Redundant parallel positioning table device

Abstract

The present invention is related a redundant parallel positioning table device. More particularly, the present invention relates to a redundant parallel positioning table device for a precise positioning of heavy load samples, instrument and/or apparatus, e.g. in the context of diffractometer machines for synchrotron facilities.

Claims

1. A redundant parallel positioning table device Rd-PPT comprising: (a) a stationary base B; (b) a moveable table T movable relative to the stationary base in all six degrees of freedom 6dof, the moveable table having a fixing surface .sub.T adapted to receive a sample Sp or related bodies Bo; (c) at least one set of four supporting legs, one being redundant, as 213 kinematics chains K, the legs arranged around a center of the base symmetrically and in opposed pairs, each leg having a base end connected to the stationary base and a table end connected to the movable table.

2. The redundant parallel positioning table device of claim 1 wherein the parallel positioning table device is modular with the supporting legs as positioning modules Pm, the positioning modules being active 2dof pillars, parallel to each other, vertical with respect to one axis of symmetry Z, and orthogonal with respect to a second axis of symmetry X/Y.

3. The redundant parallel positioning table device of claim 2 wherein the positioning modules Pm are located symmetrically about a central location of the movable table T.

4. The redundant parallel positioning table device of claim 2 wherein each of the positioning modules is a stacked combination of an active planar positioning unit Ac, a passive elevation positioning unit El, and a passive spherical guiding positioning unit Gu.

5. The redundant parallel positioning table device of claim 4 wherein the active planar positioning unit Ac is a 2dof actuation unit that includes a base b fixed to the stationary base, a mover M movable relative to the base in two orthogonal axes planar to the base, a linear actuator A11 moving the mover M in the first orthogonal axis, a linear actuator A12 moving the mover M in the second orthogonal axis, a redundant linear actuator A11 moving the mover M in the first orthogonal axis, and a redundant linear actuator A12 moving the mover M in the second orthogonal axis.

6. The redundant parallel positioning table device of claim 5 wherein the first orthogonal axis of a first opposing pair are parallel to each other and the second orthogonal axis of the first opposing pair are parallel to each other, and the first orthogonal axis of a second opposing pair are parallel to each other and the second orthogonal axis of the second opposing pair are parallel to each other.

7. The redundant parallel positioning table device of claim 4 wherein the passive elevation positioning unit El comprises a pair of wedges W21, W22 movable relative to each other on V-type inclined guiding surfaces .sub.21, .sub.22, and wherein the lower part W21 is fixed to the active planar positioning unit Ac and the upper part W22 is supporting the spherical guiding positioning unit Gu, the inclined guiding surfaces of an opposed pair of legs forming a V shape.

8. The redundant parallel positioning table device of claim 4 wherein the passive spherical guiding positioning unit Gu is a spherical joint S with a truncated conical pillar p mounted to the passive elevation positioning unit El, a precision sphere S attached to the pillar p and having convex surface .sub.31, a housing H1, H2 having an adjustable concave surface .sub.32 slidable on the convex surface .sub.31, the housing H1, H2 connected to the bottom side of the movable table.

9. Use of a redundant parallel positioning table according to claim 4 to generate simple Cartesian spatial translation (TX or TY or TZ) and rotation (RX or RY or RZ) motions, and linear (X or Y or Z) and angular (X or Y or Z) displacements, as direct involvement of motions with equal, or equivalent displacements, by using all or only some of the corresponding active planar positioning units.

10. The redundant parallel positioning table device of claim 1 wherein each of the 213 legs comprises a generalized 2dof planar actuation joint (Pl ).sub.2, as a pair of a mover M and one spherical .sub.S, or toroid .sub.Tor cylindrical .sub.C curvilinear fixed surfaces parts, the mover M being able to slide in two orthogonal directions (q1, q2) as part of general 6-4-(Pl).sub.2XS parallel mechanisms, having the spherical joints S always on the last level, and X an unspecified 1dof joint (P, R, H).

