JP2000079900A - Orbit generating device and simulated weightless condition generating device - Google Patents

Abstract

PROBLEM TO BE SOLVED: To generate the uniform rotating orbit by executing the calculation of orbit for mathematically certifying the uniformity of orbit of a point moving on a spherical surface, arbitrarily setting a period for obtaining the continuous change of angular speed and the uniform orbit, and arbitrarily setting the density of the rotating orbit. SOLUTION: A 3D clinostat as an experiment machine used in the bio- experiment disperses a sample in the gravity direction by biaxially rotating the same, so that the gravity is uniformly applied to all the sample in time average. The rotating orbit of the 3D clinostat needs the uniformity of gravity, and the continuity of angular speed. By applying the orbit generated by an orbit generating method to a rotating angle of the 3D clinostat, the uniformity of orbit and the continuity of angular speed can be ensured, and the characteristic of the rotating orbit necessary for the 3D clinostat can be obtained.

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a method of rotating a sample around its two axes so that the direction of gravity with respect to the sample becomes zero on a time average.
The present invention relates to a trajectory generator applicable to the generation of a rotational trajectory for a 3D clinostat, which is an experimental device to be used, and a pseudo zero-gravity state generator mainly used for a test relating to the growth of living organisms.

[0002]

2. Description of the Related Art (First Prior Art) Conventionally, in order to generate a uniform rotation trajectory, it is necessary to select either a method of randomly changing a rotation angular velocity or a method of randomly selecting a target rotation angle. Was common. More specifically, when the rotation angular velocity is changed at random, each of the rotation angular velocities around the two axes is changed at random every fixed time. When a target rotation angle is randomly selected, the target rotation angle is rotated at a certain time toward a randomly selected target rotation angle, and a new target position (angle) is randomly given when the target rotation angle is reached.

(Second conventional technique) In addition, gravity has a great influence on the growth of living organisms, and tests for the growth of living organisms in a zero-gravity state have been demanded mainly for academic purposes. I have. However, if a truly weightless state is to be obtained, it is desirable to perform a growth test in space such as a space shuttle, but there is a problem that the cost required for the test is high. For this reason, a pseudo zero-gravity state generating apparatus that can easily generate a zero-gravity state on the ground and can perform a test at low cost is used.

FIG. 13 is a diagram showing a driving mechanism of a conventional pseudo zero-gravity state generating device. A biological sample to be tested (mainly plant cells) is attached to the stage 11. The posture of the stage 11 is such that the outer motor 12 and the inner motor 13 are mounted so that the respective rotation axes are orthogonal to each other.
, And rotating the outer frame 2 and the inner frame 3 respectively, can be freely determined.

FIG. 14 is a diagram showing a control method of a conventional pseudo zero-gravity state generating device. In the conventional apparatus, the outer motor 12 and the inner motor 13 rotate at a speed proportional to the outer motor speed command signal 15 and the inner motor speed command signal 16 output by the controller 14, respectively. The controller 14 is provided with a random number generator 7 which transmits two independent random numbers and is used as an outer motor speed command signal 15 and an inner motor speed command signal 16, respectively.

As described above, the outer motor speed command signal 15
And the inside motor speed command signal 16 are changed in a random manner, and the result is described by Masamichi Yamashita et al., "3D-Crinostat and Its Operating Characteristics", Space Biological Science Vol. 11, N
o. 2 (1997), stage 1
On 1, it is said that the direction of gravity changes every moment, and the influence of gravity is canceled out as a temporal average, and a pseudo weightless state can be generated.

[0007]

(Problems of the first prior art) Both the above-mentioned conventional method of randomly changing the rotational angular velocity and the method of randomly selecting a target rotational angle are described below.
Since the velocity or the target position is given at random, it can only be stochastically shown that the trajectory is uniformly distributed on the spherical surface, and cannot be proved mathematically. For example, to determine whether the trajectory is uniform, it is necessary to actually generate the trajectory and check the result.

