WO2017017181A1

WO2017017181A1 - A contactless displacement and velocity measurement system

Info

Publication number: WO2017017181A1
Application number: PCT/EP2016/067995
Authority: WO
Inventors: Juan Fernando MARTÍN ANTOLÍN; Jordi NAQUI GAROLERA
Original assignee: Universitat Autonoma De Barcelona
Priority date: 2015-07-30
Filing date: 2016-07-28
Publication date: 2017-02-02

Abstract

A contactless displacement and velocity measurement system The system comprises: - first (1) and second (2) parts relatively movable to each other; - a planar electromagnetic resonator arrangement (3) excitable by an external electromagnetic field, and comprising a plurality of planar electromagnetic resonators (3) arranged in a row along a surface of the first part (1); - an element (4) for emitting or propagating an electromagnetic wave providing said external electromagnetic field, arranged on the second part (2); and - measuring means for detecting features on the electromagnetic wave or on an electrical signal associated thereto, and for providing, based on the detected features, relative displacement and velocity measurements of the first part (1) with respect to the second part (2), or vice versa. The propagating element can be a coplanar waveguide CPW to which a harmonic signal in the microwave range is fed. The passing of a resonator in front of the CPW causes a notch in the signal magnitude of the transmitted signal. The output signal is applied to an envelope detector which will show an amplitude modulated signal. The speed may be derived from the time between amplitude peaks. In order to suppress inter-resonator coupling, two fixed split ring resonators SRR may be arranged on the static substrate on which the CPW is provided, with the same distance as the resonators on the movable element, but with their slits arranged on the opposite side.

Description

A contactless displacement and velocity measurement system

Field of the Invention

The present invention generally relates to a contactless displacement and velocity measurement system, based on symmetry-related control of the coupling between a sensing element and a planar electromagnetic resonator arrangement, and more particularly to a system where the planar electromagnetic resonator arrangement comprises a plurality of planar electromagnetic resonators arranged in a row.

The invention is particularly applied to the measurements of angular displacements and angular velocities.

Background of the Invention

Metamaterial-based or -inspired sensors have attracted a lot of attention in the last few years [1 ]. In particular, many sensors have been reported where the variation of frequency, phase, and/or quality factor in resonator-loaded lines, caused by the physical magnitude under measurement (linear or angular displacement, velocity, permittivity, etc.), is the sensing principle [2], [3]. In general, sensor performance may be degraded by cross-sensitivities on environmental changes, such as temperature and humidity, and microwave sensors are not an exception.

Recently, a different principle for microwave and contactless sensing based on the symmetry-related electromagnetic properties of transmission lines loaded with symmetric metamaterial resonators (such as the split ring resonator -SRR), was proposed [4]. The main advantage of these new sensors is the fact that they are robust against environmental changes, and are therefore of high interest in applications where extreme and variable ambient conditions can be found (e.g. space). The reason for such a major robustness, as compared to the previous conventional sensors, is that the novel sensors are based on symmetry disruption. For the reference state, the sensor (line plus resonator) is symmetric, and this symmetry is not affected by environmental variations. When the variation of the magnitude under measurement breaks this reference symmetry, this can be detected by the presence of a transmission zero (or notch) of the resonator-loaded line. In these sensors, typically (not exclusively) the variation of the notch magnitude is used for sensing. These sensors are of special interest in applications where the detection of alignment/misalignment between two different surfaces is required.

Next, the sensing principle is described, considering a transmission line loaded with an electrically small and symmetric resonator, such as a coplanar waveguide (CPW) loaded with an SRR etched on the back substrate side (see Fig. 1 ). At the fundamental resonance frequency, this particle exhibits an electric wall at its symmetry plane. Conversely, the symmetry plane of the CPW is a magnetic wall for the fundamental CPW mode. Thus, if the CPW is loaded with a single SRR symmetrically etched in the line, the structure is transparent at the fundamental SRR resonance. The reason is that, under these conditions, there is neither a net axial magnetic field (to the SRR) nor a coplanar electric field (with the SRR) able to excite the particle, and therefore the SRR is not coupled to the line. However, if symmetry is perturbed by any means (lateral displacement, rotation, asymmetric dielectric loading, etc.), then this perfect cancelation of electric and magnetic field components vanishes, a net coupling arises, the particle is driven, and the transmission coefficient exhibits a notch at the fundamental SRR resonance (Fig. 1 ) [4]. Moreover, the notch magnitude depends the level of asymmetry.

