The invention relates to a mechanical linear guide for making a body move in an axial direction, comprising at least four inter¬ connected suspension means, of which a first suspension means is connected at one end at a first point to a fixed base and is movably connected by the other end at a predetermined angle at a second point to a second suspension means, which second suspension means is movably connected by its other end at a third point to the body, and of which a third suspension means is movably connected at one end at the third point to the body and is movably connected at a predetermined angle at a fourth point to a fourth suspension means, whose other end is connected to a fixed base at a fifth point.

Such a construction forms part of a mechanical linear guide which is known from the lecture synopsis of M.P. Koster, "Construc- tieprincipes voor het nauwkeurig bewegen en positioneren" ("Con¬ struction principles for accurately moving and positioning") , WA- 163, University of Twente, October 1990, p. 172. In order to make only an axial movement possible in the known construction, the above-mentioned four suspension means and five points cannot lie in a flat plane. In the known construction the first three points lie in a first plane, and the third, fourth and fifth points lie in a second plane, which planes form an angle of 120° with each other. Further suspension means are also provided, in such a way that a three-dimensional, symmetrical construction is produced and move¬ ment possibilities other than in the axial direction are elimin¬ ated. The known construction makes it possible for the body to move substantially only in an axial direction and for the lateral move¬ ment possibilities to be very small. However, for certain applica- tions, the lateral deflections occurring herewith are still too great.

An object of the present- invention is therefore to provide a mechanical linear guide which further reduces the lateral deflec¬ tion possibilities of a body, while retaining a certain desired minimum axial deflection possibility.

For this purpose, a mechanical linear guide according to the invention is characterized in that the first point is also con-

nected to a sixth point by way of a fifth suspension means, which sixth point is connected by way of a sixth suspension means to the fifth point, while between the second point and the sixth point and the fourth point and the sixth point respectively a seventh suspen- sion means and an eighth suspension means respectively are pro¬ vided, all this in such a way that both the sixth point and the third point can undergo substantially only an axial movement.

With such a mechanical linear guide, an extremely accurate linear movement can be given to a body, while the lateral deflec- tions are less than 10 nm in the case of an axial deflection of, for example, 3 mm.

In a first embodiment of the mechanical linear guide, the first three points lie in a first plane, and the third, fourth and fifth points lie in a second plane, which planes form an angle of 120° with each other, while at the third point the body is con¬ nected to a ninth suspension means, which at the other end is con¬ nected at a seventh point to a tenth suspension means, which tenth suspension means at the other end is connected to an eighth point connected to a fixed base, and also between the sixth point and the eighth point and between the sixth point and the seventh point respectively an eleventh suspension means and a twelfth suspension means respectively are provided, and the third, the seventh and the eighth point define a third plane which forms an angle of 120° with both the first and the second plane. In a further embodiment, the invention relates to a mechan¬ ical linear guide which is extended by a construction which arises through mirroring of the original linear guide about a plane situ¬ ated perpendicular to the axial direction, by means of which ninth to sixteenth points are defined, corresponding to the respective first to eighth points, and also thirteenth to twenty-fourth sus¬ pension means, corresponding to the respective first to twelfth suspension means, the body being fixed between the third point and the eleventh point.

In a preferred embodiment, all suspension means are formed from leaf springs. Rotational rigidity about the axial direction is achieved in this way.

In a further embodiment, springs are provided in order to exert a laterally directed force, so that the axial rigidity is

reduce .

The mechanical linear guide is preferably made up of three substantially identical monolithic parts.

The mechanical linear guide according to the invention is preferably used in a calibration unit for a gravitational field measuring device, based on acceleration recorders, which calibra¬ tion unit comprises three substantially identical calibration devices, the respective bodies of which vibrate substantially along the axes of an orthogonal coordinate system, and thus also deter- mine a coordinate system of the acceleration recorders.

