PARALLEL MOVING MECHANICAL SYSTEMS
Florian Ion Tiberiu Petrescu
Bucharest Polytechnic University, Romania
Email:
petrescuflorian@yahoo.com
Relly
Victoria Virgil Petrescu
Bucharest Polytechnic University, Romania
Email: petrescuvictoria@yahoo.com
Submission:
27/09/2013
Revision:
02/01/2014
Accept:
10/01/2014
ABSTRACT
Moving mechanical systems parallel structures are
solid, fast, and accurate. Between parallel systems it is to be noticed Stewart
platforms, as the oldest systems, fast, solid and precise. The work outlines a
few main elements of Stewart platforms. Begin with the geometry platform, kinematic
elements of it, and presented then and a few items of dynamics. Dynamic primary
element on it means the determination mechanism kinetic energy of the entire
Stewart platforms. It is then in a record tail cinematic mobile by a method dot
matrix of rotation. If a structural mottoelement consists of two moving elements
which translates relative, drive train and especially dynamic it is more convenient
to represent the mottoelement as a single moving components. We have thus seven
moving parts (the six motoelements or feet to which is added mobile platform 7)
and one fixed.
Keywords: mechatronics, robotics, a Stewart structure, parallel
moving mechanical systems, direct kinematics, inverse kinematics.
1.
INTRODUCTION
Moving mechanical structures are used
increasingly in almost all vital sectors of humanity (CAO et al., 2013). The
robots are able to process integrated circuits sizes micro and nano, on which
the man they can be seen even with electron microscopy (GARCIA et al., 2007).
Dyeing parts in toxic environments (TONG; GU; XIE, 2013), working in chemical
and radioactive environments, or at depths and pressures at the bottom of huge
oceans, or even cosmic space conquest and visiting exoplanets, are now
possible, and were turned into from the dream in reality, because mechanical
platforms sequential gearbox (PERUMAAL; JAWAHAR, 2013).
Robots
were developed and diversified, different aspects, but today, they start to be
directed on two major categories: systems serial and parallel systems (PADULA;
PERDEREAU, 2013). Parallel systems are more solid, but more difficult to designed
and handled, which serial systems were those which have developed the most. In
medical operations or radioactive environments is preferred mobile systems
parallel to their high accuracy positioning (REDDY; SHIHABUDHEEN; JACOB, 2012).
2.
THE STRUCTURE AND GEOMETRY OF A STEWARD
SYSTEM
Figure
1: The basic structure of a Stewart System
Figure 1
shows unit vectors route along items 1 and 2 from the bottom to mobile
platform. The coordinates (_{}, system 1) of vectors unit (_{}, system 2) belonging to
mottoitems 16 (variablelength) are given by the system (1), where l_{i} is the length (module)
of vectors _{} (system 3); with
i=16 (GARCIAMurillo, 2013).
_{} (1)
Where
these lengths of vectors unit are given by the system (2), and actual lengths
of the six mottoelements (variables) is expressed by the system (3).
_{} (3)
In Figure 2 is represented a motto
element (motto element 1) in a position snapshots. If a structural mottoelement
consists of two moving elements which translates relative, drive train and
especially dynamic it is more convenient to represent the mottoelement as a
single moving components. We have thus seven moving parts (the six motoelements
or feet to which is added mobile platform 7) and one fixed.

Figure
2: The basic structure of a motto element
For the stem 1, one writes relations
(47). The length l_{1}=AD is
variable (_{}); in the
same way and the distance a_{1} which defines the position of the
center point of gravity G_{1} (and the center of gravity G_{1}
is continuously changed, even if rod mass formed from virtually two kinematic
elements in relative movement of translation is virtually constant).
_{} (4)
_{} (5)
_{} (6)
_{} (7)
Kinetic energy of the mechanism (8)
is being written while taking account of the fact that the translation center
of gravity of each mottoelement already contains and the effect of different
rotations. Each motoelement (rod) will be studied as a single kinematic element
variablelength to constant mass and the position of the center of gravity
variable. Each mottoelement movement is one of spatial rotation (PETRESCU et
al., 2009; PETRESCU; PETRESCU, 20112013).
_{} (8)
After
the model system (7) is determined velocities of centers of the weight of the
six rods (see equations 9). Speeds _{} are known. The masses
are weighed and mass moment of inertia after axis N shall be calculated on the
basis of a approximate formula (10).
_{} (9)
_{} (10)
Where mp shall mean the mass mobile
tray 7 (obtained by weighing).
3. The Geometry and Cinematic of Mobile Tray 7, by a
Matrix Rotation Method
In Figure 3 is represented mobile
plate 7, consisting of an equilateral triangle DEF with the center S. Attach
this triangle a system of axs rectangular, mobile, jointly and severally liable
with the platform, x_{1}Sy_{1}z_{1} (LIU et al., 2013).
