-k ~k ~k ~k

Field of the invention

The present invention relates to devices for measuring the deformations and displacements of a mechanical component. More precisely, the present invention regards a measuring device that employs a number of position transducers.

General technical problem

Measuring the displacements and deformations of an object that is subject to a load is an operation that is frequently made with a rather low precision on account of the intrinsic limits of the measuring devices themselves.

In other words, in the case where the component has a complex geometry and/or the deformations that it undergoes regard displacements along a number of degrees of freedom, possibly in combination with one another, the measuring devices currently available frequently only enable very simplified measurements to be made .

Considering, for example, the case of a wire extensometer or of a linear position transducer, it is evident that they are able to detect a displacement only in one direction, and in the case of complex states of deformation it is evident that an extensometer associated to each of the directions in which the deformations take place is required. However, as mentioned previously, said measurements are far from accurate since they are frequently affected by factors such as the positioning of the extensometers on the object and are consequently affected by low repeatability and reproducibility. Moreover, the quality is markedly dependent upon the experience of the person making the measurement. Object of the invention

The object of the present invention is to overcome the technical problems described previously. In particular, the object of the present invention is to provide a device for measuring displacements and deformations with a higher measuring precision as compared to devices of a known type and at the same time for detecting any state of deformation irrespective of its complexity.

Summary of the invention

The object of the present invention is achieved by a measuring device having the features forming the subject of the ensuing claims, which form an integral part of the technical disclosure provided herein in relation to the invention.

Brief description of the drawings

The invention will now be described with reference to the annexed drawings, which are provided purely by way of non-limiting example and wherein:

- Figure 1 is a perspective view of a measuring device according to a first embodiment of the present invention;

- Figure 2A is a schematic representation of a measuring device according to the present invention, comprising references for kinematic calculation;

- Figure 2B is a perspective view of the device of Figure 1 during the execution of a measurement;

- Figure 3 is a perspective view of a variant of the measuring device of Figure 1; and

- Figure 4 illustrates a measuring device according to a second embodiment of the present invention .

Detailed description of the invention

With reference to Figure 1, the reference number 1 designates a measuring device according to a first embodiment of the present invention. The device 1 comprises a first plate 2, a second plate 4, and first, second, third, fourth, fifth, and sixth position transducers designated by the reference numbers 6, 8, 10, 12, 14, 16, respectively.

The aforesaid position transducers 6, 8, 10, 12, 14, 16 are set between the first and second plates 2, 4, connect the latter and are transducers of a linear type; i.e., each one is provided for detecting rectilinear displacements along its own axis, namely, H6, H8, H10, H12, H14, H16, respectively.

Each transducer is preferably of the type comprising a first body and a second body that are able to slide with respect to one another (for example, a stem and a tubular body that receives the aforesaid stem) . A corresponding type of position transducer is the LVDT (linear variable differential transformer) transducer, which can hence be used on the device 1.

The plates 2, 4, in this embodiment, are both substantially C-shaped, namely:

- the first plate 2 comprises a first arm 18 and a second arm 20, which are parallel to one another and are joined together by a first header 22; and

- the second plate 4, in a similar way, comprises a third arm 24 and a fourth arm 26, which are parallel to one another and are joined together by a second header 28.

The headers 22, 28 are preferably orthogonal to the corresponding arms.

The six position transducers 6, 8, 10, 12, 14, 16 are arranged between the plates 2, 4, grouped in pairs, each arranged in a V-shaped formation.

The first and second position transducers 6, 8 each comprise a first end 30, 32, respectively, and a second end 34, 36, respectively. The first ends 30, 32 are connected, respecti ely, at a first connection point A and a second connection point B in the proximity of opposite ends of the arm 18. In the present description, the term "connection point" corresponds substantially to an intersection between geometrical entities associated to the components of the device 1, said intersection being associated to each coupling between the transducers 6, 8, 10, 12, 14, 16 and the plates 2, 4. This means that each position transducer is coupled to the plates 2, 4 by means of respective joints arranged at the aforesaid connection points .

The first ends 30, 32 are consequently connected to the arm 18 by means of a first joint Jl and a second joint J2, respectively, represented schematically, which are of a spherical type.

The second ends 34, 36 are instead both connected to the arm 24 of the second plate 4 in a third connection point C by means of a single third joint J3 (which basically comprises a double joint of a spherical type) .