With the aforementioned considerations, it follows that symmetry disruption can be used for sensing alignment, displacements or velocities [4]-[9]. Indeed, sensors based on this principle are versatile in the sense that can be implemented by considering different lines and symmetric resonators exhibiting symmetry planes of different electromagnetic nature (one an electric wall and the other one a magnetic wall). It is also clear that if the notch depth is very sensitive to the lack of symmetry, these devices may also be especially useful as detectors, comparators or differential sensors.

It is worth mentioning that other sensors based on symmetry-related electromagnetic properties of resonator-loaded lines have been reported recently, where sensing is based on resonance frequency splitting [10]-[1 1 ]. Thus, in the reference (symmetric) state, the structure exhibits a single notch, but two notches appear when symmetry is disrupted, and the frequency separation between them is related to the level of asymmetry.

A contactless angular displacement and velocity measurement system designed according to a design strategy associated to an axial configuration is disclosed in [8], where a CPW is placed on a fixed stator and an electric-LC is placed on a rotor, in respective close parallel planes. Said system includes the features of the preamble clauses of claim 1 of the present invention.

Said axial configuration allows for measurements of speeds that are constant or do not change rapidly (relative to a semi-period of rotation). The reason is that the sampling rate is assumed to be discrete. A continuous measurement may be also possible (mapping every amplitude level to a particular angle), but at the expense of accuracy. Said axial configuration doesn't allow to perform instantaneous angular velocity measurements, so there is a need for improving the system disclosed in [8].

References:

[1 ] M. Sc ^ler, C. Mandel, M. Puentes, and R. Jakoby "M eta mate rial inspired microwave sensors," IEEE Microw. Magazine, vol. 13, no. 2 pp. 57-68, Mar. 2012.

[2] C. Mandel, B. Kubina, M. Sc ^ler, and R. Jakoby, "Passive chipless wireless sensor for two-dimensional displacement measurement," Europ. Microw. Conf., Manchester, UK, Oct. 201 1 , pp. 79-82.

[3] M. Puentes, C. Weiss, M. Sc ^ler, and R. Jakoby, "Sensor array based on split ring resonators for analysis of organic tissues," IEEE MTT-S Int. Microw. Symp.,

Baltimore, MD, Jun. 201 1 .

[4] J. Naqui, M. Duran-Sindreu and F. Martin, "Novel sensors based on the symmetry properties of split ring resonators (SRRs)," Sensors, vol. 1 1 , no. 8, pp. 7545-7553,

Jul. 201 1 .

[5] J. Naqui, M. Duran-Sindreu, and F. Martin, "Alignment and position sensors based on split ring resonators," Sensors, vol. 12, no. 9, pp. 1 1790-1 1797, Aug. 2012.

[6] A. Karami Horestani, C. Fumeaux, S.F. Al-Sarawi, and D. Abbott, "Displacement sensor based on diamond-shaped tapered split ring resonator," IEEE Sensors J., vol. 13, no. 4, pp. 1 153-1 160, Apr. 2013.

[7] A. Karami Horestani, D. Abbott, C. Fumeaux, "Rotation sensor based on horn- shaped split ring resonator," IEEE Sensors J., vol. 13, no. 8, pp. 3014-3015, Aug. 2013.

[8] J. Naqui, and F. Martin, "Transmission lines loaded with bisymmetric resonators and their application to angular displacement and velocity sensors," IEEE Trans. Microw. Theory Techn., vol. 61 , no. 12, pp. 4700-4713, Dec. 2013.