11. A redundant parallel positioning table device comprising: (a) a stationary base; (b) a moveable table movable relative to the stationary base in all six-degrees-of-freedom, the moveable table having a fixing surface adapted to receive a sample and/or related instruments; (c) at least one set of four supporting legs symmetrically arranged around a center of the stationary base, each leg having a base end connected to the stationary base and a table end connected to the movable table; (d) the table positioning device being modular with the supporting legs as positioning modules, the positioning modules being vertical, parallel to each other and to one axis of symmetry, and orthogonal to another axis of symmetry, each of the positioning modules being a combination of an active positioning unit, a first passive positioning unit, and a second passive positioning unit.

12. The redundant parallel table positioning device of claim 11 wherein the active positioning unit provides two degrees of freedom along at least a first orthogonal axis and a second orthogonal axis.

13. The table positioning device of claim 12 wherein all of the active positioning units are mounted to the stationary base such that the first orthogonal axis of a first opposing pair are parallel to each other and the second orthogonal axis of the first opposing pair are parallel to each other, and the first orthogonal axis of a second opposing pair are parallel to each other and the second orthogonal axis of the second opposing pair are parallel to each other, all axes being parallel to the stationary base.

14. The table positioning device of claim 11 wherein the first passive positioning unit is an elevation component with an inclined guiding surface between a lower part fixed to the active positioning unit and an upper part supporting the second passive positioning unit.

15. The table positioning device of claim 14 wherein on each of the elevation units are perpendicularly mounted guiding positioning units that permit orientation motions and displacements for the positioning modules, and by their combined work, the entire table device to be translated and/or oriented.

16. The table positioning device of claim 11 wherein the second passive positioning unit is a guiding component with sliding, corresponding convex-concave surfaces and connecting the first passive positioning unit with the bottom side of the table.

17. A methodology for generating spatial motions and displacements as combination sequences of all or some of the active translational motions and/or displacements generated by the table positioning device according to claim 11.

Description

EXAMPLES

(1) In the actual context of invention precision relates with few (less than 10) micrometers (or, arc-seconds) and refers to accuracy, repeatability, resolution; and, the stability (several micrometers or arc-seconds/hour).

(2) For the purpose of illustrating the invention the following drawings are included:

(3) FIG. 1 represents the 6-4-2topological concept of the redundant parallel positioning table device,

(4) FIG. 2 represents the 6-4-(Pl).sub.2XS general kinematic model for redundant parallel positioning table device,

(5) FIG. 3 represents the kinematic model of 6-4-(2P)PS mechanism for redundant parallel positioning table device,

(6) FIG. 4 is a 3D view of the redundant parallel positioning table device design concept,

(7) FIG. 5 is an example of a Positioning module (Pm) and two assembly embodiments,

(8) FIG. 6 is describing the basic operational principle for the positioning table device.

(9) The followings notations have been used:

(10) TABLE-US-00001 Type Kinematics/Geometry Type Design/Drawings A.sub.i, A Guiding, Center platform points Ac (A) Actuators B.sub.i, B.sub.i0 Actuation, Fixed base points B, (Bo) Base, Body(e.g. instrument) C.sub.i, C, Sliding points, Rotation center El Elevation unit a.sub.i, b.sub.i Guiding, actuation points distance F Fixing means(e.g. screw) q.sub.i Generalized (actuated) coordinates Gu, g Guiding unit, means J Joint H Housing Dof, (f) Degree-of-freedom (joints) L, I Lengths K Kinematic chain M (m) Mover (motor) P, (Pl).sub.2, S Prismatic, Planar(2dof), Spherical Joints Pm (Pu) Positioning module (unit) R(Rx, Ry, Rz) Rotational Motion p Pillar T(XYZ) Translational Motion (Displacement) r, D Radius, Diameter (), (C) Surface, Curve S, s Spherical (Joint), Sphere d Distance Sp Sample l Links T Table I, . . . , IV Kinematic Levels W Wedge 1, 2, 3, 4 Actuated joints motion , , , Angle/Angular Motion , , (displacements) i, j = 1, . . . , 4 Index (number of points, chains, etc) , || Perpendicular, Parallel(ax)

(11) The architecture of a positioning device is an important factor regarding its capabilities. The chosen structure, kinematics, geometry, and optimum design affect the required final static, kinematic and dynamic parameters.