The projection on the plate 2 of the connection point C is in a position intermediate between the connection points A, B when the plates 2, 4 are parallel to one another. In this way, a substantially V-shaped geometry is obtained, the vertex of the V coinciding with the point C.

In a basically similar way, the third and fourth position transducers 10, 12 comprise a respective first end 38, 40 and respective second ends 42, 44. The first ends 38, 40 are connected to the header 22 by means of a fourth joint J4 and a fifth joint J5, respectively, of a spherical type set at a fourth connection point D and a fifth connection point E that are distinct from one another and located in the proximity of opposite ends of the header 22 itself.

The second ends 42, 44 are instead both connected to the header 28 of the plate 4 in a sixth connection point F by means of a single sixth joint J6 (which basically comprises a double joint of a spherical type) .

The projection of the connection point F on the plate 2 is in a position intermediate between the connection points D, E when the plates 2, 4 are parallel to one another.

Finally, the fifth and sixth position transducers 14, 16 comprise a respective first end 46, 48 and a respective second end 50, 52. The first ends 46, 48 are connected to the second arm 20 by means of a seventh joint J7 and an eighth joint J8, respectively, of a spherical type set at a seventh connection point G and an eighth connection point H that are distinct from one another and located in the proximity of opposite ends of the arm 20.

The second ends 50, 52 are both connected to the arm 26 in a ninth connection point I by means of a single ninth joint J9 (which basically comprises a double joint of a spherical type) .

The projection of the connection point I on the plate 2 is in a position intermediate between the connection points G, H when the plates 2, 4 are parallel to one another.

In this way, the three pairs of position transducers 6-8, 10-12, and 14-16 are arranged to define an array with a substantially C-shaped development, each along a different portion of the two plates 2, 4, leaving the area comprised between the arms 18, 24 and 20, 26 and facing the headers 22, 28 completely free. It will on the other hand be appreciated that the arrangement of the position transducers 6, 8, 10, 12, 14 does not present circular symmetry: said characteristic, as will emerge clearly from the ensuing description, is particularly advantageous during processing of the data to obtain measurements.

At a general level, whilst the embodiment described herein comprises a first plate 2 and a second plate 4, which are basically C-shaped and substantially reproduce the development of the array of the position transducers 6, 8, 10, 12, 14, 16, for the purposes of the present invention the shape of the plates 2, 4 can vary widely. The priority aspect is the C-shaped geometry of the array of the position transducers 6, 8, 10, 12, 14, 16.

Preferably (Figure 2A) , the connection points G, E and B, D are arranged on the plate 2 in such a way that if the straight lines joining the points G-H, E-D and A-B were to be drawn and the intersections between them were to be identified,

- the points G and E are equidistant from a first intersection II between the straight lines joining the points G, H and D, E;

- the points D and B are equidistant from a second intersection 12 between the straight lines joining the points A, B and D, E; and

- the distances referred to above, designated by b in Figure 2A, are all identical to one another.

Nonetheless, preferably the arrangement of the connection points C, F, I is chosen in such a way that in conditions of parallelism between the plates 2, 4 the axes of each pair of transducers 6-8, 10-12, 14-16 will define a respective plane orthogonal to the plates 2, 4.

Finally (Figure 2A) , a fixed cartesian reference system is introduced, designated by 0, which is fixed with respect to the device 1 and is of a right-handed type and comprises three orthogonal axes x, y, z, where the axes x and y define a plane substantially parallel to the plate 2 (and to the plate 4 when this is parallel to the plate 2) . The system 0 is preferably centred at the intersection II.

Operation of the device 1 is described in what follows .

With reference to Figure 2B, an object the deformations and displacements of which are to be measured, for example under load or following upon an assembly in which it is necessary to deform the object, is inserted between the plates 2, 4, exploiting the free area between the arms of the latter. By way of example, as object on which to carry out the measurements, a flexible connection element made of metal braid for automotive uses, designated by the letter S, is considered.

The flexible connection element S is coupled to the device 1 by arranging the plates 2, 4 substantially bestriding it. Preferably, a particular shape of the areas of connection between the arms and the header of each individual plate is provided so as to conform better to the geometry of the component being measured. In Figure 2, for example, the headers have an edge shaped like the arc of a circumference that reproduces the cylindrical geometry of the flexible connection element S. This is aimed at achieving a coupling of a rigid type between the plates 2, 4 and the element S, i.e., such that the displacements of the element S are not uncoupled from those of the plates 2, 4.

