EP3266737B1 - Programmable multistable system - Google Patents

Programmable multistable system Download PDF

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Publication number
EP3266737B1
EP3266737B1 EP16178012.7A EP16178012A EP3266737B1 EP 3266737 B1 EP3266737 B1 EP 3266737B1 EP 16178012 A EP16178012 A EP 16178012A EP 3266737 B1 EP3266737 B1 EP 3266737B1
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Prior art keywords
multistable
elastic member
stable
elastic members
elastic
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German (de)
French (fr)
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EP3266737A1 (en
Inventor
Mohamed Zanaty
Simon Henein
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Patek Philippe SA Geneve
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Patek Philippe SA Geneve
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    • G—PHYSICS
    • G04—HOROLOGY
    • G04B—MECHANICALLY-DRIVEN CLOCKS OR WATCHES; MECHANICAL PARTS OF CLOCKS OR WATCHES IN GENERAL; TIME PIECES USING THE POSITION OF THE SUN, MOON OR STARS
    • G04B31/00—Bearings; Point suspensions or counter-point suspensions; Pivot bearings; Single parts therefor

Definitions

  • the present invention relates to a multistable system.
  • a system is considered stable if it is able to maintain its state when subjected to an external disturbance.
  • a multistable system is a system with several different stable states.
  • Multistable systems are described in the literature, for example in the article "Synthesis of compliant multistable mechanisms through use of a single bistable mechanism", Journal of Mechanical Design August 2011, Vol 133, Guimin, Chen et al, which describes methods for obtaining multistable mechanisms comprising a defined number of stable states.
  • a common feature of these different multistable systems is that they have a specific and predetermined number of stable positions, which can not be changed after manufacture.
  • An object of the present invention is to provide a multistable system whose number of stable states achievable is adjustable.
  • the position of the second end or the force applied to the second end of each of the n elastic members is adjustable.
  • each of the ends not joined to a connection zone and of which neither the position nor the force applied to it is adjustable is joined to a frame carrying said multistable system.
  • each of said connection zones is located in the middle of the elastic member which carries it.
  • the or each of the adjustable end (s) of the elastic members of rank r is able to move in translation along an axis A r .
  • the axes A r defined above are typically in the same plane.
  • connection zones are movable in translation.
  • the connection zone of a link member of rank r, with r between 1 and (n-1) can typically move in translation along an axis perpendicular to the axis A r .
  • each axis A r is perpendicular to the axis A r-1 .
  • the multi-stable system comprises one or more guiding device (s) for guiding the or each adjustable end (s) of the elastic members of rank r, with r between 1 and n, along the corresponding axis A r .
  • said one or more guiding device (s) are mounted on a frame carrying said multistable system.
  • Each guiding device may, for example, be an elastic guiding device such as an elastic leaf system, possibly multistable, or a non-elastic guiding device such as a groove or a rail.
  • At least one of the ends of said multistable system whose position is adjustable is associated with a position adjustment device comprising a set screw.
  • At least one of the ends of said multistable system to which an adjustable force is applied is associated with a force adjusting device comprising a spring constrained by a screw, said screw making it possible to adjust the force exerted by said spring on the adjustable end in corresponding strength.
  • the resilient members according to the invention typically comprise deformable buckling blades and / or articulated arms subjected to the action of at least one spring.
  • at least one of the elastic members comprises several deformable blades buckling.
  • the elastic members are integral with each other and, preferably, also with the frame.
  • the multistable system thus obtained is capable of changing its multistability, that is to say of changing the number of stable positions that it can reach as well as the forces necessary to move from one stable position to another.
  • Each adjustable end of the multistable system according to the invention can be adjusted in position, it will speak of end adjustable in position, or be subjected to a force whose intensity is adjustable, it will speak of adjustable end force.
  • multistable system programmable by displacement we speak of “multistable system programmable by displacement ".
  • multistable system programmable by force it is called “multistable system programmable by force”.
  • the invention also relates to multistable systems “mixed” or “hybrid” in which some ends are adjustable in position and other ends are adjustable in strength.
  • chassis means a fixed structure on which at least a part is fixed the multistable system.
  • elastic member is meant a member of which at least part is elastically deformable.
  • the first elastic member 1 comprises two blades 1a, 1b, parallel and deformable buckling, extending between first 2 and second 3 ends, and a connecting zone 4, preferably rigid, interrupting the blades 1a and 1b between said first 2 and second 3 ends, preferably in their middle, the first end 2 being joined to a frame 5 carrying said multistable system.
  • the second elastic member 10 comprises a deformable buckling blade extending between first and second ends and is joined at its first end 20 to the connection zone 4 of the first elastic member 1.
  • the positions of the second end 3 of the first elastic member 1 and the second end 30 of the second elastic member 10 are adjustable so as to define, for the multistable system, at least four configurations having different stable states numbers, at least one monostable configuration, a bistable configuration, a tristable configuration and a quadristable configuration.
  • Such a multistable system whose all adjustable ends are adjustable in position is a multistable system programmable by displacement.
  • the adjustable ends 3, 30 of the elastic members 1, 10 are respectively able to move in translation along axes A 1 and A 2 respectively parallel to the blades 1a and 1b at rest and to the elastic member 10 at rest, the axis A 2 being preferably perpendicular to the axis A 1 .
  • the connecting zone 4 is mobile, it typically moves in translation along an axis perpendicular to the axis A 1 .
  • the multistable system represented at figure 1 comprises two guiding devices 6, 60 for guiding the adjustable ends 3, 30 of the elastic members 1, 10 respectively along the axes A 1 and A 2 .
  • the guiding devices 6, 60 of the first embodiment may comprise non-elastic guiding devices, for example of the rail or groove type, as shown schematically in FIG. figure 1 or elastic guiding devices.
  • the elastic guide devices may be simple elastic guides, as shown in FIG. figure 2a , or bistable elastic guides (cf. figure 2b ), tristable (cf. Figure 2c ) and more generally multistable.
  • stops 6 ', 60' may be provided to define positions just after unstable positions.
  • the guiding devices 6, 60 for the adjustable ends 3, 30 may be the same, as represented for example in the figure 2 , or be different from each other.
  • the various types of guiding devices 6, 60 that can be envisaged are typically mounted on the frame 5 carrying the multistable system according to the invention, as illustrated schematically in particular in FIGS. figures 1 and 2 .
  • the multistable system represented at figure 1 comprises two position adjusting devices 7, 70 each comprising a set screw 8, 80, the position adjusting devices 7, 70 for adjusting the position along the axes A 1 and A 2 of the adjustable ends 3, 30.
  • a an elastic guiding device 6, 60 when it is multistable, as illustrated in Figures 2b and 2c , can also play a role of position adjusting device 7, 70.
  • each stable position of said multistable elastic guiding device corresponds to a discrete adjustment value ⁇ .
  • each of the adjustable ends 3, 30 varies respectively by a distance ⁇ 1 and ⁇ 2 (cf. figure 3a ), hereinafter “adjustment value”, with respect to its rest position, by the actuation of the position adjusting device 7, 70.
  • adjustment value a distance ⁇ 1 and ⁇ 2 (cf. figure 3a ), hereinafter “adjustment value”, with respect to its rest position, by the actuation of the position adjusting device 7, 70.
  • the tightening of the adjusting screws 8, 80 of the position adjusting devices 7, 70 causes compression of the elastic members 1, 10 thus their buckling.
  • the second elastic member 10 comprises an application zone 90 of an input force F e making it possible to switch the multistable system from one stable state to another, in the case where the multistable system is in a multistable configuration, i.e. having at least two stable states.
  • the application zone 90 is preferably rigid and located in the middle of the second elastic member 10, it is movable in translation along an axis perpendicular to the axis A 2 .
  • the adjustment values ⁇ 1 and ⁇ 2 allow, to switch the multistable system from one stable state to another by acting elsewhere on the system, for example at the link zone. 4 of the first elastic member 1.
  • the number of attainable stable states depends in particular on the position of the adjustable ends 3, 30 and the physical and geometrical characteristics of the elastic members 1, 10 (for example their length and their buckling capacity).
  • the elastic members 1, 10 being mounted in series, the compression forces exerted on each of them are dependent on each other.
  • the respective positions of the adjustable ends 3, 30 of the first 1 and second 10 elastic members make it possible to adjust the configuration of the multistable system, that is to say to adjust the number of stable states of the multistable system. and the tilting force necessary to pass each elastic member 1, 10 from one stable state to another. Indeed, depending on the position of the ends 3, 30, the elastic members 1, 10 are subjected to a more or less strong compression under the effect of which they will deform, more specifically flambé.
  • the first elastic member 1 is a bistable. An actuating force is required for its movement. The force required to move it from one stable state to another is designated Rb 1 (tilting force).
  • the figure 3b represents the evolution of the reaction force R 1 occurring on the first elastic member 1 in response to the extension of the second elastic member 10 under the effect of the input force F e applied in the application zone 90 of said second elastic member 10 as a function of the transverse displacement "x" of the connection zone 4 of the first elastic member 1.
  • the figure 3c is a graph showing the evolution of the axial force R 2 as a function of the transverse displacement "y" of the input force application zone 90 of the second elastic member 10. It is divided into three regions 1, 2 and 3
  • the values of Rb 1 relative to regions 1, 2 and 3 define the multistability of the system.
  • the operation of the multistable system according to the invention depends forces R 2 and Rb 1 which themselves depend on the positions of the adjustable ends 3, 30 and therefore the adjustment values ⁇ 1 and ⁇ 2 .
  • the multistable system therefore operates as a bistable system.
  • FIGS. 4a to 4e illustrate various possible configurations that can take the multistable system, according to the first embodiment of the invention.
  • the multistable system is a quadristable system.
  • the figure 4e illustrates the four stable positions of the multistable system.
  • the diagram of the figure 5 depends on the physical and geometrical characteristics of the elastic members 1, 10 used. Such a diagram can be obtained by MEF finite element method (FEM) simulations. In the case of a multistable system having two elastic members 1, 10 this diagram is in two dimensions, as in the figure 5 . In the case where one would have three elastic members, one could establish a three-dimensional diagram predicting the behavior of the multistable system. For a multistable system which would have more than three elastic members, the behavior of the multistable system according to the adjustment values of different adjustable ends would also be predictable by analogous methods but these would not allow a graphical representation.
  • FEM finite element method
  • FIGS. 6a to 6h represent different multistable configurations of a multistable system according to the first embodiment of the invention comprising three elastic members 1, 10, 100, the third elastic member 100 extending parallel to the first elastic member 1, being joined by its first end 200 to a connecting zone 40 of the second elastic member 10 and having its second end 300 adjustable in position.
  • the multistable system can assume a monostable configuration ( figure 6a ), bistable ( figure 6b ), tristable ( Figure 6c ), quadristable ( figure 6d ), pentastable ( figure 6e ), hexastable ( figure 6f ), heptastable ( figure 6g ) or octastable ( figure 6h ).
  • the transition from one stable state to another is obtained by applying an input force F e at an application zone 900, preferably located in the middle of the third elastic member 100.
  • the adjustment values ⁇ 1 , ⁇ 2 , and ⁇ 3 permit, to switch the multistable system from one stable state to another by acting elsewhere on the system, for example at the connection zones 4, 40 of the first and second elastic members 1, 10.
  • This multistable system can be generalized to n elastic members, where n is an integer greater than or equal to 2. The maximum number of possible stable states is then 2 n .
  • a multistable system according to a second embodiment of the invention differs from the multistable system according to the first embodiment of the invention in that it is a multistable system programmable by force.
  • the adjustable ends 3, 30 of such a multistable system instead of being adjustable in position as in the first embodiment of the invention, are adjustable in force, each end 3, 30 adjustable in force of an organ elastic of rank r, with r between 1 and n, being subjected to a force F r .
  • the multistable system according to the second embodiment of the invention comprises a force adjusting device 7 ', 70' such as a spring constrained by a screw 8 ', 80' to adjust the force applied thereto.
  • the number of stable positions attainable depends in particular on the force applied to the adjustable ends 3, 30 and the physical and geometrical characteristics of the elastic members 1, 10 (for example their length and their capacity to buckling).
  • the resulting compressive force exerted on the corresponding elastic member 1, 10 will be lower in the case of the multi-programmable force-programmable system than in the case of the multistable system that is programmable by displacement. .
  • the ratio between the distance traveled by the screw and the compressive force exerted on the elastic member is therefore higher for a programmable displacement adjusting device than in the case of a programmable force adjustment device.
  • a force-programmable multistable system is more appropriate.
  • the multi-programmable force-programmable system according to the second embodiment of the invention behaves in the same way as the multi-programmable displacement-shift system according to the first embodiment of the invention with the difference that in operation (after adjustment ) the adjustable ends 3, 30 of the multistable system according to the second embodiment are movable (they can move during the transition from one stable state to another) while they are fixed in the case of the first embodiment.
  • a diagram for predicting the behavior of the multistable system according to the second embodiment of the invention is feasible similarly to the first embodiment.
  • the figure 8 is an example of a multistable system "mixed" according to a third embodiment of the invention wherein some ends are adjustable in position and other ends are adjustable in force.
  • This system comprises double elastic members 1, 10 comprising pairs of long rigid portions 11 and short elastic portions 12.
  • the first elastic member 1 has a first end 2 joined to the frame 5.
  • the connection zone 4 of the first elastic member 1 consists of a spacer 4 which blocks the rotation of the first elastic member 1.
  • the second end 3 of the first flexible member 1 corresponds to an adjustable block in position or that can be subjected to an adjustable force.
  • the block constituting the end 3 moves axially parallel to the axis A 1 under the effect of a force exerted by two parallel leaf springs 13, 13 '.
  • the spring blades 13, 13 ' are constrained by a block 14 whose displacement is guided by a guide blade 6.
  • the displacement of the blocks 3, 14 is limited by abutments 18, 18', as illustrated in FIG. figure 8 .
  • the block constituting the end 3 and the block 14 are rigidly connected by a bridge (not shown) so that the axial displacement of the block 14 of a distance ⁇ 1 causes an equivalent axial displacement of the block constituting the end 3.
  • the second elastic member 10 has a first end 20 joined to the connection zone 4 of the first elastic member 1.
  • the second end 30 of said second flexible member 10 corresponds to a block 30 whose position is adjustable (by displacement of a distance ⁇ 2 ) and guided by a guiding device 60 consisting of flexible parts 15 and rigid parts 16.
  • the second elastic member 10 further comprises a hinge 17 comprising two rigid parts 17a and 17b interconnected by two non-parallel spring blades 17c and 17d which form a flexible pivot allowing two rigid portions 17a and 17b to pivot relative to each other.
  • a hinge 17 comprising two rigid parts 17a and 17b interconnected by two non-parallel spring blades 17c and 17d which form a flexible pivot allowing two rigid portions 17a and 17b to pivot relative to each other.
  • the n resilient members are typically integral with each other and, preferably, also integral with the frame 5.
  • the set of elastic members can be made of any suitable material, for example for example a metal or a metal alloy (according to for example LIGA technology) or silicon (according to for example DRIE technology).
  • the elastic members may have different shapes. Each of these members may consist of a single elastic member, such as the second elastic member 10 of the figure 1 , or consist of a double elastic member, such as the first elastic member 1 of the figure 1 .
  • the elastic members of a multistable system according to the invention may also all consist of simple elastic members, as in the Figures 6a to 6h or all of them consist of double elastic members, as illustrated in figure 8 .
  • the figure 9 illustrates an example comprising three double elastic members.
  • the multistable system represented in the figure 9 comprises three elastic members 1, 10, 100, each comprising a first elastic blade 1a, 10a, 100a and a second elastic blade 1b, 10b, 100b.
  • Each of the elastic members may also comprise a first half consisting of a single elastic blade 1e, 10e, 100e and a second half consisting of two elastic blades 1c, 1d, 10c, 10d, 100c, 100d, the two halves being separated by the connection zone 4, 40 of the elastic member or by the force application zone 900, as shown in FIG. figure 10 .
  • Each of the elastic members may also comprise long rigid portions 11 and short elastic portions 12 as illustrated by FIG. figure 11 and as already described in relation to the figure 8 .
  • each elastic member 1, 10 may comprise articulated arms 1.1, 1.2, 10.1, 10.2 subjected to the action of minus a spring 1.3, 10.3 as illustrated in the figure 12 . Under the effect of compression, such elastic members bend instead of flambé, the operating principle of the multistable system remaining the same.
  • the figure 12 also illustrates a force application device consisting of an arm 91 articulated at a first end to the force application zone 90 of the second elastic member 10, its second end 92 being guided by a device for guiding the application of force. 93 force type groove or rail.
  • the multistable system thus obtained is capable of changing its multistability, that is to say of changing the number of stable positions that it can reach as well as the forces necessary to move from one stable position to another.
  • Such a system can be used in very diverse applications such as in the watch industry, in threshold detectors (for example in acceleration sensors), in switches, in valves, in positioners or in robots reconfigurable.