(12) The graphical representation of a structure working as positioning table device is proposed in FIG. 1. The topological kinematic concept is fundamentally based on two rigid bodies (or, elements)a first element (1) called the base (B), generally fixed to the ground and the second element (2) supposed to move called platform, or table (T). Both of them are connected with four identical kinematic chains or, legs (K.sub.i), i=1, . . . , 4a succession of mobile rigid pairs of links (l.sub.i.1, l.sub.i.2) and triplets of joints (J.sub.i.j) arranged on three levels (j=l, . . . , lll) in the same succession regarding joints' dof (f.sub.ij=213) starting from the primary element (1). All joints at the first level (I) situated on the base are called actuated (active) joints (J.sub.il) are actuated (bold and underlined noted), whereas the remaining ones situated on levels two (II) and three (III) are non-actuated called passive joints (J.sub.iII, J.sub.iIII). By this symmetric structural arrangement, the total degrees of freedom or mobility (M) of the mechanism computed with Kuzbach-Grbler formula: M=6n.sub.i.sup.j(6fi) for spatial mechanisms is resulting as six (M=6), because moving parts n=9, number of joints j=12 and their degrees of freedom f.sub.i=2,1 and 3, (j=1 . . . 4,5 . . . 8,9 . . . 12). The result is qualifying the kinematic mechanism (6-4-213) to have full spatial mobility; however, obtained with the price of redundancy. The degree of redundancy is coming from one chain addition (Rd.sub.K=1) and the actuators number (Rd.sub.A=2). In fact, the above graph is representing not only one type of the mechanisms' topology, but an entire QUATTROPOD's (QP) 6dof redundant PM family. Each of the members are depending on particular choice of joints, e.g. 1-P (Prismatic), 2-PR (R-Rotation) 3-S(Spherical). These particular very symmetric, over actuated, and over-constrained members are prone to perform heavy load stable motions with increased static and dynamic capabilities because of supplementary contact/acting points and power compared with three ones (tripod) being in the same time more versatile than six points(hexapod) structures.

(13) A general kinematic model is helping to define a particular mechanism based on the actual existent (or, developed) portfolio of kinematic joints and their general reciprocal arrangements. It is useful also to formulate the methodology of establishing the input/output (closure) equations. The above 6-4-213 graph permits to freely choose the actuated and non-actuated type of joints as: 1dof-linear (P), rotation (R), helicoidally (H), 2dof-(PP), (PR), (RR) and 3dof-spherical (S), (UR), (RRR) ones. A couple of active 2dof joints based on surface/mover principle could be used havingplanar (.sub.P), spherical (.sub.S), cylindrical (.sub.C) or toroid (.sub.T) fixed surfaces, on which the linear or curvilinear pathways motions (1, . . . , 8) of the sliders are moving accordingly, as shown in FIG. 2, representing 2P, 2R.sub.S, PR and 2R.sub.T driving joints. Through their simultaneously, or separated combined actions, each of the surface movers (m.sub.1, . . . , m.sub.4) or acting points B.sub.i (X.sub.Bi, Y.sub.Bi, .sub.Bi, i=1, . . . , 4) defined by a pairs of mechanisms' curvilinear generalized coordinates (q.sub.i, q.sub.i+1),i=1, . . . , 4 are changing the spherical joints (S) center A.sub.i (X.sub.i, Y.sub.i, .sub.i, i=1, . . . , 4) positions, which in turn, is moving the attached sample (Sp) and instrument body (Bo) generally in three spatial translational and/or rotational directions (3T/3R). With other words, this is to say that A.sub.i points are moving on curves (C.sub.i), i=1, . . . , 4 having each 2dof (l.sub.icurvilinear coordinate variable, see also FIG. 3). Following this, the resulted posepositions (XYZ) and orientation (, , ) values respectively, of manipulated objects is depending on: a) the actuation displacements (q.sub.1, i=1, . . . , 8) and b) geometrical (a.sub.i, b.sub.i, li, d.sub.i, L, I, R, r) parameters values for a general case of a 6-4-(Pl).sub.2XS mechanisms (X-undefined 1dof, (Pl).sub.2generalized curvilinear planar 2dof joints).Compact Spherical (S) joints is given a simplification in to formulate and solve the motion (position) equation. In this context, the (C.sub.i) and A.sub.i are called guiding curves and guided points, respectively. The closure equations can be easy derived by expressing their coordinates in both Cartesian systemsfix (B-XYZ) and mobile (A-xyz); the input (or, output) parameters (X, Y, Z, , , and q.sub.i) are implicit included.

