Method and device for displacing a moving body on a base mounted elastically with respect to the ground

Description

BACKGROUND OF THE INVENTION

The present invention relates to a method and to a device for displacing a moving body on a base mounted elastically with respect to the ground.

In the context of the present invention, said device comprises, in addition to the moving body and the base, a controllable actuator, for example an electric motor, intended to bring about a linear displacement of the moving body on the base.

The latter is mounted on the ground via elastic mounts which are intended to isolate it from vibration originating from said ground.

However, when the moving body is made to move, during its acceleration and deceleration phases, the base is subjected to the reaction of the force applied to the moving body by the actuator. This reaction force excites the base which then oscillates on its supports. This disturbs the relative position of the moving body with respect to the base, and has a very harmful effect on the precision of the device.

This error in relative position remains after the end of displacement of the moving body and does not disappear until after the base is stabilized (which takes place a great deal later).

DESCRIPTION OF THE PRIOR ART

Various solutions for overcoming this drawback are known. Some of these solutions in particular envisage:

immobilizing the base during the acceleration and deceleration phases using a locking system, for example an electromagnetic locking system, which is mounted in parallel with the elastic mounts. This known solution does, however, prevent the mounts from isolating the base from vibration originating from the ground during said acceleration and deceleration phases;

canceling the effect produced by the force generated by the actuator by providing an additional actuator which is arranged between the base and the ground and which generates an additional force of the same amplitude but of opposite sense; or

displacing an additional moving body on the base with a similar displacement but of opposite sense with respect to the displacement of the moving body, so as to cancel the inertial effects.

However, none of these known solutions is satisfactory because their effectiveness is low and they all require additional means (locking system, additional actuator, additional moving body) which, in particular, increase the complexity, cost and bulk of the device.

SUMMARY OF THE INVENTION

The object of the present invention is to overcome these drawbacks. The invention relates to a method for displacing a moving body extremely precisely and at a low cost on a base mounted elastically with respect to the ground, said moving body being displaced linearly with a predetermined displacement in terms of distance and time, under the action of a controllable force.

To this end, said method is noteworthy according to the invention in that:

a) a mathematical relationship illustrating the movements of the entity formed by the base and the moving body and dependent on parameters related to the base and to the moving body and which vary during a displacement of the latter, is defined;

b) using said mathematical relationship, mathematical processing is used to determine a force which, applied to said moving body, produces a combined effect:

on the one hand, on the moving body so that it performs said predetermined displacement; and

on the other hand, on the base at least so that it is immobile at the end of the displacement of the moving body; and

c) the force thus determined is applied to said moving body.

Thus, the force applied to the moving body allows the latter to effect the envisaged predetermined displacement, particularly in terms of time and in terms of distance, while at the same time rendering the base immobile at the end of the displacement so that it does not oscillate and does not disrupt the relative positioning between it and the moving body.

In consequence, because of this combined effect or control of the moving body and of the base, an extremely precise displacement of the moving body is obtained in a frame of reference that is independent of the base and linked, for example, with the ground.

It will be noted that the implementation of the method according to the invention is not restricted to a displacement along a single axis, but can also be applied to displacements along several axes which may be considered as being independent.

In the context of the present invention, it is possible to use various mathematical relationships, particularly a mathematical relationship obtained, for example, by deconvolution.

However, in a preferred and simplified embodiment, by way of mathematical relationship in the aforementioned step a), use is advantageously made of the following relationship:

y = x - \frac{k1}{k0} \dot{x} + \frac{1}{m} (mB - \frac{{k1}^{2}}{k0}) xB - \frac{mB}{m} \cdot \frac{k1}{k0} \dot{x} B .

in which:

y represents an imaginary variable;

k

0

and k

1

respectively represent the natural frequency and the damping of the elastically mounted base;

m and mB represent the masses of the moving body and of the base, respectively;

x and xB represent the displacements of the moving body and of the base, respectively; and

{dot over (x)} and {dot over (x)}B represent the speeds of displacement of the moving body and of the base, respectively.

As far as step b) of the method according to the invention is concerned, various mathematical processing operations may be performed, particularly processing operations which employ:

a sum of sinusoidal functions; or

a polynomial decomposition.