Description

La présente invention concerne un système multistable.The present invention relates to a multistable system.

Un système est considéré comme stable s'il est capable de se maintenir dans son état lorsqu'il est soumis à une perturbation extérieure. Un système multistable est un système présentant plusieurs états stables différents.A system is considered stable if it is able to maintain its state when subjected to an external disturbance. A multistable system is a system with several different stable states.

Des systèmes multistables sont décrits dans la littérature, par exemple dans l'article « Synthesis of compliant multistable mechanisms through use of a single bistable mechanism », Journal of Mechanical Design August 2011, Vol 133, Guimin, Chen et al, qui décrit des méthodes pour obtenir des mécanismes multistables comprenant un nombre défini d'état stables. Un point commun de ces différents systèmes multistables est qu'ils possèdent un nombre de positions stables spécifique et prédéterminé, qui ne peut pas être modifié après la fabrication.Multistable systems are described in the literature, for example in the article "Synthesis of compliant multistable mechanisms through use of a single bistable mechanism", Journal of Mechanical Design August 2011, Vol 133, Guimin, Chen et al, which describes methods for obtaining multistable mechanisms comprising a defined number of stable states. A common feature of these different multistable systems is that they have a specific and predetermined number of stable positions, which can not be changed after manufacture.

Il serait pourtant intéressant de pouvoir modifier et adapter le nombre de positions stables d'un système multistable aux besoins de l'utilisateur.It would be interesting, however, to be able to modify and adapt the number of stable positions of a multistable system to the needs of the user.

Un but de la présente invention est de fournir un système multistable dont le nombre d'états stables atteignable est réglable.An object of the present invention is to provide a multistable system whose number of stable states achievable is adjustable.