(14) A kinematics scheme is helping to understand the working behavior of a mechanism and to formulate the motion equations. The positioning related problems (direct/invers) are then solved based on the input/output displacements and geometric parameters. A parallel mechanisms kinematics for positioning table based on above 6-4-(Pl).sub.2XS model is represented in FIG. 3. It is consisting from a symmetric arrangement in-pairs of four identical (PI).sub.2XS, i=1, . . . , 4, open kinematic chains, each comprising one planar actuated joint (2P) and twoprismatic (P) and spherical (S) non-actuated joints linking a quadrilateral platform like table (T) with the base (B) of the same shape. The (2P) joints are providing 2dof in a plane being located on substantially a planar base surface (.sub.B). Each of the opposite actuated joints (2P.sub.1, 2P.sub.3/2P.sub.2, 2P.sub.4) being symmetrically arranged, have all their linear motion axis orthogonally to each other (e.g. P.sub.11.sup.P.sub.12, etc) and subsequently orthogonally with other joints axis (P.sub.11.sup.P.sub.22.sup.P.sub.33.sup.P.sub.44). This symmetric combination of actuated axis is forming a general 42P planar Actuation module (A.sub.m), providing a simple and direct way for moving the table along each of the horizontal Cartesian planar axesX (X.sub.1, X.sub.2, X.sub.3, X.sub.4) and Y(Y.sub.1, Y.sub.2, Y.sub.3, Y.sub.4), respectively. Non- actuated opposite prismatic joints pairs (P.sub.13P.sub.33/P.sub.23P.sub.43) have all an identical inclined angles (.sub.i, i=1, . . . , 4) in respect with one of the actuated axis. By the two sets of in-pair actuators motion through simultaneously and concurrent displacements, the platform are moving in a orthogonal direction (Z) to the previously ones (X and Y) on a V type kinematics principle based. The inclined angles can be any from 0 to (except /2) radian; in figure </2. By simultaneously and motions of a pairs of actuated joints in the directions not related with the axis of rotation, or with another words orthogonally on rotation axis location, the result is the rotations around one of the planar orthogonal axis (e.g. X.sub.1, X.sub.3/Ry); the same procedure applied for Rx(Y.sub.2, Y.sub.4). The third rotational motion (Rz) is obtained by the action of all four (2P) joints in the same direction of rotation (and, in the same time)e.g. Rz/(X.sub.1, Y.sub.1/X.sub.2, Y.sub.2/X.sub.3, Y.sub.3/(X.sub.4, Y.sub.4). Through this specific arrangement 6-4-(2Pl)PS (or, 6-4-(PP)PS) a device can do some of the simple translational or rotational motions along or around tri-orthogonal directions very easy and intuitively through decoupled motor motions, which greatly simplify its control. As fundamentally is stated everywhere, the number of minimum points to position a body in space is enough to be three (3), however in this over constrained, but over-actuated parallel mechanism, the fourth actuator (4) is acting as a means for increasing the kinematics (speed/acceleration) and/or dynamic (inertia) capabilities, beside of an evident fundamental static stability. Moreover, if damage occurs somehow in a motion axis, the remaining ones could support the work till at least one (or, two) motorized axis (or, a leg) will be repaired. Note: The entire kinematics of de mechanism is built on using two typeslinear and spherical joints, only. This small diversity could reduce the total manufacturing costs.