For this last type of processing operation, the force F is advantageously determined from the following relationship:

F = m \ddot{y} + m \frac{k1}{k0} y^{(3)} + \frac{mmB}{k0} y^{(4)}

ÿ, y

(3)

and y

(4)

being the 2nd, 3rd and 4th-order derivatives of the variable y, respectively, and using the following polynomial decomposition of y(t):

y(t)=y

0

+(y

1

−y

0

)s

5

(126−420s+540s

2

−315s

3

+70s

4

)

with

s = \frac{t - t0}{t1 - t0}, y0 = y (t0) and y1 = y (t1),

t being time and t

0

and t

1

being the instants of the start and end of the displacement of the moving body.

The present invention also relates to a device of the type comprising:

a base mounted elastically with respect to the ground;

a moving body which can be displaced linearly on said base; and

a controllable actuator capable of applying a force to said moving body with a view to displacing it on said base.

According to the invention, said device is noteworthy in that it additionally comprises means, for example a computer:

which carry out steps a) and b) of the aforementioned method to calculate a force which, applied to said moving body, makes it possible to obtain the aforementioned combined effect; and

which determine a control command and transmit it to said actuator so that it applies the force thus calculated to the moving body at the time of displacement.

Thus, in addition to the aforementioned advantages, the device according to the invention requires no additional mechanical means, and this reduces its cost and bulk and simplifies its production, compared with the known and aforementioned devices.

BRIEF DESCRIPTION OF THE DRAWINGS

The figures of the appended drawing will make it easy to understand how the invention may be achieved. In these figures, identical references denote similar elements.

FIG. 1

is the block diagram of a device in accordance with the invention.

FIGS. 2 and 3

depict graphs which illustrate the displacements of the moving body and of the base respectively when said moving body is made to move in accordance with the invention.

DESCRIPTION OF THE PREFERRED EMBODIMENT

The device

1

in accordance with the invention and depicted diagrammatically in

FIG. 1

is intended for the displacement of a moving body

4

, for example a moving carriage, on a base

2

, particularly a test bench.

This device

1

may, for example, be applied to high-speed XY tables used in microelectronics, to machine tools, to conveyors, to robots, etc.

In a known way, said device

1

comprises, in addition to the base

2

and the moving body

4

:

elastic mounts

3

of a known type arranged between the base

2

and the ground S and allowing the base

2

to be isolated from vibration originating from said ground S. The natural frequency of the base

2

on said elastic mounts

3

is generally a few hertz;

means, not depicted, for example a rail, fixed to the base

2

and allowing the moving body

4

to be displaced linearly on said base

2

; and

a controllable actuator

5

, preferably an electric motor, capable of applying a force F to said moving body

4

with a view to displacing it on the base

2

.

According to the invention, said device

1

has been improved in such a way as to obtain, directly at the end of a displacement of the moving body

4

, a precise positioning of the latter in a reference frame, not depicted, that is independent of the moving body and of the base and linked, for example, with the ground, at the same time overcoming the problems due to the base

2

beginning to oscillate when the moving body

4

accelerates and decelerates.

To achieve this, the device

1

additionally comprises, according to the invention, calculation means

6

which calculate a particular force F which is intended to be transmitted in the form of a control command to the actuator

5

and which is such that, when applied to said moving body

4

, it produces a combined effect (and therefore combined control):

on the one hand on (over) the moving body

4

so that it carries out exactly the intended displacement, particularly as far as the prescribed duration and distance of the displacement are concerned; and

on the other hand, on (over) the base

2

at least so that it is immobile at the end of the displacement of the moving body

4

.

Thus, since by virtue of the device

1

, the base

2

is immobilized at the end of the displacement, it does not disturb the positioning of the moving body

4

in the aforementioned reference frame and this means that said moving body

4

is positioned in a stable position right from the end of its displacement. Furthermore, as its displacement is performed precisely, its position corresponds exactly within said reference frame to the desired position.

To achieve this, according to the invention, said means

6

:

a) define a mathematical relationship illustrating the movements of the entity formed by the base

2

and the moving body

4

and dependent on parameters relating to the base

2

and to the moving body

4

and which vary as the latter is displaced; and

b) from said mathematical relationship use mathematical processing to determine a force F which, applied to said moving body

4

, produces the aforementioned combined effect.

Within the context of the present invention, there are a number of mathematical relationships that may be used and a number of different mathematical processing operations which may be performed.

