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13th World Congress in Mechanism and Machine Science, Guanajuato, Mxico, 19-25 June, 2011 A11_400

1

Synthesis of a RRSS Linkage for tracking a Two Axis Photovoltaic System

M M.Vtescu

*

I.Via

D.Diaconescu

R.Sulescu

Renewable Energy Systems and RecyclingResearch Centre, Transilvania University of Braov, Romnia

AbstractUsing and implementing renewable energy

systems is a prerequisite for insuring a sustainable

future. The use of solar energy conversion systems has

many advantages (clean, without by-products and wastes,

insuring security) but two major drawbacks limit their

implementation: the high costs and the low efficiency.

Mechatronics offers viable solutions to these problems,

especially for photovoltaics by using solar tracking

mechanical systems. This paper proposes a novel

solution: a non-adjustable RRSS four bars spatiallinkage, able to perform bi-axial tracking by using a

single driving element, offering a reliable, functional

model. The proposed RRSS tracking linkage represents a

flexible solution, based on a synthesis algorithm which

allows the optimum dimensional configuration for any

latitude. The optimised solution also eliminates the

blocking tendencies of the mechanisms in extreme

positions.

Keywords1

: azimuth tracking, PV system, four bars spatial linkage,

mono-actuator bi-axial tracking system

I. Introduction

An unsolved problem in the solar energy conversionsystems remains the high price and the still low conversionefficiency (lower than 18% in in-field conditions) for

photovoltaic materials [1]. A viable solution to enhance the

energetic output of photovoltaic (PV) systems is to providethe PV modules with a mechatronic tracking equipment [2];

this type of system will contain: (1) a PV solar energy

converter (the PV module/platform); (2) a mechanical

structure (e.g. planar linkages [3], spatial linkages [4], [5],

[6] gears [7]); (3) a driving unit (one or multiple

motors/actuators); (4) a control panel unit and (5) a sensorunit. The last fifth component is used only for the open-loop

tracking systems and is not included in the closed-loop

models [8].The bi-axial tracking systems develop the highest

tracking efficiencies [3] (over 99%), being able to perform

both diurnal and elevation movements of the Sun. The on

market bi-axial tracking solutions use two actuators/motors,

one for each solar movement.A novel tendency on bi-axial tracking systems design is

to obtain the bi-axial movement by using a single

* [email protected] [email protected]@unitbv.rorsaulescu @unitbv.ro

actuator/motor. Literature mentions two relevant patents,

published in 2009: a Greek patent [9] (Fig. 1) which

proposes an azimuth-elevation tracking system where the

elevation stroke is obtained from the input azimuthmovement; herein the rotational azimuth movement is

transformed into a vertical translational movement by

running a pin after a spatial cam profile (Fig. 1).

Fig. 1. Bi-axial, single-drive solar tracking, Greek patent [9]

Fig. 2. Bi-axial, single-drive solar tracking, Spanish patent, [10]

Another 2009 published solution is presented by aSpanish Patent [10] (Fig. 2) which also proposes an

azimuth-elevation tracking system where the dependent

elevation stroke results from the input azimuth

movement, according to a swing arm movement linking

the PV platform to the ground. For a seasonal adaptationof the elevation movement, the swing arm is equipped

with a screw length adjusting system (9) and a similar

device is set to adjust the distance between the swing arm

foot and the vertical pole.A critical analysis on these two state of the art

solutions show some weak points:
mailto:[email protected]:[email protected]

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The first solution (Fig. 1) relies on a complex

mechanical structure and has a reduced mechanicalresistance, leading to an unsafe working regime in high

wind speed conditions. Moreover, the point contact

between the pin and the spatial cam profile reduces the

structure stiffness.The second referential solution (Fig. 2) performs a

twice adjustable tracking movement, according to the on-swing arm and to the on-ground screw adjusting devices;

therefore, this model is relative complex, hard adjustableand attains a reduced structure stiffness.

Also, both state of the art solutions do not specify

any information about a dimensional algorithm or about

the optimum dimensional ratios.

To solve these critical aspects, a derived solution is

proposed to track a PV platform after two axes,

according to the azimuth model (Fig.3), by using a single

driving element: a non-adjustable RRSS four bars spatial

linkage (Fig. 4); the optimal relative dimensions areformulated according to the geo-meteorological features

of the location where the system is implemented. This

solution represents a development of a previous

optimised adjustable tracking linkage [6].

