RO125589B1 - Multi-hexapodal robotic positioning system - Google Patents

Description

The invention relates to a multihexapod robotic positioning system, consisting of two or more superimposed Stewart-Gough hexapod platforms. These are positioning systems with six degrees of freedom, and are known for their positioning accuracy and robustness.

The first practical uses of the Stewart-Gough hexapod platforms took place after 1965, in the field of flight simulators. The latest research is aimed at the development of platforms operated with piezoelectric actuators, for applications in the field of nanodeplacements.

Most existing hexapod modules are made in two constructions:

a) the couples on the lower (fixed) platform are spherical couplings, which allow three orthogonal rotations, and the couples on the upper (mobile) platform are cardan couplings, which allow two orthogonal rotations or vice versa; translations are provided by prismatic translation pairs (only allow translation); this solution has the disadvantage that it uses two types of rotating couplings, spherical and cardan, which complicates the construction;

b) the lower and upper couplings are cardan couplings, and the translations are provided by cylindrical translation couplings (which also allow rotation and translation); The disadvantage of this solution is that it is not possible to use certain types of linear motors that kinematically correspond to the prismatic pairs.

The main disadvantage of the single Stewart-Gough platforms is the relatively limited operating space.

Such a platform can be found in US 20030106230 A1 and refers to a micromanipulator comprising a hexapod provided with a type of parallel mechanism, and each kinematic link of the hexapod comprises a linear piezometric motor. The technical configuration obtained by the combination realized between the parallel mechanism and the linear piezometric motors allows its movement with the resolution of 10 mm or greater. In addition, each micromanipulator has six degrees of freedom.

US 5354158 discloses a machine tool containing a pair of Stewart-Gough platforms spaced apart, by means of six legs, motorized and extendable by means of hydraulic cylinders. The upper platform contains a tool fixed in the vertical axis, and the lower platform contains a workpiece fixed in the vertical axis. The length of the legs can be individually modified so that the position of the platform and the position of the tool relative to the workpiece are modified according to the six degrees of freedom of the assembly.

The technical problem that the invention aims to solve is the development of a robotic positioning system with extended mobility, for interventions in hard-to-reach spaces. The solution to this problem is provided by the robotic system having the technical characteristics presented in independent claim 1. The robotic system consists of a mechanical structure that includes the linear motor drive system, the motion control system and the control program. The mechanical structure consists of two or more identical, overlapping hexapod platforms, called hexapod modules. The number of degrees of freedom of the system is 6 n, where n is the number of modules. If it is required that all modules have identical configurations, the number of degrees of freedom of the system is reduced to 6, regardless of the number of modules.

The multihexapod robotic positioning system is composed of modules made in the following construction: the lower and upper couplings are cardan couplings, and the motor shaft is fixed by the upper cardan coupling through a radial bearing, the linear motor being kinematic equivalent to a prismatic coupling; this solution simplifies the construction and allows miniaturization, compared to the existing solutions. From a constructive point of view, the motor support ensures coaxiality between the lower cardan coupling and the motor shaft.

RO 125589 Β1 (1)

The mobility degree M of the hexapod module is calculated by the formula:

M = 6-n- ^ mN _m m- \ where n is the number of movable elements, and N _m - the number of couplings of class m.

in the proposed construction, the translation module consists of three kinematic elements:

- engine support + engine body;

- motor shaft + motor shaft adapter + outer ring bearing;

- inner ring bearing + cardan coupling adapter.

Thus, the 6 legs represent 18 elements, and the mobile platform, the 19th, ie n = 19. So we have the following kinematic couplings:

-12 class 4 cardan couplings;

- 6 pure translation couplings (linear motors) of class 5;

- 6 rotating couplings (bearings) of class 5.

The degree of mobility becomes as follows:

M = 6 · 19 - (4 · 12 + 5 · 6 + 5 · 6) = 114 - (48 + 30 + 30) = 114 - 108 = 6 (2) which corresponds to the number of actuating elements of the hexapod module .

The hexapod modules are assembled by means of connecting elements that are designed and sized so as to ensure the precise relative positioning of two adjacent modules, one relative to the other, allow the assembly of the desired hexapod modules, and ensure the coplanarity of the centers of the upper cardan couplings belonging to the module. inferior, and of the centers of the lower cardan couplings of the upper module; this is a condition that derives from the theoretical model.

The development of the invention is the result of the following theoretical premises:

To define the position of the platform, three parameters are used: the x, y, z coordinates of the center of the platform; To define the orientation of the platform, three independent angles are introduced (Euler angles):

- ψ - the rotation angle around the fixed vertical axis;

- θ - the inclination angle of the platform about a horizontal axis rotated with the angle ψ;

- Φ - the angle of rotation of the platform around the axis perpendicular to the center of the platform.

To determine the coordinates of the peaks of hexagons B · ,, and B _2i , i = 1 ... 6, we use a matrix method, with the notations:

X MOW// - sin i // 0 ' Cart # 0 Sin # cosţz » - sin </> 0 [r] = y M = sin ψ mow// 0 0 1 0 sinţz » cosţz » 0 z 0 0 1 - without # 0 Cart # 0 0 1

[V] being the position vector, and [ψ], [θ], [φ] - the elementary rotation matrices.

The following coordinate systems are defined (fig. 1): the fixed system O ₀ x ₀ y ₀ z ₀ , the system O _l x _l y _l z _l attached to the intermediate mobile platform 1 and the system O ₂ x ₂ y ₂ z ₂ attached to the mobile platform end 2.

