applied voltage, it was observed that the

PPy linear actuator produced the shape as shown in

Figure 8. In this case, the outer PPy layer of the

upper components is oxidised and the inside layer is

reduced, and under no constraints, almost uniform

curvature may be experienced. The lower

components may be activated; however the possible

oxidation of the Cu tape suggests that the lower

components remain either inactivated. This linear

design restricts the bending motion of the actuators

due to the presence of the magnets used to clamp the

copper tape to the actuators (Figure 8). For the

shorter lengths, a greater percentage of the actuator

is affected by the clamping induced by the magnets

and as a result, the actuator has a more elongated

appearance (Figure 9). Due to this elongation, it

doesn’t move as far in the vertical direction as it

potentially could. To overcome this limitation,

another method of electrically connecting the upper

and lower actuator components that does not restrict

the motion is necessary. For this to be possible, the

electrical connection must be flexible and able to

bond to the actuator without the assistance of

magnets. Although the magnets restrict motion, they

do provide some stability which is important in

attempting to control the actuator.

(a)

(b)

Figure 7: Linear PPy actuator in neutral position.

4 PERFORMANCE

CHARACTERISATION

RESULTS

Linear actuators shown in Figures 6-7 with link

lengths of 10mm, 15mm, 20mm and widths of 2mm,

3mm, 4mm were manufactured and tested under a

series of applied loads. Loads were added to the

bottom tip of the actuators and the overall

displacement of the base tip was measured visually

using a grid paper, as illustrated in Figure 10a. The

initial load used was the non-magnetic wire hook

and a 0.266g NdFeB magnet glued to its base

(Figure 10b), with incremental loads applied by

FROM BENDING TO LINEAR MOVEMENT - A Linear Actuation Mechanism based on Conducting Polymer Actuators

adding magnets of either 0.266g or 0.54g to the base

of the wire hook. Voltage was maintained at +/-1V

to avoid over-oxidation and reduce the variation in

results that may arise due to early onset of fatigue.

The frequency of the square voltage inputs was held

constant for all experiments at 0.5Hz to allow

sufficient response time. Typical voltage, current

and charge data recorded by the datalogging system

used is presented in Figure 11.

Figure 8: Shape of actuator under actuation.

Figure 9: Shape of shorter actuators under actuation.

(a) (b)

Figure 10: (a) PPy linear actuator with a load. (b) Wire

hook; used to separate magnet loads from magnets on the

actuator.

Figures 12(a)-(i) provide an overview of the base

tip position in extended and contracted positions

under given applied loads, with the electrode

contacts as the reference point. In all actuators, as

the load increases the position of the base tip below

the reference point also increases. Generally, as the

width decreases the position below the electrode

increases and is more evident in the 15mm long

actuators. As width increases, the actuator becomes

stiffer which allows a smaller deflection below the

reference point under a load than an actuator of a

small width.

Figure 11: Example voltage, current and charge input data

for 20mm x 2mm linear PPy actuator at 0.5Hz.

Displacement increases and then decreases for

increasing load as shown in Figure 12(d)-(i) for the

15mm and 10mm long actuators. This behaviour is

because under no load, the actuators are restricted in

their movement by the magnets clamping the Cu

tape in place. The clamping effect has a greater

impact on shorter actuators because, as a percentage,

a greater proportion of the actuator is restricted than

longer actuators. Under applied loads, the shorter

actuators are able to move because the load forces

the actuator base tip to be displaced to lower than

the original position, and under an applied voltage

the actuator attempts to return to the original

position and produces an upward motion.

For this

reason, the shorter actuators may only be suitable for

applications requiring a pulling load, and if shorter

actuators are required for pushing, then another

method of connecting the actuators that provides less

restriction on motion is required.

A comparison of load and displacement output

between the linear and cantilever actuators of

corresponding length has revealed that the cantilever

actuators provide a greater range of motion in the

vertical direction, while the linear actuator lifted

heavier loads. The linear actuators are effectively 4

times the volume of their corresponding bending

actuator.

Base tip of

actuator

ICINCO 2009 - 6th International Conference on Informatics in Control, Automation and Robotics

Load v position, 4 x 20m m

-30

-25

-20

-15

-10

-5

0510

Load (mN)

contracted

extended

Position of base tip

below electrode (mm)

Load v position, 3 x 20mm

-30

-25

-20

-15

-10

-5

0510

Load

(

)

contracted

extended

Position of base tip

below electrode (mm)

Load v position, 2 x 20mm

-30

-25

-20

-15

-10

-5

0510

Load (mN)

contracted

extended

Position of base tip

below electrode (mm)

(a) (b) (c)

Load v position, 4 x 15mm

-20

-15

-10

-5

0 5 10 15

oad

(

)

contracted

extended

Position of base tip

below electrode (mm)

v pos

iti

on,

-20

-15

-10

-5

0 5 10 15

Load

(

)

contracted

extended

Position of base tip

below electrode (mm)

v pos

iti

on,

-20

-15

-10

-5

0 5 10 15

Load (mN)

contracte d

extended

Position of base tip

below electrode (mm)

(d) (e) (f)

Load v position, 4 x 10m m

-10

-8

-6

-4

-2

0 5 10 15

Load

(

)

contracted

extended

Position of base tip

below electrode (mm)

Load v position,

-10

-8

-6

-4

-2

0 5 10 15

Load (mN)

contracted

extended

Position of base tip

below electrode (mm)

Load v position, 2 x 10mm

-10

-8

-6

-4

-2

051015

Load (mN)

contracte d

extended

Position of base tip

below electrode (mm)

(g) (h) (i)

Figure 12: Position of base tip of linear actuators under applied load.