At a more general level, as will emerge clearly in what follows it is in any case sufficient that there is a rigid coupling at least between the plate 4 and the element S for the execution of the measurement, since the coupling between the displacements of the element S and of the plate 2 can be obtained in some other way.

The second plate 4 is movable with respect to the first plate 2 according to six degrees of freedom. Said degrees of freedom comprise, with respect to the reference system 0,

- three translations δχ, 5y, δζ along the axes x, y, z, respectively; and

- three rotations θχ, By, Qz about the axes x, y, z, respectively.

The movement of the plate 4 with respect to the plate 2 is possible thanks to the lengthening and contraction of the position transducers 6, 8, 10, 12, 14, 16, as well as to rotations thereof with respect to the plates 2, 4 themselves.

The lengthenings and contractions of the position transducers 6, 8, 10, 12, 14, 16, designated respectively by 56, 58, 510, 512, 514, 516, take place in directions joining the first and second ends of each position transducer 6, 8, 10, 12, 14, 16 and can both have the directions illustrated in the figures.

Keeping the plate 2 substantially fixed (in particular with respect to the reference system O) while making a measurement, any displacement or deformation that the flexible connection element S has undergone (for example, owing to the application of a load or of a displacement) results in a movement of the second plate 4 with respect to the first plate 2.

There exists a clearly determined functional link between the displacements of the second plate 4 with respect to the first plate 2 (according to the degrees of freedom 5x, 5y, δζ, θχ, Sy, θζ) and the displacements 56, 58, 510, 512, 514, 516 that are covered and detected by the position transducers 6, 8, 10, 12, 14, 16. In greater detail, the kinematics of the device 1 can be described by means of a system of equations with nine unknowns, the solution of which will be discussed hereinafter.

To carry out the measurement it is necessary to acquire, for example by means of an electronic processing unit (not illustrated) connected to the device 1, the displacements 56, 58, 510, 512, 514, 516 detected by the corresponding position transducers and resulting from the movement of the second plate 4 imposed by the deformation of the flexible connection element S.

By solving then the system of equations that describes the device 1 kinetically, it is possible, starting from the displacements 56, 58, 510, 512, 514, 516, to arrive at the displacements 5x, 5y, 5z, and at the rotations θχ, 9y, θζ and thus, in practice, to measure the deformations that the flexible connection element S undergoes.

In this connection (with reference to Figure 2A) , there now follows a brief description of the construction of the system of equations associated to the device and used for processing the data coming from the transducers 6, 8, 10, 12, 14, 16.

The following quantities are introduced for the purpose:

- θΐ, θ2, θ3 are angles comprised, respectively, between the transducer 16 and the straight line joining the points G and H, between the transducer 12 and the straight line joining the points E, D and between the transducer 8 and the straight line joining the points A, B;

- a is the distance between the connection points A and B, D and E, G and H (the distances being the same as one another) ;

- b (which has been introduced previously) is the distance between 0 and the connection points E, G, which from what has been described previously is equal to the distance between the points, E, B and the intersection 12;

- 11, 12, 13, 14, 15, 16 are distances, respectively, between the connection points H and I, G and H, E and F, D and F, B and C, A and C and depend upon the displacements 56, 58, 510, 512, 514, 516 (they are equal but for a constant);

- xl, yl, zl is a first set of co-ordinates referred to the connection point I with respect to the reference system 0;

- x2, y2 , z2 is a second set of co-ordinates referred to the connection point F with respect to the reference system 0;

- x3, y3, z3 is a third set of co-ordinates referred to the connection point C with respect to the reference system 0;

- B is the distance between the connection points B and I; and

- c is the distance between the connection points I, F and F, C (the distances being the same as one another) .

It is moreover assumed, as has been described, that the planes identified by each pair of position transducers (6-8, 10-12, 14-16) are orthogonal to the plate 2 (and to the plate 4) when they are parallel.