The invention will be explained further below with reference to a number of drawings, in which:

Fig. 1 shows diagrammatically a device in a satellite for measuring the gravitational field on earth; Fig. 2a shows an arrangement of a gravitational field measur¬ ing device in a satellite provided with calibration means;

Fig. 2b shows the same arrangement as Fig. 2a, but viewed from a plane perpendicular to the plane of Fig. 2a;

Fig. 3 shows a block diagram of a control circuit for the calibration means;

Fig. 4 shows a view of a basic concept for a mechanical lin¬ ear guide system;

Fig. 5a shows a further embodiment of the basic concept shown in Fig. 4; Fig. 5b shows a variant of the embodiment shown in Fig. 5a;

Figs. 6a, 6b and 6c show the design principles for a mechan¬ ical linear guide system;

Fig. 7 shows a diagrammatic representation of a mechanical linear guide in three dimensions, based on the design principles of Fig. 6c;

Fig. 8 shows a preferred embodiment of a mechanical linear guide based on Fig. 7;

Fig. 9 shows an explanation of the principle of a constant energy system; Fig. 10 shows a diagrammatic view of a realized mechanical linear guide;

Fig. 11 shows one of the three monolithic parts which together form the mechanical linear guide shown in Fig. 10.

The point of departure for the design of a mechanical linear guide was the need for having the most accurate calibration unit possible for a gravitational field measuring device in satellites. Figure 1 shows diagrammatically the measurement of the gravitation- al field on earth 1 from space 2 with the aid of four three-dimen¬ sional acceleration meters 3, 4, 5, 6 situated in a satellite (not shown). The four acceleration meters are placed on a rigid plate 7, so that they assume a fixed position relative to each other. The letters x, y and z in Fig. 1 indicate a coordinate system which is fixed in relation to the four acceleration meters 3, 4, 5, 6. The satellite moves around the earth in such a way that the z-axis is always directed substantially exactly towards the centre point of the earth.

Direct measurement of the gravitation in a free-flying satel- lite is not possible. It is possible to determine the gravitational gradient by means of the four acceleration meters 3, 4, 5, 6, and to determined the gravitational field from this. The gravitational field on earth must be determined with very great accuracy by means of the four acceleration meters 3, 4, 5, 6: the accuracy must be at least 5 x 10 ^-5 m/s ² and the resolution 100 km x 100 km at earth level. Such a high accuracy requires the acceleration meters 3, 4, 5, 6 to be calibrated constantly on board the satellite. For this purpose, a calibration unit of very high accuracy is necessary.

The calibration unit preferably consists of three calibration devices 9, 10, 11, which generate three orthogonally directed har¬ monic forces (Figure 2). Each of these forces makes the satellite as a whole vibrate in each .of the three respective directions, each with its own frequency. For the x-, y- and z-direction, it is poss¬ ible to select, for example, a frequency of 4/12, 5/12 and 6/12 Hz respectively, while the acceleration amplitude is the same for all three directions and is, for example, 10 ^~s m/s ² . Through these vibrations, calibration measuring points in the x-, y- and z-direc¬ tion are obtained in the acceleration meters 3, 4, 5, 6, the fre¬ quencies of which points correspond to the above-mentioned values of 4/12, 5/12 and 6/12 Hz respectively. These frequency values lie outside the frequency range of approximately 0.005 - 0.125 Hz, which is important for the determination of the gravitational field, so that by filtering calibration signals are obtained. The

coordinate system defined by the calibration units 9, 10, 11 need not coincide with the coordinate system of the satellite.

Figure 2a shows the position of the calibration units 9, 10, 11 in the centre of the four acceleration meters 3, 4, 5, 6, viewed from the x-direction. Figure 2b shows a view of the arrangement according to Figure 2a, but viewed from the negative z-direction. This latter figure also shows a box 12, in which, inter alia, the necessary electronics and electrical supply are housed.

