The invention relates to a method for manufacturing a motion simulator. The invention moreover relates to a motion simulator.

For simulating movements, in particular vehicle movements such as for instance movements of airplanes, motorcars, trains and the like, and of working environments, motion simulators are used which comprise a movable deck supported by a number of legs. The deck of such motion simulator, known as Stewart platform, can be moved within a movement envelope by changing the lengths of the legs, while the envelope is determined by the extreme positions that can be adopted by the deck.

The design of a Stewart platform starts from the maximum translation necessary in the directions of movement of the deck for simulating a vehicle or environment. On the basis thereof, a symmetrical motion simulator is built up, in which a deck is supported by six legs. These legs are arranged in three pairs between the deck and a base part, with three pairs of first pivot points connecting the legs to the deck and three pairs of second pivot points connecting the legs to the base part. The three first pairs of pivot points are evenly distributed over the circumference of a(n imaginary) circle around the deck, the three pairs of second pivot points are evenly distributed over the (imaginary) circumference of the base part, so that in each case, an

angle of 1200 is included between the first and second pairs respectively. The pairs of first pivot points are located in a first plane, the pairs of second pivot points are located in a second plane located parallel thereto. All six legs are equal and, accordingly, have equal adjusting ranges. At least in an intermediate position, the legs always include equal angles relative to each other, while, in top plan view, a pair of first pivot points is always located centrally between two pairs of second pivot points. With a thus obtained motion simulator, different vehicles and working environments can be simulated.

An major drawback of a thus obtained motion simulator of the Stewart platform type is that it is not optimized for the simulation of the desired vehicle or the desired working environment. The movement envelope of the deck deviates substantially from the required movement space for the accurate simulation of the relevant vehicle movements or working environment. As a consequence, usually more mass should be accelerated and decelerated than is necessary, while moreover a larger space is needed for installing the motion simulator. Further, this known motion simulator has the drawback that in at least a number of directions of movement, there is the danger of undesired extreme positions being reached of at least a number of the legs, so that singularities occur, which complicates the steering and control of the deck movements and has an adverse effect on the accuracy. Another consequence is that the power

transmission on and through the legs is not optimal, which is disadvantageous to the construction of the motion simulator and to the possible accelerations and the forces required therefor.

The object of the invention is to provide a method of the type described in the preamble, in which the drawbacks mentioned are avoided while the advantages thereof are retained. To that end, a method according to the invention is characterized by the features of claim 1.

In a method according to the invention, the design of the motion simulator starts from a minimum movement space necessary for the deck for accurately simulating the movements of a working environment, in particular of a vehicle. For that purpose, in a number cf translation directions and a number of rotation direcions, and for combinations of these translation and/c- rotation directions, a minimum circumscribing ellipse is determined within which translation and rotation movements o; tre deck that are located within the relevant plane are located. On the basis of these ellipses, a hyper-ellipsold S determined, at least a relevant part of the shell of suc Dc~-. The center of such hyper-ellipsoid body is preferably located on the intersection of a principal axis of movement of the motion simulator and a vertical axis through the center of the deck between the legs, at least in the starting position of the deck. This hyper-ellipsoid body determines the minimum volume of the movement envelope of the deck which in turn depends

on the mutual positions of the first and second pivot points and the adjusting range of the different legs. Starting from the hyper-ellipsoid found, an optimum configuration of the flight simulator can be obtained manually or preferably by means of a suitable algorithm the positions of the different pivot points, related to the lengths and adjusting ranges of the different legs, such that the hyper-ellipsoid can be included into the movement envelope of the deck with minimum space.

In further elaboration, a method according to the invention is characterized by the features of claim 2.

By determining the movements in three independent translation movements and three independent rotation movements, as in a motion simulator having six degrees of freedom, fifteen ellipses can be determined for combinations of translations and/or rotations. From these fifteen ellipses, said hyper-ellipsoid body can be determined. Thus, an optimum configuration of a motion simulator having six degrees of freedom can be obtained.

In a particularly advantageous embodiment, a method according to the invention is characterized by the features of claim 5.