The structural features and the kinematical synthesis

of the non-adjustable spatial linkage are furtherpresented, based on an improved variant of the previous

synthesis algorithm.

II. The RRSS Linkage for bi-axial, azimuth tracking

The shift towards the bi-axial mono-actuated solar

tracking must comply with the following prerequisites:

increased reliability of the entire system;reduced mechanical complexity of the

mechanisms;reduced costs of the system.

These three objectives can be successfully reached by

a non-adjustableRRSS four bars spatial linkage designed

to track a PV platform after two axes, according to the

azimuth model (Fig. 3), by using a single drivingelement. It consists (Fig. 4) of a vertical pole (0) on top

of which is articulated a fork (1) by a revolute joint

(R=0;1); a rotating slew drive (1) spins the fork (1) and

transmits the azimuth motion, *, to the PV platform (2)through a horizontal (A-A) revolute joint (R=1;2). Thus,

the PV platform (2) follows the sun according to itsazimuth movement, (Fig. 3). A swing arm (3)embodies a mobile connection between the platform (2)and the basis (0) by two theoretical spherical joints (S);

because the angular capacities of the spherical joints are

relative small for this application, these are replaced by

(Fig.4a and b): a bi-mobile Cardan joint between arm (3)and platform (2) and a tri-mobile Cardan joint (3-4-0)

between arm (3) and the basis (0). Thus, the passive

mobility of the arm (3), allowed by the two spherical

joints, is eliminated.

Fig. 3 The azimuth solar angles () and the corresponding trackingangles (* *) [3]

a)

b)

Fig. 4. a) The 3D embodiment scheme and b) the 3D kinematic schemewith specific parameters for the tracking linkage;

Therefore, during the angular azimuth displacement

(*, Fig.4b), the swing arm (3) constrains the platform(2) to perform simultaneously the angular elevation

displacement, *, (homologue to suns altitudedisplacement, , Fig.3).

Additionally, the proposed non-adjustable RRSS

azimuth four bars spatial linkage has no dimension

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adjusting devices to reduce its stiffness or its tracking

accuracy.To fulfil the requirementsof a competitive bi-axial,

mono-actuator, solar tracking system, an optimum

dimensioning algorithm is developed for the proposed

non-adjustable RRSS structure, to fit in any chosenterrestrial location. A numerical application is presented

for Brasov, Romania implementing location (latitude=45.6 N).

III. The kinematical synthesis prerequisites

To ensure the efficient functioning of the non-

adjustable RRSS for azimuth solar tracking linkage, the

kinematical synthesis was done assuming the Equinox2

day as a referential solar moment; therefore, the

transmission angle between the PV platform (2) and theswing arm (3) was imposed to reach its maximum (of

90o) at the Equinox day noon [6]. Accordingly, the

motion transmitting function3was deducted. To simplifythe calculations, the number of four unknown dimensions

(h, r, l, e) (Fig. 4b) was reduced to a number of three

unknown parameters, defined as ratios:H = h/e; R = r/e;L = l/e [4], [5], [6].

Fig. 5. The three working angles restricted on the sunset/sunrise

position:155,235,365, [6]

The kinematical synthesis of the adjustabletracking

RRSS linkage [6] started form an input data variation for

R; then H and L were calculated according to theimposed extreme tracking angle values and the optimum

dimensions were identified by formulating the conditions

to avoid blocking.

2The Spring and the Autumn Equinox days are consider to have similar

solar characteristics3

see equations (1) and (2) from the logical scheme

In the kinematical synthesis of the non-adjustable

RRSS tracking linkage, all three parameters areunknowns in the beginning and H is calculated according

to the imposed extreme tracking angle values, while L

and R are calculated according to the equations, for

avoiding blocking. Moreover the new algorithm is moreeasily adaptable for any latitude implementing location.

Further, for insuring a highly reliable tracking, threeblockage avoiding restrictions were imposed, as detailed

in [6], describing three working angles: 1, 2and 3andtheir extreme allowable values for a non-blocking bi-

axial, azimuth tracking: 1 55, 2 35, 3 65 aspresented in Fig. 5.

Thus, considering a referential solar moment [4], [5],

[6] and imposing the blockage avoidance restrictions [6],an improved synthesis algorithm is developed to calculate

the optimum dimensions of the non-adjustable spatial

linkage, for any latitude.