(15) A good way to materialize the kinematic principle is a key factor to fulfill the required static, kinematic and/or dynamic performances. In FIG. 4, a general design concept is proposed based on 6-4-(2P)PS mechanism kinematic model. Redundant Parallel Positioning Table (Rd-PPT) design consists from a set of four active Positioning Modules (Pm.sub.i, i=1, . . . , 4) arranged on a substantially planar basic surface (.sub.B) and supporting a platform-like table (T) having both polygonal (quadrilateral) shapes. Each of the (Pm) comprises two types of Positioning units (Pu.sub.i, i=1, 2) in respect with their participation at the general motion; the first ones are called actuated and the second ones non-actuated (passive). The Actuation (Ac.sub.i, i=1, . . . , 4 Pu are driving means providing 2dof planar motion activated by any of the actual or further developed linear bidirectional motorized drivers, as direct driven (DD), e.g. planar motors, coming from each or combination of stepping, servo, magnetically or piezo effects, or including in-parallel or serial or hybrid (parallel-serial/serial-parallel) electromechanical actuation principles, or standard (motor-gearhead-motion screw-guides) solution. The last one, in the case of a XY stage is providing high stability of motion over the time, however, not very much to be preferred, because of cable management difficulties and the resulted reciprocal errors (e.g. perpendicularity, etc.) with the direct effect on precision. (Note: DD means driving the load directly without any transmission mechanism, such as pulleys, timing belts, ball screws and gears enabling both, high-precision and high-speed positioning. For long strokes, they have to rely on advanced servo technology for assuring high stability).

(16) The second types of Pu are including the Elevation (El) and Guiding (Gu) means, respectively.

(17) The (El.sub.i) units are based on planar wedge motion principle consisting from twolower, fixed on (Ac.sub.i) and upper, supporting (Gu.sub.i) parts having reciprocal inclined planar surfaces of motion and auxiliary guiding means (g.sub.i). By their relative motion, and following the result of the combined actuated unit(s) motions, the upper part will move up and down constrained by the distance of two opposite (Pm.sub.i). For heavy loads and precision motions the simple way of materializing them is to have flat sliding surfaces. However, others contact surfaces, as rolling/rolled (rails) or fluid (air, liquid) based principles can be also taken in to consideration if fit with the final required performances.

(18) The Guiding (Gui) Pu are based on spherical motion principle and are consisting from at least two partslower, fixed on upper part of (El.sub.i) and upper, supporting and giving the opportunity the table (T) to be oriented in 3D. The relative motion of the above parts is involving a spherical guiding surface in order the table (T) to perform the required rotational motions. The type can be any from compactrolling, sliding spherical joints (S) principle or even separatedsimple rotations joints (RRR) and combination of them (UR/RU) design. Other functional principle, as air or any fluid can be also taken in to consideration depending on the applications.

(19) The optimum design including the size and type of components are affecting not only the final performances but the entire characteristics and life of the device. In FIG. 5, a Positioning module (Pm) embodiment and two particular arrangements for whole devices are shown. The (Pm) is based on a stacked combination of three basic Positioning units (Pu.sub.i, i=1, 2, 3): a) first one (Pu.sub.i)-active/actuated (A) and b) second (Pu.sub.2) and third (Pu.sub.3) inactive (passive)wedge (W) and Spherical Joint (S) types, respectively.

