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Design of a precision rotary-linear dual-axis positioning system
with a surface encoder
Shinji Sato, Wei Gao and Satoshi Kiyono
Department of Nanomechanics Engineering, Tohoku University,
Aramaki-aza Aoba 6-6-01, Aoba-ku, Sendai, 980-8579 Japan
ABSTRACT
This paper presents a prototype rotary/linear dual-axis positioning system consisting of a θ-Z actuator and a rotary-
linear angle sensor. In the system, an aluminum rotor (moving element) can be moved along and rotated about the axis
(Z) of a ceramic cylinder (driving rod). The θ-Z actuator is composed of a Z-piezoelectric actuator (maximum stroke: 12
µm) for linear motion, two θ-piezoelectric actuators (maximum strokes: 9.1 µm) with an added weight for rotation, a
driving rod and a rotor. The two θ-piezoelectric actuators with the added weight are attached to the driving rod via a
clamping device made with steel. The inner face of the rotor is made contact to the driving rod with a certain friction
force. The linear-axis positioning employs the smooth impact drive mechanism to achieve a large stroke by applying a
periodic saw-toothed motion from the Z-piezoelectric actuator to the rotor via the driving rod. Sinusoidal motions are
applied to the θ-piezoelectric actuators for rotary positioning, which is with a different mechanism form the smooth
impact drive mechanism. The stroke of the prototype system along the Z-axis, which is limited by the length of the
cylinder, is designed to be 10mm and there is no limitation in the rotary motion. The positioning resolution and
maximum speed along the Z-direction are approximately a few nanometers and 2.4mm/sec, respectively. The maximum
revolution speed is approximately 50 rpm. An optical surface encoder is also designed for precision positioning of the
rotor.
Keywords: Rotary-linear Dual-Axis Positioning, Piezoelectric Actuator, Precision Positioning, Surface Encoder
1. INTRODUCTION
Various linear single-axis positioning systems driven by piezoelectric actuators have been developed because the
piezoelectric actuator has advantages of high resolution and fast response [1, 2]. On the other hand, precision rotary-
linear dual-axis positioning systems with nanometric resolution, high-speed and wide moving stroke are also desired in
various areas of nanotechnology, such as nano-manipulation of cells, micro-parts, etc. Some new mechanisms have been
developed to achieve rotary-linear motions [3]. One of them is a rotary-linear induction motor whose stator possesses
two windings generating the rotating and traveling fields. But the mechanisms are too complex to make compact
designs. Precision positioning is also difficult because there does not exist proper rotary-linear dual-axis position
sensors.
In this paper, a rotary-linear dual-axis positioning system consists of a θ-Z actuator and a rotary-linear surface encoder
[4] is presented. The Z-actuator utilizes the smooth impact drive mechanism (SIDM) [1, 2]. The SIDM actuator has
advantages such as simple construction, long stroke, and high resolution. A SIDM actuator is composed of a
piezoelectric actuator, a friction component, and a moving body. One side of the piezoelectric actuator is mounted on
the SIDM base and the other side is connected with the friction component. The friction component is attached to the
moving body with a small friction. When a saw-toothed voltage is applied to the piezoelectric actuator, a saw-toothed
motion of the friction component is generated. The moving body can then be moved along the Z-direction based on the
stick-and-slip phenomenon determined by the inertia and friction force generated on the moving body. The friction
component is with a cylinder shape so that rotary motion can also be generated. The θ-actuator employs a different
driving mechanism, in which a sinusoidal voltage is applied to a piezoelectric actuator so that a sinusoidal motion is
generated along the tangential direction of the cylindrical friction component. Consequently a rotary-linear dual motion
can be realized. The designed θ-Z actuator system is composed of a piezoelectric actuator for the linear motion, two
piezoelectric actuators with an added weight for the rotary motion. A driving rod is used as a friction component, and a
rotor is used as a moving body. On the other hand, however, the generated motions in the Z- and θ-directions are not
Optomechatronic Systems Control, edited by Farrokh Janabi-Sharifi, Proc. of SPIE
Vol. 6052, 60520J, (2005) · 0277-786X/05/$15 · doi: 10.1117/12.647931
Proc. of SPIE Vol. 6052 60520J-1
accurate without a feedback control system based on a proper rotary-linear dual-axis position sensor. The feedback
control system is also essential for reducing the interference between the motions along the two directions. In this paper,
a rotary-linear surface encoder is presented for detecting the relative motions between the moving body (rotor) and the
sensor in the rotational and axial directions. The rotary-linear surface encoder is modified from a surface encoder for
planar motion detection [5, 6]. The surface encoder consists of a two-directional (2D) slope (angle) sensor and a
sinusoidal micro-structured grid surface (angle grid) generated on the rotor periphery [7]. The angle sensor is used to
read the two-directional local slopes of an angle gird surface. Since the angle grid surface is a superposition of sine
waves along the rotational and axial directions, the rotational and linear motions of the rotor relative to the rotary-linear
angle sensor can be independently obtained from the 2D outputs of the sensor.
