PLATFORM USING LAB VIEW

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The Modeling and Simulation of the Stewart’s Platform Using Lab VIEW



The Romanian Review Precision Mech
anics, Optics & Mec
hatronics,
20
12, No. 42

78

THE MODELING AND SIMULATION OF THE STEWART’S
PLATFORM USING LAB VIEW


Nina Gorie, Valer Dolga

“Politehnica” University of Timisoara,

Bd.Mihai Viteazu 1, Timisoara, Romania, cod 300222

E
-
mail: nina_gorie@yahoo.com

Abstract
:

The study of the architecture,

the geometrical structures and the mechanical linkages of a
parallel manipulator allows knowing its physical limits. This paper discusses the current state of the
Stewart’s Platform that is considered as a parallel ro
bot with six degrees of freedom.
Due o
f the
advantages and drawbacks of the parallel manipulators make it useful for specific applications. The
simulation
-
control software is not intended simply to operate the platform as quickly as possible. This is a
teaching program in automated mechanics.
At each step of calculating a “movement”, the elements
necessary to control position are worked out, and also various mechanical calculations are performed.

Lab
VIEW was designed for making available the facilities of the graphical interfaces with the user

that are
developed by the modern operating systems and is dedicated to data acquisition , analyzing processing
and displaying information. The objective of this application made in LabVIEW is to analyze the
movements of Stewart’s platform and help people
with this application to correct the disabilities of upper
and lower limb
.
.

Keywords
:

LabVIEW, the Stewart’s platform, parallel manipulator, inverse kinematics, forward
kinematics
.
1.
Introduction


The
parallel robots can be defined as mechanisms
with clos
ed kinematic chains composed of a terminal
body with n degrees of freedom located on a mobile
platform that is connected to a fixed platform by n
independent kinematic chains: [1].

The use of parallel robots has the following
advantages:
a)

a very good rep
ort of manipulated
table/table robot, thanks to its structure each engine
supporting 1/n of manipulated table, where n is the
number of independent kinematic chains,
b)

the small
table in motion ensure a good dynamic behavior that
ensure high speeds and ac
celerations (maximum 6m/s
respectively 22 g),
c)

the simple geometric model
provide a easy driving,
d)

the great positional accuracy
(0.010
-
0.005). The disadvantages are: the reduced
workload comparative with the parallel robots and the
use of upper joints

with more technological problems:
[1].

In further
we will present a small historical about
development of parallel robots in chronological order.
The first application of parallel robots was the testing
machine for robots of V.E.Gough in 1954. He used six

linear actuators mounted in three cardan both in the
fixed platform and mobile platform. V.E.Gough build a
platform for a flight simulator which was materialized
later by NASA. The first author who made the
kinematic analysis of a closed kinematic chain
m
echanism was D.Stewart, the platform of Stewart’s is
a mechanism with six degrees of freedom, with
hydraulically actuators that directs a triangular platform.
D.Stewart made a study of the workspace called “the
limitations amplitudes” solving for the first

time the
inverse problem of the mechanism, based on parallel
mechanisms built a flight simulator, a orientation
mechanism of a radar antenna, an offshore drilling a
device for machine tools: [1]. W.Koevermans [KOE 75]
made a flight simulator with four deg
rees of freedom. It
consists of four arms which two are linked by a double
patella on mobile plate of triangular shape, a passive
arm ensure the constraint of the mobile plateau ensuring
four degrees of freedom in relation to the frame.
McCallion [MCC 79]
made in the University of
Canterbury (New Zealand) a robot type KPS used in
assembly stations, the linear actuators are made of
mechanisms screw nut whose action is given by the
engine step by step through cardan joints. By varying
the arm length under the

command of a computer the
mobile plate execute complex movements: [1].