However, they produced much less displacement

due to the restriction in motion provided by the

magnet connections. The cantilever actuators have

the ability to move above and below the electrodes

whereas the linear actuators are limited to motion

below the electrodes only. Although much less

displacement is achieved, the benefit of a linear

actuator is that motion in one direction is more

controlled than for a bending actuator. For

displacement output, the linear actuators with 20mm

PPy links, produced the greatest displacement than

actuators with shorter PPy links over a range of

loads. Figure 13 depicts the displacement in the

vertical direction for linear actuators of varied width

with 20mm length. As width of the PPy links

increases, a greater displacement output for a given

load may be expected. However, as width increases,

the PPy film has a tendency to curl across the width,

particularly in actuators for 4mm wide or greater

(Alici, 2007). Curling increases stiffness and thus

decreases the potential displacement output, hence

the 4mm wide actuator produced a slightly smaller

displacement than actuator with 3mm wide PPy

links.

0 1 2 3 4 5 6 7 8 9

20 x 2 mm, Y= -0.7348X+4.2350

Displacement (mm)

0 1 2 3 4 5 6 7 8 9

20 x 4 mm, Y= -0.3871X+4.2312

Displacement (mm)

Load (mN)

0 1 2 3 4 5 6 7 8 9

20 x 3 mm, Y= -0.6900X+6.0927

Figure 13: Variation of the tip displacement of the linear

actuation module with the payload.

FROM BENDING TO LINEAR MOVEMENT - A Linear Actuation Mechanism based on Conducting Polymer Actuators

5 CONCLUSIONS

A linear actuator system based on the bending

motion of conducting polymer actuators operating in

air is presented, including an analytical model to

estimate the linear movement and the force output of

the mechanism. The mechanism is basically a

motion and force transmission system, converting

the bending work provided by the electroactive

polymer actuators into Cartesian work. The

experimental results presented demonstrate that the

conducting polymer actuators generate enough

displacement and force to handle a range of practical

payloads. Another outcome of this study is that

when the bending type- low power consuming

polymer actuators are tailored properly, they can be

used to generate a rectilinear motion with enough

force output.

Future work involves deriving a more accurate

analytical model taking into account the deflections

of the mechanism links and verifying the model

experimentally. Improvements may also be made to

the hinge connections of the linear actuator, by

replacing the copper connections with an inert,

conductive material such as gold or platinum.

ACKNOWLEDGEMENTS

The authors thank Dr Stephen W. John for his help

in synthesizing the bulk actuator sheet and

construction of the actuation module.

REFERENCES

Alici, G 2000, ‘Determination of Singularity Contours for

Five-bar Planar Parallel Manipulators’, Robotica,

vol.18, no.6, pp.569-575.

Alici, G & Huynh, NN 2007, ‘Performance Quantification

of Conducting Polymer Actuators for Real

Applications: A Microgripping System’, IEEE/ASME

Transactions. on Mechatronics, vol.12, no.1, pp.73 -

84.

Alici, G, Metz, P & Spinks, G 2005, ‘A mathematical

model to describe bending mechanics of Polypyrrole

(PPy) Actuators’, Proceedings of the 2005

IEEE/ASME International Conference on Advanced

Intelligent Mechatronics, 2005, 24-28 July, Monterey,

California.

Alici, G & Shirinzadeh, B 2004 “Optimum synthesis of

parallel manipulators based on kinematic isotropy and

force balancing”, Robotica, vol.22, no.1, pp. 97 – 108.

Alici, G & Shirinzadeh 2005, ‘Enhanced Stiffness

Modelling, Identification and Characterisation for

Robot Manipulators’, IEEE Transactions on Robotics,

vol.21, no.4, pp. 554 – 564.

Alici, G, Spinks, GM, Huynh, NN, Sarmadi, L, &

Minato, R 2007, ‘Establishment of a Biomimetic

Device Based on Tri-layer Polymer Actuators –

Propulsion Fins’, Journal of Bioinspiration &

Biomimetics, vol.2, no.2, pp. S18-S30.

EAMEX Corporation n.d., accessed 15/06/2008,

http://www.eamex.co.jp/index_e.html.

John, SW, Alici, G & Cook, CD 2008, ‘Validation of a

Resonant Frequency Model for Polypyrrole Trilayer

Actuators’, IEEE/ASME Transactions on

Mechatronics, vol.13, no.4, pp.401 - 409.

Metz, P, Alici, G & Spinks, G 2006, ‘A finite element

model for bending behaviour of conducting polymer

electromechanical actuators’, Sensors and Actuators

A, vol.130-131, pp1-11.

Otero, TF, Cortes, MT & Vazquez Arenas, G 2007,

‘Linear movements from two bending triple-layers’,

Electrochimica Acta, vol. 53, pp1252-1258.

Thompson, F.W. 2007. ‘Hybrid linear actuator based on

conducting polymers’, Bachelor of Engineering

(Mechatronics) Honours Thesis, Faculty of

Engineering, University of Wollongong.

Yamakita, M, Kamamichi, N, Yashuaki, K, Asaka, K &

Luo, Z 2004 ‘Development of an artificial muscle

linear actuator using ionic polymer metal composites’,

Advanced Robotics, vol.18 , pp383-399.

ICINCO 2009 - 6th International Conference on Informatics in Control, Automation and Robotics