The angles θΐ, θ2, θ3 can be computed using the following relations:

θ ₃ = cos ^"1 (01 + a ² - ll / C2l-a)) This enables the co-ordinates yl, x2, and y3 to be obtained y ₁ = b ÷ l ₁ cos9 _{1 ( 1 )}

x _t = b -r l ₃ cos9 _{3 ( 2} )

y ₃ = b -r l _s cos9 _{5 ( 3 )}

It is hence possible to write three equations that link the mutual positions of the plate connection points I, F, C to obtain the moduli of the distances B, c starting from the co-ordinates of the three points I, F, C themselves: c ² = (x _t x _. ) ^: + (y-t - y _: ^' ) ^: - ( z _t - z, ) (4) I-F

c ^c2 = - ( vx ₂ - x ₃ ) ² + ^ (y ₂ I -- yY ₃ B) ² + (¾ - z ₃ ) (5) C-F

B ² = (x _j - x ₃ ) ² + (y _t - y ₃ ) ² + (z ₁ - z ₃ ) ^: (6)

where, with simple passages

The system made up of Eqs. (4), (5) and (6) has nine unknowns. Three unknowns can be obtained from Eqs. (1), (2) and (3), so that there remain still six unknowns to find.

It is hence necessary to write a further three equations so as to render the system soluble. Said equations can be obtained by computing the distances 11, 13 and 15 starting from the co-ordinates of the points I, F, C (Figure 2A) :

I ² = x ² + (b + a - y _t ) ² + zf ₍ η l ² = (x, -b) ² ~y ² -Z ² (8)

l ² = ia + 2b-x ₃ ) ² - (y ₃ -b) ÷zf (9)

From this we have a system made up of six equations, in particular Eqs . (4), (5), (6), (7), (8), and (9) .

In order to render the notation more compact, the following equivalencies are introduced:

t = y

I = t| - (y ₃ - b) ²

n = (yi -y ₃ ) ²

d = a + 2b

2ot = c"— s ^~ — tr— u— q

2β = c ² — s ² — I ² — q— 1+ d ²

2y = B ² — n— u— I + d ² whence, after a number of simple passages, + sx ₁ + ty ₂ + u - q-yf 1 = 0 (10)

β + x ₃ (s - d) - iy ₂ + q - yfv' ¹ - ( ^d - ¾) ^{2 = 0} (11) y + x _t x ₃ - dx ₃ + u -x ² _v ^; I - (d - x ₃ ) ² = 0 (12)

Developing Eqs. (10), (11) and (12) it is possible obtain, respectively, xl as a function of y2, x3 as function of y2 , and x3 as a function of xl: x ^z {s ² + q — y ) + x-iilas + 2sty ₂ ) + {a ² + t y; + 2 ty ₂ — uq + uyi) = 0

(13)

qd ^: = 0

(15)

Solving for xl in Eq. (13) and substituting it in Eq. (15), it is possible to obtain an equation that expresses x3 as a function of y2 (said equations are of the second degree and consequently have two solutions;

the inventor has found that the correct solution is the one with the positive sign of the discriminant) . i ^ ^ ^

-(2as + 2sty ₂ ) + ^! (2as + 2sty ₂ ) ² — 4(s ² + q - y )(or ² + t ² y ₂ - + 2aty ₂ - uq + uy _? )

2(s ² + q - y ₂ ² )

Equating Eq. (15), obtained with the value of xl given above, with Eq. (14), an equation is obtained where the only unknown is y2 :

(16) ((-(2kly ₂ -2qd+2dy2 ² +2bk)+((2kly ₂ -2qd+2dy ₂ ² +2bk) ² -4(k ² +q- y ₂ ² )(b ² + ² )(y ₂ ² )+2bly ₂ -l+ly ₂ ² +qd ² -(d ² )(y ₂ ² )))^

(2as+2sty2)-((2as+2sty ₂ ) ² -4(s ² +q 2 ² )(a +(t ² )Cy2 ² )+2aty2-uq+uy2W ⁵ )/(2(s2+q- y ₂ ² ) ))-2gd-2du+2d((-(2as+2sty ₂ )-((2as+2sty ₂ ) ² -4(s ² +q-y ₂ ² )(a ² +(t ² )(y ₂ ² ]+2aty ₂ - uq+uy ₂ ² ))° ^(2(s ² +qy ₂ ² ))) ² )+((2g((-(2as+2sty ₂ )-tf^