K.Hunt [HUN 83] proposed a model with three identical
arms articulated at the base by the pivotal connections
120
˚ and the mobile plate through spherical joints, this
model was studied by other researchers as K.M.LEE
and Roth, B [LEE 93]. Inoue [INO 85] from University
of Tokyo developed an active hand in the pantograph
mechanism that positions the mobile platform ar
e driven
by DC motors through planetary gear. F.Sternheim built
the robot DELTA with three respectively four degrees
of freedom, R.Clavel [CLA 91] was studied this model
The Modeling and Simulation of the Stewart’s Platform Using Lab VIEW



The Romanian Review Precision Mech
anics, Optics & Mec
hatronics,
20
12, No. 42

79

in his PhD thesis. The three engines set at 120˚ on a
fixed platform suspended on a su
pport act the three
arms.

The arms that leaves the mobile platform is tied to
rotations mechanisms parallelogram (with four rotule)
that transmit moments to the mobile plate through
torque moments, the workspace has an amplitude of 200
mm at a manipulated
table of 30 g: [1].
Compared with
serial manipulators, parallel manipulators have a high
rigidity in its structure and therefore have a high load
-
carrying capacity, moreover since there is no
accumulation of errors on the mobile platform is
possible to obt
ain a better accuracy. In exchange for
these advantages, parallel manipulators have a very
limited workspace. Despite their poor dexterity, parallel
manipulators have interesting applications such as flight
and vehicle simulators, high
-
precision machining
centers, mining machines, and so on
: [2]
.

Similarly
serial robots, parallel robots can adopt configurations in
which joint forces cannot balance the forces on the
mobile platform. It is important to determine these
settings in whose precinct the joint forc
es tend to
infinity and the robot may collapse. A complete
description and characterization of the singularities
would be completely parameterized hyper surfaces in
the workspace of the robot. This analysis would identify
regions of the workspace where the

singularities restrict
the maneuverability of the robot
: [2]
.

The paper is organized as follow: in the first section we
have a short introduction about parallel robots and a
short history, in the second section we have the
architecture of the Stewart’s pl
atform and it presents the
geometrical parameters. Then the third section presents
the problematic of the parallel manipulators between the
use of the inverse and forward model. Finally the last
part is dedicated to the process control of the Stewart’s
pla
tform using programming tools as the relevant
software to the Stewart’s platform and Lab VIEW 8.2.


2.
Geometrical parametrisation of the Stewart’s
platform


The Stewart’s platform is a parallel structure which
comprises a fixed platform and a mobile platf
orm
connected by six axes identical telescopic spherical
joints at the ends. The platform top is guided in space
around by varying lengths of six axis hexapod limit the
building permits. The construction with several closed
kinematic chains presents a stru
cture much better
mechanical strength compared with serial structures on
the other, as all actuators can be placed on the fixed
platform is possible to obtain advantages of mechanism
with acceleration and high speed such as can be seen in
the figure.1: [3]
.

Type of parallel structure
meets the advantages of
high working speeds, precision and high rigidity that
required the adaptation of this structure in different
variants in the design and construction of parallel
robots. The research in the field of paral
lel robots fall
among the top research worldwide, theoretical and
practical contributions to research parallel robots took
her over the years many researchers around the world:
[3].


Figure
1
: The Stewart’s platform


The kinematic

structure allows the parallel robots to
be sued by actuators positioned on the robot, in contrast
the serial robots don’t contain closed kinematic chains
and are typically operate in each pair kinematic chain.
In the structure of parallel robots the weigh
t of the
actuators isn’t supported by manipulator arms this
allowing the parallel robot arms to get much easy than
those of a serial robot: [3]. In the figure 2 we can see the
components of the Stewart’s platform which are: the
mobile platform, the fixed p
latform, six actuators and
twelve cylindrical joints.


Figure
2
: The Stewart’s platform with its components


We can see in the figure 3 the parameters of the mobile
platform and the fixed platform:



Figure
3
: Frame of reference of the upper platform: [4]

Lower base: this is related to the fixed frame of
reference
(O
F
;

x
F

,

y
F

,

z
F
).

Upper platform: this is related to the mobile frame of
reference
(O
M
;

x
M
,

y
M

,

z
M
)
.

The Modeling and Simulation of the Stewart’s Platform Using Lab VIEW



The Romanian Review Precision Mech
anics, Optics & Mec
hatronics,
20
12, No. 42

80

We can observe from the figure 3 that AiBi is gi
ven by
length Li called actuator length.