As result of its simplified mechanical structure of thenon-adjustable RRSS spatial tracking linkage, this new

algorithm proves to be an improved solution comparing to

the previous calculations [4], [5], [6].

IV. Linkage kinematical synthesis developed for a

given application

According to the kinematical prerequisites, the on-

latitude optimum dimensioning algorithm for the non-adjustable tracking linkage can be synthesised in a

specific input data set and a 5 step calculation process:

The INPUT data set: for the two axis photovoltaic system

(Fig. 4) there are given:1.the structural scheme (Fig. 4b) with four unknown

dimensions (h, r, l, e);2.the motion transmitting law, with the implicit (1) and

explicit (2) forms (Fig.16);

3.the angular restrictions for avoiding blocking: theworking angles restrictions(Fig. 5); the corresponding

equations (3), (4) and (5), given in the logical scheme

from Fig.16;

4. The geo-meteorological data for the implementing

location (the latitude and the annual turbidity factorvariation TR [11])

5. The extreme angular values which ensure a high

harvest of the available direct solar radiation on the PVsurface; these values are presented in the logical

scheme (Fig.16) at point 5 from the input data block.

The required RESULTS are the H, R, L values, able to

ensure the highest tracking efficiency while fulfilling theworking angles restrictions and thus developing a safe,

reliable and energetic efficient solar tracking, for the

considered location specific conditions. The improvedalgorithm developed for the synthesis of the non-adjustable

spatial linkage has the following five steps:

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Step 1 (blocksaefrom Fig.16; Fig. 6a and b):

H variation is calculated, on each latitude, considering

the relevant values for *m; then, H variation for the locationlatitude () is selected. A family of unchecked4H curves isobtained as in Fig.6a; for an increased calculation accuracy,

from the previous curve family (Fig.6a) a single variation

curve is extracted (Fig.6b) for the considered latitude

(=45.6 lat N).

a)

b)

Fig. 6. a) the variation curves of H (H-unchecked) for the entire latitudedomain (0-90) while the sunrise/sunset elevation angle (*m)

variation is considered; b) the single variation curve of H as a function

of *m for Brasov, Romania latitude (= 45,6lat. N)

Step 2 (blocksfhfrom Fig. 16; Fig. 7):

The ideal value of 1forthe Spring Equinox noon is1 = 0, allowing to obtain the maximum transmissionangle. To cover an enlarged and a more relevant domain

of solutions, 1willbe assigned with the following values|1| = {15; 10; 5; 0}; for each discreet value of |1| acorresponding L = L (*m) value is calculated,considering each relevant set of values obtained on Step

1. Thus, an unchecked2 family of curves is obtained for

the L ratio (Fig.7).

Step 3 (blocks i...kform Fig. 16; Fig. 8):

To insure a large and relevant domain of solutions,

|3| is assigned with the following values: 65, 60 and55 respectivelly; for each discreet value of |3|, R = R(*m) values are calculated for each (H, L) pair obtainedin Steps 1 and 2. Thus the unchecked2curve families for

R ratio are obtained, as in Fig.8.

4Due to the fact that these values are not yet verified according to the

blockage avoiding conditions

Fig. 7. The variation curves for L as a function of *m , whenconsidering three discrete values for|1M| = 0; 5; 10; 15, for Brasov,

Romania (= 45,6lat. N)

Fig. 8. The three families of R-curves, for each |3m| = 65, 60and 55,described as functions of *m, while considering three discrete valuesfor|1M| = 0; 5; 10; 15, for Brasov, Romania (= 45,6lat. N)

Step 4 (blocks lmfrom Fig. 16; Figs. 9, 10, 11, 12, 13):The restrictions for avoiding blockage are verified for

all pairs (H, L, R, *m) developed in the previous Steps.

Thus. the H, L and R validated solutions are selected,

from the initial set of solutions obtained in Steps 1, 2 and3, as presented in Figs. 9, , 13.

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.Fig. 9. The H-curve solutions (red) lapped over the initial H-curve

(blue) for *m(030) considering = 45,6lat. N

Fig. 10.The L-curves solutions (continuous line) lapped over the init ialL-curves (dashed) for *m(030), calculated for 1M={0, 5, 10,15}; the marked solutions correspond to the discrete values for *m=

{15, 16, 18, 20, 22, 24, 26, 28, 30}, for = 45,6lat. N

Step 5 (blocksnqfrom Fig. 16; Figs. 14, 15; Table 1):

The energy calculation is done for each pair obtained

during the previous step, to identifythe optimum solution,leading to the highest tracking efficiency, along with the

most reliable working conditions (155, 235, 365). As result, 12 curves are obtained, corresponding toeach restriction imposed on 1 and 3 (Fig. 14).