Before discussing a preferred means of calculation, the conditions and assumptions of the relevant problem will be specified, namely:

the moving body

4

has a mass m and is displaced without friction on the base

2

of mass mB;

the base

2

is connected to the ground S elastically with a stiffness k

0

and damping k

1

; and

the movements of the base

2

are assumed to be restricted to displacements parallel to the displacement of the moving body

4

.

By way of illustration, masses:

{\begin{matrix} m = 40 kg \\ mB = 800 kg \end{matrix},

give:

\begin{matrix} {\begin{matrix} k0 = {mB (5.2 π)}^{2} = 5 Hz \\ k1 = 0.3 \sqrt{k0 . mB} = 0.3 \end{matrix} \end{matrix}

Further incorporating:

x the position of the center of mass of the moving body

4

in the aforementioned reference frame linked, for example, with the ground S;

xB the position of the center of mass of the base

2

in said reference frame; and

F the force applied to the moving body

4

, the equation of forces can be written:

&AutoLeftMatch; {\begin{matrix} m \ddot{x} = F \\ m B \ddot{x} B = - F - k0 x B - k1 \dot{x} B \end{matrix}

In a preferred embodiment, the means

6

by way of mathematical value in the aforementioned step a) make use of the following imaginary variable y:

\begin{matrix} y = x - \frac{k1}{k0} \dot{x} + \frac{1}{m} (mB - \frac{{k1}^{2}}{k0}) xB - \frac{mB}{m} \cdot \frac{k1}{k0} \dot{x} B . & (1) \end{matrix}

This variable has the noteworthy property of summarizing all the movements of the entity formed by the moving body

4

and the base

2

. This is because the position and speed of the base

2

and moving body

4

, and the force F can be expressed as a function of y and its derivatives up to the 4th order derivatives (y

(i)

being the ith-order derivative of y).

\begin{matrix} {\begin{matrix} x = y + \frac{k1}{k0} \dot{y} + \frac{mB}{k0} \ddot{y} \\ \dot{x} = \dot{y} + \frac{k1}{k0} \ddot{y} + \frac{mB}{k0} y^{(3)} \\ xB = - \frac{m}{k0} \ddot{y} \\ \dot{x} B = - \frac{m}{k0} y^{(3)} \\ F = m \ddot{y} + m \frac{k1}{k0} y^{(3)} + \frac{mmB}{k0} y^{(4)} . \end{matrix} & (2) \end{matrix}

Thus, if it is sought to bring about the required displacements of the moving body

4

and of the base

2

, all that is required is to provide a trajectory of y, which is a polynomial with respect to time, which interpolates the initial and final conditions, namely the moving body

4

is displaced from a position x

0

at rest ({dot over (x)}0=0) at an instant t

0

marking the start of the displacement, to a position x

1

at rest ({dot over (x)}1=0) at an instant t

1

marking the end of the displacement, and the base

2

is immobile ({dot over (x)}B=0) at the instants t

0

and t

1

at the position of equilibrium xB.

This therefore gives:

&AutoLeftMatch; {\begin{matrix} x (t0) = x0, \dot{x} (t0) = 0, x B (t0) = 0, \dot{x} B (t0) = 0, F (t0) = 0 \\ x (t1) = x1, \dot{x} (t1) = 0, x B (t1) = 0, \dot{x} B (t1) = 0, F (t1) = 0 \end{matrix}

namely:

&AutoLeftMatch; {\begin{matrix} y (t0) = x0, \dot{y} (t0) = 0, \ddot{y} (t0) = 0, y^{(3)} (t0) = 0, y^{(4)} (t0) = 0 \\ y (t1) = x1, \dot{y} (t1) = 0, \ddot{y} (t1) = 0, y^{(3)} (t1) = 0, y^{(4)} (t1) = 0. \end{matrix}

To obtain a polynomial trajectory that is exploitable in terms of y, the minimal degree, given the fact that there are 10 initial and final conditions, is equal to 9, namely:

y(t)=y

0

+(y

1

−y

0

)s

5

(126−420s+540s

2

−315s

3

+70s

4

) (3)

with

s = \frac{t - t0}{t1 - 1 t0}, y0 = y (t0) and y1 = y (t1) .

The force F, and the parameters x, {dot over (x)}, xB and {dot over (x)}B are then deduced from the aforementioned relationships (2) and from the relationship (3).