The parametrisation of the lower base is: [4].

The bars are anchored at the points Ai arranged around
a circle of radius
r
F
.

The points Ai are positioned in pairs every 120°.

The two points in each pair are separate
d by the angle
2
α

The parametrisation of the upper platform is:

The bars are anchored at the points Bi arranged around a
circle of radius
r
M
;

The points Bi are arranged in pairs every 120°.

The two points in each pair are separated by the angle
2
β

The initial position of

the platform is characterised by
the point O
M

and O'
M

with the upper platform parallel
to the lower base

as in the figure 4.
The upper platform
has six

degrees of freedom with respect to the lower
base
: three degrees of freedom in translation
characterize
d by the position of the point
O'
M

which is
the origin of the moving frame
R
M

in the fixed frame
R
F.

In other words by the following vector with respect to
the reference position we have: [4].

O
'
O
=
x

x

+
y

y

+
z

z
M
M
M
F
M
F
M

F





(
1
)

But the upper platform has thre
e degrees of freedom in
rotation characterized by the orientation of the frame
R
M

with respect to the fixed frame
R
F
.

This orientation
is given by three angles as:
θ
1,
θ
2 and
θ
3, in the figure 4
is represented the parametrisation of the lower base and
the
platform with reference position: [4].



Figure
4
: The parametrisation of the lower base and the
platform: reference position: [4]


3.
Inverse and forward model


We must distinguish two aspects: the inverse
kinematics and the forw
ard kinematics. The inverse
kinematics problem, a difficult problem for robots
series, is easy for parallels robots. However, the forward
kinematics is more complicated.

A.

Inverse model

The inverse problem is the following: knowing the
position of the end co
mponent (in this case the upper
platform), to determine the values of the articulation
variables (in this case the length of the legs).

The
question here is therefore to calculate the length L
i

of
each leg n°i, using the 6 position parameters of the
upper
platform with respect to the lower base.

The
movement of the Stewart’s platform is described using
the data from parametric equations of the platform’s
angular and linear positions. We have u which is
parameter and [ui, uf] its area of definition, it is
im
portant not see any physical meaning whatsoever in
this parameter. Then we have six scalar functions that
describe: the three degrees of freedom in translation
characterized by the position of the point
O
M
which is
the origin of the mobile frame

in the fixed frame
,
with regard to the reference position by the vector: [5].


(2)

and the three degrees of freedom in rotation
characterized by the orientation of the frame

with
respect to the fixed frame
. Th
e three angle θ1(u),
θ2(u) and θ3(u) described previously fix this orientation.
From a numerical standpoint the number of points N in
the calculation remain to be defined. The interval [ui,
uf] is then broken down into N
-
1 equal intervals, N
calculated pos
itions are then generated corresponding to

such that we obtain: [5].


(3)

The results obtained with the help of inverse model are:
determination of Qi using the inverse model, the lengths
of actuators in function of the position and we can
d
escribe a trajectory which looks like in the figure
below:


Figure
5
: Determination of Qi using inverse model

The Modeling and Simulation of the Stewart’s Platform Using Lab VIEW



The Romanian Review Precision Mech
anics, Optics & Mec
hatronics,
20
12, No. 42

81


Figure
6
: The lengths of actuators in function

of the position



Figure
7
: Described trajectory


B.

The forward model


The direct problem is as follows: knowing the
different values of the articulation variables (in this case
the extension of each leg
,
the question is to define the
position of the end component (in this ca
se the upper
platform), using the 6 parameters
(

1
,

2
,

3
, x
M
, y
M
,
z
M
)
. The movement is described using the data from the
parametric equations of the lengths Li of the legs
supporting the platform. We consider u be this
parameter and [ui, uf] be its area
of definition, then we
have six scalar functions that define the functions
associated with the changes in length of the legs. From a
numerical standpoint the number of points N in the
calculation remain to be defined. The interval [ui, uf] is
then broken d
own in N
-
1 equal intervals, N calculated
positions are then generated corresponding to

such
that we obtain
: [5].