Further, in both methods, a temporally discontinuous angular velocity may occur due to its randomness. For example, in the case of a method of randomly giving a rotational angular velocity, when the angular velocity is changed, the angular velocity before the change and the angular velocity after the change may be discontinuous. Also, in the case of randomly selecting the target rotation angle, when the target rotation angle is changed, the angular velocity before the change and the angular velocity after the change toward the new target rotation angle may be discontinuous. is there.

That is, when a specific object is to be rotated along the generated rotation trajectory, and when the rotating body is not completely rigid, the rotating body vibrates due to a discontinuous angular velocity with respect to time. In some cases, there is a problem.

Further, since the characteristics of the object to be rotated are various, it is necessary to arbitrarily set the time period at which the trajectory becomes uniform, and it is necessary to arbitrarily set the density of the rotating trajectory. None can be set in a random way.

(Problem of the second conventional technique) The above-mentioned conventional method has two problems. The first issue is reproducibility. Since the pseudo-gravity-free state generating device is mainly intended for slow-growing ones such as plant cells, the operation period is usually one month or longer. If the operation is performed for about one month, the friction characteristics of the rotary bearings increase with time, so that the relationship between the motor speed command signals 15 and 16 and the actual motor speed inevitably fluctuates with time.

Therefore, in the conventional method, the attitude of the stage 11 is not determined only by the motor speed command signals 15 and 16, but also depends on the friction characteristics. Assuming that the attitude of the stage 11 is not determined only by the motor speed command signals 15 and 16, even if the same trajectory of the motor speed command signals 15 and 16 is given for the purpose of retesting a certain test, the friction characteristics Is indeterminate, so that the posture of the stage 11 cannot be reproduced as intended.

The second problem is the statistical bias of gravity.
In the conventional method, the speeds of the outer motor 12 and the inner motor 13 are changed at random. In the method of changing randomly, after a sufficient time has elapsed since the start of the experiment, the influence of the direction of gravity is canceled out as a time average, as shown in the above-mentioned paper by Masamichi Yamashita et al. However, if attention is paid to a short period of time, for example, about 10 minutes during the test period, it is inevitable that there is a bias in the direction of gravity.

That is, if the time when gravity is critical in the growth process of an organism matches this bias, it is not an effective test. In order to improve the quality of the test, when the whole test period is divided into short periods, for example, about 10 minutes,
Although it is necessary that the direction of gravity is uniform in any period, it cannot be realized by a conventional method based on a random number method.

As described above, the conventional method has disadvantages in a short term. Furthermore, the problem of the conventional method is not limited to short-term bias, but also has a problem from a long-term viewpoint. In the conventional method, attention is paid only to making the time variation value of gravity uniform, but making uniform only the average value is insufficient. An example is shown below.

As shown in FIG. 15, the rotation axis of the outer motor 2 is set on the x-axis, the rotation axis of the inner motor 3 is set on the z-axis, and the rotational displacement angle of the outer motor 2 and the inner motor 3 from the reference angle is φ. θ. The reference angle is selected for φ so that the z-axis is opposite to the gravity vector. θ
For, the reference angle is arbitrary. The direction and magnitude g of gravity of the stage 1 (hereinafter referred to as gravity vector) are φ and θ.
Is given by

[0017]

(Equation 1) Here, g0 is the magnitude of the gravitational acceleration. The conventional method aims to make the gravity vector zero on a time average. For example,

(Equation 2) When the motor is rotated along the orbit, the gravity vector becomes

(Equation 3) Becomes This average is

(Equation 4) Is the average value from time 0 to T

(Equation 5) Is given by

[0018]

(Equation 6) In this example, the x component of the gravity vector is always 0, and x
Since the components and the other y and z components are obviously non-uniform, they satisfy the requirement that the time-average value of the gravitational vector be zero, although this is not intended.
This problem can be solved not only by simply setting the gravity vector to 0 on a time average, but also by making the variances of the x, y, and z components of the gravity vector uniform.