This paper describes the design and construction of the precision rotary-linear dual-axis positioning system. The
principle of the rotary-linear position detection by the surface encoder is illustrated. Results of driving experiments by
the rotary-linear dual-axis are also presented.
2. θ-Z ACTUATOR
2.1 Schematic of the rotary-linear positioning system
Fig.1 shows a schematic of the rotary-linear dual-axis positioning system. The rotary-linear positioning system
consists of a θ-Z actuator and a rotary-linear angle sensor. An aluminum rotor (moving element) can be moved along
and rotated about the axis (Z) of a ceramic cylinder (driving rod) and a rotary-linear angle sensor detects the rotary-
linear dual motion of the rotor relative to the rotary-linear angle sensor independently. The feedback control system for
precision positioning will be developed based on the results of this paper.
θ-Z actuator
Weight X
Ring actuator with casing (PZTA)
Piezoelectric actuator (PZT B, C)
I Rotor
Y
Driving rod
Z
Rotary-linear angle sensor
Z
Fig.1 Schematic of the rotary-linear positioning system
Proc. of SPIE Vol. 6052 60520J-2
Fig.2 Photograph of the θ-Z actuator
Table.1 Specification of the PZT B (PZT C)
Table.1 Specification of the PZT A
Dimensions 5×5×10mm
Dimensions φout15mm×3.5mm (φin9mm) Resonance frequency 138kHz
Resonance frequency 30kHz Displacement /Voltage 9.1µm/150V
Displacement /Voltage 12µm/150V Curry temperature 145degree
Stiffness 250N/µm Young’s modulus 4.4×1010N/m2
Fig.2 shows a photograph of the θ-Z actuator. The θ-Z actuator is composed of a ring actuator with a stainless casing
(PZT A: maximum stroke: 12 µm) for linear motion, two piezoelectric actuators (PZTs B, C: maximum stroke: 9.1 µm)
with an added weight for rotation, a driving rod made with ceramic, and a rotor made with aluminum. The driving rod is
attached to PZT A so that the driving rod can be moved with the displacement of PZT A. The inner surface of the rotor
is made contact to the periphery of the driving rod with a certain friction force. The driving rod serves as not only the
friction component driving the rotor but also the guide of the linear motion along and rotation about the Z-axis. PZT B
and PZT C with an added weight are attached to a driving rod via a clamping device made with steel. PZT B and PZT C
are used to twist the neck of the driving rod by inertial force caused by rapid deformation. The weights attached to the
top of PZT B and PZT C, respectively, have a mass of 6 g. The weights enlarge the inertial force to increase the angle of
the driving rod. The rotor is made from aluminum for the purpose of fabricating a sinusoidal micro-structures on the
periphery of the rotor with the diamond turning process. The outer and inner diameters of the rotor are designed to be 20
mm and 8.5 mm, respectively. The outer diameter of the driving rod is 8.45 mm and the surface roughness of the
periphery is designed to 1µm(Ra). Tables 1 and 2 show specifications of PZTs A, B and C, respectively.