Known vector _{} coordinates and the
coordinates of the pixel S (in relation with the fixed mark considered
initially, linked to the fixed platform, be taken as the basis); we know so the
coordinates of rectangular axis Sz_{1}, in such a way that can be
calculated for a start axis coordinates Sx_{1} (relations 11), axis
determined by points S, D (known). The
coordinates are obtained vector Sx_{1}. This, along with the
coordinates of the pixel S causes axis Sx_{1} (11) (PETRESCU et al.,
2009; PETRESCU; PETRESCU, 20112013).
Figure 3: The
geometry and kinematics mobile platform 7
_{} (11)
By screwing axis _{} by (over) axis _{}, weve axis _{} (12). The coordinates are thus obtained mobile
system x_{1}Sy_{1}z_{1} (12).
_{} (12)
In Figure 4 is given a positive
rotation to axis _{} around the axis _{} (_{}), the angle _{}.
Figure 4.
Rotation around the axis N (within mobile platform)
Using relations (13) to be written
about the system matrix (14), which is determined directly (using rotation
matrix) absolute coordinates (in accordance with the mark fixed cartesian) of
a point D^{1} that is part of the plan of mobile top plate. This point
moves on the circle of radius R and center S in accordance with rotation
imposed by the rotation angle _{}. Final coordinates are explained in the form (15) (PETRESCU
et al., 2009; PETRESCU; PETRESCU, 20112013).
_{} (13)
_{} (14)
_{} (15)
Rotation matrix method
is used to obtain
the point F (for a deduction
point coordinates F). Point D shall be
superimposed over the point F, if assigns to point D a positive rotation of 120^{0}
(relations 1617). Derive the system
(17) and we obtain directly velocities (18) and accelerations (19) of the point
F (HE et al., 2013).
_{} (16)
_{} (17)
_{} (18)
_{} (19)
For the purpose of determining point
coordinates E're still circling the point D with _{} (20). Velocities (21) and accelerations (22) point
E is determined by deriving system (20) (LEE, 2013).
_{} (20)
_{}
(21)
_{} (22)
4.
ApplicationS
Presented system can be useful in
particular to the surgical robot that operate patients who require an accuracy
of positioning very high (see figure 5).
Figure 5: Surgical robot that operate patients who
require an accuracy of positioning very high
These
platforms can position very accurately even very large weights, such as a
telescope modern stationary (see Fig. 6).
Figure 6: A
modern stationary telescope positioned by a Stewart system
Other applications of the platform
Stewart are handling and precise positioning of objects large and heavy.
Spatial Stewart platforms may
conquer outer space in the future (MELO; ALVES; ROSÁRIO, 2012).
The latest PCbased digital
controllers, facilitated by openinterface architecture providing a variety of
highlevel commands, allow choosing any point in space as the pivot point for
the rotation axes by software command (TANG; SUN; SHAO,
2013). Target
positions in 6space are specified in Cartesian coordinates, and the controller
transforms them into the required motionvectors for the individual actuator
drives. Any position and any orientation can be entered directly, and the specified
target will be reached by a smooth vector motion. The pivot point
then remains fixed relative to the platform (TABAKOVIĆ et al., 2013).
In
addition to the coordinated output of the six hexapod axes, these new hexapod
controllers provide two additional axes that can be used to operate rotary
stages, linear stages or linear actuators. Some include a macro language for
programming and storing command sequences. These controllers feature flexible
interfaces, such as TCP/IP interface for remote, network and Internet
connection.
New
simulation tools are being incorporated for graphical configuration and
simulation of hexapods to verify workspace requirements and loads. Such software provides full
functionality for creation, modeling, simulation, rendering and playback of
hexapod configurations to predict and avoid interference with possible
obstacles in the workspace.
With
the new design developments that hexapod systems are experiencing,
manufacturers and researchers that have a need for extreme high resolutions and
high accuracy can now capitalize on them for improvements within their
workplace. Hexapod
technology has advanced considerably in a few short years, now it is up to
industry to embrace these new developments and put them to work to reduce their
setup and processing time, overall production cycle times, and ultimately
reduced cost of operation.
5.
CONCLUSIONS
The presented method manages to synthesize
(in theory) the best option parameters for any desired
parallel system. Moving mechanical systems
parallel structures are solid, fast, and accurate. Between parallel systems (WANG
et al., 2013) it is to be noticed Stewart platforms, as the oldest systems,
fast, solid and precise.
The work outlines a few main elements of Stewart
platforms. Begin with the geometry platform, kinematic elements of it, and
presented then and a few items of dynamics. Dynamic primary element on it means
the determination mechanism kinetic energy of the entire Stewart platforms. It
is then in a record tail cinematic mobile by a method dot matrix of rotation.
If a structural mottoelement consists of two moving
elements which translates relative, drive train and especially dynamic it is
more convenient to represent the mottoelement as a single moving components.
We have thus seven moving parts (the six motoelements or
feet to which is added mobile platform 7) and one fixed.
Proposed method (in this work) may determine kinematic
parameters system position when required the coordinates of the endeffector S.
This is clearly a reverse motion (an inverse kinematics)
(LIN et al., 2013).
Method is direct, simple, quick and
accurate.
Information display method presented
is much simpler and more direct in comparison with methods already known.
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