FIGS. 2 and 3

depict t he displacements L and d between the instants t

0

and t

1

, of the moving body

4

and of the base

2

, respectively, not in the aforementioned reference frame linked with the ground, but in unidirectional frames of reference associated with these items.

Thus, the moving body

4

is displaced by a distance LA, such that LA=x

1

−x

0

.

The base

2

is displaced to the maximum of distances d

1

and d

2

on each side of the position of equilibrium xB, respectively, this position of equilibrium corresponding to the distance d=0 of FIG.

3

.

Of course the embodiment described above is not the only possible embodiment in the context of the present invention.

Thus, in the aforementioned step a), it is possible to use other mathematical relationships that yield the same result.

Furthermore, in a particular embodiment, it is possible to use a different formulation than the aforementioned one, also taking account of the imaginary variable y [aforementioned relationship (1)]. In this case, use is made of:

Y the Laplace transform of said imaginary variable y; and

X, Xb and F

1

, the Laplace transforms of the temporal variables x, xB and F defined in the aforementioned relationships (2).

This formulation comprises three polynomials P

0

(p), Px(p) and Pb(p) of the Laplace variable p, which satisfy:

&AutoLeftMatch; {\begin{matrix} F1 = P0 (p) \cdot Y \\ X = P x (p) \cdot Y \\ X b = P b (p) \cdot Y \end{matrix}

Furthermore, in step b), instead of employing a mathematical processing operation comprising a polynomial decomposition, as described hereinabove, it is possible to employ a mathematical processing operation that comprises, for example, a sum of sinusoidal functions.

In particular, it is possible to use a sinusoidal decomposition of the form:

y (t) = y0 + (y1 - y0) \cdot \sum_{k = 1}^{k = n} ak \cdot \sin [(k π / 2) \cdot (t - t0 / t1 - t0) + φ k]

in which:

y

1

and y

0

are the final and initial positions; and

t

1

and t

0

are the final and initial times, as indicated above.

Furthermore, ak and (pk are parameters which are determined using the same initial and final conditions as those mentioned earlier.