[9] J. Naqui, and F. Martin, "Angular displacement and velocity sensors based on electric-LC (ELC) loaded microstrip lines," IEEE Sensors J., vol. 14, no. 4, pp. 939- 940, Apr. 2014.

[10] A. K. Horestani, J. Naqui, Z. Shaterian, D. Abbott, C. Fumeaux, and F. Martin, "Two-dimensional alignment and displacement sensor based on movable broadside- coupled split ring resonators," Sensor Actuat. A-Phys., vol. 210, pp. 18-24, Apr. 2014.

[1 1 ] J. Naqui, C. Damm, A. Wiens, R. Jakoby, L. Su, F. Martin, "Transmission lines loaded with pairs of magnetically coupled stepped impedance resonators (SIRs): modeling and application to microwave sensors," IEEE MTT-S Int. Microw. Symp., Jun. 2014, Tampa, FL, USA.

[12] D. Schurig, J. J. Mock, and D. R. Smith, "Electric-field-coupled resonators for negative permittivity metamaterials," Appl. Phys. Lett., vol. 88, paper 041 109, Jan. 2006.

[13] R. Marques, F. Medina, and R. Rafii-EI-ldrissi, "Role of bianisotropy in negative permeability and left-handed metamaterials," Phys. Rev. B, vol. 65, paper 144440, 2002. Description of the Invention

It is an object of the present invention to offer an alternative to the prior state of the art, with the purpose of providing a contactless displacement and velocity measurement system which covers the gaps found in the prior art, providing a system allowing to perform instantaneous velocity measurements, including angular velocity measurements, and high precision relative displacement measurements, including angular displacement measurements.

To that end, the present invention relates to a contactless displacement and velocity measurement system, comprising:

- first and second parts which are relatively movable to each other,

- a planar electromagnetic resonator arrangement excitable by an external electromagnetic field, and being arranged on said first part;

- at least one element for at least propagating an electromagnetic wave providing said external electromagnetic field, said at least one element being arranged on said second part without contact with said planar electromagnetic resonator arrangement, such that said at least one element is loaded with said planar electromagnetic resonator arrangement at least for some positions of the first part with respect to the second part along said relative motion; and

- measuring means configured and arranged for detecting features on said electromagnetic wave or on an electrical signal associated thereto, said features induced by the planar electromagnetic resonator arrangement, and also configured for providing, based on said detected features, relative displacement and velocity measurements of said first part with respect to said second part, or vice versa.

Contrary to the known systems, particularly contrary to the system disclosed in [8], in the system of the present invention, in a characteristic manner, the above cited planar electromagnetic resonator arrangement comprises a plurality of planar electromagnetic resonators arranged in a row along at least one surface of said first part.

Depending on the embodiment, said at least one element also generates said electromagnetic wave. That is the case of a preferred embodiment for which said at least one element is a transmission line electrically fed through an input port and generating said electrical signal at an output port, and wherein said measuring means are connected to said output port of said transmission line for detecting said generated electrical signal and said features thereof.

According to a preferred variant of said embodiment, said transmission line is a coplanar waveguide (CPW) having a central conductor strip and two return conductors, one to either side of the central strip, and separated therefrom by respective slots, wherein said planar electromagnetic resonators are arranged side by side such that during the relative movement of the first and second parts they pass transversally to the transmission line, in a parallel plane, causing attenuation peaks in said electrical signal when any of the planar electromagnetic resonators is aligned with any of said slots.

For alternative embodiments, said at least one element is a waveguide or part of a transmitting/receiving unit of a wireless link. Other electromagnetic propagation means can also be used to constitute said at least one element, for other embodiments.

For an embodiment, the above cited row follows at least one of a straight path and a curved path following at least an arc. For some embodiment, the row follows a combination of different paths (straight, curved, meander, etc.), according to one or more directions.