(20) The (A) Pu is based on in-parallel actuation principle, consisting from in principle a square shape base (b) on which a pair of two similar linear actuation units (A.sub.11,A.sub.12) having each of the motion axis (t.sub.1,t.sub.2) orthogonal each other is moving in principle a rectangular mover (M) solidary being with a table (t) of the in principle same shape with (b) and fixed through several (at least four) fixing (f.sub.i,) and centered (e.g. pin, at least one) means. In addition, the (t) has in principle a flat surface supporting the next Pu (W). Each of the single actuation units (A.sub.11) and (A.sub.12) are comprising preferably a linear actuated motor (m.sub.11), and (m.sub.12) with a part fixed on the base and other (pusher) moving free and having a perpendicular and coplanar guide assembly (g.sub.1,g.sub.2) at one end with one part (preferable, the rail) fixed on (M). By pushing (or, pulling) the (A.sub.11) or (A.sub.12), the (M) is forced to move in and along each of the orthogonal directions (t.sub.11 or t.sub.12), but more specific in a (general) planar motion (t.sub.1) through their combined action. This orthogonal actuation unit (A) could be developed further, by enforcing its power through the addition of another preferably orthogonal actuation unit A(A.sub.11,A.sub.12). By this, each of the simple main actuation units are working in tandem with the additional ones (A.sub.11, A.sub.11/A.sub.12, A.sup..sub.12) to perform heavy duty motions cycles by the full working of all four (4) actuators or helping as partial work, in the case of working only three (3), for example. This complete new actuation unit (A,A) is fitting even better with the square base (b) and table (t) shape forming a strong and compact well balanced powered unit, if necessary. There is no particular limitation in the specific uses of several other in-parallel linear actuators number, as for example three, five, etc and the corresponding base/table polygonal shape accordingly; however, the two is the minimum. In principle, the guiding means (g.sub.11,g.sub.12) are preferably from sliding principle, but could be any other, e.g. rolling, magnetic, etc, as well. This at the base in-parallel actuation solution, beside the advantage of being able to provide no moving cable solution with direct effect on increased precision may use specific heavy load guiding means for the mover (M), e.g. 2dof planar bearings (.sub.1). And, in the case of more than two actuators is opening the way to choose smaller size motors and components for a more compact low profile actuation module inside of the same power parameters as two units. In all cases sensors may apply for better accurate motion.

(21) The Pu.sub.2 unit consists from a wedge (W) assemblya fixed lower part (W.sub.21) and movable upper part (W.sub.22) which in principle, is having the same support shape surface as similar to that of the table (t) A unit.

(22) By the relative motion of this pair, through the specific guiding means (g.sub.21,g.sub.22) with V groove profile surfaces (.sub.21, .sub.22), the upper part can be precisely adjusted for smooth and accurate motion against lower one through a flexible nervure (n) sliced along one of the sliding guides (g.sub.21,g.sub.22) and fixed then with several (at least two) fixing means (f.sub.2), e.g. screws. The (g.sub.21,g.sub.22) guides could have any another form which fit the scope, e.g. angular or even other means for performing the translational resulted motion (t.sub.2), based on rolling principle e.g. balls, cross-roller rails and carriages; or, for more precise motion requirements, the air guides.

(23) The Pu3 is the Spherical joint (S) positioning unit preferably comprising a sphere (s), e.g. calibration ball manufactured for metrological purpose with small roundness errors encapsulated (but, moving) in two houses (H.sub.1, H.sub.2) with reciprocal concave surfaces (.sub.31, .sub.32), and supported by a truncated conic pillar (p). (H.sub.1) is holding (H.sub.2) and it has an external guiding surface (g) for precise and smooth assembly with the table (T) using several (at least four) screws fixing means (f.sub.3). The (H.sub.1) and (H.sub.2) are adjustable to permit the smooth rotation of the convex-concave spheres with the center substantially coaxial; the conical pillar support axis is perpendicularly mounted in principle on the planar support surface of upper wedge (W.sub.22). Between the relative motions of the three surfaces the sliding contact principle is preferable to exist.