Assuming symmetry of the motion simulator relative to a plane through a principal direction of movement and the vertical axis offers the advantage that the number of design quantities to be freely chosen (position of the pivot points, adjusting range, legs) is limited considerably. This enables

for instance a reduction of the number of freedoms of design from 48 (the three degrees of freedom of each of the six top and the six bottom pivot points and the minimum length and maximum length of each of the six legs) to a considerably more limited number of freedoms of design. Preferably, for instance nine freedoms of design are allowed, by positioning the first pivot points in one plane, positioning the first pivot points in three pairs while the mutual distance in each of the pairs is chosen to be fixed and relatively small and the plane of symmetry mentioned extends through one of the pairs. The second pivot points are likewise divided into three pairs, while the mutual distance between the second pivot points in each pair is likewise chosen to be fixed and relatively small and the plane of symmetry mentioned likewise extends between the second pivot points of one of the pairs.

Moreover, the ratio between the maximum and the minimum length of each of the legs is chosen to be fixed. Limiting the number of freedoms of design to 9 offers a particularly suitable ratio between the required computing time for optimizing the design of a motion simulator and the necessary freedom of design. However, it is also possible to involve in the design fewer or, in particular, more, for instance all 48 freedoms of design, as a result of which, it is true, the required computing time increases, yet a further optimization will be possible.

A motion simulator according to the invention is characterized by the features of claim 6.

Underlying the invention is the surprising concept that by adjusting at least the mutual position of the first and/or second pivot points and/or the minimum and/or maximum length, choosing at least the adjusting range of at least one of the legs to be different relative to the other legs, a motion simulator can be obtained with a movement envelope of minimum dimensions, while the complete movement space of the deck, necessary for an accurate simulation of a selected vehicle, can yet be enclosed by the relevant movement envelope.

Depending on the vehicle to be simulated and the selected freedoms of design, the first and second pivot points respectively can each be displaced relative to each other in one plane, such that they are positioned on the circumference of an ellipse, while moreover, the pivot points can be displaced relative to each other in vertical direction. In addition, a number of pivot points can cf course be moved away from the above-described ellipse. Moreover, to optimize the relevant motion simulator, the adjusting ranges and lengths of the different legs can be selected in connecting with the selected positions of the pivot points.

In further elaboration, a motion simulator according to the invention is characterized by the features of claim 8.

Displacement, in top plan view, of the first pivot points relative to the second pivot points, preferably along said ellipse, offers the advantage that thus the starting position of the legs between the relevant first and second pivot points is adjusted, whereby a different force direction

is obtained, optimized for the desired local movement speeds and accelerations. Moreover, this influences the extreme positions of the legs, so that in each position of the deck during use an optimum power transmission from the deck to the base part can be obtained. Unlike a motion simulator of the known Stewart platform type, simulator movements during simulation of the relevant vehicle can be started from. The result of decreasing the angle a and/or increasing the angle t3 is that the legs, when the lengths remains the same, will assume a more vertical position in the starting position, while an increase of the average length of the legs, when the distance between the deck and the base part remains the same in the starting condition will cause a increase of the angle a and a decrease of the angle P respectively. As a result, the legs will obtain a flatter angle of inclination in the starting position. Comparable changes will occur during an adjustment of the mutual positions of for instance the second pivot points relative to each other in a least the vertical direction.

The use of three pairs of legs offers the advantage that in a particularly suitable manna, a motion simulator having six degrees of freedom can b sained.

Further advantageous exemplary embodiments of a method and motion simulator according to the invention are given in the subclaims.

The invention further relates to the use of a universal motion simulator, preferably having six degrees of freedom,

for simulating a vehicle or environment for optimizing a specific motion simulator according to the invention, which use is characterized by the features of claim 13.

Such use of a known, universal motion simulator for simulating the movements of a vehicle or working environment for which a specific motion simulator should be designed, offers the advantage that the maximum movement space necessary for a deck of such specific motion simulator can thereby be registered in a simple and accurate manner. These values found can then be used in a suitable manner for determining a hyper-ellipsoid body within which all necessary extreme positions of the deck of the specific motion simulator should be located, on the basis of which an optimum configuration of such specific motion simulator can be obtained.