2.2 Driving mechanism
To achieve a rotary-linear dual-motion is the primary interest of this research. The smooth impact drive mechanism
(SIDM) is employed in the θ-Z actuator. A SIDM actuator has characteristics such as simple construction, a long stroke,
and fine positioning resolution. SIDM actuators possess two operational modes. One mode is called the precise
positioning drive mode, which is simply operated by applying a DC input voltage to the piezoelectric actuator. The
displacement of the rotor is proportional to the input voltage because a friction force existing between the moving body
and the driving rod can prevent slippage. The positioning resolution of a SIDM actuator with a precise positioning drive
mode, is equivalent to the nanometer resolution of the piezoelectric actuator. The other mode is called a long stroke
mode, which is mainly mentioned in this paper. This mode utilizes the difference between the friction force and the
Proc. of SPIE Vol. 6052 60520J-3
inertia force. In the long stroke mode, the input voltage is composed of a slowly increased period and a rapidly
decreased period. The displacement of the piezoelectric actuator is proportional to the input voltage if the driving
frequency is much below the resonant frequency. Therefore a saw-toothed input voltage is used to generate alternately
slow and rapid motions of a piezoelectric actuator.
Fig. 3 shows the principle of the rotary-linear dual motion. As shown in Fig.1, a ring actuator with a stainless casing
(PZT A) and two piezoelectric actuators (PZTs B, C) with an added weight are used for linear motion and rotary
motion, respectively. Consider that an input voltage is applied to PZT A. When the input voltage is in the slowly
increased period, the rotor is moved along the Z-axis because the inner surface of the rotor and the periphery of the
driving rod is attached with the friction force, as shown in Fig. 3(a). On the other hand, when the input voltage is in the
rapidly decreased period, the rotor cannot follow the quick movement and remains on site with slip because of the
inertia, as shown in Fig. 3(b). Consequently, the displacement of the rotor is equivalent to the carried distance in the
slowly increased period and the slipped distance in the rapidly decreased period. By repeating the operation, the rotor
can be driven along the Z-axis over a long stroke. Displacement of the piezoelectric actuator and the rotor with respect
to time are shown in Fig. 4. In the second stage of applying the input voltage slowly to PZT B (PZT C), the driving rod
and rotor rotate slightly about the Z-axis because the driving rod guides the motion of the rotor along the rotational and
axial directions, as shown in Fig. 3(c). On the other hand, by applying the rapidly decreased voltage, the rotor slips and
remains on site as shown in Fig. 3(d). By repeating these operations, the rotor can rotate continuously about the Z-axis
in the same mechanism as the linear motion.
The driving characteristics of the rotor are affected mainly by the two factors. One is the input voltage, including
driving frequency, amplitude, and duty-ratio. The other is the friction force between the rotor and the driving rod. Duty-
ratio is defined by using the parameters listed in Fig. 4 as
B
Du = × 100 % (1)
A
Parameters such as driving frequency, amplitude, and duty-ratio are easily controlled by controlling the electrical source
to optimize the driving characteristics. Although it is difficult to control the friction force on purpose, it is desired to
keep the friction force to be constant. For this purpose, the surface roughness of the periphery of the driving rod is
designed to be small.
Displacement of Rotor
Z Displacement of PZTA in the axial direction
X
Y Y
Initial state
_inri1iiiii 111111
Displacement of Rotor in
the rotational direction
4—
(a) Slow expansion (c)
nuni..iii
(b) Rapid contraction (d)
iiiiiiiii
Fig.3 Principle of the rotary-linear dual-motion
Proc. of SPIE Vol. 6052 60520J-4
Displacement of piezo
Displacement of rotor
A
Displacement
B C
II
I I'
I'
II
II
I
It
I
II
—
%
I I
Time
Fig.4 Driving mechanism with saw-toothed motion of the piezoelectric actuator
3. ROTARY-LINEAR SURFACE ENCODER
Since there are no individual guide ways for the rotor in the rotational and axial directions, to increase the positioning
accuracy and reduce the interference between the motions in the two-directions, the rotary-linear dual-axis positioning
system has to include feedback control for precision positioning. A rotary-linear encoder is thus proposed to detect the
relative motion between the rotor and the rotary-linear angle senor in the rotational and axial directions, respectively.
Fig. 5 shows the schematic of the principle of rotary-linear position detection. The surface on which sinusoidal micro-
structures are generated is called the angle grid. The surface profile of the angle grid on the periphery of the rotor can be
expressed as:
⎛ 2π ⎞ ⎛ 2πr ⎞
f (θ, z ) = Az sin ⎜ ⎜ λ z ⎟ + Aθ sin ⎜ λ θ ⎟
⎟ ⎜ ⎟ (5)
⎝ z ⎠ ⎝ θ ⎠
where λz and λθ are wavelengths of the periodic sine functions in the axial and circumferential directions, respectively.