L'invention propose à cette fin un système multistable comprenant :

  • un premier organe élastique de rang r=1 comprenant des première et deuxième extrémités et une zone de liaison entre lesdites première et deuxième extrémités, et
  • (n-1) autres organes élastiques de rang r comprenant chacun des première et deuxième extrémités, avec r compris entre 2 et n, n étant un nombre entier supérieur ou égal à 2 ; lorsque n>2 chacun desdits autres organes élastiques de rang r avec r compris entre 2 et (n-1) comprenant une zone de liaison entre ses première et deuxième extrémités ; chacun desdits autres organes élastiques de rang r avec r compris entre 2 et n étant joint par sa première extrémité à la zone de liaison de l'organe élastique de rang (r-1);
et caractérisé en ce qu'il est agencé de façon à ce que la position d'au moins une desdites première et deuxième extrémités du premier organe élastique ou la force appliquée à au moins une desdites première et deuxième extrémités du premier organe élastique, et/ou la position de la deuxième extrémité d'au moins un desdits (n-1) autres organes élastiques ou la force appliquée à la deuxième extrémité d'au moins un desdits (n-1) autres organes élastiques est réglable, ledit système multistable étant tel qu'un réglage de la position et/ou de la force appliquée à ladite ou auxdites extrémités réglables permet de faire passer ledit système multistable d'une configuration multistable à une autre, lesdites deux configurations multistables ayant des nombres d'états stables différents. De préférence, n=2 ou n=3.The invention proposes for this purpose a multistable system comprising:
  • a first elastic member of rank r = 1 comprising first and second ends and a connection zone between said first and second ends, and
  • (n-1) other elastic members of rank r each comprising first and second ends, with r between 2 and n, n being an integer greater than or equal to 2; when n> 2 each of said other elastic members of rank r with r between 2 and (n-1) comprising a connection zone between its first and second ends; each of said other elastic members of rank r with r between 2 and n being joined at its first end to the connecting zone of the elastic member of rank (r-1);
and characterized in that it is arranged in such a way that the position of at least one of said first and second ends of the first elastic member or the force applied to at least one of said first and second ends of the first elastic member, and / or the position of the second end of at least one of said n-1) other elastic members or the force applied to the second end of at least one of said (n-1) other elastic members is adjustable, said multi-stable system being such that a position and / or force adjustment applied to said one or more adjustable ends makes it possible to pass said multistable system from one multistable configuration to another, said two multistable configurations having different stable state numbers. Preferably, n = 2 or n = 3.

De préférence, la position de la deuxième extrémité ou la force appliquée à la deuxième extrémité de chacun des n organes élastiques est réglable.Preferably, the position of the second end or the force applied to the second end of each of the n elastic members is adjustable.

Avantageusement, chacune des extrémités non jointes à une zone de liaison et dont ni la position ni la force qui lui est appliquée ne sont réglables est jointe à un châssis portant ledit système multistable.Advantageously, each of the ends not joined to a connection zone and of which neither the position nor the force applied to it is adjustable is joined to a frame carrying said multistable system.

Dans un mode de réalisation préféré, chacune desdites zones de liaison est située au milieu de l'organe élastique qui la porte.In a preferred embodiment, each of said connection zones is located in the middle of the elastic member which carries it.

De préférence, la ou chacune des extrémité(s) réglable(s) des organes élastiques de rang r, avec r compris entre 1 et n, est apte à se déplacer en translation selon un axe Ar.Preferably, the or each of the adjustable end (s) of the elastic members of rank r, with r between 1 and n, is able to move in translation along an axis A r .

Les axes Ar définis ci-dessus sont typiquement dans un même plan.The axes A r defined above are typically in the same plane.

Avantageusement, les zones de liaison sont mobiles en translation. La zone de liaison d'un organe de liaison de rang r, avec r compris entre 1 et (n-1) peut typiquement se déplacer en translation selon un axe perpendiculaire à l'axe Ar.Advantageously, the connection zones are movable in translation. The connection zone of a link member of rank r, with r between 1 and (n-1) can typically move in translation along an axis perpendicular to the axis A r .

De manière préférée, chaque axe Ar, avec r compris entre 2 et n, est perpendiculaire à l'axe Ar-1.Preferably, each axis A r , with r between 2 and n, is perpendicular to the axis A r-1 .

Dans un mode de réalisation préféré, le système multistable selon l'invention comprend un ou plusieurs dispositif(s) de guidage pour guider la ou chacune des extrémité(s) réglable(s) des organes élastiques de rang r, avec r compris entre 1 et n, le long de l'axe Ar correspondant. Avantageusement, ledit ou lesdits dispositif(s) de guidage sont montés sur un châssis portant ledit système multistable. Chaque dispositif de guidage peut, par exemple, être un dispositif de guidage élastique tel qu'un système à lames élastiques, éventuellement multistable, ou encore un dispositif de guidage non élastique tel qu'une rainure ou un rail.In a preferred embodiment, the multi-stable system according to the invention comprises one or more guiding device (s) for guiding the or each adjustable end (s) of the elastic members of rank r, with r between 1 and n, along the corresponding axis A r . Advantageously, said one or more guiding device (s) are mounted on a frame carrying said multistable system. Each guiding device may, for example, be an elastic guiding device such as an elastic leaf system, possibly multistable, or a non-elastic guiding device such as a groove or a rail.

Avantageusement, au moins une des extrémités dudit système multistable dont la position est réglable est associée à un dispositif de réglage de position comprenant une vis de réglage.Advantageously, at least one of the ends of said multistable system whose position is adjustable is associated with a position adjustment device comprising a set screw.

Avantageusement, au moins une des extrémités dudit système multistable sur laquelle est appliquée une force réglable est associée à un dispositif de réglage de force comprenant un ressort contraint par une vis, ladite vis permettant de régler la force exercée par ledit ressort sur l'extrémité réglable en force correspondante.Advantageously, at least one of the ends of said multistable system to which an adjustable force is applied is associated with a force adjusting device comprising a spring constrained by a screw, said screw making it possible to adjust the force exerted by said spring on the adjustable end in corresponding strength.

Les organes élastiques selon l'invention comprennent typiquement des lames déformables en flambage et/ou des bras articulés soumis à l'action d'au moins un ressort. Avantageusement, au moins un des organes élastiques comprend plusieurs lames déformables en flambage.The resilient members according to the invention typically comprise deformable buckling blades and / or articulated arms subjected to the action of at least one spring. Advantageously, at least one of the elastic members comprises several deformable blades buckling.

Dans un mode de réalisation préféré de l'invention, les organes élastiques sont monobloc les uns avec les autres et, de préférence, aussi avec le châssis.In a preferred embodiment of the invention, the elastic members are integral with each other and, preferably, also with the frame.

Avantageusement, au moins l'organe élastique de rang r=n comprend, entre ses première et deuxième extrémités, une articulation, typiquement à pivot flexible, pour diminuer les contraintes subies par le système multistable selon l'invention.Advantageously, at least the elastic member of rank r = n comprises, between its first and second ends, a hinge, typically with flexible pivot, to reduce the stresses to the multistable system according to the invention.

Le système multistable ainsi obtenu est capable de changer sa multistabilité, c'est-à-dire de changer le nombre de positions stables qu'il peut atteindre ainsi que les forces nécessaires pour passer d'une position stable à une autre.The multistable system thus obtained is capable of changing its multistability, that is to say of changing the number of stable positions that it can reach as well as the forces necessary to move from one stable position to another.

D'autres caractéristiques et avantages de la présente invention apparaîtront à la lecture de la description détaillée suivante faite en référence aux dessins annexés dans lesquels :

  • La figure 1 est une représentation schématique d'un système multistable selon un premier mode de réalisation de l'invention.
  • Les figures 2a à 2c sont des représentations schématiques de variantes du système multistable selon le premier mode de réalisation de l'invention.
  • La figure 3a représente le système multistable selon le premier mode de réalisation de l'invention. Ce dernier est divisé en une première partie comprenant un organe élastique de rang r=1 et en une deuxième partie comprenant un organe élastique de rang r=2. Les figures 3b et 3c sont des graphiques représentant l'évolution de forces respectivement R1 et R2 dont l'analyse permet de comprendre le comportement du système représenté dans la figure 3a.
  • Les figures 4a à 4e sont des représentations schématiques de différentes configurations du système multistable selon le premier mode de réalisation de l'invention.
  • La figure 5 est un diagramme représentant les différentes configurations possibles du système multistable selon le premier mode de réalisation de l'invention, en fonction de valeurs de réglage.
  • Les figures 6a à 6h sont des représentations schématiques de différentes configurations d'une variante du système multistable selon le premier mode de réalisation de l'invention comprenant trois organes élastiques.
  • La figure 7 est une représentation schématique d'un système multistable selon un second mode de réalisation de l'invention.
  • La figure 8 est une représentation schématique d'un système multistable selon un troisième mode de réalisation de l'invention.
  • Les figures 9, 10 et 12 sont des représentations schématiques de variantes du système multistable selon l'invention.
  • La figure 11 est une représentation schématique d'une variante d'un organe élastique du système multistable selon l'invention.
Other features and advantages of the present invention will appear on reading the following detailed description given with reference to the accompanying drawings in which:
  • The figure 1 is a schematic representation of a multistable system according to a first embodiment of the invention.
  • The Figures 2a to 2c are schematic representations of variants of the multistable system according to the first embodiment of the invention.
  • The figure 3a represents the multistable system according to the first embodiment of the invention. The latter is divided into a first part comprising an elastic member of rank r = 1 and in a second part comprising an elastic member of rank r = 2. The Figures 3b and 3c are graphs representing the evolution of forces respectively R1 and R2 whose analysis makes it possible to understand the behavior of the system represented in the figure 3a .
  • The Figures 4a to 4e are schematic representations of different configurations of the multistable system according to the first embodiment of the invention.
  • The figure 5 is a diagram representing the different possible configurations of the multistable system according to the first embodiment of the invention, as a function of adjustment values.
  • The Figures 6a to 6h are schematic representations of different configurations of a variant of the multistable system according to the first embodiment of the invention comprising three resilient members.
  • The figure 7 is a schematic representation of a multistable system according to a second embodiment of the invention.
  • The figure 8 is a schematic representation of a multistable system according to a third embodiment of the invention.
  • The Figures 9, 10 and 12 are schematic representations of variants of the multistable system according to the invention.
  • The figure 11 is a schematic representation of a variant of an elastic member of the multistable system according to the invention.