The optimum (H, L, R, *m) is the one thatsimultaneously reaches a high tracking efficiency along

with the most reliable conditions for avoiding blockage

(Table 1).

Fig. 11. The R-curves solutions (continuous line) lapped over the initial

R-curves (dashed line) for *m(030), calculated for each 1M={0,5, 10, 15}, while considering 365; the marked solutions

correspond to the discrete values of *m= {15, 16, 18, 20, 22, 24,26, 28, 30}, for = 45,6lat. N

Fig. 12. The R-curves (continuous line) lapped over the initial R-curves

for *m(030) variation, calculated for each 1M={0, 5, 10,15}, while considering 360; the marked solutions correspond to

the discrete values of *m= {15, 16, 18, 20, 22, 24, 26, 28,30}, for = 45,6lat. N

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To implement this 5-steps algorithm, a logical

scheme has been developed and numerical simulationswere done for a particular implementing location:

Brasov, Romania; 45,6 lat. N; annual specific turbidityvalue: TR= 3 [11].

*m 22H 3,2893

L(1 M=15) 1,5869R(1 M=15; 3m=55) 2,5659

2[] 50.94Tracking efficiency 96,05 %

TABLE 1. The optimum dimensional parameters H, R and L calculated

according to the 5 steps synthesis algorithm, for = 45,6lat. N (Fig. 16)

The optimum solution is chosen for insuring the safestblockage avoiding restrictions and also a high tracking

efficiency. For the case study investigated, the optimum

solution reaches the following specific values: 1M = 15(55), 2M= 50,94(35), 3m= 55(65),m = 22, M =45 and a corresponding tracking efficiency of 96,05 %(Table 1).

Fig. 13.The R-curves of solutions (continuous line) lapped over theinitial R-curves for *m(030), calculated for each 1M= {0, 5,

10, 15}, while considering 355; the marked solutionscorrespond to the discrete values for *m = {15, 16, 18, 20, 22, 24,

26, 28, 30}, for = 45,6lat. N

a)

b)

Fig. 14. The tracking efficiency of the tracking mechanism according to

the discrete solutions H, R, L, for = 45,6lat. N

The results of the numerical simulations, for each

step of the algorithm, are reported through exemplifying

graphs (Figs. 6 15). The calculations along the logicalscheme of the synthesis algorithm up to block o) leads to a

large domain of solutions.

Fig. 15. a) The step variations of * and * along with the continuousvariationsand and b) the available solar radiation (curve B) and the

solar radiation received by the module (curve B PV) when using the

tracking mechanism, during the Spring Equinox, for = 45,6lat. N

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START

INPUT DATA:

1. the structural scheme of a bi-axial, mono-actuated, four bars, spatial azimuth type tracking linkage(Fig. 4),with four unknown dimensions (h, r, l , e)

2. The motion transmitting law generating the elevation movement * by the independent azimuth (daily)movement * (Fig. 4b):

Implicit form: ( ) 0coscossin2 (1)2222*** =++ herlher

Explicit form:

++

= cb

cbaa 2221*tan2 (2)

Where:e

ra ;

*cos2

=

2

2

e

rhb

= ;

2

222

e

ehrc

+ (2), (2), (2)+=

3. The geometrical conditions imposed to the mechanism for avoiding blocking:For the working angle 1 (1, Fig. 5):

= 55

coscossincos||

*1

1L

H (3)

For the working angle 2 (2, Fig. 5):

o35*sin

cos|| 12

=

L

(4)

For the working angle 3 (3, Fig. 5):

o65*cos

cos|| 13

=

L

RH (5)

4. The geographic and meteorological data, in the implementing location: latitude and monthly variation ofthe turbidity factor TR[11];

5. The extreme angular values which ensures a convenient tracking efficiency, using as reference the valuesfrom the Equinox day (Spring or Autumn): *m = 90o; *M = 0o; *M = (90o- ) and *m =0o... 0,7*M,where: M indicates the noon moment and m indicates the sunrise/sunset moment

OUTPUT DATA:

The values for the reduced dimensions:H h/e, R r/e, L l/e insuring, for any chosen implementinglocation:

a)high efficiency for the direct solar radiation harvest on the PV platform;b)avoiding blocking;c)high reliability considering the working angles restrictions and a minimum overall size.