When the row is only a straight path, the relative displacement and velocity measurements refer to relative linear displacement and linear velocity measurements, respectively.

For a preferred embodiment, said row follows a complete circumference path. Said first part has, for an embodiment, a substantially planar major face and said second part has at least a substantially planar first face facing and parallel to at least a portion of said substantially planar major face of the first part.

For a preferred embodiment, at least one of said first and second parts is a rotating part, and said planar electromagnetic resonators are arranged following a circumferential row along or near the outer edge of said substantially planar major face of the first part and said at least one element is arranged on said substantially planar first face of the second part, or on a substantially planar second face of the second part opposed to said substantially planar first face, wherein said relative displacement and velocity measurements being relative angular displacement and angular velocity measurements, respectively. For this embodiment, instantaneous angular velocity measurements can be performed with the system of the invention.

For another embodiment, the first part has an outer cylindrical surface and the second part has at least a first face facing a portion of said outer cylindrical surface of the first part, wherein at least one of said first and second parts is a rotating part, rotating about the axis of the cylinder bounded by said outer cylindrical surface, and wherein said planar electromagnetic resonators are arranged following a circumferential row along said outer cylindrical surface of the first part and said at least one element is arranged on said first face of the second part, or on a second face of the second part opposed to said first face, wherein said relative displacement and velocity measurements being relative angular displacement and angular velocity measurements, respectively.

When the specific application on which the system of the present invention is to be implemented requires a redundant measuring mechanism, two or more pluralities of planar electromagnetic resonators, arranged on different regions of the first part or on two different parts, and associated to two or more respective elements propagating electromagnetic waves, arranged on different regions of the second part or on two other different parts, are envisaged for different embodiments implementing redundancy.

One of such redundancy embodiments is that which combines the above described embodiments for angular displacement and angular velocity measurements of a rotating part, i.e. the one where a plurality of planar electromagnetic resonators are arranged following a circumferential row along or near the outer edge of a substantially planar major face of the first part and the one where a plurality of planar electromagnetic resonators are arranged following a circumferential row along an outer cylindrical surface of the first part.

According to an embodiment, the spacing left between each two contiguous planar electromagnetic resonators has been selected in order not to suffer from inter- resonator coupling.

However, as for some application a high precision for the measurements is needed which causes the spacing between each two contiguous planar electromagnetic resonators be very small, such that inter-resonator coupling could happen, for a preferred embodiment, the transmission line is arranged on the second face of the second part and the system further comprises an additional planar electromagnetic resonator arrangement arranged on the first face of the second part, configured for avoiding said inter-resonator coupling between the planar electromagnetic resonators of the first part. For a variant of said preferred embodiment, said additional planar electromagnetic resonator arrangement comprises two planar electromagnetic resonators identical or similar to the planar electromagnetic resonators arranged on the first part but oriented at 180° with respect to them, such that when two opposing pairs of planar electromagnetic resonators are perfectly aligned a notch at the resonance frequency of the resulting pair of broadside-coupled resonators occurs.

Said planar electromagnetic resonators are split ring resonators (SRR) having at least one slit, for an embodiment, preferably single loop resonators, although, for other embodiment, other kind of resonators are also covered by the invention, such as complementary split ring resonators (CSRR), where the metallic parts of the SRR are replaced with slots etched on a metallic plane.

For an embodiment, said first and second parts are dielectric parts attached to or integral with respective first and second members having a relative motion with respect to each other whose displacement and velocity is to be measured by the system. For another embodiment, said first and second parts constitute said first and second members, respectively.

For some embodiments, at least one of the first and second members and/or at least one of the first and second parts is disc-shaped, ring-shaped or cylinder-shaped.