RO 125589 Β1

Starting from the position and orientation of platform 2, defined by the coordinates of its center x ° 'Ϋο ₂ ' ^z o ₂ in the system O ₀ x ₀ y ₀ z ₀ and the orientation angles t / θ = Ψ, έ? ₂ ° = = Φ with respect to the same system, the analogous parameters must be determined for:

- intermediate platform 1 in relation to the system O _(j x _(j y _(j z _(j '. χθ, j / θ, ζθ, respectively, ζίΟ u

Ψΐ, 5 ψ \>

- the final platform 2 In relation to the system Cfx ^ zȚ.xl, y °, z °.

- ^ 2> Ψΐ '

For a certain point P we have the following relations between its coordinates expressed vectorially in the systems O ₀ x ₀ y ₀ z ₀ , O ₁ x ₁ y ₁ z ₁ , respectively, θ 2 ^ 2) ^ 2

Κ] = [ ^γ ';] ⁺ [^] - [^] - [^] - [ ^γ ϊ] < ⁴ >

[u 1 = K1 ⁺ Ml - K1 - Ml - [u 1 = K1 ⁺ M - [®l- [®] - [u 1 < ⁵ >

For identical configurations, we have identical distances θ _θ θ! - that is:

[uhu] <®>

and identical angles t / θ = = 1 //, 0 ° = έ? ₂ = θ, φ ° = φ \ = φ (7) by substituting the relation (4) into (3) and taking into account (6) and (7), we obtain:

M = [U] + W - M - M · ([U] + M · [»] · H '[U]) =

Κ] + Μ · ΜΗ · ([υψΜ · Μ · Η · [υ]) = <®>

[UHdUHdKMdUlWK]

Taking into account the relation (5), we obtain the identity:

But, by particularizing P = O ₂ in relation (1) and taking into account (4), we have [U] = [u] w Η 'Κ l = [' ·] + M · Pl · M · [U] (10 ) by substituting the relation (10) into (9), we obtain

MPi-Pil · Μυ] = Μ · [®] · [®] · Μ ου or (Μ · Ρ] · [<= [Ψ] · [Θ] [Φ] (12)

The final relationship results [v /] 'p]' W = vm [®] '[®] (1 ³ )

RO 125589 Β1

Using the same method, the relation (13) can be generalized for a system with n 1 modules:

³

The coordinates of points Β _Ή and B _2i , i = 1 ... 6 are then determined:

Ki '/ i + M-M'W'ki] < ¹⁵ > ⁵ < ¹⁶ >

From the relations (15) and (16) the lengths of the platform legs are deduced, that is to say, the 7 order sizes.

The multihexapod robotic positioning system according to the invention has the following 9 advantages:

- allows to expand the operating space, ie to increase the displacements and inclines of the final platform;

- it can be ordered so as to achieve the positioning and orientation of the useful platform 13 through six control parameters, regardless of the number of hexapod modules, imposing the condition that all the hexapod modules have identical geometric configurations at one point. 15

The following is an example of an embodiment of the invention for two hexapod modules, in connection with FIG. 2 ... 5, representing: 17

FIG. 2, view of a dual hexapod robotic positioning system;

FIG. 3 is a view of a hexapod module; 19

FIG. 4, axial section through a translation module (leg of the hexapod module);

FIG. 5, detail of the axial section through the translation module in the area of the rotating coupling. 21

The double hexapod robotic positioning system consists of identical hexapod 1 modules, three connecting elements 2 arranged at 120 °, fastened with screws 3 and 4; each 23 hexapod module consists of a fixed platform 5 and a movable platform 6, joined by six legs of variable length, called translation modules 7. 25

Each translation module is composed of the linear electric motor 8, mounted on the support 9, of the adapter 10 on which the radial bearing 11 is fixed, mounted in the box 12; 27 the translation module is fixed to the fixed platform 5 and to the mobile platform 6 by means of two cardan couplings 13, respectively 14. The support 9 provides the coaxiality between the shaft 29 of the linear motor 8 and the cardan couplings 13 and 14. The connecting elements 2 ensure the coplanarity. the centers of the upper cardan couplings 14, which belong to the lower module, and 31 the centers of the lower cardan couplings 13 of the upper module.

The multihexapod robotic positioning system can be controlled so as to achieve the positioning and orientation of the usable area by only six control parameters, regardless of the number of hexapod 1 modules; this is achieved by imposing the condition that all hexapod modules have identical geometric configurations at one point, which is obtained by using relation 14 in the control algorithm. 37

Claims (2)

claims 1. Multihexapod robotic positioning system, composed of a plurality of identical hexapod modules (1), comprising a fixed lower platform (5) and a mobile upper platform (6), the platforms (5, 6) being linked between they are via six translation modules (7), comprising a lower cardan coupling (13), fixed on the fixed lower platform (5), an upper cardan coupling (14), fixed on the movable upper platform (6), and an engine linear electric (8), mounted on a support (9), which ensures the coaxiality between the linear motor shaft (8) and the cardan couplings (13.14), characterized in that the hexapod modules (1) are assembled together so that the fixed lower platform (5) of the upper module is positioned below the movable upper platform (6) of the previous module, by means of three connecting elements (2), arranged at 120 °, and of screws (3, 4) that ensure the coplanarity c the inputs of the upper cardan couplings (14), which belong to the lower hexapod module, and the centers of the lower cardan couplings (13), which belong to the next upper hexapod module. 2. System according to claim 1, characterized in that the positioning and orientation of the upper mobile platform (6), comprising the last hexapod module (1), is achieved by using a six-parameter control software, and by imposing the condition that all the hexapod modules (1) initially have identical geometric configurations.