Step I:

H curves calculation, according to equation (6), as a variation of the latitude value (), for the specific discretevalues of the PV platform sunrise/sunset elevation angle: *m= *mi= (i-1)5, with i = 1, 2, 3, ..., ~0,7*M/5.Equation (6) is deducted from equation (1) in which the numerical values for *m i *M are set in direct correlationwith the implementing location latitude value :

Mm

mmMMH

**

****

coscos

cossincossin)(

= (6)

a

b

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A family of curves Hi (, *mi) (Fig. 6a)

The family of curves Hi graph is crossed with a vertical which corresponds to the implementing

latitude value(for the numerical example: = 45,6 N ) (Fig. 6a)

The continuous variation H = H (*m), for the chosen latitude (for thenumerical example: = 45,6 N ),without considering the blockage avoiding

Curves L = L (*m),corresponding to the minimum considered values for |1| = 15; 10; 5; 0,without considering the blockage avoiding tendencies restrictions (Fig. 7)

A (H, L) pair of numerical values, each coresponding to one of the discrete considered values

for without considering the blockage avoiding tendencies restrictions *m

R = R (*m) curves, corresponding to |3| = 65; 60; 55, without considering theblockage avoiding tendencies restrictions (Fig. 8)

Step III:

R = R (*m) is calculated according to equation (5), for each previously obtained pair (H, L); equation

(5) is deducted form (5), by imposing |3| = 65; 60; 55:

m

m

LHR

*cos

cos)*( 3

= (5)

A triplet solution (H, L, R), for each considered discrete value *mwithout considering the blockage avoiding tendencies restrictions

c

d

e

f

g

h

i)

j)

k)

Step II:

Calculation of L = L (*m) for each previous registered values H (*m), according to equation (3), where(3) is deducted from equation (3), considering |1 | = 15; 10; 5; 0:

1

*

cos

coscossin)*(

MMML m

H =

(3)In which *M= (for the Spring/Autumn Equinox day) and *M =0(noon)

NOT

accomplished

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Are

accomplished

NOT

accomplished

Step IV:

The checking calculations, for each solution (H, L, R, *m),

concerning the accomplishment of the working restrictions:

155, 235, 365

l

m

n

o

p

q

Step V:The tracking efficiency value is calculated for each previously obtained solution (H, L, R, *m), define as a

ratio between the annual harvest of direct solar radiation energy on the PV surface (EB.PV) and the available

direct solar radiation energy (EB.S) [6], while imposing an hourly stepwise tracking program for PV platformsazimuth stroke *, maintaining an equal variation to the left, to the right, up and beyond from the solar ray

variation curve (see Fig. 15):

= EB.PV/ EB.S (7)

= dtBE PVBPVB .. , *)]cos(*coscos*sin.[sin += sBPV B (Fig. 15 b) (7)= dtBE SBSB .. ,

+

+=sin4,99,0

Texp)]72,2N.9856,0cos(0334,01.[1367B (Fig. 15 b) [12] (7)RS

In which :

N number of the day in the year;

Tr =3 the annual constant value of the turbidity factor, specific for Brasov, Romaniageographical area [11];

solar ray elevation angle (Fig. 3);* PV platform elevation angle, o tracked according to the RRSS quadrilateral spatial linkage

described in Fig.15 a., according to equation (2);

solar ray azimuth angle (Fig. 3);* PV platform azimuth angle, described through a step curve which approximates the

continuous variation of the solar ray azimuth (Fig. 15 a).

A set of solutions (H, L,R, *m)which ensures the accomplishment of the extreme

tracking angles, specific for the chosen implementing location and which ensures theavoidance of the blocking tendencies (Figs. 9, 10, 11, 12, 13)

The tracking efficiency values for each pair of solutions (H, L, R, *m) previous

obtained, for the considered location (herein: Brasov, Romania) (Fig. 14.)

The optimum solution (H, L, R,*m) (Table 1)

STOP

The analysis and the comparison of the previous obtained solutions (H, L, R, *m) to identify the set that

ensures the safest functioning conditions along with the highest tracking efficiency value.