Next, the variance of the gravity vector is obtained for the conventional method. X, y, z components of the gravity vector
Expressed as x, gy, gz, the variance of the gravity vector in the conventional method is as follows.

[0020]

(Equation 7) Thus, it can be seen that the conventional method has a statistical bias that the variance of the z component of the gravity vector is different from that of the x and y components.

An object of the present invention is to prove mathematically the uniformity of the trajectory of a point moving on a spherical surface, and to have a continuous angular velocity change,
An object of the present invention is to provide a trajectory generation device capable of arbitrarily calculating a trajectory capable of arbitrarily setting a period at which a trajectory becomes uniform and arbitrarily setting a density of a rotating trajectory.

It is another object of the present invention to provide a pseudo weightless state generating apparatus which improves reproducibility and statistical bias of gravity.

[0023]

Means for Solving the Problems In order to solve the above problems and achieve the object, a trajectory generating device and a pseudo weightless state generating device of the present invention are configured as follows.

(1) A trajectory generation device according to the present invention is a trajectory generation device for generating a trajectory of a point moving on a spherical surface, which can mathematically prove the uniformity of the trajectory of the point, and the angular velocity change becomes continuous. The cycle at which the trajectory becomes uniform can be set arbitrarily,
A calculating means for calculating a trajectory capable of arbitrarily setting the density of the rotating trajectory is provided.

(2) The pseudo zero-gravity state generating apparatus of the present invention is provided such that the respective rotating shafts are orthogonal to each other, and drives the outer motor and the inner motor to rotate the outer frame and the inner frame, respectively. In the pseudo weightless state generating device that determines a posture, an outer motor angle detector that detects a rotation angle of the outer motor, an inner motor angle detector that detects a rotation angle of the inner motor, the outer motor angle detector, Compensating means for compensating each detection result of the inner motor angle detecting means to match each angle command value of the outer motor and the inner motor, and outputting each speed command signal to the outer motor and the inner motor. It is configured.

(3) A pseudo zero-gravity state generating apparatus according to the present invention is the apparatus described in (2) above, and further includes a calculating means for calculating each of the angle command values.

[0027]

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS (First Embodiment) FIG. 1 is a diagram showing an outline of a trajectory generating device according to a first embodiment of the present invention. In the trajectory generating apparatus a of the present embodiment, the problem that the uniformity of the trajectory cannot be mathematically proved, the problem that a temporally discontinuous angular velocity is generated, and the trajectory becomes uniform In order to deal with the problem that the period cannot be set arbitrarily, the problem that the density of the rotating trajectory cannot be set arbitrarily, and the four problems that cannot be solved by the above random methods, the trajectory calculation method uses mathematics to calculate the trajectory uniformity. Can be proved that the angular velocity change is continuous,
A trajectory calculation in which the period at which the trajectory becomes uniform can be set arbitrarily and the density of the rotating trajectory can be set arbitrarily.

The trajectory calculation method by the trajectory generation device a is expressed by the following equation. The trajectory is given by the following formulas (1) and (2)
Is represented by a differential equation relating to the rotation angle (φ, θ) of the point p on the unit spherical surface.

[0029]

(Equation 8) However, the initial values of φ and θ are arbitrary.

Here, A and B are angular velocity parameters, and by adjusting these two parameter values, the period at which the trajectory becomes uniform can be adjusted. For example, the period of A = 2, B = 3 is twice the period of A = 4, B = 6. However,
A: 2m for the smallest integer n, m such that B = n: m
It is necessary to select A and B so that / n does not become an integer.
Further, the density of the rotating orbit can be set by adjusting the values of n and m. For example, n: m is 10:11 than 10:11.
The rotation density is higher when 0: 111.