Chaque extrémité réglable du système multistable selon l'invention peut être réglée en position, on parlera alors d'extrémité réglable en position, ou être soumise à une force dont l'intensité est réglable, on parlera alors d'extrémité réglable en force.Each adjustable end of the multistable system according to the invention can be adjusted in position, it will speak of end adjustable in position, or be subjected to a force whose intensity is adjustable, it will speak of adjustable end force.

Lorsque toutes les extrémités réglables du système multistable selon l'invention sont réglables en position, on parle de « système multistable programmable par déplacement ». Lorsque toutes les extrémités réglables du système multistable selon l'invention sont réglables en force, on parle de « système multistable programmable par force ». L'invention concerne également des systèmes multistables « mixtes » ou « hybrides » dans lesquels certaines extrémités sont réglables en position et d'autres extrémités sont réglables en force.When all the adjustable ends of the multistable system according to the invention are adjustable in position, we speak of "multistable system programmable by displacement ". When all the adjustable ends of the multistable system according to the invention are adjustable in force, it is called "multistable system programmable by force". The invention also relates to multistable systems "mixed" or "hybrid" in which some ends are adjustable in position and other ends are adjustable in strength.

On entend par « châssis » une structure fixe sur laquelle est fixé au moins en partie le système multistable.The term "chassis" means a fixed structure on which at least a part is fixed the multistable system.

Par « organe élastique » on entend un organe dont une partie au moins est déformable élastiquement.By "elastic member" is meant a member of which at least part is elastically deformable.

En référence à la figure 1, un système multistable selon un premier mode de réalisation de l'invention comprend un premier organe élastique 1, dit de rang r=1, et un deuxième organe élastique 10, dit de rang r=2. Le premier organe élastique 1 comprend deux lames 1a, 1b, parallèles et déformables en flambage, s'étendant entre des première 2 et deuxième 3 extrémités, et une zone de liaison 4, de préférence rigide, interrompant les lames 1a et 1b entre lesdites première 2 et deuxième 3 extrémités, de préférence en leur milieu, la première extrémité 2 étant jointe à un châssis 5 portant ledit système multistable. Le deuxième organe élastique 10 comprend une lame déformable en flambage s'étendant entre des première 20 et deuxième 30 extrémités et est joint par sa première extrémité 20 à la zone de liaison 4 du premier organe élastique 1.With reference to the figure 1 , a multistable system according to a first embodiment of the invention comprises a first elastic member 1, said rank r = 1, and a second elastic member 10, said rank r = 2. The first elastic member 1 comprises two blades 1a, 1b, parallel and deformable buckling, extending between first 2 and second 3 ends, and a connecting zone 4, preferably rigid, interrupting the blades 1a and 1b between said first 2 and second 3 ends, preferably in their middle, the first end 2 being joined to a frame 5 carrying said multistable system. The second elastic member 10 comprises a deformable buckling blade extending between first and second ends and is joined at its first end 20 to the connection zone 4 of the first elastic member 1.

Les positions de la deuxième extrémité 3 du premier organe élastique 1 et de la deuxième extrémité 30 du deuxième organe élastique 10 sont réglables de façon à définir, pour le système multistable, au moins quatre configurations ayant des nombres d'états stables différents, en l'occurrence, au moins une configuration monostable, une configuration bistable, une configuration tristable et une configuration quadristable.The positions of the second end 3 of the first elastic member 1 and the second end 30 of the second elastic member 10 are adjustable so as to define, for the multistable system, at least four configurations having different stable states numbers, at least one monostable configuration, a bistable configuration, a tristable configuration and a quadristable configuration.

Un tel système multistable dont toutes les extrémités réglables sont réglables en position est un système multistable programmable par déplacement.Such a multistable system whose all adjustable ends are adjustable in position is a multistable system programmable by displacement.

Les extrémités réglables 3, 30 des organes élastiques 1, 10 sont respectivement aptes à se déplacer en translation selon des axes A1 et A2 respectivement parallèles aux lames 1a et 1b au repos et à l'organe élastique 10 au repos, l'axe A2 étant de préférence perpendiculaire à l'axe A1.The adjustable ends 3, 30 of the elastic members 1, 10 are respectively able to move in translation along axes A 1 and A 2 respectively parallel to the blades 1a and 1b at rest and to the elastic member 10 at rest, the axis A 2 being preferably perpendicular to the axis A 1 .

La zone de liaison 4 est mobile, elle se déplace typiquement en translation selon un axe perpendiculaire à l'axe A1.The connecting zone 4 is mobile, it typically moves in translation along an axis perpendicular to the axis A 1 .

Le système multistable représenté à la figure 1 comprend deux dispositifs de guidage 6, 60 pour guider les extrémités réglables 3, 30 des organes élastiques 1, 10 respectivement le long des axes A1 et A2. Les dispositifs de guidage 6, 60 du premier mode de réalisation peuvent comprendre des dispositifs de guidage non élastique, par exemple de type rail ou rainure, comme représenté schématiquement à la figure 1 ou des dispositifs de guidage élastique. Les dispositifs de guidage élastique peuvent être de simples guidages élastiques, comme représenté à la figure 2a, ou des guidages élastiques bistables (cf. figure 2b), tristables (cf. figure 2c) et plus généralement multistables. Dans le cas de tels guidages élastiques multistables, des butées 6', 60' peuvent être prévues pour définir des positions situées juste après des positions instables.The multistable system represented at figure 1 comprises two guiding devices 6, 60 for guiding the adjustable ends 3, 30 of the elastic members 1, 10 respectively along the axes A 1 and A 2 . The guiding devices 6, 60 of the first embodiment may comprise non-elastic guiding devices, for example of the rail or groove type, as shown schematically in FIG. figure 1 or elastic guiding devices. The elastic guide devices may be simple elastic guides, as shown in FIG. figure 2a , or bistable elastic guides (cf. figure 2b ), tristable (cf. Figure 2c ) and more generally multistable. In the case of such multistable elastic guides, stops 6 ', 60' may be provided to define positions just after unstable positions.

Les dispositifs de guidage 6, 60 pour les extrémités réglables 3, 30 peuvent être les mêmes, comme représenté par exemple dans la figure 2, ou être différents l'un de l'autre.The guiding devices 6, 60 for the adjustable ends 3, 30 may be the same, as represented for example in the figure 2 , or be different from each other.

Les différents types de dispositifs de guidage 6, 60 envisageables sont typiquement montés sur le châssis 5 portant le système multistable selon l'invention, comme illustré schématiquement notamment aux figures 1 et 2.The various types of guiding devices 6, 60 that can be envisaged are typically mounted on the frame 5 carrying the multistable system according to the invention, as illustrated schematically in particular in FIGS. figures 1 and 2 .

Le système multistable représenté à la figure 1 comprend deux dispositifs de réglage de position 7, 70 comprenant chacun une vis de réglage 8, 80, les dispositifs de réglage de position 7, 70 permettant de régler la position selon les axes A1 et A2 des extrémités réglables 3, 30. Un dispositif de guidage élastique 6, 60, lorsqu'il est multistable, comme illustré dans les figures 2b et 2c, peut également jouer un rôle de dispositif de réglage de position 7, 70. Dans ce cas, chaque position stable dudit dispositif de guidage élastique multistable correspond à une valeur de réglage discrète δ.The multistable system represented at figure 1 comprises two position adjusting devices 7, 70 each comprising a set screw 8, 80, the position adjusting devices 7, 70 for adjusting the position along the axes A 1 and A 2 of the adjustable ends 3, 30. A an elastic guiding device 6, 60, when it is multistable, as illustrated in Figures 2b and 2c , can also play a role of position adjusting device 7, 70. In this case, each stable position of said multistable elastic guiding device corresponds to a discrete adjustment value δ.

La position de chacune des extrémités réglables 3, 30 varie respectivement d'une distance δ1 et δ2 (cf. figure 3a), ci-après « valeur de réglage », par rapport à sa position de repos, sous l'effet de l'actionnement du dispositif de réglage de position 7, 70. En particulier, comme illustré dans la figure 1, le serrage des vis de réglage 8, 80 des dispositifs de réglage de position 7, 70 engendre une compression des organes élastiques 1, 10 donc leur flambage. En position de repos δ1=δ2=0 et les organes élastiques 1, 10 sont droits (non flambés).The position of each of the adjustable ends 3, 30 varies respectively by a distance δ 1 and δ 2 (cf. figure 3a ), hereinafter "adjustment value", with respect to its rest position, by the actuation of the position adjusting device 7, 70. In particular, as illustrated in the figure 1 the tightening of the adjusting screws 8, 80 of the position adjusting devices 7, 70 causes compression of the elastic members 1, 10 thus their buckling. In the rest position δ 1 = δ 2 = 0 and the elastic members 1, 10 are straight (not flamed).

Le deuxième organe élastique 10 comprend une zone d'application 90 d'une force d'entrée Fe permettant de faire basculer le système multistable d'un état stable à un autre, dans le cas où le système multistable est dans une configuration multistable, c'est-à-dire ayant au moins deux états stables. La zone d'application 90 est de préférence rigide et située au milieu du deuxième organe élastique 10, elle est mobile en translation selon un axe perpendiculaire à l'axe A2. Cependant, il est également possible, lorsque les valeurs de réglage δ1 et δ2 le permettent, de faire basculer le système multistable d'un état stable à un autre en agissant ailleurs sur le système, par exemple au niveau de la zone de liaison 4 du premier organe élastique 1.The second elastic member 10 comprises an application zone 90 of an input force F e making it possible to switch the multistable system from one stable state to another, in the case where the multistable system is in a multistable configuration, i.e. having at least two stable states. The application zone 90 is preferably rigid and located in the middle of the second elastic member 10, it is movable in translation along an axis perpendicular to the axis A 2 . However, it is also possible, when the adjustment values δ 1 and δ 2 allow, to switch the multistable system from one stable state to another by acting elsewhere on the system, for example at the link zone. 4 of the first elastic member 1.