For this purpose, each calibration unit 9, 10, 11 contains a body which vibrates in the x-, the y- or the z-direction, and which is driven by an actuator in an electronic control loop, and the position of which is measured by a position sensor. Figure 3 shows a block diagram of the control loop used. A control signal which is suitable for the desired sinusoidal movement of the body 18 is generated by a position generator 13 and fed to a summation unit 14. The summation unit 14 deducts from this control signal the output signal of a position sensor 22 which measures the actual position of the body 18. The summation unit 14 transmits a correc¬ tion signal, based on the deduction, to control electronics 15, which in turn generate a drive signal for actuator drive elec¬ tronics 16. The actuator drive electronics 16 generate, for example, an electromagnetic force in order to give the body 18 the desired sinusoidal movement. This electromagnetic force is counter¬ acted by spring forces generated by a spring system 21 (to be dis- cussed later), which is shown symbolically by means of the summa¬ tion unit 17. External interferences with the movement of the body are indicated by 20, the influence of which interferences is shown symbolically by the summation unit 19. The control electronics can carry out any form of regulation known per se to the person skilled in the art, i.e. P-, PI- or PID regulation.

As already said, each of the three calibration units 9, 10, 11 must be provided with a body 18 which vibrates substantially only in one direction, and the deflection of which in any other direction is substantially 0. The design principles are explained further below for a body 18 vibrating in the x-direction. The same design principles apply to the bodies vibrating in the y- and z- direction. Table 1 below gives the required design specifications for the vibrating body in the x-direction.

Table 1 parameter value

amplitude vibrating body 3 mm frequency vibrating body 4/12 Hz mass vibrating body 0.76 kg nominal movement (x-direction): force noise amplitude at

- 5/12 Hz <19.2 nm

- 6/12 Hz <13.3 nm

- 8/12 Hz <15 nm phase synchronization <1x10 ^"3 rad parasitic movement (lateral) force noise amplitude at

- 5/12 Hz <19.2 nm - 6/12 Hz <13.3 nm course accuracy 1 second of arc or 'decenter' over 3 mm <15 nm

Figure 4 shows a design which is known per se for achiev¬ ing a linear movement of a body 18, given here in order to make the mechanical linear guide according to the invention easier to under¬ stand. The body 18 is set in motion in the x-direction by means of an actuator which is not shown. At the two ends the body 18 is sus¬ pended from three leaf springs 23a, 23b, 23c and 24a, 24b, 24c respectively. The three leaf springs 23a, 23b, 23c are preferably placed at respective angles of 120° relative to each other and their ends not connected to the body 18 are connected to a fixed base. The same applies to the three leaf springs 24a, 24b, 24c. Due to the suspension of the body 18 shown in Figure 4 and the rigidity of the leaf springs in the lengthwise direction thereof, and the in-plane rigidity thereof, the body can move substantially only in the x-direction. However, the simple design shown in Fig. 4 has the disadvantage that only a very small axial movement in the x- direction is possible, because any movement in the x-direction requires expansion of the in-principle rigid leaf springs 23a, 23b, 23c, 24a, 24b, 24c. Besides, the system is many times over-deter¬ mined, inter alia in a direction φ about the x-axis (see Figure 4). For the most accurate possible undisturbed axial movement of the body 18, the system must be prevented from being over-determined in

any direction, because that is precisely what leads to undesirable and uncontrollable tensions, and therefore movement deflections.

The system shown in Figure 5a solves the first-mentioned problem of the system shown in Figure 4. The system shown in Figure 5a differs from that shown in Figure 4 to the extent that the leaf springs 23a, 23b and 23c are replaced by leaf springs 25a, 25b and 25c respectively, which are folded through a predetermined angle, and the leaf springs 24a, 24b and 24c are replaced by leaf springs 26a, 26b and 26c respectively, which are folded through a predeter- mined angle. On account of the folds in the leaf springs 25a, 25b, 25c, 26a, 26b, 26c, those parts thereof which are connected to the body 18 can carry out an axial movement without the expansion forces in the leaf spring becoming too great, because near their folds the leaf springs can move in the lateral direction. At the same time, the system is rigid for the body 18 in the lateral direction, on account of the three-point suspension of the leaf springs and the in-plane rigidity thereof. The system shown in Figure 5a is over-determined in the direction φ, which can lead to undesirable tensions. This could possibly be compensated for by giving the body 18 a relatively low torsional rigidity.

