Off-line programming of an industrial robot for manufacturing

Abstract A procedure for the automatic generation of the robot programming used in manufacturing operations is introduced in the present paper. The off-line programming system developed here includes graphical simulation of the robot and its workcell, kinematic model of the robot, motion planning and creation of the NC code for manufacturing process. The proposed system is applied in a robot with five revolute joints for manufacturing operations and in a robot with six revolute joints for welding operations Keywords Robot Æ Off-line programming Æ Simulation Æ Welding
 1 Introduction
 Robotics applications in manufacturing lead to the reduction of production time and the improvement of the quality of the workpieces. Small and medium enterprises that produce a wide variety of products require a method that generates the NC code for processes automatically. The robot off-line programming using a CAD system has the potential to produce a visual presentation of the robot when performing its task and to eliminate in the planning stage problems of robot reach, accessibility, collision, timing, etc. In this way significant time economy can be achieved, because the actual manufacturing would only have to be interrupted briefly, while the new programs are downloaded into the workcell control computers. The robot off-line programming using a CAD system has been the subject of much research in recent years. Computer graphics simulation of the robot and its workcell can be realized with different models such as wire-frame and solid models [1]. These models and adequate algorithms can be used for collision detection and for kinematic and dynamic behaviour of the robot [2,3,4].
 In the present paper, the procedure for automatic generation of the programming of the manipulator used for manufacturing is described. The off-line programming system developed here includes graphical simulation of the robot and its workcell, kinematics of the robot, motion planning and creation of the NC code. With the aid of this procedure it is possible to simulate the behaviour of the robot during the process. The developed system is demonstrated in two cases: a robot with five degrees of freedom and five revolute joints (RV-M1) used for general manufacturing processes and a robot with six degrees of freedom and six revolute joints (RV6) used for welding.
 2 Graphical simulation
 In the first step of the procedure, the graphical simulation of the manipulator, tool, workpiece and workspace  is achieved using the SolidWorks program [5]. Geometrical characteristics such as size and shape of the robot links and the kinematics are introduced into a database. The description of the robot kinematics contains information about the degrees of freedom, the type of joints, the Denavit-Hartenberg parameters [6], the joint functionality limits, etc. After the drawing of the manipulator links in solid three-dimensional space, they are assembled taking into account the position of the joints and the relative motion between the links.
 Figure 1 shows the simulating model of a robot with five revolute joints. The simulating model of the robot environment contains geometrical data of the workspace including the workpieces, which will be processed and can be

Fig. 1 Robot with five revolute joints described in the same way as the geometry of the robot.
 3 Robot kinematics  In order to plan and simulate the robot motion, the forward and inverse kinematics must be solved. In this view the robot consists of an open spatial kinematic chain. Figure 2 shows the simulating model of a robot with six revolute joints. Using the homogeneous transformation matrices and the Denavit-Hartenberg parameters given in the table of Fig. 2, the motion equations of the manipulator are developed. These equations can be used for the direct or inverse kinematics of the manipulator. For a prescribed position and orientation of the endeffector, the problem of the inverse kinematics of the manipulator is solved analytically. The manipulator in
 Fig. 2 has a closed form solution, because the axes 4, 5 and 6 intersect [7]. In this way all eight solutions of the