To clarify the invention, exemplary embodiments of a method and motion simulator according to the invention will hereinafter be discussed in more detail, with reference to the accompanying drawings. In these drawings: Fig. 1 is a schematic top plan view of a deck having first pivot points for a motion simulator according to the invention, together with a deck, shown in broken lines, of a known, comparable motion simulator; Fig. 2 is a schematic top plan view of a base part for a motion simulator according to the invention with associated second pivot points, in which a base part of a known,

comparable motion simulator is schematically included in broken lines; Fig. 3 is a schematic side elevation of a motion simulator according to the invention; Fig. 4 is a schematic, perspective view of a motion simulator according to the invention; and Fig. 5 is a view of the hyper-ellipsoid for three translation planes.

Fig. 4 shows a motion simulator according to the invention, comprising a deck 1, which deck 1 is supported by six legs 2. Each leg 2 has a top end 3 thereof connected to the deck 1 via a first pivot point 4, and each bottom end 5 of each leg 2 is connected to a base part 7 via a second pivot point 6. Each leg 2 comprises an assembly of a double- acting, for instance hydraulically drivable piston and cylinder, whereby the length of the leg 2 can be dynamically set. The second pivot points 6 are arranged in pairs on the circumference of an ellipse 9A, viewed from the top, which ellipse encloses the base part 7, while the first pivot points 4 are arranged in pairs on the circumference of an ellipse 9 enclosing the deck 1. The positions of the first 4 and second pivot points 6 will be discussed in more detail hereinbelow. By adjusting the lengths of the legs 2, the deck 1 can be moved relative to the base part 7, whereby the deck can be accelerated and decelerated such that motions of a specific vehicle or a specific environment can be simulated.

Suitable control systems for a deck supported by such

adjustable legs are generally known and are for instance discussed in international patent application PCT/NL94/00178, British patent specification 1 160 471 and US Patent 5 182 150, which are understood to be incorporated herein as examples by reference. On the deck 1, an environment to be simulated can be built up in a manner known per se, for instance a cockpit of an airplane or another working environment, while moreover, the deck may for instance be of shell-shaped construction, as is discussed at length in the above international patent application PCT/NL94/00178, which is understood to be incorporated herein by reference.

As is clearly demonstrated in Fig. 1, the first pivot points 4 are positioned on the circumference of an ellipse 9 in three pairs 4A, 4B and 4C, the mutual distance between the first pivot points 4 of each pair 4A, 4B, 4C being selected to be relatively small compared with the distance between the pairs 4A, 4B, 4C. For the motion simulator depicted in the drawing, a principal direction of movement X is located along the long axis of the ellipse 9, a second direction of movement Y is located along the short axis of the ellipse 9, while a third axis of movement Z extends vertically through the center of the ellipse 9, at right angles to the directions of movement X and Y. The first pair of first pivot points 4A is located adjacent the intersection of the principal direction of movement and the ellipse 9, one first pivot point 4 on either side of the principal direction of movement X. The second pair 4B and third pair 4C are located

on either side of the principal direction of movement X on the circumference of the ellipse 9. In Fig. 1, lines through the center M and the second pair 4B and third pair 4C respectively are represented by a dash-dot line K1 and K2 respectively. The line K1 includes an angle al with the principal direction of movement X, the line K2 includes an angle a2 therewith. In the exemplary embodiment shown, the angles al and a2 are identical and about 140°. As appears from Fig. 1, in the known motion simulator of the Stewart platform type, this angle is exactly 120°, so that the pairs of first pivot points of the known motion simulator are symmetrically distributed over a circle.

Fig. 2 schematically shows a base part 7 between three pairs of second pivot points 6 of the legs 2, which pairs are designated by 6a, 6b and 6c. For clarification, the principal direction of movement X is shown in Fig. 2, although the base part 7 is of course in principle stationary. The first pair of second pivot points 6a is located on the circumference of the ellipse 9a adjacent the top thereof, at the crossing with the principal direction of movement X, on the side of the short axis Y opposite the side where tne first pair of pivot points 4a is located. The second pair 6 and third pair 6c are located on the opposite side of the short axis Y, on lines K3 and K4 respectively, indicated as dash-dot lines, which two lines intersect the center M of the ellipse 9a. The line K3 includes and angle 1 with the principal direction of movement X, the line K4 includes an angle P therewith. In

the exemplary embodiment shown, the angles P1 and P2 are identical. The distance 2p between the second pivot points 6 of each pair 6a, 6b, 6c is chosen to be relatively small compared with the distance between the pairs 6a, 6b, 6c.