Claims

1. A method for displacing a moving body (4) on a base (2) mounted elastically with respect to the ground (S), said moving body (4) being displaced linearly with a predetermined displacement under the action of a controllable force (F), wherein:a) a mathematical relationship illustrating the movements of the entity formed by the base (2) and the moving body (4) and dependent on parameters related to the base (2) and to the moving body (4) wherein said parameters vary during a displacement of the moving body, is defined; (b) using said mathematical relationship, mathematical processing is used to determine a force (F) which, applied to said moving body (4), produces a combined effect: on the one hand, on the moving body (4) so that it performs said predetermined displacement; and on the other hand, on the base (2) at least so that it is immobile at the end of the displacement of the moving body (4); and (c) the force (F) thus determined is applied to said moving body (4).
2. A method as claimed in claim 1, wherein by way of mathematical relationship in step a), use is made of the following relationship: y=x-k1k0⁢ ⁢x.+1m⁢ ⁢(mB-k12k0)⁢ ⁢xB-mBm·k1k0⁢ ⁢x.⁢B.in which:y represents an imaginary variable; k0 and k1 respectively represent the natural frequency and the damping of the elastically mounted base (2); m and mB represent the masses of the moving body (4) and of the base (2), respectively; x and xB represent the displacements of the moving body (4) and of the base (2), respectively; and x and xB represent the speeds of displacement of the moving body (4) and of the base (2), respectively.
3. A method as claimed in claim 1, wherein, in step b), the mathematical processing operation employs a sum of sinusoidal functions.
4. A method as claimed in claim 1, wherein, in step b), the mathematical processing operation employs a polynominal decomposition.
5. A method as claimed in claim 2, wherein, in step b), the force F is determined from the following relationship: F=m⁢ ⁢y¨+m⁢k1k0⁢ ⁢y(3)+mmBk0⁢ ⁢y(4),ÿ, y(3) and y(4) being the 2nd, 3rd and 4th-order derivatives of the variable y, respectively, and using the following polynomial decomposition of y(t):y(t)=y0+(y1−y0)s5(126−420s+540s2−315s3+70s4) with s=t-t0t1-t0,y0=y⁢ ⁢(t0)⁢ ⁢and⁢ ⁢y1=y⁢ ⁢(t1),t being time and t0 and t1 being the instants of the start and end of the displacement of the moving body (4).
6. A device, comprising:a base; a body coupled to said base; an actuator coupled to said body; and, a computer that provides a control command to said actuator, said control command induces a force profile that causes said body to move from a start position at a start time to an end position at an end time, so that said base has a zero displacement at the end time, the force profile being dependent on parameters related to said base and said body, said parameters vary as said body moves from the start to end positions.
7. The device of claim 6, wherein the force profile is dependent upon an imaginary variable.
8. The device of claim 7, wherein the imaginary variable is the expression y=x−k1/k0·{dot over (x)}+1/m·(mB−k0)·xB−mB/m·k1/k0·{dot over (x)}B, where y is the imaginary variable, x is a position of a center of said body, xB is a position of a center of said base, {dot over (x)} and {dot over (x)}B are the time base derivatives of x and xB, respectively, m is a mass of said body, mB is a mass of said base, k0 is a natural frequency of said base and k1 is a damping of said base.
9. The device of claim 8, wherein the force profile causes said base to have a positive displacement and then a negative displacement when said body is moved by said actuator.
10. The device of claim 8, wherein the imaginary variable is expressed as a polynomial.
11. The device of claim 8, wherein the imaginary variable is expressed as a sinusoidal decomposition.
12. A device, comprising:a base; a body coupled to said base; an actuator coupled to said body; and, calculation means for generating a control command that is provided to said actuator, said control command induces a force profile that causes said body to move from a start position at a start time to an end position at an end time, so that said base has a zero displacement at the end time, the force profile being dependent on parameters related to said base and said body, said parameters vary as said body moves from the start to end positions.
13. The device of claim 12, wherein the force profile is dependent upon an imaginary variable.
14. The device of claim 13, wherein the imaginary variable is the expression y=x−k1/k0·{dot over (x)}+1/m·(mB−k1/k0)·xB−mB/m·k1/k0·{dot over (x)}B, where y is the imaginary variable, x is a position of a center of said body, xB is a position of a center of said base, x and {dot over (x)}B are the time base derivatives of x and xB, respectively, m is a mass of said body, mB is a mass of said base, k0 is a natural frequency of said base and k1 is a damping of said base.
15. The device of claim 14, wherein the force profile causes said base to have a positive displacement and then a negative displacement when said body is moved by said actuator.
16. The device of claim 14, wherein the imaginary variable is expressed as a polynomial.
17. The device of claim 14, wherein the imaginary variable is expressed as a sinusoidal decomposition.
18. A method for moving a body relative to a base, comprising:calculating a control command to move the body with a force; and, exerting a force onto the body, the force having a force profile that causes the body to move from a start position at a start time to an end position at an end time, so that said base has a zero displacement at the end time, the force profile being dependent on parameters related to said base and said body, said parameters vary as said body moves from the start to end positions.
19. The method of claim 18, wherein the force profile is dependent upon an imaginary variable.
20. The method of claim 19, wherein the imaginary variable is the expression y=x−k1/k0·{dot over (x)}+1/m·(mB−k1/k0)·xB−mB/m·k1/k0·{dot over (x)}B, where y is the imaginary variable, x is a position of a center of the body, xB is a position of a center of the base, {dot over (x)} and {dot over (x)}B are the time base derivatives of x and xB, respectively, m is a mass of the body, mB is a mass of the base, k0 is a natural frequency of the base and k1 is a damping of the base.
21. The method of claim 20, wherein the imaginary variable is expressed as a polynomial.
22. The method of claim 20, wherein the imaginary variable is expressed as a sinusoidal decomposition.

Priority Claims (1)

Number	Date	Country	Kind
99 02224	Feb 1999	FR

US Referenced Citations (178)