Fig. 2 Robot with six degrees of freedom and its Denavit-
Hartenberg parameters sets of the joint variables and the corresponding configurations of the robot are determined [8]. From the sets of the joint variables the one that guarantees collision avoidance, joint limits and avoidance of singular configurations is chosen. The CAD package used has a high potential for collision detection. The joint angles are calculated for every point along the end-effector path using the Fortran programming language.
 4 Motion planner From the workpiece CAD model, the programmer generates a list of the initial and final points of each movement and the workpiece features to be processed as position, material, width, depth of the process, etc. The motion planner, based on the robot and workpiece CAD model, is divided in gross and fine motion planning. The gross motion planner deals with the planning of the approach and departure motions of the end-effector to and from the process operations. The generation of a collision-free path is realized with a ‘‘hypothesize and test’’ approach [9]. The approach utilizes heuristic rules to provide an efficient solution. For a candidate path from the start to the goal end-effector pose, the user can define the number of points, and using a linear or spline interpolation the intermediate points are calculated. At each location, the inverse kinematics is solved, and considering joint limits the collision avoidance is checked. If a collision is found, a new candidate path is proposed by examining the obstacles involved in the collision. The procedure continues until a collision-free path is found. An example of a collision-free path generated by the gross motion planner is shown in Fig. 3. The fine motion planner plans the operation path from the initial to the final point of each process. During the process the robot must hold the tool at the correct orientation, at the correct distance and move at a constant velocity. Taking into account the tool holder orientation, the orientation of the end-effector relative to the base frame of the robot is determined. Due to the fact that sometimes such orientations lead to a collision of the end-effector with the workpiece, the user can modify the end-effector orientation angles until the collision is avoided. A linear interpolation is used for trajectory planning. The obtained trajectory is saved to file and the graphical simulator displays the sequence of robot motions for verification before the actual process. 5 NC-code generation To generate the NC code, the robot motion program is completed with commands regarding the process (pulse velocity, spin velocity, coolant flow, etc for manufacturing processes and arc current, arc voltage, welding speed, feed wire, etc for welding processes), taking into account the technological data of the process (workpiece
Fig. 3 Path optimising for
 obstacles avoidance

 and electrode material, process position, etc) and the interpolation facilities of the robot controller. The program can then be downloaded to the robot controller. The structure of the NC-code generating system for manufacturing processes is illustrated in Fig. 4. The path planning part, developed in the Visual Basic environment, simulates manipulator movement working parallel with the inverse kinematics problem solution, which is solved in Fortran and parallel with the CAD models constructed in SolidWorks design software. While taking into account the process parameters, path planning simulation-software creates the NC code for manufacturing automatically. Simulation software is developed so that the method of automatic trajectories programming mentioned above is easy for the user [10]. All the movements set on the platform of this software are interactive with the Solid-

Fig. 4 Automated robotic welding system structure
 Works platform to ensure user supervision of trajectory programming. The movement control of the robot is achieved through the end-effector position and orientation definition. In order to improve the accuracy of the process simulation, a procedure which interpolates points along the selected trajectory is carried out. This linear interpolation refers not only to the coordinates but also to the orientation of the end-effector. The trajectory is saved to file, in order to have easy access to each trajectory. The developed software includes three forms. The main form called ‘‘Points Base’’ is presented in Fig. 5 and contains the points along the trajectory. The endeffector trajectory can be produced in four ways: – By choosing a pre-designed path – By choosing a designed path of lines and splines in
 SolidWorks – By setting points, which belong to the trajectory of the end-effector, in the 3D workspace of the robot – By choosing vertices or edges (lines, arcs, splines, parabolas and ellipses) of the part to be processed The path points are presented in a table and the parameters of the selected point can be changed. For each point, there is the ability to set the coordinates (X,Y,Z) and the orientation angles (A,B,C) of the endeffector to approach the target point with the right orientation, according to the process techniques. The joint angles values are presented for each point, and there is the ability to see the overstepping of the joint angles limits and the collision of any part of the robot with an obstacle in the workspace. The ‘‘welding’’ and ‘‘OSAP’’ boxes can be marked to set the starting point of a process (welding in the present example) and an ‘‘Oscillation Auxiliary Point’’ respectively. There is also the opportunity to interpolate points among the final trajectory points, to simulate the entire trajectory
 Fig. 5 Robot control program