(24) Two preferred embodiments using above (Pm.sub.i) as parts of entire parallel table positioning device assemblies are materialized in FIG. 5b. The embodiments are consisting in using the preferably identic four from above modules (Pm) coupled in pairs (Pm.sub.1,Pm.sub.3/Pm.sub.2,Pm.sub.4) being in a circumferential and equidistant way arranged around a common vertical axis of symmetry of both, the base and table with the same square shapes size (a=b). The actuation/supporting legs axis of symmetry are intersecting: a) the middle-points, FIG. 5b1 and b) the corners, FIG. 5b2 of the actuation (b)/supporting (a) square, respectively. The rigid base (B) in both cases is expected to be a flat surface (plate) attached direct to a more generally flat surface of the machine basic structure (diffractometer); or, through additional device (e.g. gonio stages). Note, the base and the flat table could have also various planar polygonal shapes beside the square one, e.g. octagonal. In both embodiments, preferably the spherical joints are fixed in the table through partially through holes (h.sub.i) machined in the lower table surface and the precision manufactured guiding surfaces (g.sub.3) through screws. The working diagram of obtaining simple motions, e.g. X and Y translations are the same, in both variants. But for the remaining, they are as the followings; 1) Z motion is coming asa) four (4) and b) eight (8) and 2) Rx and Rya) two (2) and b) eight (8) axes together work (FIG. 5.b1) with direct influence on positioning parameters and subsequently, the performances. In addition, the distance (d) between modules are different: a) d.sub.a and b) d.sub.b (d.sub.a<d.sub.b), respectively. This means the device in the b) case can be designed with smaller footprint (compact) or with larger central aperture (D) for the same footprint for easier cable management as in the diffractometers' environments very often is necessary. By the above design both, the (Pm) component and whole assembly, the parallel positioning table is exhibiting a high degree of modularization and re-configurability; and, with an acceptable cost-effective product because relative few and simple parts are involved.

(25) The way of producing the output motions based on the afferent input motions (or, displacements) is a necessary step to understand the working behavior and to evaluate the capabilities of a new device. The method of basic operational principle is described in FIG. 6. The Rd-PPT device is supposed to be with direct drive (planar motors) in the nominal position (Pn). This means null orientation (Rx=Ry=Rz=0) and displacements for the table center (A; X=Y=0, Z=h) which is corresponding null displacements in the actuation units Ac.sub.i (B.sub.i; X.sub.1=Y.sub.1=0; X.sub.2=Y.sub.2=0; X.sub.3=Y.sub.3=0, X.sub.4=Y.sub.4=0). The basic motion sequences: a) X, Y, or Rz and b) Rx, Ry and Z imposed to the table are seen in relation with the Actuation modules (Ac.sub.i) changes. The final position (Pf) is marked as dash-dot line.

(26) Back and forth translational motions along X axis (Tx) are realized by synchronized motion of all actuators along specified axis and in the same direction (t.sub.i1, i=1, . . . , 4); the remaining motionsalong Y axis (t.sub.i2, i=1, . . . , 4) being inactivated (or, free), FIG. 6,a1. Supposing a positive displacement (X) of point (A) from initial to final (A) position, all the motors related with the same axis must be activated and in the same direction moving with the same values (X=X.sub.1=X.sub.2=X.sub.3=X.sub.4); or, at least three of them (the forth could be inactivated on this direction). For example, if Ac.sub.1 (X.sub.1), Ac.sub.2(X.sub.2) and Ac.sub.3(X.sub.3) are moving, then Ac.sub.4 (X.sub.4) could be completely free. The following relations exist: X=X.sub.1=X.sub.2=X.sub.3 (=X.sub.4); Y.sub.1=Y.sub.2=Y.sub.3=Y.sub.4=0. The same procedure applies to second orthogonal and coplanar axis (Y), FIG. 6,a2. Back and forth translational motion along Y axis (Ty) are realized by synchronized translational motions of all actuators along specified axis (t.sub.i2, i=1, . . . , 4) and in the same direction. Supposing a linear displacement along Y axis of point A(Y), the synchronized motions of all Actuation units (Ac.sub.i, i=1, . . . , 4) related with the Y axis must be activated and move in the same direction (Y=Y.sub.1=Y.sub.2=Y.sub.3=Y.sub.4); or at least three of them. That means, for example, if Ac.sub.1 (Y.sub.1), Ac.sub.2(Y.sub.2) and Ac.sub.3(Y.sub.3) are activated and moves; Ac.sub.4(Y.sub.4) can be inactivated: Y=Y.sub.1=Y.sub.2=Y.sub.3 (=Y.sub.4); X.sub.1=X.sub.2=X.sub.3=X.sub.4=0.