FIG. 2 is a diagram showing a coordinate system according to the present embodiment, and φ and θ are defined as follows. A point p on the unit sphere represented by x ² + y ² + z ² = 1 in the rectangular coordinate system
, The position vector of the point p is (x _p , y _p , z _p )
Where φ: the angle between the vector (0, 0, 1) and the position vector of the point p, θ: the vector (1, 0, 0) and the vector when the point p is projected onto the xy plane Angle formed by (x _p , y _p , 0),

(Equation 9) It is.

(1) Continuity of angular velocity The phrase that the angular velocity of the trajectory generated by the trajectory generator a is continuous with respect to time means that φ is continuous with time at an arbitrary time and that φ is arbitrary. At

(Equation 10) Is continuous with φ.

Hereinafter, it will be shown that the trajectory generated by the trajectory generator a satisfies the continuity of the angular velocity.

(2) Proof of continuity of angular velocity

[Equation 11] If is a continuous function,

(Equation 12) Is the time derivative of φ, so it is obvious that φ is continuous with time. From equations (1) and (2),

(Equation 13) So that

[Equation 14] Is continuous with φ,

(Equation 15) Is continuous with φ. Therefore,

(Equation 16) May be shown to be continuous with φ.

From equation (1), when sin (φ)> 0,
When sin (φ) <0,

[Equation 17] Is continuous because it can be represented by a continuous function of φ.

When sin (φ) = 0, both sin (φ) = 0 as follows.

(Equation 18) Since the limits of

[Equation 19] Is continuous even when sin (φ) = 0.

[0037]

(Equation 20) That is,

(Equation 21) Is continuous with φ, which proves the continuity of the angular velocity.

(3) Uniformity of the trajectory The uniformity of the trajectory is calculated as follows: the coordinates of the points moving on the unit spherical surface in the orthogonal coordinate system have a time average of 0 for each of the x, y, and z directions, and x, y , Z are equal, the following is obtained.

The coordinates of a point moving on the unit spherical surface (x ² + y ² + z ² = 1) at a period T are represented by (x (t), y (t), z
(T)), x (t), y (t), z
The time average of (t) becomes 0, and the variances become equal.

That is,

(Equation 22) Becomes

Hereinafter, it will be proved that the trajectory generated by the trajectory generator a satisfies the above-mentioned trajectory uniformity.

(4) Proof of Uniformity of Trajectory The average and variance of the trajectory generated by the trajectory generator a are obtained as follows.

(4-1) Average in the x direction When a point on the unit sphere is at the position (φ, θ) in the polar coordinate system, this is converted into the rectangular coordinate system (x, y, z) as follows. Become.

X = cos (θ) · sin (φ) y = sin (θ) · sin (φ) z = cos (θ) Consider a case where φ changes from 0 to 2Nπ during the period T. Since how much φ changes during the time T is arbitrarily determined by the angular velocity parameter A, generality is not lost.

At this time,

(Equation 23) Therefore, if θ (0) = 0, then θ = aφ. Therefore, θ changes from 0 to 2Naπ. At this time, B is selected so that Na is an integer and 2a is a non-integer.

Also,

(Equation 24) It is.

[0047]

(Equation 25) Becomes

The above equation is

(Equation 26) In the form of a linear sum of. As shown below, this format is 0 when 2a is not an integer. That is,

[Equation 27] Becomes next,

[Equation 28] Ask for. However, Na = M for integers N and M according to the condition regarding a.

[0049]

(Equation 29) Also,

[Equation 30] It is. here,

(Equation 31) It is. Therefore, f (2aπ) = Csin (2aπ) =
0.

At this time, when 2a is not an integer,

(Equation 32) From C = 0, that is,

[Equation 33] It is.

From the above, when 2a is not an integer with respect to a where Na = M for integers N and M,

(Equation 34) Becomes

(4-2) Average in the y direction Average in the y direction is the same as average in the x direction.

(Equation 35) It is.

(4-3) Average in z direction

[Equation 36] (4-4) X-direction variance The variance V (x) in the x-direction is reduced to 1/3 as follows.