Figure 5b shows a mechanical linear guide which is known per se, and which is based on the design principle of Figure 5a. The three leaf springs 25a, 25b, 25c together form a leaf spring construction 25, and the three leaf springs 26a, 26b, 26c together form a leaf spring construction 26. The leaf spring construction 25 is pushed with the three flanged ends over the three respective flanged ends of the leaf spring construction 26, while the con¬ struction pushed together is connected to a fixed base at the three overlapping areas. At the total of six positions where each of the two leaf spring constructions 25, 26 is folded over, a spring is fitted, one 27 of which is shown in Figure 5b. Each of these springs 27 exerts a pressure force on the leaf spring construction 25, 26 in a direction perpendicular to the x-axiε. The reason for fitting these springs 27 will be explained later with reference to Figures 9 and 10. A body can be fitted within the system shown in Figure 5b at the position of the cylinder 18' shown by dashed lines. The cylinder shape is shown here only by way of example, and is not essential for the present invention.

Although with the system shown in Figures 5a, 5b a higher axial deflection (i.e. in the x-direction) of the body 18 is poss¬ ible than with the system shown in Figure 4, this is at the expense of the lateral rigidity (i.e. in directions perpendicular to the x- direction) of the system, because the leaf springs 25 (a, b, c), 26 (a, b, c) are not bounded in the lateral direction, and thus for lateral rigidity use cannot be made of the longitudinal rigidity of the leaf springs.

A system in which there is use of the longitudinal rigid- ity of the leaf springs used, and which also has the advantages of the system shown in Figures 5a and 5b, is shown in Figures 6b and 6c. Figure 6a illustrates the mode of operation of the systems shown in Figures 6b and 6c. Figure 6a shows a triangular rod sys¬ tem, which rods are interconnected by means of ball joints at points A, B, E. The point A is connected to a fixed base. If the triangle is equilateral and the angle B-A-E is 90°, then a movement of the point B in the y-direction will result in the same amount of movement of the point E in the x-direction. If the lengths EA and BA are selected so that they are unequal, these movements are, of course, not equal to each other.

The system shown in Figure 6b is based on the system of Figure 6a, but is designed so that it is double, mirrored about the x-axis, and is provided with two additional rods BF and JF. At all corner points A, B, E, F, I, J the rods are interconnected again by ball joints, while in figure 6b the system is connected to a fixed base both at point A and at point I. In rest, the rods AE and IE lie in line with each other- and the rods BF and JF also lie in line with each other, although this is not essential for the idea of the invention: in rest, the angles A-E-I and B-F-J can be smaller or greater than 180°, while they also need not be equal to each other. If point F is now moved from the rest position along the x-axis, points B and J move towards the x-axis, and point E shifts along the x-axis. Since both points A and I are fixed, the point E cannot make any lateral movement, and the elongation of the rods AE and IE must make this movement of the point E along the x-axis possible. In the system shown in Figure 6b the longitudinal rigidity of the rods must therefore be used to minimize the lateral movement possi¬ bilities. The points B and J will carry out substantially the same

movement, albeit mirrored about the x-axis. Owing to the longitudi¬ nal rigidity of the rods used, point F will be able to carry out virtually no lateral movement. It is possible to dimension the system in such a way that a very small deflection of E in the x- direction corresponds to a relatively much greater deflection of F along the x-axis. For example, a deflection of E over 0.1 mm from the rest position may correspond to a deflection of F over 3 mm from the rest position. If the triangles BAE and JIE are both equi¬ lateral and equal to each other, such a deflection also corresponds to a deflection of 0.1 mm of B and J in the y-direction.

With the system shown in Figure 6b, a point mass applied in point F can thus make a substantially true linear movement in the x-direction, while the deflection in the lateral direction is less great than in the case of the system shown in Figures 5a and 5b. In order to give the system the same rigidity in a direction z perpendicular to the plane x-y in Figure 6b, the plane AEFB can be placed at an angle of 120° to the plane EIJF and the same rod sys¬ tem EMΝF as shown in Figure 7, yet to be discussed, can be added thereto, while the plane EMΝF also forms an angle of 120° with the two other planes AEFB and EIJF mentioned.