ΑΖ and Αθ are the corresponding amplitudes. r is the radius of the periphery of the rotor. The angle grid surface on the
periphery of the rotor is designed to have identical amplitudes and wavelengths in the axial and circumferential
directions (λz = λθ =100 µm, ΑΖ = Αθ =100 nm).
The rotary-linear angle sensor detects a reflection angle of a laser beam, corresponding to the 2D local slops of the
angle grid, based on the principle of autocollimation. The 2D local slops of the angle grid, which is detected by the
angle sensor, can be described by
∂f ( z , θ) 2π ⎛ 2π ⎞
α( z ) = = Az cos⎜⎜ λ z⎟ ⎟ (6)
∂z λz ⎝ z ⎠
1 ∂f ( z , θ) 2π ⎛ 2πr⎞
β(θ) = = Aθ cos⎜
⎜λ θ⎟⎟ (7)
r ∂z λθ ⎝ θ ⎠
It can be seen that α(z) and β(θ) are periodical sine functions of z and θ, and the periods are equal to λz and λθ,
respectively. Consequently z and θ can be evaluated from the angle sensor output such as α(z) and β(θ). By using the
wavelength as the graduations, displacement of the relative motion between the rotor and the angle senor can be
measured in the rotational and axial directions, respectively.
A multiple beams are used to utilize the averaging effect, which reduce the influence of the profile errors of the angle
grid surface. The multiple beams are projected onto the periphery of the rotor at the same phase positions in difference
periods of the periodic sine waves. However, because of the curvature of the periphery of the rotor, the reflected beams
from the angle grid surface will radiate. Hence a cylindrical lens is used to converge the multiple beams to the center of
the rotor so that the measurement of the slope profile of the sinusoidal micro-structures will not be influenced by the
curvature of the periphery of the rotor.
Through employing the fast tool servo technique, the sinusoidal micro-structures on the periphery of the cylinder with
wavelengths of 100 µm has been accurately fabricated [8]. Therefore, it is expected that fabrication of the sinusoidal
micro-structures on the periphery of the rotor could be realized.
Proc. of SPIE Vol. 6052 60520J-5
Laser beam
ΑΖ Αθ
λz λθ
Axial direction Circumferential direction
Fig.5 Schematic of the principle of rotary-linear position detection
Laser head
Receiver
Retroreflector
.\j flu Encoder head
Reference cube-corner
I.. I. Encoder scale
Fig.6 Schematic of the principle Fig.7 Schematic of the principle
4. EXPERIMENT
The driving voltage generated by a function generator or a personal computer is multiplied by 15 times before it is
applied to the piezoelectric actuators. Figs. 6 and 7 show photographs of the experimental setups for measurements of
the linear motion and rotation, respectively. The linear motion of the rotor is measured by a laser interferometer, which
has a high resolution of 1.25 nm. A rotary encoder, which has a scale of 5000 pulses/revolution, measures the rotation of
the rotor. As shown in Fig. 6, the retroreflector of the laser interferometer is attached to the rotor via an acrylic plastic
tube since the reference cube-corner is used as the reference plane. The mass of the rotor is changed from 6 g to 23.5 g.
When it comes to the measurement of the rotation, the mass of the rotor is changed from 6 g to 19 g because the encoder
scale is attached. As the mass of the rotor gets heavy, the driving characteristic varies because the friction force between
the rotor and driving rod is influenced by.
Fig. 8 shows the duty ratio-velocity characteristic of the linear motion. The driving frequency is changed from 2200
Hz to 3000 Hz with a step of 200 Hz. The amplitude of the driving voltage is 7.5 V. Under this condition, the maximum
velocity of the rotor is 2.4 mm/sec where the duty ratio is 30% and the driving frequency is 2600 Hz. As shown in the
figure, the duty ratio-velocity characteristic is symmetrical about a point where the duty ratio is 50% and the velocity is
0 mm/sec. It is confirmed through the experiment that the linear motion of the rotor over a long stroke can be realized
by applying a periodic saw-toothed input voltage.