As is clearly demonstrated in Fig. 3, the first pivot points 4 in the exemplary embodiment shown are located in one plane, parallel to the deck 1. On the other hand, the second pivot points 6 are located in three parallel spaced apart planes V1, V2 and V3, in Fig. 3 indicated by broken lines. The first pair of second pivot points 6a is located in the top plane V1, slightly spaced above the base part 7. Of the second pair of second pivot points 6b and third pair of second pivot points 6c, the pivot point 6 of the relevant pair 6b, 6c located adjacent the first pair 6a is in each case located in the third plane V3 at some distance below the base part 7, while the two second pivot points 6 that are remotest from the first pair 6a are located in the second plane V2, in which the base part 7 is located. This displacement of the second pivot points 6 relative to each other in vertical direction causes the working direction of the adjustable legs 2 to be adjusted thereby, which working direction influences the power transmission on at least the deck 1, as a result of which for instance better and accurate control of the movements of the deck 1 is possible, singularities are avoided and the dexterity is increased, which will be explained in more detail hereinbelow.

In the exemplary embodiment shown, the motion simulator is symmetrical relative to the plane through the principal direction of movement X and the vertical axis Z. The motion simulator comprises six legs 2 distributed over three pairs of legs 2a, 2b, 2c. The top ends of the first pair of legs 2a are connected to the deck 1 in the first pair of first pivot points 4a, while the bottom ends of the legs of the first pair 2a are connected to the second pivot points 6, located in the plane V2, of the second and third pairs of second pivot points 6b, 6c respectively. The top ends of the legs 2 of the second pair of legs 2b are connected to the foremost, i.e. located closest to the short axis Y, first pivot points 4 of the second pair 4b and third pair 4c respectively, while the bottom ends of the relevant legs 2 of the second pair 2b are connected to the second pivot points 6 located in the plane V3 of the second pair 6b and third pair 6c respectively of the second pivot points. The top ends of the legs 2 of the third pair 2c are connected to the rearmost first pivot points 4 of the second pair 4b and third pair 4c respectively, while the bottom ends are connected to the second pivot points, located in the plane V1, of the first pair of second pivot points 6a. In the exemplary embodiment shown, the legs in each pair 2a, 2b, 2c are identical to each other, while the pairs 2a, 2b, 2c have mutually different leg lengths and/or adjusting ranges. This aspect will be discussed in more detail hereinbelow.

The optimum configuration of a motion simulator according to the invention is obtained in accordance with a method to be described in more detail hereinbelow, in which, as an example, simulation of an airplane of the type Boeing 747-400 is mainly started from. This example should not be construed as being limitative in any way.

By means of a known flight simulator of the Stewart platform type, a relatively large number of flight movements of a Boeing 747-400 are simulated, while the resulting motion and displacement quantities have been passed through a so- called "unity-gain classical wash out filter" as described by Nahon, M. et al., "Simulator motion-drive algorithms: a designer's perspective", Journal of Guidance, AIAA, Vol. 13, No. 2, 1989, pp. 356-362, for predicting the paths of movement of the motion simulator. On the basis of these paths of movement, a working space is determined on the basis of which the layout of the motion simulator is subsequently determined which fits the found, necessary working space best.

The flight simulation of the Boeing 747-400 with the known motion simulator is performed by a qualified pilot, in which 31 critical maneuvers are fixed. For the 15 relevant combinations of translations and rotations of the motion simulator, ellipses have been determined for all 31 flight situations, which ellipses fittingly enclose the maximum paths of movement for each relevant combination. These serve as weighting factors for the design phase. The ellipses found

are joined together to form a "hyper-ellipsoid" in a multidimensional space.

For the design of the motion simulator of the present type, there are in principle 48 degrees of freedom of design, viz. a three-dimensional positioning for each first pivot point, a three-dimensional positioning for each second pivot point, a maximum length for each of the six legs and a minimum length for each of the six legs (6*3 + 6*3 + 6*2 = 48). Variation of one of these variables directly influences the behavior of the motion simulator. Moreover, the influence of each of the individual variables on this behavior is non- linear and depends on the values of each of the other variables. In the example here described, the number of freedoms of design is reduced to a practically more realistic subset. By experiment, a subset of 9 degrees of freedom of design has been determined. This is in the first place realized by said selected symmetry around the X-Z plane.