(27) Vertical back and forth translational motions (Tz) of the table can be performed by simultaneously concurrent motions of all actuation unit (Ac.sub.i, i=1, . . . , 4), FIG. 6,b3 or at least three of them. Supposing A point displacement along Z axis (Z), then all the Actuation units (Ac) are activated and pairs move together concurrently in opposite direction towards the Z axis Z=tgX.sub.1=tgY.sub.2=tg X.sub.3 (=tgY.sub.4) or the point (B)the base center; or, at least three of them (the corresponding forth one being inactivated). That means, for example, Ac.sub.1(X.sub.1), Ac.sub.2(Y.sub.2) and Ac.sub.3(X.sub.3) are activated and moves, and A.sub.4(Y.sub.4) not.

(28) Symmetric rotations around X or Y axis (Rx or Ry) are achieved by combined back and forth linear motions (t.sub.i1(2), i=1, 2) of a pair of two actuators Ac.sub.i (i=1, 2), or at least one non-collinear with the axis of rotation, FIG. 6,b1 and b2. In order to obtain a positive angular displacement () simultaneously linear displacements actions in opposite directions along the correspondent orthogonal axis must be performed. For example, for Rx() imposes A.sub.2(Y.sub.2) and/or A.sub.4(Y.sub.4) and for Ry() imposes A.sub.1(X.sub.1) and A.sub.3(X.sub.3) to work for which ()=arctg(Z.sub.i/a.sub.i), where Z.sub.i=X.sub.i(Y.sub.i)arctg(.sub.i). Symmetric rotations around Z axis (Rz) are achieved by combined back and forth linear motions (t.sub.i12, i=1, . . . , 4) of the entire set of four actuators Ac.sub.i (i=1, . . . , 4), or at least three of them, FIG. 6,b3. In order to obtain a positive angular displacement y simultaneously linear displacements actions in the same direction around the Z axes must be performed. For example, for Rz() imposes A.sub.1(X.sub.1,Y.sub.2), A.sub.2(X.sub.2,Y.sub.2) and A.sub.3(X.sub.3,Y.sub.3) to work for which =arctg (Y.sub.i/X.sub.i).

(29) As resulted from above, by choosing a number of four-legs acting and supporting points as a number in-between three points necessary for minimum stability and maximum six imposed for full motion capabilities, and by using compact bi-directional linear actuators, this parallel positioning table is providing a trade-off, between an increased accuracy, speed and stability and the dexterity, being able to deliver high power, high-energy efficient 3D positioning trajectories.

(30) The above Redundant Parallel Positioning Table (Rd-PPT) concept can be applied for accurate, high speed, table-like automated or manually driven applications, as for example: alignment, simulation, machining, assembly, measurement, control, or testing or any other operations, from mechanical, optics, semiconductors (lithography, LCD, wafer, printing, etc) processes in manufacturing, aviation, medical or bio-technological fields including their use in extreme environments (vacuum, cryogenic, magnetic, etc).

(31) The examples as described above provide a device and method to automatically (or, manually) pose one body or several heavy bodies in space with required precision, speed and stability. The positioning table device is based on symmetric redundant six-degrees-of-freedom spatial parallel kinematic mechanism, a member of the Quadropods family. Each pod (leg) is being built as a vertical supporting positioning module actuated by an in-parallel two-degrees-of-freedom motorized unit with motors located at the base and supporting two non-motorizedthe elevation and the guiding positioning units, respectively. The elevation units consist from two opposite wedge systems arranged in pairs following the guiding positioning units from spherical bearings types. Through their combined actions, a platform-like table can be easily and intuitively moved in linear and rotational Cartesian directions. In order to manipulate heavy loads as usually in synchrotron applications they are, the device has the characteristics of compact size, low profile, and simple structure providing increased stiffness, precision, and speed positioning capabilities compared with prior art.