(4)

One can therefore consider reducing this problem to the
following: knowing the lengths L
i

of the 6 legs, to
determine the v
alues of the 6 parameters (

1

,

2
,

3
,
x
M
, y
M
, z
M

)
.
Solving the inverse problem enabled us
to express the length L
i

of each leg as a function of the
variables (

1

,

2

,

3
, x
M

, y
M

, z
M
) . We must
therefore resolve a system of non
-
linear equations of t
he
type: f
i

(

1

,

2

,

3
, x
M

, y
M

, z
M

) = L
i.
. We can
consider the system: [5].












6
M
M
M

3
2
1

6
5
M
M
M

3
2
1

5
4
M
M
M

3
2
1

4
3

M
M
M

3
2
1

3
2
M
M
M

3
2
1
2
1
M
M
M

3
2
1
1
L

=

)

z

,

y

,

x
,

,


,

(
f
L

=

)

z

,

y

,

x
,

,


,

(
f
L

=

)

z

,

y

,

x
,

,


,

(
f
L

=
)
z

,

y

,

x
,

,


,

(
f
L

=

)

z

,

y

,

x
,

,


,

(

f
L

=

)

z

,

y

,

x
,

,


,

(

f



















(5)

In general such a system cannot be resolved
analytically, and only numerical methods can produce a
solution
. We can use the Newton
-
Raphson iterati
ve
method to solve the system and the results obtained with
the forward model looks like in the figure below and we
can observe that the described trajectory is very
different of trajectory obtained with inverse model: [5].



Figure
8
: Described trajectory of forward model


4.
The programming of the Stewart’s platform in
Lab VIEW 8.2


The platform is not operated in real time. If it is
wished to impart a movement to the platform, it is
necessary first of all
:
a)

t
o describe the mov
ement using
a definition in parametric coordinates using any
parameter u (geometrical calculations) or the t
ime t
(kinematic calculation), t
his formal parametric
definition is interpreted
,
b)

f
or calculatin
g appropriate
actuator lengths, t
hese actuator len
gths are stored in a
results file (.RES )
,
c)

t
o check the calculated actuator
lengths. In particular it is important to ensure that the
actuator travels and the movements of the ball joints are
not exceeded
,
d)

to read the file (.RES) and to transmit
the
length set points in sequence for controlling the
platform.

To realize the programming using LabVIEW
8.2, is necessary to do use of the functional chain
controlled

as in the figure 9.
To begin, the Stewart´s
Platform used, is commanded by a Controller Boar
d
(APCI
-
3120) inserted in one the PCI slot of the CPU.

This board allows the data exchange with the
peripheral. The board has up to 16 input channels and 8
output channels for processing analog signals and 4
input channels and 4 output channels for proces
sing
digital 24V signals

as in the figure 10.
The entrance
position setpoints is done from a computer with a
simulation/control Software (LabVIEW 8.2), interfaced
with the controller board. The interface board
analog/digital between the computer and the mo
tion
control electronics allows the both, in real time
:
transmit the calculated set points by the computer to
The Modeling and Simulation of the Stewart’s Platform Using Lab VIEW



The Romanian Review Precision Mech
anics, Optics & Mec
hatronics,
20
12, No. 42

82

each of the controlled axes

and

acquire the various
measures of position velocity and the couple to view
them
: [6].

A lab VIEW program is composed

by a front panel
for in/out data and block diagram for processing
information. Lab VIEW application is composed by six
sections: Recording, Modify, Play, Drawing, edit and
Wait. These sections are included in a Case structure
with six subdiagrams that can

be selected from the front
panel using Case selector, the subdiagram in which the
application is running at one time is lighted by an
indicator placed on the front panel. The obtaining data
can be saved in a file using the function Array to
Spreadsheet St
ring that converts a matrix into a string
format table. Data obtained in this way is written into
the text file using Write to Text File.vi subroutine. For
saving the obtained file the path and the file extension
must be specified, the file name generated
on the front
panel delimitation characters and the file extension are
appended into a character string: [6].