y2 ² )(a ² +(t ² )(y2 )+2aty ₂ -uq+uy2 ² )) ⁰ ^(2(s ² +q-y ₂ ² )))-2gd-2d

((2as+2sty ₂ ) ² -4(s ² +q-y ₂ ² )(a ² +(t ² )(y ₂ ² )+2aty ₂ -uq+uy ₂ ² ) ) ^{0 5} )/(2 *(s ² +q-y ₂ ² )) ) ² ) ² - 4(d ² -2d((-(2as+2sty ₂ )-((2as+2sty2) ² -4(s +q-y2 ² )(a ² +(t ² )Cy2 ² )+2aty2- uq+uy ₂ ² ))° ^(2(s ² +q-y ₂ ² )))+u)(g ² -ul+l((-(2as+2sty ₂ )-tf^

y ₂ ² )(a ² +(t ² ){y2 ² )+2aty ₂ -uq+uy2 ² )) ⁰ ^/(2(s ² +q-y2 ² ))) ² ((2as+2sty ₂ ) ² -4(s ² +q-y2 ² )(a ² +(t ² )(y2 ² )+2aty ₂ -uq+uy2 ² )) ⁵ )/f2(s ² +q- y ₂ ² )))W ⁵ )/(2(d ² -2d((-(2as+2sty2)-((2as+2sty ₂ ) ² -4 (s ² +q-y ₂ ² )

(a ² +(t ² ) y ₂ ² )+2aty2-uq+uy2 ² ))°- ⁵ )/(2(s ² +q-y2 ² )))+u)))=0 Eq. (16) does not have an analytical solution and must consequently be solved numerically, for example with the bisection method.

Once the co-ordinate y2 is known, it can be substituted in the other equations, and all the other unknowns can be computed analytically. The solution of the system is consequently of a semi-numeric type.

Once the co-ordinates of the three points I, F and C are obtained, the deformations of the element S, understood as the relative displacements between the plate 4 and the plate 2, can be calculated.

It should moreover be noted, recalling what was mentioned previously, that the constraint imposed on the plate 2 can be imposed also on the structure or on the object on which the measurement is made, without any need for a rigid coupling with the plate 2 itself.

By way of example, if the element S undergoes a measurement by means of the device 1 in a laboratory environment, it is possible to fix the portion of the element S that is located in a position corresponding to the plate 2 on the same support as that on which the plate 2 itself is fixed. The coupling in this way would be indirect, and moreover it would be possible to arrange a "universal" plate 2, i.e., one designed for making measurements on different objects which can be combined to different plates 4 shaped according to the geometry of the object on which the measurement is made .

In brief, a measuring method is thus defined that, in general terms, comprises the following steps:

- rigidly coupling an object at least to the second plate 4 and possibly to the first plate 2 ;

- keeping the first plate 2 substantially fixed with respect to the reference system 0 that is fixed with respect to the device 1;

- detecting the displacements 66, 68, 610, 612,

614, 516 by means of the position transducers 6, 8, 10, 12, 14, 16 resulting from the movement of the second plate 4 with respect to said first plate 2 imposed by a deformation of the object coupled to them; and

- calculating displacements and rotations δχ, 6y, δζ, θχ, 9y, θζ of the second plate 4 with respect to the first plate 2 starting from the displacements 66, 68, 610, 612, 614, 616 detected by the position transducers 6, 8, 10, 12, 14, 16.

The implementation of said measuring method is very simple and advantageous both in computational terms and in mechanical terms.

From the computational standpoint, according to an advantageous aspect of the present invention, the non- circular symmetry with which the position transducers are arranged enables a solution of a semi-numeric type to be obtained, such as the one described previously, for the system of equations that is considerably simpler (hence less burdensome from the computational standpoint) as compared to the case where the transducers 6, 8, 10, 12, 14, 16 were arranged according to circular symmetry.

The algorithm used for solving the system of equations calculates iteratively only one of the nine unknowns, subsequently obtaining in an analytical way the further unknowns starting from the numeric calculation of the first. This enables a reduction in the computational power required, or, in a dual way, results can be obtained in a shorter times given the same computational power. From the mechanical standpoint, it will be appreciated that the device 1 can be used either in the laboratory (in which case, the electronic processing unit can be a fixed station with a computer) or on board a vehicle or a structure of which it is intended to measure the deformations in real time (in which case, the electronic processing unit can be an electronic control unit installed on board the vehicle or the structure) . For example, in the case of the flexible connection element S it is possible to couple thereto the device 1 directly in the underbody of the vehicle, connecting it with a control unit of the vehicle itself possibly provided for co-operating with other systems of the vehicle. Moreover, the constraints necessary to maintain the position of the first plate 2 can be easily reproduced on board the vehicle (or any structure on which the device 1 is installed) .