[0054]

(37) here,

(38) Integrating this gives:

[Equation 39] Becomes

When this is substituted into the above equation, almost all the terms become 0 as in the case of the average, and the following terms remain.

[0056]

(Equation 40) Here, since T = 4 N / A, V (x) = 1/3.

(4-5) Dispersion in the y direction Dispersion in the y direction is reduced to 1/3 in the same manner as dispersion in the x direction.

(4-6) Z-direction variance The variance V (z) in the z-direction is reduced to 1/3 as follows.

[0059]

[Equation 41] (5) Periodicity of orbit uniformity By setting the velocity parameters as follows, uniformity can be provided at an arbitrary period.

According to the angular velocity equation (1), the time required for φ to change from 0 to π / 2 is 1 / A as follows.

[0061]

(Equation 42) -Cos (φ) = At φ = 0, t ₀ = −1 / A φ = π / 2, t ₁ = 0 t ₁ −t ₀ = 1 / A Therefore, from the symmetry, φ is 0 The time required to change to 2π (one round) is 4 / A. On the other hand, since θ changes at a speed of B / A times φ, the time required for θ to change from 0 to 2π (one round) is 4 / B. Therefore, the period T is a time of the least common multiple of 4 / A and 4 / B, and can be set to an arbitrary time depending on how the parameters A and B are selected.

(6) Arbitrary Arbitrary Density of Trajectory FIGS. 3, 4 and 5 show parameter patterns 1 and 2, respectively.
FIG. 4 is a perspective view showing trajectories 2 and 3, and FIGS.
FIG. 5 shows the setting of the velocity parameter having a higher orbital density. Integers n and m representing the ratio of parameters A and B
By adjusting, the orbital density can be adjusted. Actually, trajectories are generated in the case of three patterns in which the values of A and B are almost the same but the ratios of A and B are slightly different. FIGS. 3, 4 and 5 show examples. In these figures, a trajectory is generated with the velocity parameters shown in Table 1, and the trajectory is seen through in the y-axis direction. It is understood that the orbital density can be increased by increasing the values of n and m representing the ratio of A: B.

Table 1 Pattern A [rad / sec] B [rad / sec] A: B 1 (FIG. 3) 0.1 0.3 1: 3 2 (FIG. 4) 0.1 0.28 5: 143 (FIG. 5) 0.1 0.296 25:74 FIG. 6 is a diagram showing a configuration of a 3D clinostat to which the trajectory generation device a is applied. In the present embodiment, 3D
Regarding the specific problem of generating the rotation trajectory of the clinostat, the uniformity and continuity required for the 3D clinostat were realized using the trajectory generator a.

The 3D clinostat shown in FIG. 6 includes a gantry 1, an outer frame 2, an inner frame 3, motors 4 and 5,
It is composed of A sample (not shown) is set at the center of the inner frame 3. The outer frame 2 is rotated by a motor 4 attached to the gantry 1, and the inner frame 3 is rotated by a motor 5 attached to the outer frame 2.

The 3D clinostat is an experimental machine used for a biological experiment. The purpose of the 3D clinostat is to disperse the direction of gravity by rotating the sample around two axes so that gravity is uniformly applied to the entire sky of the sample on a time average basis. The rotation trajectory of the 3D clinostat requires uniformity of gravity and continuity of angular velocity. When the angular velocities are not continuous, there is a problem that the 3D clinostat main body vibrates due to the dynamic characteristics of the 3D clinostat main body, which causes a problem.

These problems have been solved by applying the present trajectory generation method to a 3D clinostat. Since the rotation around the two axes is represented by the rotation angle around the two axes, the rotation angle directly corresponds to the angle representing the position of the point on the unit spherical surface used in the present trajectory generation method. From this, by applying the trajectory generated by the trajectory generation method to the rotation angle of the 3D clinostat, the trajectory uniformity, which is a feature of the trajectory,
In addition, the continuity of the angular velocity and the continuity of the angular velocity are guaranteed, and the characteristics of the rotational orbit required for the 3D clinostat can be obtained. In an actual application, the generated trajectory is sampled at an arbitrary sampling period because digital control is performed.