According to an embodiment of the system of the present invention, for which the above cited at least one element is a transmission line electrically fed through an input port and generating an electrical signal at an output port, the measuring means comprises at least:

- a power source connected to said input port and configured to feed the transmission line with a harmonic signal tuned at said resonance frequency of the pair of broad-side coupled resonators; and

- an envelope detector connected at said output port of the transmission line to demodulate the generated electrical signal which has been modulated in amplitude due to the relative motion of the first and second parts, where the time distance between adjacent amplitude peaks of the demodulated signal gives the displacement and velocity measurements, and even position. In this case, the above mentioned detected features induced by the planar electromagnetic resonator arrangement are the above mentioned time distance between adjacent amplitude peaks of the demodulated signal.

For an embodiment, the planar electromagnetic resonators are metamaterial resonators. For another embodiment, the planar electromagnetic resonators are closed resonators in the sense that are excited by external electromagnetic fields rather than by feeding ports. Brief Description of the Drawings

The previous and other advantages and features will be better understood from the following detailed description of embodiments, with reference to the attached drawings, which must be considered in an illustrative and non-limiting manner, in which:

Fig. 1 illustrates the sensing principle on which the present invention is based, where the SRR symmetry plane is aligned (a) or misaligned (b) with the CPW axis.

Fig. 2 schematically shows an embodiment of the system of the invention, illustrating the sensing concept for an edge configuration, where the chain of resonators is etched along a planar face near the outer perimeter of the rotor (only shown in part) forming a circumferential row and the sensing element is placed over a portion of the circumferential row.

Fig. 3 shows an embodiment of the system of the present invention for which the CPW is placed on a face of the stator while in an opposing face a pair of fixed resonators are arranged, where (a) shows the layout of the CPW with fixed resonators and the chain of resonators (schematically shown following a straight row, for clarity sake, although for the present embodiment the chain of resonators follow a circumferential row, as shown in part in Fig. 2), and (b) shows a cross section for the aligned position where the CPW is coupled to a BC SRR for the edge configuration. Dimensions are (in mm): W = 1.3, G = 0.9, P_m = 2, = .6, l₂ = 6.2, c = 0.4, and g = 0.2. The thicknesses of the substrates are 0.635 mm (stator) and 1 .27 mm (rotor).

Fig. 4 is a diagram showing the simulated transmission coefficient (amplitude) for the reference aligned position (0T_m) and for different misalignments between the fixed and movable split rings, which are separated by an air gap of 0.5 mm, where the simulations have been made for the embodiment of Fig. 3.

Fig. 5 shows the schematic of the measuring means of the system of the present invention, for an embodiment, including a sensing line, a circulator and an envelope detector.

Fig. 6 is a diagram showing the measured output waveform for a rotating speed of 2 rps in the edge configuration of the system of the present invention, for an embodiment. Fig. 7 schematically shows a further embodiment of the system of the present invention for which the array or chain of resonators are arranged along an outer cylindrical surface. Detailed Description of Several Embodiments

With reference to Figures 2 to 6 a main embodiment of the system of the present invention is described in this section, which implements what has been named as edge configuration. The depicted embodiments are also limited to the case for which the displacement and the velocity to be measured are of an angular nature, i.e. refer to the relative rotation between first and second members.

In the edge configuration, an array of resonators 3 is etched along the edge of the rotor and coupled broadside to the transmission line 4, as illustrated in Fig. 2. In this approach, the resonators are supposed to pass transversally to the line 4, so that when any of the resonators of the chain 3 is aligned with the line 4, the structure is transparent (Fig. 1 (a)). By contrast, the line exhibits a strong notch when a resonator is aligned with one of the slots of the CPW (Fig. 1 (b)). Obviously, the larger the number of transmission peaks, the higher the accuracy in the determination of the instantaneous rotation speed. The number of peaks is proportional to the number of resonant elements. However, increasing the number of resonators means to reduce the resonator transverse dimension and the inter-resonator spacing. A minimum transverse dimension is necessary to guarantee a reasonable attenuation at resonance. Because of the inter- resonator coupling, a minimum spacing between contiguous resonators is also restricted. It has been found that if the resonators are close to each other, inter- resonator coupling degrades sensor performance considerably.