Finally, it is to be noted that the device 1 can also be used as global position transducer for the measurement of displacements with respect to a fixed reference, for example by rigidly coupling the plate 4 to a structure or to an object (possibly movable) and fixing the plate 2 to a different object or structure that functions as fixed reference. Hence, in this case it is more evident than ever how in general just the coupling with the second plate 4 is sufficient to make a measurement (where, in any case, the previous considerations apply) .

The device 1 according to the invention thus presents a series of considerable advantages. In the first place, the structure of the plates 2, 4 and the consequent arrangement of the transducers with respect thereto is without the circular symmetry, which enables an area to be obtained in which the object of which the deformations are to be measured can be easily arranged. Furthermore, the possibility of solving the system of eguations that describes the kinematics of the device 1 in a semi-numeric way enables a drastic reduction in the computing times, rendering it possible, given the same computational power installed on the electronic processing unit connected to the device 1, to acquire and process data in a shorter time .

With reference to Figure 3, an advantageous variant of the instrument 1 is designated by the reference number 1' . All the components that are identical to those described previously are designated by the same reference numbers. The difference of the device 1 ' with respect to the device 1 lies only in the fact that the third and fourth position transducers 10, 12 are arranged in a reversed way with respect to the instrument 1. The axes H10, H12 define a plane orthogonal to the first plate 2.

In particular, the first ends 38, 40 of the transducers 10, 12 are connected to the first header 20 in a single connection point D' by means of a single fourth joint J4 ' (which basically comprises a double joint of a spherical type), whereas the second ends 42, 44 are connected to the second plate 4 at the second header 28 in two separate connection points E', F' by means of respective joints J5 ' J6 ' of a spherical type. The position of the connection point D' is such that its projection on the plate 4 is in an intermediate position with respect to the points E', F' when the plates 2, 4 are parallel.

Said arrangement enables further optimization of the overall dimensions of the position transducers and widening of the area dedicated to insertion of an object on which a measurement is to be made.

With reference to Figure 4, a second embodiment of a measuring device according to the present invention is designated by the reference number 100 (appearing in this figure is also the element S partially sectioned to show some components that otherwise would not be visible ) .

The measuring device 100 comprises a first plate 102, a second plate 104, and six wire extensometers 106, 108, 110, 112, 114, 116. The aforesaid wire extensometers 106, 108, 110, 112, 114, 116 are set between the first and second plates 2, 4, connect the latter, and comprise respective drums D106, D108, DUO, D112, D114, D116, which have respective axes H016, H108, H110, H112, H114, H116 and wound on which are corresponding wires W106, W108, WHO, W112, W114, W116 made of a substantially inextensible material.

The first plate 102 comprises, in this embodiment, a base element 118 of a quadrilateral shape having a through hole 120 shaped for receiving the element S or any object on which the measurement is to be made, and a first bracket 122, a second bracket 124, a third bracket 126, and a fourth bracket 128, which are fixed to the base element 118 in positions corresponding to four vertices of a quadrilateral, here coinciding with the vertices of the base element 118.

The first and second brackets 122, 124 are substantially L-shaped and are fixed so as to have, respectively, a first flap 130 and a second flap 132 orthogonal to the base element 118. They are moreover aligned to one another and are on one and the same side with respect to the brackets 126, 128.

The third bracket 126 is of an angular type; i.e., it comprises a third flap 134 and a fourth flap 136, which are mutually orthogonal, and is fixed to the base element 118 in such a way that the flaps 134, 136 are orthogonal thereto. The fourth bracket 128 is identical to the third bracket 126 and comprises a fifth flap 138 and a sixth flap 140, which are mutually orthogonal, and is fixed to the base element 118 in such a way that the aforesaid flaps 138, 140 are orthogonal thereto.