Fig. 6 Graphical simulation of
robot and its workcell

Fig. 7 Four points of the
welding process path

 and check the point’s parameters in the table of points.
 The second form called ‘‘Read Points’’ is the channel connecting the user with the environment of SolidWorks software. All the selections of the workpiece (points, curves, surfaces, etc) in the SolidWorks space can be read, identified and checked for sequences among them. An adjustable number of interpolated points are
 Table 1 Welding process parameters

 calculated for each selection. All these points (selected and interpolated) can be added to the points of the final trajectory.
 The third form called ‘‘Navigation’’ is used for the control of the end-effector’s coordinates and orientation, without changing any point of the trajectory. Hypothesizing a position, it checks the overstepping of the joint angles limits and the collision of any part of the robot with an obstacle in the workspace. Passing these tests, the programmed point could be added in the points base trajectory. NC code for the robot control is created automatically, working with the three forms on parallel, hypothesizing and testing points, checking the joint angles limits and the collision-free movement, simulating  the movement and reaching the desired result of trajectory.
 6 Application The above methodology is applied in a six degrees of freedom manipulator used for the welding of office furniture frames [11]. An example of the graphical simulation of the robot and an office chair base adjusted on its worktable is presented in Fig. 6. The end-effector path is shown in the figure also (Detail A). Four linear segments 3–4, 7–8, 11–12 and 15–16 for welding and three intermediate spline curves 4–5–6–7, 8–9–10–11 and 12–13–14–15 for movement with collision avoidance compose the path. The sequence of the welding lines is picked in order to reduce the welding process duration. Another application of the proposed methodology is presented in the following. The graphical simulation of the robot and workpieces to be welded is shown in Fig. 7. The programmed points of the entire path are inserted in point’s table in Fig. 5. The inverse kinematics problem is solved for all points along the trajectory. Four main points of the welding process are illustrated in Fig. 6 in the SolidWorks environment. Welding parameters used in this application like current intensity, arc voltage, wire feed, etc presented in Table 1, are selected so as to satisfy all welding technology conditions. These parameters are determined in the
 Fig. 8 NC code for welding

Fig. 9 Application in robot real
workspace
 procedure ‘‘WELDON’’ called by the main program of NC code. The ‘‘WELDON’’ procedure uses linear interpolation movement (CP_Line) and constant velocity. The NC code presented in Fig. 8 is created using the programmed points of the entire path. Applying it to the robot controller, it executes this code, moves the endeffector to the specified positions and generates the seam as presented in Fig. 9.
 7 Conclusions
 By means of the developed procedure the NC code for processes can be generated, taking into account the technological data of the process and the interpolation facilities of the robot controller. The proposed system can be further used for optimisation of the process planning of workpieces by reducing the cycle duration of the workcell.
 The off-line programming application using a CAD/ CAM system significantly reduces the robot downtime and the production process becomes more efficient. Future development of the robot’s dynamic model is required in order to improve the path planning of the end-effector and reduce limits to the control of movements such as speed, acceleration and actuator torque. Acknowledgements Special thanks are expressed to Dromeas industry for the opportunity to perform experiments on their robot. References
 1. Megahed SM (1993) Principles of robot modeling and simulation. Wiley, New York
 2. Mitsi S, Bouzakis K-D, Mansour G (1995) Optimization of robot links motion in inverse kinematics solution considering collision avoidance and joint limits. J Mech Mach Theory 30:653–663
3. Mitsi S, Bouzakis K-D, Tsiafis I, Mansour G (1997) Dynamic behavior simulation of a manipulator with five degree of freedom considering joints friction. J Balkan Tribological Assoc 3:51–60
4. Mitsi S, Bouzakis K-D, Mansour G (2000) Automatic NC code generation for welding by means of an industrial robot. In: TCMM, Technical Publishing House, Bucharest, 40:311–316
5. SolidWorks (2001) User’s guide. SolidWorks Corporation
6. Denavit J, Hartenberg RS (1955) A kinematic notation for lower pair mechanisms based on matrices. ASME J Appl Mech 22:215–221
7. Craig JJ (1986) Introduction to robotics, mechanics and control. Addison-Wesley, Reading
8. Mitsi S, Bouzakis K-D, Mansour G (1999) Automatic NC code generation for welding by means of an industrial robot considering workcell. In: Proc 5th EEDM Conf Mach Tools Manuf Process, Thessaloniki, pp 367–375
9. McKerrow PJ (1993) Introduction to robotics. Addison-Wesley, Wokingham
10. Sagris D (2001) Software development for off-line programming of industrial robot RV6. Dissertation, EEDM, Aristoteles University of Thessaloniki
11. Reis Robot Manual. Reis GmbH and Co Maschinenfabrik
Fig. 9 Application in robot real workspace 267