Although the present invention also covers embodiments for which the spacing between each two contiguous resonators of the chain 3 is enough not to suffer from said inter-resonator-coupling problem, preferred embodiments implement a strategy aimed at avoiding inter-resonator coupling.

The proposed strategy to solve the inter-resonator coupling problem has been to use an additional (fixed) resonant arrangement on the stator, particularly formed by a pair of resonators 5. The specific CPW-based configuration is depicted in Fig. 3. A CPW 4 etched on a second face 2b of dielectric substrate part 2 (for the example is Rogers RO3010) is loaded with a pair of fixed single loop rectangular SRRs 5, etched on a first face 2a, opposed to second face 2b, of the dielectric substrate part 2, acts as the stator S. The rotor R is formed by a rotating member M to which a dielectric substrate part 1 is attached, and contains the chain of movable resonators 3 (movable because part 1 moves together with member M), single loop SRRs identical to those fixed 5, but oriented with the slits etched on the opposite side. When a pair of SRRs 3 of the rotor R is perfectly aligned with the fixed pair 5, a notch at the resonance frequency of the resulting broadside-coupled SRRs (BC-SRRs) [13] occurs. Since this resonance frequency is distant (lower) from the resonance frequency of the single SRRs, the coupling problem disappears. Fig. 4 demonstrates that the resonance frequency shifts downwards as a result of the broadside coupling that depends on the rotor-to-stator angular position.

For the measurement of both angular displacement and velocity, the CPW is fed with a harmonic signal tuned at the resonance frequency of the pair of BC-SRRs. The rotation modulates the carrier frequency in amplitude at the output port (Port 2) of the CPW. For angular displacements, the input dynamic range is n/n. Note that, by aligning pairs of resonators with the line 4, the required number of resonators for n amplitude peaks is n+l. For angular velocities, the distance between adjacent peaks gives the rotation speed (ω_Γ= 2n/nT_m with T_m = T_r/n and T_r is the rotation period). In the limit where n->∞, then r_m->0, and ω_Γ becomes the instantaneous speed. The setup for the measurement of the rotation speed is represented in Fig. 5, and includes an envelope detector Ed for rectifying the modulated signal, such that the time between adjacent amplitude peaks, T_m, allows for rotation speed measurements. In order to avoid unwanted reflections caused by the envelope detector Ed, a circulator Ci is cascaded between the output of the CPW and the input of the envelope detector Ed, as depicted in Fig. 5

The time-domain waveform at the envelope detector Ed output obtained through an oscilloscope, for a rotation speed of 2 rps (revolutions per second), is plotted in Fig. 6, whose period is coherent with the nominal speed. From this waveform, the angular velocity can be measured with high accuracy and precision, including instantaneous angular velocity measurements. Said time-domain waveform has been obtained for the edge configuration arrangement shown in Figures 2 and 3 for a fabricated chain of 300 resonators arranged on a rotor with 101.6-mm radius.

It should be highlighted that, though the principle for velocity sensing is based on a geometrical alignment, the proposed sensors are robust against small mechanical vibrations or misalignments that may occur in real systems. In fact, the reported proof- of-concept demonstrators were measured in the absence of perfect alignments.

Figure 7 shows an alternative embodiment, also applied to the measurement of angular displacements and angular velocities, but where the chain of resonators 3 (in this case circular SRRs) is arranged on an outer cylindrical surface 1 c of a dielectric substrate part 1 (which in the depicted embodiment is an annular dielectric strip 1 ), attached to the outer cylindrical surface of a rotating cylinder member M (such as a reaction wheel), surrounding the same. The transmission line 4 is, in this case, arranged on face 2a of the dielectric substrate part 2, i.e. directly facing some of the resonators of the chain of resonators 3, as for the illustrated embodiment the pair of fixed resonators are not included. However, a slight modification of the embodiment depicted in Figure 7 envisages placing, like in the embodiment of Figure 3, the transmission line 4 on face 2b of dielectric substrate part 2 and including a pair of fixed resonators 5 on face 2a (equal or similar to the ones of the chain 3).