FIGS. 7, 8, and 9 are diagrams showing examples in which the trajectory generation method according to the first embodiment is applied to a real machine and the trajectory is sampled at a sampling period of 0.1 second. . FIG. 7 shows the time history of the time average of the coordinates for each axis direction in the orthogonal coordinate system of the generated trajectory. The solid line is the average in the x direction, the broken line is the average in the y direction, and the dashed line is the average in the z direction. . FIG. 8 shows the time history of the time variance of the coordinates of each generated axis in the orthogonal coordinate system in the orthogonal coordinate system. The solid line is the variance in the x direction, the broken line is the variance in the y direction, and the dashed line is the variance in the z direction. . FIG. 9 shows the time history of the rotational angular velocities. The solid line indicates the angular velocity in the φ direction, and the broken line indicates the angular velocity in the θ direction.

FIG. 7 shows an average time history in the x, y, and z directions. It can be seen that the average is 0 in the period T (= 200 seconds). Even after time T, the average becomes 0 for each cycle T. FIG. 8 shows a time history of dispersion in the x, y, and z directions. It can be seen that the variances of x, y, and z coincide (1/3) in the period T. Even after time T, the variances are identical for each cycle T. FIG. 9 shows the time history of the angular velocity. It can be seen that the angular velocity is continuous over time.

(Second Embodiment) FIG. 10 is a diagram showing a configuration of a driving mechanism 26 and a controller 20 of a pseudo weightless state generating apparatus according to a second embodiment of the present invention. In this device, the outer motor 12 and the inner motor 13 are provided with an outer motor angle detector 21 and an inner motor angle detector 22, and transmit signals indicating an angle φ and an angle θ, respectively. Controller 20 integrates outer motor speed command signal 15 and inner motor speed command signal 16 corresponding to angles φ and θ by integrators 23 and 24, respectively, and outputs angle command signals φ _r and θ _r . Compensator 25 inputs the angle command signal phi _r and theta deviation of the actual angle phi and theta for _r [delta] _phi and [delta] _theta, an outer motor speed signal 151, such as to zero [delta] _phi and [delta] _theta inner The motor speed command signal 161 is transmitted. Compensator 25
Then, for example, the speed command signals _vφ and _vθ are calculated by the following arithmetic expression of PID control.

[0070]

[Equation 43] As described above, by measuring the actual angles φ and θ and controlling them so that they correspond to the command angles φ _r and θ _r , the motor can be driven as instructed. It is also possible to obtain reproducibility.

(Third Embodiment) FIG. 11 is a diagram showing a configuration of a driving mechanism 26 and a controller 27 of a pseudo weightless state generating apparatus according to a third embodiment of the present invention. 11, the same parts as those in FIG. 10 are denoted by the same reference numerals, and the description thereof will be omitted.

In the controller 27, in the trajectory calculation unit 28,
X gravity vector of the stage 11, y, statistically bias in the z-axis component of the angle command signal theta _r calculated output of the angle command signal phi _r and the inner motor 13 of the outer motor 12 so as not to occur. Compensator 25, the actual angle of inputs deviation [delta] _phi and [delta] _theta, [delta] _phi and the outer motor speed signal 152, such as to zero [delta] _theta inner motor corresponding to the angle command signal phi _r and theta _r A speed command signal 162 is transmitted.

The trajectories of the angle command signals φ _{r and} θ _r that do not cause a statistical deviation in the x, y, and z axis components of the gravity vector are not unique, but are numerous. Therefore, the calculation formula of the trajectory calculation unit 28 is not uniquely determined. Here, an example of the calculation formula is shown. Conventionally, φ _{r and} θ _r are shown in FIG.
As shown in 0 of the controller 20, to set the respective differential value v _phi and v random number _theta, it was calculated by integrating it. For example, v _φ and v _θ are determined as follows by using constants k ₁ and k ₂ .