Le nombre d'états stables atteignables dépend notamment de la position des extrémités réglables 3, 30 et des caractéristiques physiques et géométriques des organes élastiques 1, 10 (par exemple leur longueur et leur capacité de flambage).The number of attainable stable states depends in particular on the position of the adjustable ends 3, 30 and the physical and geometrical characteristics of the elastic members 1, 10 (for example their length and their buckling capacity).

Les organes élastiques 1, 10 étant montés en série, les forces de compression qui s'exercent sur chacun d'eux sont dépendantes les unes des autres.The elastic members 1, 10 being mounted in series, the compression forces exerted on each of them are dependent on each other.

Les positions respectives des extrémités réglables 3, 30 des premier 1 et deuxième 10 organes élastiques permettent de régler la configuration du système multistable, c'est-à-dire de régler le nombre d'états stables du système multistable ainsi que la force de basculement nécessaire pour faire passer chaque organe élastique 1, 10 d'un état stable à un autre. En effet, selon la position des extrémités 3, 30, les organes élastiques 1, 10 sont soumis à une compression plus ou moins forte sous l'effet de laquelle ils vont se déformer, plus précisément flamber.The respective positions of the adjustable ends 3, 30 of the first 1 and second 10 elastic members make it possible to adjust the configuration of the multistable system, that is to say to adjust the number of stable states of the multistable system. and the tilting force necessary to pass each elastic member 1, 10 from one stable state to another. Indeed, depending on the position of the ends 3, 30, the elastic members 1, 10 are subjected to a more or less strong compression under the effect of which they will deform, more specifically flambé.

Les conditions de multistabilité du système multistable selon l'invention seront plus facilement comprises en divisant ledit système en deux parties :

  • une première partie incluant le premier organe élastique 1 et
  • une deuxième partie incluant le deuxième organe élastique 10.
The multistability conditions of the multistable system according to the invention will be more easily understood by dividing said system into two parts:
  • a first part including the first elastic member 1 and
  • a second part including the second elastic member 10.

Pour chacune de ces parties les forces de réaction respectives R1 et R2 sont estimées au point de connexion correspondant à la zone de liaison 4. La figure 3a illustre ces deux parties.For each of these parts, the respective reaction forces R 1 and R 2 are estimated at the connection point corresponding to the connecting zone 4. figure 3a illustrates these two parts.

Lorsque l'on actionne le système avec une force d'entrée Fe dans la direction latérale «y», le deuxième organe élastique 10 s'étend axialement, ce qui produit la force axiale R2.When the system is actuated with an input force F e in the lateral direction "y", the second elastic member 10 extends axially, which produces the axial force R 2 .

Le premier organe élastique 1 est un bistable. Une force d'actionnement est requise pour son déplacement. La force nécessaire pour le faire passer d'un état stable à l'autre est désignée par Rb1 (force de basculement).The first elastic member 1 is a bistable. An actuating force is required for its movement. The force required to move it from one stable state to another is designated Rb 1 (tilting force).

La figure 3b représente l'évolution de la force de réaction R1 apparaissant sur le premier organe élastique 1 en réponse à l'extension du deuxième organe élastique 10 sous l'effet de la force d'entrée Fe appliquée dans la zone d'application 90 dudit deuxième organe élastique 10 en fonction du déplacement transversal « x » de la zone de liaison 4 du premier organe élastique 1.The figure 3b represents the evolution of the reaction force R 1 occurring on the first elastic member 1 in response to the extension of the second elastic member 10 under the effect of the input force F e applied in the application zone 90 of said second elastic member 10 as a function of the transverse displacement "x" of the connection zone 4 of the first elastic member 1.

La figure 3c est un graphique représentant l'évolution de la force axiale R2 en fonction du déplacement transversal « y » de la zone d'application 90 de force d'entrée du deuxième organe élastique 10. Elle se divise en trois régions 1, 2 et 3. Les valeurs de Rb1 par rapport aux régions 1, 2 et 3, définissent la multistabilité du système. Ainsi, le fonctionnement du système multistable selon l'invention dépend des forces R2 et Rb1 qui elles-mêmes dépendent des positions des extrémités réglables 3, 30 et donc des valeurs de réglage δ1 et δ2.The figure 3c is a graph showing the evolution of the axial force R 2 as a function of the transverse displacement "y" of the input force application zone 90 of the second elastic member 10. It is divided into three regions 1, 2 and 3 The values of Rb 1 relative to regions 1, 2 and 3 define the multistability of the system. Thus, the operation of the multistable system according to the invention depends forces R 2 and Rb 1 which themselves depend on the positions of the adjustable ends 3, 30 and therefore the adjustment values δ 1 and δ 2 .

Dans le cas où la valeur de réglage δ1 implique que Rb1 se situe dans la région 1 de la figure 3c, la force axiale R2 du deuxième organe élastique 10 est toujours supérieure à la force Rbi nécessaire pour basculer la position de l'organe élastique 1, le premier organe élastique 1 est donc toujours dans son premier état stable et ne peut pas passer dans son deuxième état stable. Dans ce cas, selon la valeur de réglage de δ2, le système multistable peut fonctionner comme un système monostable ou bistable :

  • si δ2 est inférieur à une valeur critique δ2a, le système multistable a une seule position stable, il est monostable ;
  • si δ2 est supérieur à la valeur critique δ2a, le système multistable a deux positions stables, il est bistable.
In the case where the setting value δ 1 implies that Rb 1 is in region 1 of the figure 3c , the axial force R 2 of the second elastic member 10 is always greater than the force Rbi necessary to swing the position of the elastic member 1, the first elastic member 1 is always in its first stable state and can not pass in its second stable state. In this case, depending on the setting value of δ 2 , the multistable system can operate as a monostable or bistable system:
  • if δ 2 is smaller than a critical value δ 2a , the multistable system has a single stable position, it is monostable;
  • if δ 2 is greater than the critical value δ 2a , the multistable system has two stable positions, it is bistable.

Dans le cas où la valeur de réglage δ1 implique que Rb1 se situe dans la région 2 de la figure 3c, le système multistable peut fonctionner soit comme quadristable, soit comme tristable :

  • si δ2 ≤ D1, le système multistable fonctionne comme un système tristable, où D1 représente la valeur maximale du déplacement transversal « x » de la zone de liaison 4 du premier organe élastique 1 après l'application des valeurs de réglage δ1 et δ2 avec Fe=0.
  • sinon, le système multistable fonctionne comme quadristable.
In the case where the adjustment value δ 1 implies that Rb 1 is in region 2 of the figure 3c , the multistable system can function either as quadristable or as tristable:
  • if δ 2 ≤ D 1 , the multistable system functions as a tristable system, where D 1 represents the maximum value of the transverse displacement "x" of the connection zone 4 of the first elastic member 1 after the application of the adjustment values δ 1 and δ 2 with F e = 0.
  • otherwise, the multistable system functions as quadristable.

Dans le cas où la valeur de réglage δ1 implique que Rb1 se situe dans la région 3 de la figure 3c, la force axiale R2 du deuxième organe élastique 10 n'est jamais suffisante pour basculer le premier organe élastique 1 entre ses deux positions stables, le système multistable fonctionne donc comme un système bistable.In the case where the setting value δ 1 implies that Rb 1 is in region 3 of the figure 3c , the axial force R 2 of the second elastic member 10 is never sufficient to tilt the first elastic member 1 between its two stable positions, the multistable system therefore operates as a bistable system.

Les figures 4a à 4e illustrent différentes configurations possibles que peut prendre le système multistable, selon le premier mode de réalisation de l'invention.The Figures 4a to 4e illustrate various possible configurations that can take the multistable system, according to the first embodiment of the invention.

Dans le cas où aucune valeur de réglage n'est programmée, c'est-à-dire lorsque δ1=δ2=0, le système multistable n'a qu'une position stable, il est donc monostable, comme représenté dans la figure 4a.In the case where no setting value is programmed, that is to say when δ 1 = δ 2 = 0, the multistable system only has a stable position, it is therefore monostable, as represented in FIG. figure 4a .

Lorsque l'on augmente la valeur de réglage δ2, le deuxième organe élastique 10 flambe et fonctionne comme un bistable. Si l'on augmente davantage la valeur de réglage δ2, la bistabilité augmente, conduisant à des forces de basculement plus élevées et à des courses plus grandes entre les positions stables. En ce qui concerne le basculement entre différents états stables, il y a deux possibilités :

  • soit la force axiale R2 du deuxième organe élastique 10 est suffisante pour pousser le premier organe élastique 1 et le faire flamber, comme illustré dans la figure 4b,
  • soit la force nécessaire pour basculer le premier organe élastique 1 est suffisamment importante pour que le deuxième organe élastique 10 flambe dans son état de transition entre ses deux positions stables, comme illustré dans la figure 4c.
When increasing the adjustment value δ 2 , the second elastic member 10 flames and operates as a bistable. If the setting value δ 2 is further increased, the bistability increases, leading to higher tilting forces and greater strokes between the stable positions. With regard to switching between different stable states, there are two possibilities:
  • the axial force R 2 of the second elastic member 10 is sufficient to push the first elastic member 1 and flamish it, as illustrated in FIG. figure 4b ,
  • the force required to tilt the first elastic member 1 is large enough for the second elastic member 10 to flare in its transition state between its two stable positions, as illustrated in FIG. figure 4c .