Although, for the embodiment of Figure 7, the resonators could be bended, due to the fact that they are arranged on a curved surface, the radius of the rotating cylinder member M generally has a high value and the number of resonators is selected, based on said radius, to be high enough so as said bending is only a slight bending, such that the operation of the system is not highly affected by the negative effects that said bending can generate. Alternatively, the dielectric substrate part 1 can be formed by a plurality of contiguous small planar faces, each supporting a respective resonator in a planar form, i.e. without bending, thus said possible negative effects are avoided.

Applications:

Both, the edge configuration and the configuration of the embodiment of Figure

7, are especially suitable for the measurement of instantaneous rotation speeds, contrary to the axial configuration disclosed in [8]. Therefore, said configurations are of interest for the measurement of the angular velocity of reaction wheels, present in space vehicles (satellites) for the attitude control, or even for antenna or solar panel pointing mechanisms. Indeed, the proposed edge-based microwave sensors offer a robust alternative to optical encoders (more sensitive to aging effects due, e.g., to thermal cycling or radiation accumulated dose), and to potentiometer-based sensors, where mechanical wearing due to harsh tribology conditions is critical (the materials used in the sensor must maintain electrical parameters after years of continuous friction under largely changing temperatures). Nevertheless, many other applications of the proposed microwave contactless sensors can be envisaged (servomechanisms, automotive industry, etc.).

A person skilled in the art could introduce changes and modifications in the embodiments described without departing from the scope of the invention as it is defined in the attached claims.

Claims

1 .- A contactless displacement and velocity measurement system, comprising:

- first (1 ) and second (2) parts which are relatively movable to each other;

- a planar electromagnetic resonator arrangement (3) excitable by an external electromagnetic field, and being arranged on said first part (1 );

- at least one element (4) for at least propagating an electromagnetic wave providing said external electromagnetic field, said at least one element (4) being arranged on said second part (2) without contact with said planar electromagnetic resonator arrangement (3), such that said at least one element (4) is loaded with said planar electromagnetic resonator arrangement at least for some positions of the first part (1 ) with respect to the second part (2) along said relative motion; and

- measuring means configured and arranged for detecting features on said electromagnetic wave or on an electrical signal associated thereto, said features induced by the planar electromagnetic resonator arrangement (3), and also configured for providing, based on said detected features, relative displacement and velocity measurements of said first part (1 ) with respect to said second part (2), or vice versa;

characterised in that said planar electromagnetic resonator arrangement comprises a plurality of planar electromagnetic resonators (3) arranged in a row along at least one surface of said first part (1 ).

2.- The system according to claim 1 , wherein said at least one element (4) is a transmission line electrically fed through an input port (Port 1 ) and generating said electrical signal at an output port (Port 2), and wherein said measuring means are connected to said output port (Port 2) of said transmission line for detecting said generated electrical signal and said features thereof.

3.- The system according to claim 2, wherein said transmission line is a coplanar waveguide (CPW) having a central conductor strip and two return conductors, one to either side of the central strip, and separated therefrom by respective slots, wherein said planar electromagnetic resonators (3) are arranged side by side such that during the relative movement of the first (1 ) and second (2) parts they pass transversally to the transmission line, in a parallel plane, causing attenuation peaks in said electrical signal when any of the planar electromagnetic resonators (3) is aligned with any of said slots.

4. - The system according to claim 1 , wherein said at least one element (4) is a waveguide.

5. - The system according to claim 1 , wherein said at least one element (4) is part of a transmitting/receiving unit of a wireless link.

6. - The system according to any of the previous claims, wherein said row follows at least one of a straight path and a curved path following at least an arc.

7. - The system according to claim 6, wherein said row follows a complete circumference path.

8.- The system according to claim 6 or 7, wherein said first part (1 ) has a substantially planar major face (1 a) and said second part (2) has at least a substantially planar first face (2a) facing and parallel to at least a portion of said substantially planar major face of the first part (1 ).