If a body with slightly greater dimensions has to undergo a linear movement, it is advantageous to mirror the system shown in Figure 6b again about the y-axis, with the result that the addi¬ tional system CDGHKL shown in Figure 6c is obtained. The body 18 can then be fixed between the points FG. The rod system CDGHKL is preferably exactly the same as the rod system ABEFIJ, only mirrored about the y-axis, so that a further description thereof can be omitted.

In the same way as the system shown in Figure 6b has a three-dimensional equivalent ABEFIJMΝ (see left side of Figure 7), the system shown in Figure 6c also has a three-dimensional equival¬ ent which is shown in its entirety in Figure 7. In Figure 7 rods are also shown between the points B and C, J and K and Ν and 0 respectively. However, these three rods are not strictly necessary. The system shown in Figure 7 gives the body 18 two degrees of freedom between the points F and G, namely translation in the direction of the x-axis and rotation in the φ direction. The degree of freedom in the x-direction is desirable, but that in the φ-

direction must be eliminated. This can be achieved by means of the system shown in Figure 8, in which all rods of the system shown in Figure 7 are replaced by leaf springs. The leaf springs BC, JK and NO are not strictly necessary. The system shown in Figure 8 does introduce an over-determination in the direction of both the y-axis and the z-axis, and also in the rotations, but this is negligible, because the over-determination forces occurring in those directions are connected with the in-plane bending rigidities of the leaf springs used, and these are, of course, already far exceeded by the longitudinal rigidity of the leaf springs. Figure 8 shows a three- dimensional structure, but it will be clear to the person skilled in the art that it is also possible to design two two-dimensionsal structures (not shown) which are identical to those of Figures 6b and 6c, in which the rods concerned are replaced by leaf springs. With the embodiment shown in Figure 8 it is possible to move the body 18 over a distance of 3 mm, while the points E and H are moved only over a distance of approximately 0.1 mm in the x-direction.

The rigidity of the system in the lateral direction must be as great as possible. This is related to the shape and the material of the leaf springs used. TiAl ₆ V _d is selected as the pre¬ ferred material, on account of the high fatigue stress, but other materials such as aluminium, spring steel and beryllium can also be used. The thicker the leaf springs, the greater the lateral rigid¬ ity of the system. However, this corresponds to a greater bending rigidity of the leaf springs, so that with increasing thickness the axial rigidity also increases. Increasing axial rigidity can be overcome, for example, by using an actuator with greater capacity, but that can be undesirable.

A way of making the lateral rigidity great enough while reducing the axial rigidity of the system was therefore sought. For this purpose, the starting point taken was the principle of con¬ stant energy, the basic principle of which is shown in Figure 9. A rigid beam 28 rests without friction on a wall 32 and leans without friction against a wall 31. The point with which the beam 28 rests against the wall 31 is connected to a spring 29 with spring con¬ stant cy, which draws the beam 28 in the direction of the wall 32. The point with which the beam 28 rests on the wall 32 is connected to a spring 30 with spring constant ex, which draws the beam 28 in

the direction of the wall 31. If the distance of the point with which the beam 28 rests on the wall 32 from the wall 31 is equal to x and the distance between the point with which the beam 28 leans against the wall 31 and the wall 32 is equal to y, then the follow- ing applies for the total spring energy U stored in the system (provided that the springs 29, 30 are in rest at deflections of y=0 and x=0 respectively):

U = 1/2.ex.x ² + 1/2.cy.y ² (1)

If the spring constants ex and cy are selected so that they are equal to one another, then the following applies:

U = 1/2.c.(x ² + y ² ) = 1/2.c.I ² = constant (2)

in which 1 is the length of the beam 28.