A New Electrothermal Microactuator with Z-shaped Beams

Abstract
A new class of thermal microactuators, Z-shaped thermal
actuator, is introduced in comparison with the wellestablished
V-shaped thermal actuator. Though they share
many features in common, Z-shaped thermal actuator offers
several advantages: compatibility with anisotropic etching,
smaller feature size, larger displacement, and larger variety
of stiffness and output force. While the Z-shaped thermal
actuator was modeled analytically and verified by
multiphysics finite element analysis (FEA), the beam width
and length of the central beam were identified as the major
design parameters in tuning the device displacement,
stiffness, stability and output force. Experimental
measurements were taken on three arrays of Z-shaped
thermal actuator with variable parameters. Results agreed
well with the finite element analysis. The development of Zshaped
thermal actuator is applicable in simultaneous
sensing and actuating applications. During the quasi-static
test of individual Z-shaped thermal actuator, the average
temperature in the device structure was estimated based on
electric resistivity at each actuation voltage.
Nomenclature
fij Compliance coefficients
Fx Internal (reaction) axial force
P Virtual unit force
M Internal (reaction) moment
α Thermal expansion coefficient
U Deflection at the tip
L Length of the long arm beam
l Length of the central beam
w Beam width
h Beam thickness
E Young’s modulus of silicon
I Beam moment of inertia (=w3h/12)
k Stiffness of a Z-shaped beam
kp Thermal conductivity of silicon
V Applied voltage across a Z-shaped beam
ρ Resistivity of silicon
Introduction
Electrostatic actuator [1] and electrothermal actuator [2-4]
are the two major in-plane actuators in microelectromechnical
systems (MEMS). Electrostatic actuators,
also known as comb drive actuators, have an output force
typically on the order of 1 μN when actuation voltage is more
than 30 V [5], while thermal actuators can easily generate a
force of 1 mN at an actuation voltage around 5-10 V [6].
Since comb drive actuators require high actuation voltage (>
30 V), which is not compatible with microelectronic power,
and large area of comb structures, thermal actuators have
attracted significant attentions in recent years, as they are
demonstrated as a compact, stable and high-force actuation
apparatus [4].
Thermal expansion is the operating principle of all kinds of
thermal actuators. As for in-plane thermal actuator, Ushaped
and V-shaped thermal actuators have been explored
and implemented for a few years. Former, also known as
thermal actuator [8-10], employs asymmetrical thermal
beams with different cross-sectional areas (cold arm and hot
arm). The locus of motion of single U-shaped thermal
actuator is an arc, which a pair of U-shaped thermal actuator
could translate linear motion. The latter, also known as bentbeam
thermal actuator [6,7,11-13], utilizes thermal
expansion of symmetric, slanted beams to generate
rectilinear displacement of the central shuttle. The V-shaped
thermal actuators, especially, have been implemented in
many applications including linear and rotary microengines
[6], nanoscale material testing systems [11,12], and
nanopositioners [14].
The advantages of V-shaped thermal actuators are large
force (on the order of mN), huge stiffness, low actuation
voltage and small features size. However, the slanted beams
in V-shaped actuator usually are not oriented along a
crystalline orientation, so that anisotropic etching cannot be
used for fabricating these structures, which largely limits the
available fabrication methods as well as materials. Also, the
slanted beams pose challenges for fabricating small
features, which deteriorates as the beam width gets close to
the resolution of photolithography (typically ~ 2 μm). Though
large stiffness makes the V-shaped thermal actuator a
perfect displacement controlled actuator, it cannot be used
as a simultaneous sensor and actuator as the electrostatic
devices. Thus an additional load sensor is always required
for such applications as nanomechanical testing [12] and
nanomanufacturing [15].
The Z-shaped thermal actuator introduced in this paper is a
new class of thermal actuators with Z-shaped beams for inplane
motion. It offers a large range of stiffness and output
force that is complementary to the comb drives and VProceedings
of the SEM Annual Conference
June 7-10, 2010 Indianapolis, Indiana USA
©2010 Society for Experimental Mechanics Inc.
T. Proulx (ed.), MEMS and Nanotechnology, Volume 2, Conference Proceedings of the Society for Experimental Mechanics Series 2,
shaped actuators. Similar to V-shaped actuators, the
structure and operating principle of the Z-shaped actuators is
first described and modeled analytically. Finite element
multiphysics simulations were then performed to verify the
experimental results that were measured in vacuum. The
devices were fabricated using the SOI-MUMPs (silicon-oninsulator
multi-user MEMS process) (MEMSCAP, Durham,
NC) with 10 μm thick silicon as the structural layer.
Concept and Modeling
A. Structure
Schematic of the Z-shaped and V-shaped thermal actuator is
shown in Fig. 1 for comparison. It is seen that the basic unit
of a Z-shaped actuator is a pair of Z- shaped beams and a
shuttle in the middle. Despite of principle similarity, Z-shaped
actuators rely on bending of the symmetric Z-shaped beams
induced by thermal expansion to achieve rectilinear
displacement of the central shuttle. Due to Joule heating, the
device is heated up when a current is passed through. The
temperature rise leads to thermal expansion of all the beams
especially the long beams; the long beams cannot expand
straight due to symmetry constraint of the structure, rather
they bend to accommodate the length expansion. As a result
the shuttle is pushed forward. Figure 1(c) shows a scanning
electron microscopy (SEM) image of a Z-shaped thermal
actuator with two pairs of Z-shaped beams.
(a) (b)
(c)