9. - The system according to claim 8, wherein at least one of said first (1 ) and second (2) parts is a rotating part, and wherein said planar electromagnetic resonators

(3) are arranged following a circumferential row along or near the outer edge of said substantially planar major face (1 a) of the first part (1 ) and said at least one element (4) is arranged on said substantially planar first face (2a) of the second part (2), or on a substantially planar second face (2b) of the second part (2) opposed to said substantially planar first face (2a), wherein said relative displacement and velocity measurements being relative angular displacement and angular velocity measurements, respectively.

10. - The system according to claim 6 or 7, wherein said first part (1 ) has an outer cylindrical surface (1 c) and said second part (2) has at least a first face (2a) facing a portion of said outer cylindrical surface (1 c) of the first part (1 ), wherein at least one of said first (1 ) and second parts (2) is a rotating part, rotating about the axis of the cylinder bounded by said outer cylindrical surface (1 c), and wherein said planar electromagnetic resonators (3) are arranged following a circumferential row along said outer cylindrical surface (1 c) of the first part (1 ) and said at least one element (4) is arranged on said first face (2a) of the second part (2), or on a second face (2b) of the second part (2) opposed to said first face (2a), wherein said relative displacement and velocity measurements being relative angular displacement and angular velocity measurements, respectively.

1 1 . - The system according to any of the previous claims, wherein the spacing left between each two contiguous planar electromagnetic resonators (3) has been selected in order not to suffer from inter-resonator coupling.

12. - The system according to claim 9 or 10 when depending on claim 2 or 3, wherein the transmission line is arranged on said second face (2b) of the second part (2), and wherein the system further comprises an additional planar electromagnetic resonator arrangement arranged on the first face (2a) of the second part (2), configured for avoiding inter-resonator coupling between the planar electromagnetic resonators (3) of the first part (1 ).

13. - The system according to claim 12 when depending on claim 2, wherein said additional planar electromagnetic resonator arrangement comprises two planar electromagnetic resonators (5) identical or similar to the planar electromagnetic resonators (3) arranged on the first part (1 ) but oriented at 180° with respect to them, such that when two opposing pairs of planar electromagnetic resonators are perfectly aligned a notch at the resonance frequency of the resulting pair of broadside-coupled resonators occurs.

14. - The system according to any of the previous claims, wherein said planar electromagnetic resonators (3, 5) are split ring resonators having at least one slit.

15.- The system according to claim 14, wherein said planar electromagnetic resonators (3, 5) are single loop resonators.

16. - The system according to claim 14, wherein said planar electromagnetic resonators (3, 5) are complementary split ring resonators.

17. - The system according to any of the previous claims, wherein said first (1 ) and second (2) parts are dielectric parts attached to or integral with respective first and second members having a relative motion with respect to each other whose displacement and velocity is to be measured by the system.

18. - The system according to claim 17, wherein at least one of said first and said second members and/or at least one of said first (1 ) and second (2) parts is disc- shaped, ring-shaped or cylinder-shaped.

19. - The system according to claim 13 or to any of claims 14 to 18 when depending on claim 13, wherein said measuring means comprises at least:

- a power source (v_c(t)) connected to said input port (Port 1 ) and configured to feed the transmission line with a harmonic signal tuned at said resonance frequency of the pair of broad-side coupled resonators; and

- an envelope detector (Ed) connected at said output port of the transmission line to demodulate the generated electrical signal which has been modulated in amplitude due to the relative motion of the first (1 ) and second (2) parts, where the time distance between adjacent amplitude peaks of the demodulated signal gives the angular displacement and velocity measurements, and even position.

20. - The system of any of the previous claims, wherein said planar electromagnetic resonators (3, 5) are metamaterial resonators.

21 . - The system of any of the previous claims, wherein said planar electromagnetic resonators (3, 5) are closed resonators in the sense that are excited by external electromagnetic fields rather than by feeding ports.