Fig. 9 shows results of the minimum step-drive of the linear motion. The driving frequency, amplitude of input
voltage, and duty ratio are 400 Hz, 0.75 V, and 99%, respectively. The minimum step width is approximately 70 nm.
The step width cannot be smaller even if the amplitude of input voltage is below 0.75 V because of an elastic
Proc. of SPIE Vol. 6052 60520J-6
deformation of friction parts. When the input voltage is increased gradually to the threshold voltage, the rotor moves
and the step width jump from 0 to the minimum step width of 70 nm.
Figs. 10 and 11 show the rotation characteristics. The displacement of the driving rod in the XY-plane is measured by
an optical fiber displacement sensor. The results indicate that the rotation mechanism is different from the smooth
impact drive mechanism. The rotor rotates because of an elliptic oscillation of the driving rod in the XY-plane.
Although the saw-toothed input voltage is essential for a linear motion, the sinusoidal input voltage is applied to realize
the rotary motion. As shown in Fig. 10, when an input voltage is applied to the PZTB, the rotor rotates continuously
about the Z-axis and the rotation speed is kept constant where the amplitude of input voltage and driving frequency are
15 V, 30 V, and 45 V, and 1.6 kHz, respectively. The rotation direction is defined by which piezoelectric actuator is
driven, as shown in Fig. 11. As the input voltage increases, the rotation speed gets faster. The maximum rotation speed
is approximately 50 rpm. Fig. 12 shows the minute step rotation. The input voltage is composed of a sinusoidal and
constant waveform as shown in Fig. 13. The step width is determined by the amplitude and frequency of the sine wave,
and time period when the sine wave is applied (Ts). The results in the figure indicates that a 0.6 degree of the minute
step rotation is realized where the amplitude, driving frequency, and time period (Ts) are 10.5 V, 1250 Hz, 10 msec,
respectively
3
2200 Hz
L
2 400 Hz > PZT Rotor 0
—t—2000Hz 0
2000 Hz
E 70nm
3000 Hz =
0 0
0
2
N 0
=
0-
0 0 0
= 0
0 0
E
1
0
C-, 0
0 =
a
0 2
0 a
C
0 20 40 60 80 100 Time I msecIdiv
Duty ratio %
Fig.8 Relationship between velocity and duty-ratio Fig.9 Minimum step-drive of linear motion
700
tZTA
600 PZTB
40
0 PZTB
2 500 45V E
a
0)
0
V 20
o 400 0
0) a
300 30V =
.2 PZTC
0
C,
0
o 200
-20
100 15V
0 -40
0 0.5 1 1.5 2 0 20 40 60 80
Time Sec Driving voltage V
Fig.10 Rotation of the rotor Fig.11 Relationship between rotation speed and driving voltage
Proc. of SPIE Vol. 6052 60520J-7
Rotation angle O.2degreeIdiv
0.6° Tf Ts
Voltage
Time
Fig.12 waveform of the input voltage
Fig.13 minute step rotation
5. CONCLUSION
A rotary-linear dual-axis positioning system consisting of a θ-Z actuator and a rotary-linear angle sensor for precision
positioning of rotary-linear dual-axis motions has been proposed. The principle of the rotary-linear position detection
based on the measurement result of the rotary-linear surface encoder is described. A cylindrical lens is used in the
rotary-linear angle sensor to converge the multiple beams to the center of the rotor so that the measurement of the slope
profile of the sinusoidal micro-structures will not be influenced by the curvature of the periphery of the rotor. The θ-Z
actuator is designed and developed to achieve the rotary-linear dual-axis motion. The experimental results have
indicated that a linear motion of the rotor over a large stroke can be realized by applying a periodic saw-toothed input
voltage and a rotary motion can be realized by applying a sinusoidal input voltage. It has also been verified that the
driving mechanisms of the linear motion and rotary motions are different.
A new θ-Z actuator that can realize the rotary-linear dual-axis motion with the same driving mechanism will be
developed to simplify the control of the rotor. The feedback control of the positioning system for precision positioning
is also our future work.
ACKNOWLEDGEMENTS
This research was financially supported by Osawa scientific studies grants foundation.
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