Number	Name	Date	Kind
1143165	Begusch	Jun 1915	A
1306906	Jaques, Sr.	Jun 1919	A
2367139	Ress	Jan 1945	A
3357268	Richter	Dec 1967	A
3442475	Rivin	May 1969	A
3460786	Rivin	Aug 1969	A
3478608	Met	Nov 1969	A
3533012	Johnson et al.	Oct 1970	A
3565515	De Mey, II	Feb 1971	A
3577791	Vanden Broek	May 1971	A
3578278	Pickering	May 1971	A
3601476	MacKenzie	Aug 1971	A
3620558	MacMillan	Nov 1971	A
3667525	Spieth	Jun 1972	A
3751025	Beery et al.	Aug 1973	A
3917201	Roll	Nov 1975	A
3945245	Wadensten	Mar 1976	A
4030811	Khoe et al.	Jun 1977	A
4065203	Goell et al.	Dec 1977	A
4079404	Comerford et al.	Mar 1978	A
4088396	Edelstein	May 1978	A
4119363	Camlibel et al.	Oct 1978	A
4144504	Leggett et al.	Mar 1979	A
4164363	Hsu	Aug 1979	A
4167744	Nyul	Sep 1979	A
4199222	Ikushima et al.	Apr 1980	A
4237474	Ladany	Dec 1980	A
4268113	Noel, jr.	May 1981	A
4295152	Khoe et al.	Oct 1981	A
4296998	Dufft	Oct 1981	A
4316678	F'Geppert	Feb 1982	A
4332469	Wendland	Jun 1982	A
4350867	Kinoshita et al.	Sep 1982	A
4355323	Kock	Oct 1982	A
4357072	Goodfellow et al.	Nov 1982	A
4387956	Cline	Jun 1983	A
4403243	Hakamada	Sep 1983	A
4435037	Abramson et al.	Mar 1984	A
4469399	Cowen et al.	Sep 1984	A
4469929	Rosen et al.	Sep 1984	A
4479698	Landis et al.	Oct 1984	A
4500165	Scholl et al.	Feb 1985	A
4506108	Kersch et al.	Mar 1985	A
4523802	Sakaguchi et al.	Jun 1985	A
4523810	Goss et al.	Jun 1985	A
4525659	Imahashi et al.	Jun 1985	A
4550410	Chenausky et al.	Oct 1985	A
4615031	Eales et al.	Sep 1986	A
4623220	Grabbe et al.	Nov 1986	A
4647147	Pikulski et al.	Mar 1987	A
4647331	Koury, Jr. et al.	Mar 1987	A
4657429	Morris	Apr 1987	A
4664732	Campbell et al.	May 1987	A
4673244	Miles	Jun 1987	A
4673245	Kling et al.	Jun 1987	A
4677290	Mitch	Jun 1987	A
4678271	Beaulieu	Jul 1987	A
4679908	Goodwin	Jul 1987	A
4701013	Jurczysayn et al.	Oct 1987	A
4702556	Ishii et al.	Oct 1987	A
4708429	Clark et al.	Nov 1987	A
4714315	Krause	Dec 1987	A
4720163	Goodwin et al.	Jan 1988	A
4746195	Auracher et al.	May 1988	A
4747657	Chaoui et al.	May 1988	A
4748632	Preston	May 1988	A
4759600	Caron et al.	Jul 1988	A
4763979	Heywang	Aug 1988	A
4767174	Carenco et al.	Aug 1988	A
4773730	Sedlmayr	Sep 1988	A
4779946	Pimpinella et al.	Oct 1988	A
4779959	Saunders	Oct 1988	A
4782223	Suzuki	Nov 1988	A
4787691	Lorenzo et al.	Nov 1988	A
4800262	Lentine	Jan 1989	A
4807750	Ryder et al.	Feb 1989	A
4823220	Milster et al.	Apr 1989	A
4837768	Schmid	Jun 1989	A
4842397	Eisler	Jun 1989	A
4850261	Greene	Jul 1989	A
4850671	Finzel	Jul 1989	A
4854667	Ebata et al.	Aug 1989	A
4913527	Jessop	Apr 1990	A
4914867	Saito et al.	Apr 1990	A
4915482	Collins et al.	Apr 1990	A
4938564	Romero	Jul 1990	A
4966474	Geiger	Oct 1990	A
4978910	Knox et al.	Dec 1990	A
4988159	Turner et al.	Jan 1991	A
4988165	Ishii et al.	Jan 1991	A
5000415	Sandercock	Mar 1991	A
5044719	Nakamura	Sep 1991	A
5058124	Cameron et al.	Oct 1991	A
5062012	Maeda et al.	Oct 1991	A
5068749	Patel	Nov 1991	A
5077747	Hemmer et al.	Dec 1991	A
5132824	Patel et al.	Jul 1992	A
5138496	Pong	Aug 1992	A