Moreover, positioning of the first pivot points 4 and the second pivot points 6 on an ellipse 9 and 9a respectively, at least in top plan view, is primarily opted for. The lengths of and the ratio between the short and the long axis of each of the ellipses 9, 9a are chosen to be variable, resulting in two freedoms of design for the deck 1 and the base part 7.

The mutual distance between the pivot points of each pair 4a- 4c and 6a-6c respectively is chosen to be fixed at a minimum reachable distance (2d for the deck 1, 2p for the base part 7). One pair of first pivot points 4a and one pair of second

pivot points 6a are fixed, symmetrically on the principal axis of movement X. The other two pairs of first pivot points 4b, 4c and the other two pairs of second pivot points 6b, 6c are positioned symmetrically relative to the principal direction of movement X on the circumference of the ellipse 9, 9a while including an angle a and P respectively with said principal direction of movement X. The angles a and P determine two further freedoms of design. Further, the minimum leg length Qmin is chosen as freedom of design, the symmetry of the motion simulator having as a result that this leads to only three further freedoms of design. The maximum leg length Qmax is related to the minimum leg length Qmin according to the formula Qmax = 2 x Qmin - c.

The constant value in this equation is preferably selected between 0.98 and 0.99, in particular 0.981. These represent a family of adjustable legs with comparable mechanical hardware, with the cylinders and pistons being set at different lengths. This ratio is determined empirically and based on existing movement hardware. It is further pointed out that each of said fixedly chosen values can be added as further design variable, so that a further optimization of the motion simulator can be achieved, in respect of which it should however be understood that this considerably prolongs the computing time required for optimization.

The angles a and are chosen depending on the desired power transmission from in particular the legs 2 to the deck

1 and preferably range between 900 and 1700, while more in particular preferably at least one of the angles a, P deviates from 1200. Partly on account hereof, singularities of the assembly of legs 2 and deck 1 are avoided within the suitable movement space.

The "hyper-ellipsoid", obtained by joining together the two-dimensional ellipses as described hereinabove, describes the required movement volume and is mathematically defined as <BR> <BR> <BR> <BR> <BR> <BR> <BR> <BR> (X-Xo)² + (Y-Yo)² + (Z-Zo)² + (#-#o)² + (#-#o)² + (#-#o)² # 1<BR> <BR> #x #r #z #v #@ #@<BR> <BR> <BR> <BR> <BR> <BR> <BR> <BR> <BR> <BR> <BR> <BR> <BR> <BR> <BR> <BR> <BR> where x0 ..., 90 represent the neutral position of the motion simulator (in which all legs are set at the center of the adjusting range). This is also the center of the "hyper- ellipsoid". The weighting factors Px ., p,, give the length of the hyper-ellipsoid axis in each cL toe directions. By means of the ellipses found, the "hyper-ellipsoid" can be fitted.to the data which comprise the centers and the weighting factors.

To obtain the optimum value, toe unction to be maximized can be determined as X²+Y²+Z²+#²+#²+#² = R where x, y . . represent a scaled, non-dimensional distance from the neutral position of the deck 1, for instance

x x-xo Px The factor R, referred to as the weighted radius of the "hyper-ellipsoid", gives a proportional scaling of the ellipsoid without change of shape. The function to be maximized attempts to find the maximum weighted radius Rmax which describes the greatest "hyper-ellipsoid" fitting with minimum space within the required working space of the deck 1. When hax > # 1, the working space of the deck 1 comprises the paths of movement.

Due to the chosen symmetry of the motion simulator along the X-Z plane, y0 = Co = * =O The X0-Z0 position of the deck determines the neutral position relative to the base part 7 and the horizontal position of the deck 1.

To realize an optimization of the "hyper-ellipsoid" in a relatively simple manner, limitation of the analysis of the working space to cross-sectional planes of the "hyper- ellipsoid", the 15 ellipses mentioned, has been opted for.

The ellipse having the smallest value for Rmax is chosen as critical, which results in Rm²x # min {Rxy, Rxz ,..., ) R##}.