Figure
9
: The programming system in LabVIEW



Figure
10
: Controller Board APCI
-
3120


LabVIEW
8.2 is used as compiler to allow the
communication between the Board APCI
-
3120 and the
Stewart’s Platform EX800. With this graphic interface
is possible to write a numerical value to control the
length of the Platform’s actuators using the channels of
Anal
ogic I/O of the Board to apply a value of voltage

as
in the figure 11:


Figure
11
: Control of Stewart’s platform since
LabVIEW 8.2


The front panel in LabVIEW 8.2 displays the
information necessary to know if the controller board

is
working and obtain data to inspect the steps in the
process control. Another characteristic that include this
panel is the possibility to control the initial position of
the platform by changing the output voltage range ( 2
modes: Unipolar and Bipolar
)and then write an analog
output value which drives the actuator selected to travel
a certain distance

as in the figure 12 and table 1: [7].



Figure
12
: Control of the initial position

Table 1. The control of parameters

pb_Polar
ityArray Parameter

Voltage Range

WriteValueArray
Parameter

APCI3120_UNIPOLAR

0
-

10V with gain 1

0 to 8192

APCI3120_BIPOLAR

+/
-

10V with gain 1

0 to 13383


Then

there is a selector which allows to choice a whish movement and a selector to set the numb
er of times the
program will execute such

movement

as in the figure 13:


F
igure
13
: Control of movements

The Modeling and Simulation of the Stewart’s Platform Using Lab VIEW



The Romanian Review Precision Mech
anics, Optics & Mec
hatronics,
20
12, No. 42

83


Finally in the
figure 14

is presented the hierarchy of the
main program did in LabVIEW 8.2, which contains all
the API fo
nctions that manage the controller board
APCI3120 and the pre
-
programmed movements to
execute.















Figure
14
: Program Hierarchy



Figure
15
: The program developed in Lab VIEW



Figure
16
: The algorithm of program developed

in Lab VIEW


5.
Conclusion


The Forward Model is applied with this kind of
programming but with Lab VIEW is not possible to
determinate limits to respect the physical limitation of
the kinematics c
omponents of the Stewart’s Platform;
considering all the calculus necessaries to move the
upper platform in the wished position this is one
disadvantage for the study of the system.

This program
developed in Lab VIEW was made in order to purpose
motion in
the actuators of the Stewart’s platform and
help people with different disabilities to do
rehabilitation exercises.


6.
References


[1]

Ispas Virgil, “The robots for medical applications
.”
Publishing Dacia
.
1999;7
,
2
3.

[2]

Grigore Gogu, “Structural Synthesis of Parallel
Robots, Part 3: Topologies with Planar Motion of
the Moving Platform
.”
Springer Dordrecht
Heidelberg
.
2010;pp.685
.

[3]

Cristian Szep. , “Theoretical and experimental
research on mechatronic systems with applicati
ons
in robotics
.”
PhD Thesis
, Cal.

2011

[4]

Innocenti. , “Forward Kinematics in Polynomial
Form of the General Stewart’s Platform
.”
Proc.1998
ASME Design Engineering Technical Conference,
CD
-
ROM, paper DETC 98/MECH
-
5894

[5]

DELTALAB. , “Six
-
Axis Platform EX 800
.”

Technical Manual

[6]

Panoiu

and

colab
. , “Memorizing, Playing and
Editing Songs Using Lab VIEW Environment
.”
Science Direct
, Cal.

2012

[7]

Lab VIEW 8.2 User Manual, National instruments
.

Acknowledgment

This work was partially supported by the strategic
grant POSD
RU 107/1.5/S/77265, inside POSDRU
Romania 2007
-
2013 co
-
financed by the European
So
cial Fund


Investing in People.

Main Program

I_APCI3120_
WriteMoreAnalogValue
.vi

I_APCI3120_
GetHardwareInformation
.vi

I_APCI3120_
SetBoardInformation
.vi

I_APCI3120_
CheckAndGetPCISlotNumber
.vi

I_APCI3120_InitCompiler.vi