5140470	Luecke	Aug 1992	A
5146532	Hodge	Sep 1992	A
5150236	Patel	Sep 1992	A
5172160	Van Eijk et al.	Dec 1992	A
5179618	Anton	Jan 1993	A
5183350	Kramer	Feb 1993	A
5189725	Bensel, III et al.	Feb 1993	A
5191587	Hanson et al.	Mar 1993	A
5194993	Bedzyk	Mar 1993	A
5214735	Henneberger et al.	May 1993	A
5218258	Shirasu et al.	Jun 1993	A
5218610	Dixon	Jun 1993	A
5219051	Davis	Jun 1993	A
5245552	Andersson et al.	Sep 1993	A
5251863	Gossman et al.	Oct 1993	A
5285995	Gonzalez et al.	Feb 1994	A
5289559	Wilson	Feb 1994	A
5300755	Nishitani et al.	Apr 1994	A
5311278	Rosencher	May 1994	A
5319435	Melle et al.	Jun 1994	A
5321539	Hirabayasi et al.	Jun 1994	A
5327061	Gullapalli	Jul 1994	A
5337383	DeAngelis et al.	Aug 1994	A
5367140	Jonaneh et al.	Nov 1994	A
5410145	Coroy	Apr 1995	A
5428225	Silva et al.	Jun 1995	A
5428635	Zhiglinsky et al.	Jun 1995	A
5434944	Kerry et al.	Jul 1995	A
5434945	Burek et al.	Jul 1995	A
5446519	Makinouchi	Aug 1995	A
5463647	Pan	Oct 1995	A
5469265	Measures et al.	Nov 1995	A
5499261	Welch et al.	Mar 1996	A
5502598	Kimura et al.	Mar 1996	A
5528718	Ray et al.	Jun 1996	A
5530547	Arnold	Jun 1996	A
5530785	Sakamoto et al.	Jun 1996	A
5553186	Allen	Sep 1996	A
5563972	Krausse et al.	Oct 1996	A
5564537	Shoureshi	Oct 1996	A
5570444	Janssen et al.	Oct 1996	A
5581077	Chirovsky et al.	Dec 1996	A
5598500	Crespel et al.	Jan 1997	A
5603387	Beard et al.	Feb 1997	A
5617501	Miller et al.	Apr 1997	A
5619609	Pan et al.	Apr 1997	A
5638482	Winterhoff et al.	Jun 1997	A
5653317	Wakui	Aug 1997	A
5655045	Morlion et al.	Aug 1997	A
5660255	Schubert et al.	Aug 1997	A
5668906	Yamamura et al.	Sep 1997	A
5673350	Song et al.	Sep 1997	A
5689607	Vincent et al.	Nov 1997	A
5717804	Pan et al.	Feb 1998	A
5725066	Beard et al.	Mar 1998	A
5737132	Luecke et al.	Apr 1998	A
5745633	Giebel et al.	Apr 1998	A
5748821	Schempp et al.	May 1998	A
5751877	Ishizaka et al.	May 1998	A
5757561	Sechrist et al.	May 1998	A
5758004	Alarcon et al.	May 1998	A
5761360	Grois et al.	Jun 1998	A
5765800	Watanabe et al.	Jun 1998	A
5774614	Gilliland et al.	Jun 1998	A
5793920	Wilkins et al.	Aug 1998	A
5793921	Wilkins et al.	Aug 1998	A
5794912	Whittaker et al.	Aug 1998	A
5812958	Mayama	Sep 1998	A
5823307	Schubert et al.	Oct 1998	A
5825558	Farmiga et al.	Oct 1998	A
5852519	Do et al.	Dec 1998	A
5909324	Bryant et al.	Jun 1999	A
5930057	Sechrist et al.	Jul 1999	A
5941920	Schubert	Aug 1999	A
5946023	Blanding	Aug 1999	A
5963695	Joyce	Oct 1999	A
6016230	Nunnally et al.	Jan 2000	A
6022005	Gran et al.	Feb 2000	A
6198580	Dallakian	Mar 2001	B1
6209841	Houghton, Jr. et al.	Apr 2001	B1

Foreign Referenced Citations (7)

Number	Date	Country
2199423	Mar 1996	CA
2 124 402	Jul 1982	GB
2 131 971	Jun 1984	GB
03021894	Jan 1991	JP
08088167	Apr 1996	JP
09330875	Dec 1997	JP
10144601	May 1998	JP

Non-Patent Literature Citations (1)

Entry
US 5,880,594, 03/1999, Blakley (withdrawn)

Method and device for displacing a moving body on a base mounted elastically with respect to the ground

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