Lorsque les deux conditions ci-dessous sont réunies :

  • premièrement, Rb1 se situe dans la région 2 de la figure 3c ; et
  • deuxièmement, la condition δ2 ≤ D1 est respectée,
le système multistable fonctionne comme un système tristable. La figure 4d illustre les trois positions stables de cette configuration.When the two conditions below are met:
  • firstly, Rb 1 is in region 2 of the figure 3c ; and
  • secondly, the condition δ 2 ≤ D 1 is respected,
the multistable system works like a tristable system. The figure 4d illustrates the three stable positions of this configuration.

Enfin, dans le cas où Rb1 n'est ni toujours supérieur à R2, ni toujours inférieur à R2 (région 2 de la figure 3c) et où la relation δ2 > D1 est satisfaite, le système multistable est un système quadristable. La figure 4e illustre les quatre positions stables du système multistable.Finally, in the case where Rb 1 is neither always greater than R 2 , nor always less than R 2 (region 2 of the figure 3c ) and where the relation δ 2 > D 1 is satisfied, the multistable system is a quadristable system. The figure 4e illustrates the four stable positions of the multistable system.

Le diagramme de la figure 5 représente les différentes configurations dans lesquelles se trouve le système multistable en fonction des valeurs de réglage δ1 et δ2. Ainsi, l'utilisateur utilise un tel diagramme pour adapter la position des extrémités des organes élastiques 1, 10 selon qu'il veuille obtenir un système monostable, bistable, tristable ou quadristable.

  1. 1) Dans le cas où aucune valeur de réglage n'est programmée, c'est-à-dire lorsque δ1=δ2=0, le système multistable est monostable et les deux organes élastiques 1, 10 déformables en flambage ont une rigidité positive. En augmentant les valeurs de réglage, la rigidité diminue.
  2. 2) En augmentant la seconde valeur de réglage δ2 au-delà d'une valeur critique δ2a, le système multistable commence à fonctionner comme un bistable (configuration dite « bistable 1 »). En augmentant la valeur de δ1, la rigidité du premier organe élastique 1 diminue. Aussi, une plus grande valeur de δ2 est nécessaire pour maintenir le flambage du deuxième organe élastique 10.
  3. 3) En augmentant la valeur de réglage du premier organe élastique 1 au-delà d'une valeur critique δ1a, le premier organe élastique 1 flambe. Afin de produire une tristabilité, la valeur de réglage δ1 doit être suffisante pour que la force Rb1 nécessaire pour faire basculer le premier organe élastique 1 se situe dans la région 2 de la figure 3c. Dans ces cas, le système multistable fonctionne comme un tristable tant que δ2 ≤ D1.
  4. 4) En augmentant la valeur de réglage δ2, la condition δ2 > D1 est vérifiée, le système multistable est alors dans une configuration quadristable.
  5. 5) En augmentant la valeur de réglage δ1, la force Rb1 nécessaire pour faire basculer le premier organe élastique 1 d'un état stable à un autre augmente. Lorsque δ1 atteint une valeur critique δ1c, la force de basculement Rbi entre dans la région 3 de la figure 3c. Ainsi, le deuxième organe élastique 10 n'apporte pas assez de force pour faire basculer le premier organe élastique 1 vers un autre état stable. Le système multistable est donc dans une configuration bistable (dite « bistable 2 ») obtenue uniquement par le flambage du deuxième organe élastique 10.
  6. 6) A partir de certaines valeurs de réglage δ1 et δ2, le matériau constituant le système multistable atteint sa limite de contrainte maximale.
The diagram of the figure 5 represents the different configurations in which the multistable system is located as a function of the adjustment values δ 1 and δ 2 . Thus, the user uses such a diagram to adapt the position of the ends of the elastic members 1, 10 according to whether he wants to obtain a monostable system, bistable, tristable or quadristable.
  1. 1) In the case where no setting value is programmed, that is to say when δ 1 = δ 2 = 0, the multistable system is monostable and the two elastic members 1, 10 which are deformable in buckling have a rigidity positive. By increasing the setting values, the stiffness decreases.
  2. 2) By increasing the second adjustment value δ 2 beyond a critical value δ 2a , the multistable system begins to function as a bistable (so-called "bistable 1" configuration). By increasing the value of δ 1 , the rigidity of the first elastic member 1 decreases. Also, a greater value of δ 2 is necessary to maintain the buckling of the second elastic member 10.
  3. 3) By increasing the adjustment value of the first elastic member 1 beyond a critical value δ 1a , the first elastic member 1 flames. In order to produce a tristability, the adjustment value δ 1 must be sufficient so that the force Rb 1 needed to tilt the first elastic member 1 is in the region 2 of the figure 3c . In these cases, the multistable system functions as a tristable as long as δ 2 ≤ D 1 .
  4. 4) By increasing the adjustment value δ 2 , the condition δ 2 > D 1 is verified, the multistable system is then in a quadristable configuration.
  5. 5) By increasing the adjustment value δ 1 , the force Rb 1 necessary to tilt the first elastic member 1 from one stable state to another increases. When δ 1 reaches a critical value δ 1c , the tilting force Rbi enters the region 3 of the figure 3c . Thus, the second elastic member 10 does not bring enough force to tilt the first elastic member 1 to another stable state. The multistable system is therefore in a bistable configuration (called "bistable 2") obtained only by the buckling of the second elastic member 10.
  6. 6) From certain adjustment values δ 1 and δ 2 , the material constituting the multistable system reaches its maximum stress limit.

Le diagramme de la figure 5 dépend des caractéristiques physiques et géométriques des organes élastiques 1, 10 utilisés. Un tel diagramme peut être obtenu grâce à des simulations de type méthode des éléments finis MEF (ou FEM pour « finite elements method »). Dans le cas d'un système multistable présentant deux organes élastiques 1, 10 ce diagramme est en deux dimensions, comme dans la figure 5. Dans le cas où l'on aurait trois organes élastiques, on pourrait établir un diagramme en trois dimensions prédisant le comportement du système multistable. Pour un système multistable qui comporterait plus de trois organes élastiques, le comportement du système multistable selon les valeurs de réglage de différentes extrémités réglables serait également prévisible par des méthodes analogues mais celles-ci ne permettraient pas une représentation graphique.The diagram of the figure 5 depends on the physical and geometrical characteristics of the elastic members 1, 10 used. Such a diagram can be obtained by MEF finite element method (FEM) simulations. In the case of a multistable system having two elastic members 1, 10 this diagram is in two dimensions, as in the figure 5 . In the case where one would have three elastic members, one could establish a three-dimensional diagram predicting the behavior of the multistable system. For a multistable system which would have more than three elastic members, the behavior of the multistable system according to the adjustment values of different adjustable ends would also be predictable by analogous methods but these would not allow a graphical representation.

Les figures 6a à 6h représentent différentes configurations multistables d'un système multistable selon le premier mode de réalisation de l'invention comprenant trois organes élastiques 1, 10, 100, le troisième organe élastique 100 s'étendant parallèlement au premier organe élastique 1, étant joint par sa première extrémité 200 à une zone de liaison 40 du deuxième organe élastique 10 et ayant sa deuxième extrémité 300 réglable en position. Selon les valeurs de réglage δ1, δ2 et la valeur de réglage δ3 de la deuxième extrémité 300 du troisième organe élastique 100, le système multistable peut prendre une configuration monostable (figure 6a), bistable (figure 6b), tristable (figure 6c), quadristable (figure 6d), pentastable (figure 6e), hexastable (figure 6f), heptastable (figure 6g) ou octastable (figure 6h). Le passage d'un état stable à un autre s'obtient en appliquant une force d'entrée Fe au niveau d'une zone d'application 900, située de préférence au milieu du troisième organe élastique 100. Cependant, il est également possible, lorsque les valeurs de réglage δ1, δ2, et δ3 le permettent, de faire basculer le système multistable d'un état stable à un autre en agissant ailleurs sur le système, par exemple au niveau des zones de liaison 4, 40 des premier et deuxième organes élastiques 1, 10. Le nombre maximum d'états stables atteignables est de 23=8. Ce système multistable peut être généralisé à n organes élastiques, où n est un nombre entier supérieur ou égal à 2. Le nombre maximum d'états stables possibles est alors de 2n.The Figures 6a to 6h represent different multistable configurations of a multistable system according to the first embodiment of the invention comprising three elastic members 1, 10, 100, the third elastic member 100 extending parallel to the first elastic member 1, being joined by its first end 200 to a connecting zone 40 of the second elastic member 10 and having its second end 300 adjustable in position. According to the adjustment values δ 1 , δ 2 and the adjustment value δ 3 of the second end 300 of the third elastic member 100, the multistable system can assume a monostable configuration ( figure 6a ), bistable ( figure 6b ), tristable ( Figure 6c ), quadristable ( figure 6d ), pentastable ( figure 6e ), hexastable ( figure 6f ), heptastable ( figure 6g ) or octastable ( figure 6h ). The transition from one stable state to another is obtained by applying an input force F e at an application zone 900, preferably located in the middle of the third elastic member 100. However, it is also possible when the adjustment values δ 1 , δ 2 , and δ 3 permit, to switch the multistable system from one stable state to another by acting elsewhere on the system, for example at the connection zones 4, 40 of the first and second elastic members 1, 10. The maximum number of attainable stable states is 2 3 = 8. This multistable system can be generalized to n elastic members, where n is an integer greater than or equal to 2. The maximum number of possible stable states is then 2 n .

En référence à la figure 7, un système multistable selon un deuxième mode de réalisation de l'invention diffère du système multistable selon le premier mode de réalisation de l'invention en ce qu'il s'agit d'un système multistable programmable par force. Les extrémités réglables 3, 30 d'un tel système multistable, au lieu d'être réglables en position comme dans le premier mode de réalisation de l'invention, sont réglables en force, chaque extrémité 3, 30 réglable en force d'un organe élastique de rang r, avec r compris entre 1 et n, étant soumise à une force Fr.With reference to the figure 7 , a multistable system according to a second embodiment of the invention differs from the multistable system according to the first embodiment of the invention in that it is a multistable system programmable by force. The adjustable ends 3, 30 of such a multistable system, instead of being adjustable in position as in the first embodiment of the invention, are adjustable in force, each end 3, 30 adjustable in force of an organ elastic of rank r, with r between 1 and n, being subjected to a force F r .