Fig.1. Schematics of (a) a Z-shaped thermal actuator and (b)
a V-shaped thermal actuator before and after motion. Drawn
not to scale. (c) SEM image of the Z-shaped thermal
actuator. The black area is an etched hole underneath. I is
the current passing through thermal beams, while DC is the
power source.
B. Mathematical Modeling
Following assumptions have been made for analytical
derivation: central shuttle is rigid and its thermal expansion is
neglected; thermal expansion of short beam (with length l in
Fig.1) is neglected; small strains and displacements are
considered; average temperature rise in a Z-shaped beam is
given [11].
Mechanical response of the structure in Fig.1 can be
equivalently modeled by considering half of the structure
without the shuttle, as shown in Fig. 2. In energy method,
three reaction forces, axial force Fx, virtual force P and
moment M, can be obtained by solving the following set of
equations [8]
11 12 13
21 22 23
31 32 33
2
0
x f f f F TL
f f f P U
f f f M
⎡ ⎤ ⎡ ⎤ ⎡ αΔ ⎤
⎢ ⎥ ⎢ ⎥ = ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥
⎢⎣ ⎥⎦ ⎢⎣ ⎥⎦ ⎢⎣ ⎥⎦
(1)
where
3 2
11
2
3
f L l Ll
EA EI EI
= + +
2 2
12
3
2 2
f L l Ll
EI EI
= +
2
13 2
f l Ll
EI EI
= − −
2 2
21
3
2 2
f Ll L l
EI EI
= +
2 3
22
8
3
f l L l L
EA EI EI
= + +
2
23
f 2L Ll
EI EI
= − −
2
31 2
f l Ll
EI EI
= − −
2
32
f 2L Ll
EI EI
= − − 33
f 2L l
EI EI
= +
Set virtual force P equal to zero, deflection in the y direction
is derived as
3
2
2
12
6
3
U TL
w l L l
l
αΔ
=
⎛ ⎞
+ ⎜ + ⎟
⎝ ⎠
(2)
The stiffness of a Z-shaped beam is given by
( )
( )
3 3 2 2
3 3 2 4 2 4 4 4 2 2 3
2 6
8 16 2 12 6
Ew h l Lw Ll
k
Ll wl wL wLl Ll wLl
+ +
=
+ + + + +
(3)
The internal force is given by
3 2 2
24
2 x
F TEIL
l Ll Lw
αΔ
=
+ +
(4)
The output force f is given by the product of displacement
and stiffness, f=kU. The stiffness of a Z-shaped actuator with
a pair of beams is 2k, thus the output force is 2f accordingly.
Fig.2. Free-body diagram of a single Z-shaped beam.
There are three possible modes of heat transfer: conduction,
convection, and radiation. Convection and radiation are
generally neglected in MEMS structures; conduction through
the air layer between the device and the substrate is a major
heat transfer mechanism for surface micromachined
devices, since the air layer is typically very thin (on the order
of a few μm) [8,10-12]. But in SOI devices, the only heat
transfer mechanism is heat conduction to the anchors across
the beams, since the underneath silicon substrate is totally
etched as shown in Fig.1(c).
The performance of Z-shape thermal actuator is geometry
dependent. The peak displacement of one single Z-shaped
beam at a given temperature can be increased by simply
increasing the length of the long arm (L). The device
thickness (h) is not related to the displacement, but affects
the stiffness and loading force in direct proportion. In our
design, all the long beams (L) length was 88 μm and
structural thickness is 10 μm as specified in the SOIMUMPs.
Widths of all the long beams and central beams are
the same for simplicity. The central beam length (l) and
beam width (w) are variables for parametric study.

