PARALLEL MOVING MECHANICAL SYSTEMS

Florian Ion Tiberiu Petrescu

Bucharest Polytechnic University, Romania

E-mail: petrescuflorian@yahoo.com

Relly Victoria Virgil Petrescu

Bucharest Polytechnic University, Romania

E-mail: 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 exo-planets, 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 to-day, 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 co-ordinates (, system 1) of vectors unit (, system 2) belonging to motto-items 1-6 (variable-length) are given by the system (1), where l_i is the length (module) of vectors (system 3); with i=1-6 (GARCIA-Murillo, 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).

(2)

(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 (4-7). The length l₁=AD is variable (); in the same way and the distance a₁ which defines the position of the center point of gravity G₁ (and the center of gravity G₁ 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 variable-length 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, 2011-2013).

(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, x₁Sy₁z₁ (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 co-ordinates of rectangular axis Sz₁, in such a way that can be calculated for a start axis coordinates Sx₁ (relations 11), axis determined by points S, D (known). The co-ordinates are obtained vector Sx₁. This, along with the coordinates of the pixel S causes axis Sx₁ (11) (PETRESCU et al., 2009; PETRESCU; PETRESCU, 2011-2013).

Figure 3: The geometry and kinematics mobile platform 7

(11)

By screwing axis by (over) axis , weve axis (12). The co-ordinates are thus obtained mobile system x₁Sy₁z₁ (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 co-ordinates (in accordance with the mark fixed cartesian) of a point D¹ 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, 2011-2013).

(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 120⁰ (relations 16-17). 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 PC-based digital controllers, facilitated by open-interface architecture providing a variety of high-level 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 6-space are specified in Cartesian coordinates, and the controller transforms them into the required motion-vectors 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 set-up 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 co-ordinates 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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