Le système multistable selon le second mode de réalisation de l'invention comprend un dispositif de réglage de force 7', 70' tel qu'un ressort contraint par une vis 8', 80' pour régler la force qui lui est appliquée.The multistable system according to the second embodiment of the invention comprises a force adjusting device 7 ', 70' such as a spring constrained by a screw 8 ', 80' to adjust the force applied thereto.

Dans ce second mode de réalisation de l'invention, le nombre de positions stables atteignables dépend notamment de la force appliquée aux extrémités réglables 3, 30 et des caractéristiques physiques et géométriques des organes élastiques 1, 10 (par exemple leur longueur et leur capacité de flambage).In this second embodiment of the invention, the number of stable positions attainable depends in particular on the force applied to the adjustable ends 3, 30 and the physical and geometrical characteristics of the elastic members 1, 10 (for example their length and their capacity to buckling).

L'avantage d'un système multistable programmable par force est qu'il permet un réglage plus précis qu'un système multistable programmable par déplacement.The advantage of a force-programmable multistable system is that it allows a more precise adjustment than a multi-programmable, displacement-based system.

En effet, si l'on compare le réglage d'une extrémité du système multistable selon l'invention selon que l'on considère un système multistable programmable par déplacement dont le dispositif de réglage de position 7, 70 est une simple vis de réglage 8, 80 ou un système multistable programmable par force dont le dispositif de réglage de force 7', 70' est également une vis 8', 80' mais dans lequel cette vis 8', 80' agit par l'intermédiaire d'un ressort dont elle détermine l'état de compression, le serrage de la vis entraîne dans le premier cas (vis de réglage de position 8, 80) un déplacement d'une distance À de la position de l'extrémité 3, 30 à régler et dans le second cas (vis de réglage de force 8', 80') une compression du ressort d'une distance À affectant ainsi la force exercée par ledit ressort sur l'extrémité 3, 30 de l'organe élastique 1, 10 correspondant. Pour un même serrage de la vis et une même distance À, la force de compression résultante exercée sur l'organe élastique 1, 10 correspondant sera plus faible dans le cas du système multistable programmable par force que dans le cas du système multistable programmable par déplacement. Le rapport entre la distance parcourue par la vis et la force de compression exercée sur l'organe élastique est donc plus élevé pour un dispositif de réglage à déplacement programmable que dans le cas d'un dispositif de réglage à force programmable. Aussi, dans un système multistable dans lequel les variations de forces nécessaires pour basculer d'un état stable à un autre sont très faibles et demandent un réglage précis, un système multistable programmable par force est plus approprié.Indeed, if one compares the adjustment of an end of the multistable system according to the invention according to that we consider a multi-programmable displacement system whose position adjusting device 7, 70 is a simple adjusting screw 8 , 80 or a multi-programmable force-programmable system whose force-adjusting device 7 ', 70' is also a screw 8 ', 80' but in which this screw 8 ', 80' acts via a spring of which it determines the state of compression, the tightening of the screw leads in the first case (adjustment screw of position 8, 80) a displacement of a distance A of the position of the end 3, 30 to be adjusted and in the second case (force adjusting screw 8 ', 80') a compression of the spring of a distance To thus affecting the force exerted by said spring on the end 3, 30 of the corresponding elastic member 1, 10. For the same tightening of the screw and the same distance λ, the resulting compressive force exerted on the corresponding elastic member 1, 10 will be lower in the case of the multi-programmable force-programmable system than in the case of the multistable system that is programmable by displacement. . The ratio between the distance traveled by the screw and the compressive force exerted on the elastic member is therefore higher for a programmable displacement adjusting device than in the case of a programmable force adjustment device. Also, in a multistable system in which the force variations required to switch from one steady state to another are very small and require fine tuning, a force-programmable multistable system is more appropriate.

Le système multistable programmable par force selon le second mode de réalisation de l'invention se comporte de la même façon que le système multistable programmable par déplacement selon le premier mode de réalisation de l'invention à la différence près qu'en fonctionnement (après réglage) les extrémités réglables 3, 30 du système multistable selon le second mode de réalisation sont mobiles (elles peuvent se déplacer lors du passage d'un état stable à un autre) alors qu'elles sont fixes dans le cas du premier mode de réalisation.The multi-programmable force-programmable system according to the second embodiment of the invention behaves in the same way as the multi-programmable displacement-shift system according to the first embodiment of the invention with the difference that in operation (after adjustment ) the adjustable ends 3, 30 of the multistable system according to the second embodiment are movable (they can move during the transition from one stable state to another) while they are fixed in the case of the first embodiment.

Un diagramme permettant de prévoir le comportement du système multistable selon le second mode de réalisation de l'invention est réalisable de manière similaire au premier mode de réalisation.A diagram for predicting the behavior of the multistable system according to the second embodiment of the invention is feasible similarly to the first embodiment.

Comme dans le premier mode de réalisation de l'invention, lorsque l'on utilise n organes élastiques en série on obtient un système multistable présentant plusieurs configurations différentes et la configuration possédant le plus d'états stables différents possède 2n états stables.As in the first embodiment of the invention, when n elastic members are used in series, a multistable system having several different configurations is obtained and the configuration having the most of different stable states has 2 n stable states.

La figure 8 est un exemple d'un système multistable « mixte » selon un troisième mode de réalisation de l'invention dans lequel certaines extrémités sont réglables en position et d'autres extrémités sont réglables en force.The figure 8 is an example of a multistable system "mixed" according to a third embodiment of the invention wherein some ends are adjustable in position and other ends are adjustable in force.

Ce système comprend des organes élastiques doubles 1, 10 comprenant des paires de longues parties rigides 11 et de courtes parties élastiques 12.This system comprises double elastic members 1, 10 comprising pairs of long rigid portions 11 and short elastic portions 12.

Le premier organe élastique 1 comporte une première extrémité 2 jointe au châssis 5. La zone de liaison 4 du premier organe élastique 1 est constituée d'une entretoise 4 qui bloque la rotation du premier organe élastique 1. La deuxième extrémité 3 du premier organe flexible 1 correspond à un bloc réglable en position ou pouvant être soumis à une force réglable.The first elastic member 1 has a first end 2 joined to the frame 5. The connection zone 4 of the first elastic member 1 consists of a spacer 4 which blocks the rotation of the first elastic member 1. The second end 3 of the first flexible member 1 corresponds to an adjustable block in position or that can be subjected to an adjustable force.

Dans le cas où la deuxième extrémité du premier organe élastique 1 est réglable en force, le bloc constituant l'extrémité 3 se déplace axialement parallèlement à l'axe A1 sous l'effet d'une force exercée par deux lames ressorts parallèles 13, 13'. Les lames ressorts 13, 13' sont contraintes par un bloc 14 dont le déplacement est guidé par une lame de guidage 6. Le déplacement des blocs 3, 14 est limité par des butées 18, 18', comme illustré sur la figure 8.In the case where the second end of the first elastic member 1 is adjustable in force, the block constituting the end 3 moves axially parallel to the axis A 1 under the effect of a force exerted by two parallel leaf springs 13, 13 '. The spring blades 13, 13 'are constrained by a block 14 whose displacement is guided by a guide blade 6. The displacement of the blocks 3, 14 is limited by abutments 18, 18', as illustrated in FIG. figure 8 .

Dans le cas où la deuxième extrémité du premier organe élastique 1 est réglable en position, le bloc constituant l'extrémité 3 et le bloc 14 sont reliés rigidement par un pont (non représenté) de sorte que le déplacement axial du bloc 14 d'une distance δ1 entraîne un déplacement axial équivalent du bloc constituant l'extrémité 3.In the case where the second end of the first elastic member 1 is adjustable in position, the block constituting the end 3 and the block 14 are rigidly connected by a bridge (not shown) so that the axial displacement of the block 14 of a distance δ 1 causes an equivalent axial displacement of the block constituting the end 3.

Le deuxième organe élastique 10 comporte une première extrémité 20 jointe à la zone de liaison 4 du premier organe élastique 1. La deuxième extrémité 30 dudit deuxième organe flexible 10 correspond à un bloc 30 dont la position est réglable (par déplacement d'une distance δ2) et guidée par un dispositif de guidage 60 constitué de parties flexibles 15 et de parties rigides 16.The second elastic member 10 has a first end 20 joined to the connection zone 4 of the first elastic member 1. The second end 30 of said second flexible member 10 corresponds to a block 30 whose position is adjustable (by displacement of a distance δ 2 ) and guided by a guiding device 60 consisting of flexible parts 15 and rigid parts 16.

Le deuxième organe élastique 10 comprend en outre une articulation 17 comprenant deux parties rigides 17a et 17b reliées entre elles par deux lames ressorts 17c et 17d non parallèles qui forment un pivot flexible permettant aux deux parties rigides 17a et 17b de pivoter l'une par rapport à l'autre. Une telle articulation permet de diminuer les contraintes subies par le système.The second elastic member 10 further comprises a hinge 17 comprising two rigid parts 17a and 17b interconnected by two non-parallel spring blades 17c and 17d which form a flexible pivot allowing two rigid portions 17a and 17b to pivot relative to each other. Such articulation makes it possible to reduce the stresses to which the system is subjected.

Dans la figure 8, le système est programmé par l'intermédiaire des blocs 14 et 30 et la force d'entrée Fe est appliquée à la partie rigide 17a.In the figure 8 , the system is programmed through blocks 14 and 30 and the input force F e is applied to the rigid portion 17a.