Fig. 16. The on-latitudes dimensioning algorithm for the azimuth, non-adjustable RRSS spatial tracking l inkage, based on

the blockage avoiding tendencies restrictions

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Fig. 17. The 3D RRSS PV azimuth tracking linkage modeled

according to the optimum dimensioning algorithm, for Brasov

Romania (= 45,6lat. N), on its noon position, with a detailed viewon the Cardan transmission swing arm

The numerical simulations results showed that, for

Brasov, Romania (= 45,6lat. N, TR= 3 [11]), the bi-axial mono-actuated non-adjustable RRSS linkage has atracking efficiency of 96,05% (Table 1), with only 3%

lower than that the bi-axial, double-actuated tracking

systems [13].

A 3D model was built according to the obtainedvalues (Table 1) as shown in Fig. 17.

V. Conclusions

This paper proposes a non-adjustable RRSS four

bars spatial linkage for PV solar tracking, following the

need to develop low-cost, highly efficient systems withreduced complexity.

The model represents the improved variant of a

previous adjustable RRSS spatial linkage, designed for abi-axial, mono-actuator azimuth tracking.

A new, simplified synthesis algorithm is developed,

based on the R (known) variation and on the imposed

extreme tracking angles values.

To obtain more accurate and relevant solutions, the

new synthesis algorithm considers all three parameters(H, R, L) as unknowns and solves their equations

considering the restrictions for avoiding the mechanism

blockage. The results are the H, R, L ratios, leading tothe optimum dimensions: h, r, l, e.

A case study, develop for the Brasov, Romania

location showed that the proposed mechanisms allows

obtaining a tracking efficiency of 96 %, with only 3%

lower compared to the much complex bi-axial, bi-mobiletracking systems.

These conclude that the proposed non-adjustable

RRSS four bars spatial linkage represents a qualitative,

competitive and on all latitudes adaptable solution.

References

[1] A. Goetzberger and V.U. Hoffmann. Photovoltaic Solar Energy

Generation, Springer, Berlin, Germany, 2005;[2] G. Boyle. Renewable Energy power for a sustainable future, (2nd

edition) 2004;[3] I. Visa, D. Diaconescu, V. Popa. On the Received Direct Solar

Radiance of the PV Panel Orientated by Azimuthal Trackers,

COMEC - The 2nd International Conference ComputationalMechanics and Virtual Engineering, Brasov, Romania, October2007, p. 25-30, ISBN 978-973-598-117-4;

[4] D. Diaconescu, I. Via, M.M.Vtescu, I. Hermenean, R.Sulescu. Synthesis of a Bi-Axial Tracking Spatial Linkage with aSingle Actuator. Proceedings of SYROM 2009, Springer

Science& Media, p. 617 632, ISBN: 978-90-481-3522-6_52;

[5] M. M. Vtescu, D. V. Diaconescu, I. Via: On the Simulation ofa Mono-actuator Bi-Axial Azimuth PV System, Bulletin of theTransilvania University of Brasov Vol. 2 (51) - 2009 Series I,

p. 97 104, ISSN 2065-2119;[6] D. Diaconescu, I. Via, M. Vtescu, R.Sulescu, B. Burduhos:

The Optimization of a Bi-Axial Adjustable Mono-Actuator PV

Tracking Spatial Linkage. New Trends in Mechanism Science.Analysis And Design, volume 5, Springer Science& Media 2010,

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[7] B. Butuc, M. Late, G. Moldovean. FEM Analysis of the BevelGear Housing of an azimuthal Tracked PV Platform, OradeaUniveristy Anals. Technological Engineering and Management

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Energy Reviews 13 (2009) 18001818, Elsevier;

[9] I. Fragkiadakis.: Innovative Azimuthal Solar Tracker, Patent GR

1006107B1, publication date 2009-10-15;

[10] A. Jesus et al.: Solar Tracker with Movement in Two Axes andActuation in Only One of Them, Patent WO2008/000867 A1.,

publication date 2008-06-18;[11] M. M. Vtescu, D. Diaconescu, A. Du, B.G. Burduhos:

Atmospheric Pollution Evaluation In Brasov Romania Based On

Turbidity Factor Analysis. Analytical and Nano-anayitical

Methods for Biometrical and Environmental Sciences (IC-AMBES2010), Transilvania University Press, p. 106, ISBN 978-973-598-

722-0;

[12] M. Meliss. Regenerative Energie-quellen Praktikum, Springer,

Berlin (1997);[13] V. Popa, PhD thesis: Efficiency Increase In Photovoltaic Panels

By Azimuthal Tracking Systems, Tarnsilvania University of

Brasov, October 2009.

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