C. Multiphysics FEA Simulation
Thermomechanical finite element analysis (FEA) was
performed to verify the mathematical modeling. A 2D multifield
plane element PLANE223 was used in the FEA
(ANSYS v11.0) simulation, which involves electric, thermal
and mechanical fields. A constant temperature increase of
400 K was applied to the entire Z-shaped beam as shown in
Fig. 2. Note that, for verification of the mathematical model,
all thermal properties of single crystalline silicon (SCS) are
constants at room temperature; for comparison with the
experimental results, however, all thermal properties of SCS
are temperature dependent as listed in Table 1 in the end of
the paper.
D. Comparison between Z-shape and V-shape
A systematic comparison between the Z-shaped thermal
actuators and the V-shaped thermal actuators was carried
out to further illustrate their characteristics, as shown in Fig.
3. Fig. 3(a)

shows an excellent agreement for displacements
between the FEA and analytical solution, which confirms the
validity of the analytical model. Figures 3(a) and (b) together
show that, for both actuators, the smaller the beam width,
the larger the displacement. However, fabricating a small
beam width (especially ≤2 mm) is more challenging for
inclined beams (V-shape). In this regard, the Z-shaped
actuators can achieve relatively larger displacement.
Fig. 3(c) and (d) show that the stiffness of the Z-shaped
actuators is about one order of magnitude smaller than that
of the V-shaped actuators, when the beam width ranges
from 2 to 8 μm. The stiffness of V-shaped actuators does not
change with the beam width; by contrast, that of Z-shaped
scales approximately with square of beam width, because Vshaped
actuators are mainly based on beam extension while
Z-shaped actuators are mainly on beam bending. Since the
stiffness of bending beam is proportional to the cube of the
beam width, Z-shaped actuators possess a large stiffness
range for different beam width For some applications that
requires simultaneous sensing and actuating functions, Zshaped
thermal actuator alone could also be consider as
senor at the same time, while V-shaped thermal actuator
should combine with a certain type of sensor.
Fig. 3(e) and (f) show that both actuators share the same
column effective length factor, which means they have the
same critical buckling force and possess similar level of
stability. The output force is in the range of 30 to 490 μN,
calculated by f=kU. Apparently, the output force of the Zshaped
actuators is smaller than that of the V-shaped
thermal actuators [6,11].