Dans les trois modes de réalisation de l'invention, les n organes élastiques sont typiquement monobloc les uns avec les autres et, de préférence, aussi monobloc avec le châssis 5. L'ensemble des organes élastiques peut être réalisé dans tout matériau approprié, par exemple un métal ou un alliage métallique (selon par exemple la technologie LIGA) ou le silicium (selon par exemple la technologie DRIE).In the three embodiments of the invention, the n resilient members are typically integral with each other and, preferably, also integral with the frame 5. The set of elastic members can be made of any suitable material, for example for example a metal or a metal alloy (according to for example LIGA technology) or silicon (according to for example DRIE technology).

Les organes élastiques peuvent avoir différentes formes. Chacun de ces organes peut être constitué d'un organe élastique simple, comme le deuxième organe élastique 10 de la figure 1, ou être constitué d'un organe élastique double, comme le premier organe élastique 1 de la figure 1. Les organes élastiques d'un système multistable selon l'invention peuvent également être tous constitués d'organesélastiques simples, comme dans les figures 6a à 6h ou bien être tous constitués d'organes élastiques doubles, comme illustré dans la figure 8. La figure 9 illustre un exemple comprenant trois organes élastiques doubles. Le système multistable représenté dans la figure 9 comprend trois organes élastiques 1, 10, 100, comprenant chacun une première lame élastique 1a, 10a, 100a et une deuxième lame élastique 1b, 10b, 100b.The elastic members may have different shapes. Each of these members may consist of a single elastic member, such as the second elastic member 10 of the figure 1 , or consist of a double elastic member, such as the first elastic member 1 of the figure 1 . The elastic members of a multistable system according to the invention may also all consist of simple elastic members, as in the Figures 6a to 6h or all of them consist of double elastic members, as illustrated in figure 8 . The figure 9 illustrates an example comprising three double elastic members. The multistable system represented in the figure 9 comprises three elastic members 1, 10, 100, each comprising a first elastic blade 1a, 10a, 100a and a second elastic blade 1b, 10b, 100b.

Chacun des organes élastiques peut également comprendre une première moitié constituée d'une seule lame élastique 1e, 10e, 100e et une deuxième moitié constituée de deux lames élastiques 1c, 1d, 10c, 10d, 100c, 100d, les deux moitiés étant séparées par la zone de liaison 4, 40 de l'organe élastique ou par la zone d'application 900 de force, comme représenté dans la figure 10. Chacun des organes élastiques peut aussi comprendre de longues parties rigides 11 et de courtes parties élastiques 12 comme illustré par la figure 11 et comme déjà décrit en relation avec la figure 8.Each of the elastic members may also comprise a first half consisting of a single elastic blade 1e, 10e, 100e and a second half consisting of two elastic blades 1c, 1d, 10c, 10d, 100c, 100d, the two halves being separated by the connection zone 4, 40 of the elastic member or by the force application zone 900, as shown in FIG. figure 10 . Each of the elastic members may also comprise long rigid portions 11 and short elastic portions 12 as illustrated by FIG. figure 11 and as already described in relation to the figure 8 .

Quel que soit le mode de réalisation de l'invention, au lieu de comprendre une ou des lames déformables en flambage, chaque organe élastique 1, 10 peut comprendre des bras articulés 1.1, 1.2, 10.1, 10.2 soumis à l'action d'au moins un ressort 1.3, 10.3 comme illustré dans la figure 12. Sous l'effet d'une compression, de tels organes élastiques fléchissent au lieu de flamber, le principe de fonctionnement du système multistable restant le même.Whatever the embodiment of the invention, instead of comprising one or more deformable blades buckling, each elastic member 1, 10 may comprise articulated arms 1.1, 1.2, 10.1, 10.2 subjected to the action of minus a spring 1.3, 10.3 as illustrated in the figure 12 . Under the effect of compression, such elastic members bend instead of flambé, the operating principle of the multistable system remaining the same.

La figure 12 illustre également un dispositif d'application de force constitué d'un bras 91 articulé par une première extrémité à la zone d'application 90 de force du deuxième organe élastique 10, sa deuxième extrémité 92 étant guidée par un dispositif de guidage d'application de force 93 de type rainure ou rail.The figure 12 also illustrates a force application device consisting of an arm 91 articulated at a first end to the force application zone 90 of the second elastic member 10, its second end 92 being guided by a device for guiding the application of force. 93 force type groove or rail.

Il apparaîtra clairement à l'homme du métier que la présente invention n'est en aucun cas limitée aux modes de réalisation représentés dans les figures. Elle n'est par exemple pas limitée à un nombre d'extrémités réglables particulier. Le système multistable selon l'invention pourrait n'avoir qu'une seule extrémité réglable, chaque organe élastique pourrait avoir une extrémité réglable, ou seulement certains organes élastiques pourraient avoir une extrémité réglable.It will be apparent to those skilled in the art that the present invention is in no way limited to the embodiments shown in the figures. For example, it is not limited to a particular number of adjustable ends. The multistable system according to the invention could have only one adjustable end, each elastic member could have an adjustable end, or only some elastic members could have an adjustable end.

Le système multistable ainsi obtenu est capable de changer sa multistabilité, c'est-à-dire de changer le nombre de positions stables qu'il peut atteindre ainsi que les forces nécessaires pour passer d'une position stable à une autre. Un tel système peut être utilisé dans des applications très diverses telles que dans l'horlogerie, dans les détecteurs de seuil (par exemple dans les capteurs d'accélération), dans les commutateurs, dans les vannes, dans les positionneurs ou encore dans les robots reconfigurables.The multistable system thus obtained is capable of changing its multistability, that is to say of changing the number of stable positions that it can reach as well as the forces necessary to move from one stable position to another. Such a system can be used in very diverse applications such as in the watch industry, in threshold detectors (for example in acceleration sensors), in switches, in valves, in positioners or in robots reconfigurable.

Claims (16)

  1. Multi-stable system comprising:
    - a first elastic member (1) of rank r = 1 comprising first (2) and second (3) ends and a linking zone (4) between said first (2) and second (3) ends, and
    - (n-1) other elastic members (10, 100) of rank r each comprising first (20, 200) and second (30, 300) ends, with r being between 2 and n, n being an integer greater than or equal to 2; when n > 2 each of said other elastic members of rank r with r being between 2 and (n-1) comprising a linking zone (40) between its first and second ends; each of said other elastic members of rank r with r being between 2 and n being joined by its first end to the linking zone of the elastic member of rank (r-1);
    characterised in that it is arranged such that the position of at least one of said first (2) and second (3) ends of the first elastic member (1) or the force applied to at least one of said first (2) and second (3) ends of the first elastic member (1), and/or the position of the second end of at least one of said (n-1) other elastic members (10, 100) or the force applied to the second end of at least one of said (n-1) other elastic members (10, 100) is adjustable, said multi-stable system being such that an adjustment of the position and/or of the force applied to said adjustable end(s) allows said multi-stable system to be passed from one multi-stable configuration to another, said two multi-stable configurations having different numbers of stable states.
  2. Multi-stable system as claimed in claim 1, characterised in that the position of the second end or the force applied to the second end of each of the n elastic members (1, 10, 100) is adjustable.
  3. Multi-stable system as claimed in claim 1 or 2, characterised in that each of said linking zones (4, 40) is located in the centre of the elastic member (1, 10) which bears it.
  4. Multi-stable system as claimed in any one of claims 1 to 3, characterised in that the or each of the adjustable end(s) of the elastic members (1, 10, 100) of rank 1, with r being between 1 and n, is able to move in translation along an axis Ar.
  5. Multi-stable system as claimed in claim 4, characterised in that each axis Ar, with r being between 2 and n, is perpendicular to the axis Ar-1.
  6. Multi-stable system as claimed in claim 4 or 5, characterised in that it comprises one or more guide device(s) (6, 60, 600) to guide the or each of the adjustable ends of the elastic members (1, 10, 100) of rank r, with r being between 1 and n, along the corresponding axis Ar.
  7. Multi-stable system as claimed in claim 6, characterised in that said guide device(s) (6, 60, 600) comprise at least one elastic guide device.
  8. Multi-stable system as claimed in claim 7, characterised in that said at least one elastic guide device is multi-stable.
  9. Multi-stable system as claimed in any one of the preceding claims, characterised in that at least one of the ends of said system of which the position is adjustable is associated with a position-adjusting device (7, 70) comprising an adjusting screw (8, 80).
  10. Multi-stable system as claimed in any one of the preceding claims, characterised in that at least one of the ends of said system to which an adjusting force is applied is associated with a force-adjusting device (7', 70') comprising a spring constrained by a screw (8', 80').
  11. Multi-stable system as claimed in any one of the preceding claims, characterised in that at least one of said elastic members (1, 10, 100) comprises one or a plurality of beams which are deformable by buckling.
  12. Multi-stable system as claimed in any one of the preceding claims, characterised in that at least one of said elastic members (1, 10) comprises articulated arms (1.1, 1.2, 10.1, 10.2) subjected to the action of at least one spring (1.3, 10.3).
  13. Multi-stable system as claimed in any one of the preceding claims, characterised in that at least one of said elastic members (1, 10, 100) comprises several beams (1a, 1b) which are deformable by buckling.
  14. Multi-stable system as claimed in any one of the preceding claims, characterised in that said elastic members (1, 10, 100) are formed in one piece with each other.
  15. Multi-stable system as claimed in any one of the preceding claims, characterised in that n = 2 or n = 3.
  16. Multi-stable system as claimed in any one of the preceding claims, characterised in that at least the elastic member of rank r = n comprises an articulation between its first and second ends to decrease the constraints applied by said system.
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