The sequence of the flaps 130, 134, 136, 138, 140, 132 defines in this way an array with a substantially C-shaped geometry, as may be appreciated from Figure 4, defined substantially by three orthogonal stretches comprising:

- a first stretch defined by the flaps 130 and

134;

- a second stretch defined by the flaps 136, 138;

- a third stretch defined by the flaps 132, 140. The plate 102 further comprises six supporting elements 142, 144, 146, 148, 150, 152 fixed, respectively, to the flaps 130, 134, 136, 138, 140, 132.

The second plate 104, in this embodiment, is basically configured as an annular element comprising a first portion 154 and a second portion 156, which can be coupled by means of threaded connections and carry a fifth bracket 158, a sixth bracket 160, and a seventh bracket 162, arranged at the vertices of an isosceles triangle (the brackets 158, 162 are opposite to one another) . Finally fixed in a removable way to each bracket is a respective clamping plate, respectively, 164, 166, 168.

The drums D106, D108, DUO, D112, D114, D116 of the wire extensometers are connected to the first plate 102 by means of fixing to the supporting elements, respectively, 142, 144, 146, 148, 150, 152. In this way, the wire extensometers are arranged according to a C-shaped geometry and grouped in the pairs 106-108, 110-112 and 114-116. The drums D106, D108 are fixed, respectively, to the supporting elements 142, 144 at first and second connection point A' ', B' ' that are distinct from one another. Hence, they are connected to the plate 102 along the first stretch of the aforementioned array of flaps of the brackets.

In a way similar to the device 1, each connection point on the plate 102 is defined by the intersection of the axis of a drum with the corresponding supporting element and is understood as geometrical reference, set in a position corresponding to which is a joint between a wire extensometer and the plate 102 (preferably, a threaded connection, just like the remaining ■extensometers ) .

The corresponding wires W106, 108 are instead connected to the plate 104, in particular to the bracket 158, in a single third connection point C' ' . For the plate 104 the presumed intersection of the convergent wires on each of the brackets 158, 160, 162 is assumed as connection point.

In this case, the connection is made by fastening the clamping plate 164 on the bracket 158 (other solutions are in any case possible) pinching the two wires W106, W108 that converge on the bracket.

The drums DUO, D112 are fixed, respectively, to the supporting elements 146, 148 in a position corresponding to a fourth connection point D' ' and a fifth connection point E ^{1 1} , which are distinct from one another (hence they are connected to the plate 102 along the second stretch of the aforementioned array of flaps of the brackets), whereas the corresponding wires WHO, W112 are connected to the plate 104, in particular to the bracket 160, in a single sixth connection point F ' ' by means of tightening of the clamping plate 166. Finally, the drums D114, D116 are fixed, respectively, to the supporting elements 150, 152 in a position corresponding to a seventh connection point G' ' and an eighth connection point H' ' that are distinct from one another (hence, they are connected to the plate 102 along the third stretch of the aforementioned array of flaps of the brackets) , whereas the corresponding wires W114, W116 are connected to the plate 104, in particular to the bracket 162, in a single ninth connection point I' ' by tightening the clamping plate 168.

It should be noted that also in this case the wire extensometers are grouped in pairs, each arranged according to a V-shaped geometry, and define an array with a C-shaped geometry and without central symmetry, just like the device 1. In addition, each pair of convergent wires preferably defines a plane orthogonal to the base element 118.

The relative position of the various connection points is hence preferably identical to the one illustrated in Figure 2A (it is simply necessary to replace the points A, B, C D, E, F, G, H, I with the corresponding points A' ', B ' ' , C' ', D' ', E' ', F' ', G' ', H' ', I' ') _? as likewise identical is the choice of the reference system 0, which enables application of the system of equations described previously. There is no change at the level of the measuring method, so that, if 5106, 5108, 5110, 5112, 5114, 5116 are the displacements of the wires W106, W108, WHO, W112, W114, W116 that can be detected by means of the corresponding wire extensometers, starting from these, it is possible to compute the displacements and rotations 5x, 5y, δζ, θχ, Qy , θζ of the plate 104 with respect to the plate 102 and consequently the deformations and displacements of the flexible- connection element S (or of any other object) . Except for the different type of position transducers (and hence the different type of connection to the plates 102, 104) , operation is substantially identical to that of the device 1, with all the advantages described previously .

Of course, without prejudice to the principle of the invention, the details of construction and the embodiments may vary widely with respect to what has been described and illustrated herein purely by way of example, without thereby departing from the scope of protection of the present invention, as defined by the annexed claims.