It is therefore possible in theory to move the beam 28 with the supporting points along the wall 32 and the wall 31 with- out exerting any force thereon, of course if such a system were friction-free and loss-free. The principle of a force-free movement shown in Figure 9 can be applied to the system shown in Figure 8. The tensile forces corresponding to the leaf spring 29 shown in Figure 9 are achieved with six springs, five 33 ... 37 of which are visible in Figure 10. The sixth spring 38 (not visible) runs paral¬ lel to spring 35 between the points K and 0. The force indicated by the spring 30 in Figure 9 corresponds in the system shown in Figure 10 to the bending force of the leaf springs BF, JF, ΝF, CG, KG, OG. If the spring constant of the springs 33 to 38 is now selected at the correct value, the body 18 can be moved axially by a very small axially directed force. In practice, for example, a system such as that shown in Figure 10 is achieved, in which system a body 18 of 1.35 kg was held in vibration at an amplitude of 3 mm with a force of max. 2.5 Ν. Figure 11 shows a preferred design for a part 42 of the linear guide shown in Figure 10. In the linear guide shown in Fig¬ ure 10, three of the parts 42 shown in Figure 11 are intercon¬ nected. Each of the three identical parts 42 is connected by the two other parts to plate-shaped parts 39, 40, 41, preferably by way

of connecting means 39a, 40a (see Figure 10). Figure 10 shows the situation in which the connecting means 40a is round. This round shape is not necessary, while more than one connecting means between the respective plate-shaped part 40 and the adjacent plate shaped part 40' can also be used. Figure 10 also shows that adjac¬ ent plate-shaped parts 39 and 39' are interconnected by way of connecting means 39a, of which there are a total of three, but only one of which can be seen in the figure. The plate-shaped parts 41 of the three adjacent parts 42 are interconnected in the same way as the three plate-shaped parts 40.

Each of the three parts 42 is made in one piece, so that the whole linear guide is based on three monolithic identical parts which are interconnected and which are immovably fixed to a housing 43. For this purpose, each of the three monolithic designs shown in Figure 11 has connecting beams B1 , B2, B3 which are rigid and have substantially no bending action. The respective parts 42 are con¬ nected to the housing by means of, for example, bolts, a number of which are indicated by 44, 45, 46. With three of the parts shown in Figure 11, a mechanical linear guide whose corner points A, D, I, L, M, P are connected to a fixed base, and whose other points can move within predetermined standards, is thus obtained. The use of monolithic parts 42 simplifies the assembly of the linear guide.

Finally, attention is also drawn to the special shape of the leaf springs, which all preferably have a thick, rigid central part and only at the ends are relatively thin. As a result, the leaf springs bend only at their ends, and a great bending resis¬ tance is also achieved. All leaf springs, apart from BF, CG, JF, KG, ΝF and OG preferably have a hole-type hinge construction. The leaf springs BF, CG, JF, KG, ΝF and OG preferably have relatively elongated, thin ends, for the benefit of the axial deflection pos¬ sibilities of the body 18.

Table 2 gives an outline of the values achieved with a mechanical linear guide shown in Figure 10, compared with the required values already shown in Table 1.

Table 2 parameter required value achieved value

amplitude vibrating body 3 mm 3 mm frequency vibrating body 4/12 Hz 4/12 Hz mass vibrating body 0.76 kg 1.35 kg nominal movement (x-direction) force noise amplitude at

- 5/12 Hz <19.2 nm <10 nm

- 6/12 Hz <13.3 nm <10 nm

- 8/12 Hz <15 nm <10 nm phase synchronization <1x10 ^"3 rad <1x10 ^"3 rad parasitic movement (lateral )

Table 2 shows that all design specifications have been met, except that the body is slightly heavier. It was also found that a lateral deflection of 80 nm occurred at the first harmonic frequency of 8/12 Hz, for which no required standard is specified. Despite that, the objectives set were amply achieved.

The point of departure for the design of a mechanical linear guide was the need for providing a linear guide for a body moving in space which can be used in a calibration unit for accel¬ eration meters. Of course, use of the very accurate linear guide described here is not restricted thereto. The mechanical linear guide described can also be used, for example, in the case of pre¬ cision guidance for optical components (for example, deceleration lines) .