The Z-shaped thermal actuators were fabricated by the SOIMUMPs
process in run 27. All the Z-shaped thermal devices
in our design have the same anchor-anchor distance
(412μm); central beam length and width are two design
parameters. Three arrays of Z-shaped thermal actuators with
different beam widths (2 μm, 4 μm and 8 μm) were
fabricated for parametric study and device optimization.
Within each array, the length of the central beam varies from
1 to 20 μm. One such array of the Z-shaped thermal
actuators is shown in Fig.4. The displacement was
measured using an optical microscope with the edge
detection method [16]. Resolution is calibrated as 81.5
nm/pixel. Fig.5 shows the displacement of the Z-shaped
thermal actuators of two arrays. The array with 2 μm and 8
μm beam width were actuated under 2 V and 3 V,
respectively. Multiphysics FEA results for both arrays with
the corresponding applied voltages are also plotted in the
Figure. The displacement results agreed quite well between
experiments and FEA, which are also in line with the
analytical modeling as shown in Figure 3(a).
Fig.4 An array of Z-shaped thermal actuator with the same
beam width of 4 mm.
00 2 4 6 8 10 12 14 16 18 20
100
200
300
400
500
600
700
800
Central beam length (μm)
Displacement (nm)
Width 2μm -- FEA
Width 2μm -- Experiment
Width 8μm -- FEA
Width 8μm -- Experiment
Fig.5 Measured and FEA simulated displacements of Zshaped
thermal actuator arrays with two different beam
widths (2 mm and 8 mm). The actuation voltage on the array
with 2 μm beam width is 2 V and that on the array with 8 mm
beam width is 3 V.
The following tests were carried out inside an SEM (JEOL
6400F) on a particular Z-shaped thermal actuator with 4μm
beam width and 20 μm central beam length. Displacement
was measured with the actuation voltage from 0 to 6 V. The
measured displacement is plotted with respect to the input
current, as shown in Fig. 6(a). The stiffness of the structure
was calculated to be 273.4 N/m based on the measured
dimensions. Figure 6(b) shows the dependence of electric
resistance of the structure on the input current. Assuming
the linear dependency of resistivity on temperature as listed
in Table 1, the average temperature in the device was
estimated [8,9], and also plotted in Fig.6(b).
0 2 4 6 8 10 12
0
200
400
600
800
1000
1200
Measured Displacement (nm)
Measured current (mA)
0
50
100
150
200
250
300
Estimated force (μN)
(a)
0 2 4 6 8 10 12
150
200
250
300
Measured resistance (Ω)
Measured crrent (mA)
400
600
Estimated temperature (K)
(b)
Fig.6 (a) Measured displacement and corresponding
(calculated) force as functions of input current. (b) Measured
resistance and corresponding (estimated) average
temperature change as functions of input current.
Conclusions
A new electrothermal actuator with symmetric Z-shaped
beams was developed in this paper. Compared to V-shaped
one, it offers some unique advantages such as compatibility
with anisotropic etching, larger displacement, and smaller
stiffness and output force. The variable stiffness and force of
Z-shaped actuators fill the gap between those of the comb
drives and V-shaped thermal actuators. Additionally a Zshaped
actuator with smaller stiffness could be used as a
simultaneous load sensor. Among all of the design
parameters, the length of the central beam and beam width
were identified as the major ones in tuning the device
features. The quasi-static experimental measurements of
three arrays of Z-shaped thermal actuators agreed well with
the FEA predictions.
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Table 1. Silicon properties used in simulations of Z-shaped thermal actuators
Material properties Unit Value Reference
Young’s modulus GPa 160 [17]
Poisson’s ratio - 0.28 [17]
Thermal conductivity (constant) Wm-1K-1 146 [4]
Thermal conductivity (temperature dependent) Wm-1K-1 kt(T)=210658T-1.2747 [17]
Resistivity (constant) Ωm 5.1×10-5 Measured
Resistivity (temperature dependent) Ωm ρ(T)=5.1×10-5[1+3×10-3(T-273)] [17]
Thermal expansion coefficient (constant) K-1 2.5×10-6 [4]
Thermal expansion coefficient (temperature dependent) K-1 α(T)=-4×10-12T2+8×10-9T+4×10-7 [4]
213