Fig. 5 shows three cross-sections of the translation working space, viz. X-Y, X-Z and Y-Z. Here, the weighting factors Px = Py = 1 and pz is 0.5, the critical ellipse being located in the X-Z plane. For each of the planes comprising the relevant ellipses, the limit of the working space is determined on the basis of the relationship between the deck position and the leg lengths. Subsequently, within this space, the optimum ellipse, i.e. the RmaX, is determined. The measure of accuracy of the determination of the limit of the relevant working space directly determines the accuracy of the RmaX found.

Between the position of the deck 1 and the length of the legs 2 there is a l-to-l relationship, and problems may arise with respect to the controllability of the deck when the deck position changes relatively substantially during relatively small movements of the legs. Such situation is referred to as singularity of the deck and should be prevented within the entire working space, because this may cause malfunctioning of the deck. Moreover, designs tending to approach singularities should be avoided, as they may result in excessively high leg loads.

Singularities can be detected through analysis of the Jacobian matrix, which relates the measure of change of the deck position to the measure of change of the leg length according to q = J x

where Q describes the leg length and X describes the deck positions, for translations as well as rotations. The 6 x 6 matrix J is defined as # ### ### # J = # # ### ### J is not constant but varies within the working space.

The dexterity is the reciprocal of the condition number of J and can be defined as <BR> <BR> D = #min<BR> <BR> <BR> #max where in amin and amax determine the minimum and maximum singular value of J, obtained according to a method known per se and referred to as "singular value decomposition". The dexterity D indicates the controllability of the deck. A value of D = 1 indicates an isotropic position, in which equal forces in the pivot points 4 are necessary for obtaining motion in each direction. When a singularity of the deck is approached, amin tends towards 0 and hence, the value D = 0 indicates a singular configuration. For optimizing a motion simulator according to the invention, a dexterity in which D > 0.2 is opted for, which value is obtained as optimum from designing experience. Of course, this value can be chosen lower or higher.

In Table 1, the eventually selected values of the design variables and of the Rmax found are given as global optimums for each of three test arrangements mentioned.

Table 2 gives for each of the three exemplary embodiments given in Table 1 a cross section of the working space in X-Y direction, x-z, X-0 direction and -0 direction respectively, and the ellipses, fitting therein with minimum space, for the relevant sections. Table 2 provides a good view of the proper fit of the "hyper-ellipsoid" within the working space.

Table 3 schematically provides for each of the exemplary embodiments mentioned in Table 1 a graphical representation of the geometry of the relevant motion simulator and a three-dimensional representation of the translation and rotation working spaces thereof.

In comparison with the known motion simulator, a motion simulator according to the invention offers the advantage of requiring a smaller installation spar as all superfluous working space is left out in an optimum manner, while all paths of movement that are necessary it simulation of the relevant vehicle are nevertheless present within the movement space available. Moreover, singular~ t) e, are avoided in an optimum manner, while an optimum dexterity is retained. If required, the first pivot points 4 and,' or the second pivot points 5 can be moved relative to eac other in vertical and/or horizontal direction, while in instance a number of pivot points may be located inside or outside the ellipse 9,

9a, when this is necessary for a suitable power transmission and freedom of movement of the relevant motion simulator. By using a method according to the invention as described hereinabove, a motion simulator which fits the or each vehicle or working environment to be simulated will in each case be arrived at.

The thus optimized motion simulator moreover has the advantage that for instance response times, possible accelerations and decelerations and occurring forces can be controlled even more effectively, while the dimensioning of the deck can be optimized, whereby forces of inertia can be further reduced.

The invention is by no means limited to the exemplary embodiments shown in the specification and the Figures. Many variations thereto are possible.

For instance, more or fewer freedoms of design may be allowed, depending on the choice of fixed values, for instance iterative or based on experience. Also, more or fewer planes of symmetry may be present in the motion simulator. Moreover, other types of vehicles and working environments may be used for obtaining a suitable motion simulator. Further, the necessary paths of movement may be determined in a different manner, for instance on the basis of the use of a computer model of the relevant vehicle or the relevant working environment. Further, the necessary freedoms of design may be filled in differently, for instance by empirical research, computer simulation and the like. With this, too, a motion simulator according to the present invention with the advantages thereof may be arrived at.

However, such manner is assumably less optimal. Also, other legs or leg lengths and adjusting ranges may be applied, when a desired simulation so requires.

These and many comparable variations are understood to fall within the framework of the invention.