[0074]

[Equation 44] The following equation is obtained by integrating the above equation.

[0075]

[Equation 45] Here, τ is a periodic function related to t shown in FIG.
By the operation of the compensator 25,

[Equation 46] Is achieved, the gravity vector x,
The y and z axis components are as follows.

[0076]

[Equation 47] From the above equation, the time average value of the x-, y-, and z-axis components of the gravitational vector becomes the following equation by setting T sufficiently large.

[0077]

[Equation 48] Here, assuming that the least common multiple of 1 / k ₁ and 1 / k ₂ is T ₀ , and the remainder obtained by dividing T by T ₀ is T ₁ , the above equation becomes the following equation.

[0078]

[Equation 49] The second term of the right side of the above equation is a periodic function an is the magnitude of the period T ₀ is finite. On the other hand, the first term on the right side monotonously decreases with an increase in T, so that the above equation becomes zero when T → ∞.

Since the second term on the right side of the above equation is a periodic function that becomes _{0 for} each period T ₀ , the time average value of the gravity vector becomes ₀ for any time section of T ₀ seconds during the experimental period.
T _0, so the user by two parameters k ₁ and k ₂ can be freely selected by setting small T _0, it is possible to eliminate short-term bias was conventional problem.

Further, in the conventional method, x,
Although the dispersion of the y- and z-axis components is biased, according to the method according to the second embodiment, the uniformity can be obtained as follows from T → ∞.

[0081]

[Equation 50] The present invention is not limited to the above embodiments, and can be appropriately modified and implemented without changing the gist.

[0082]

According to the trajectory generator of the present invention, the uniformity of the trajectory of a point moving on a sphere can be mathematically proved, and the time-average existence probability of a point on the sphere at an arbitrary time period can be proved on the sphere. , The angular velocity change becomes continuous with respect to time, the period at which the trajectory becomes uniform can be arbitrarily set, and the trajectory calculation can be performed so that the density of the rotating trajectory can be arbitrarily set.

Also, by applying the present trajectory generation device to a 3D clinostat, the uniformity of the time average of the trajectory can be assured at an arbitrary time period and the continuity of the angular velocity can be assured as compared with the conventional random method. As a result, vibration does not occur in the 3D clinostat body.

Further, the period and the orbital density can be variously adjusted according to the difference in the characteristics of the test object.

According to the pseudo weightless state generating apparatus of the present invention, the actual angles of the outer motor and the inner motor are measured and compensated so that each of them coincides with the angle command value to control the outer motor and the inner motor. Accordingly, the outer motor and the inner motor can be driven as instructed, so that reproducibility can be obtained even when disturbance such as friction occurs.

Further, the angle command values of the outer motor and the inner motor can be calculated so that no statistical deviation occurs in each axis component of the gravity vector of the stage.

[Brief description of the drawings]

FIG. 1 is a diagram showing an outline of a trajectory generation device according to a first embodiment of the present invention.

FIG. 2 is a diagram showing a coordinate system according to the first embodiment of the present invention, showing a definition of an angle.

FIG. 3 is a perspective view showing a trajectory of a parameter pattern according to the first embodiment of the present invention.

FIG. 4 is a perspective view showing a trajectory of a parameter pattern according to the first embodiment of the present invention.

FIG. 5 is a perspective view showing a trajectory of a parameter pattern according to the first embodiment of the present invention.

FIG. 6 is a diagram showing a configuration of a 3D clinostat to which the trajectory generation device according to the first embodiment of the present invention is applied.

FIG. 7 is a diagram showing a time history of a time average of coordinates in each axis direction in a rectangular coordinate system of a generated trajectory according to the first embodiment of the present invention.

FIG. 8 is a diagram showing a time history of time variance of coordinates in each axis direction in a generated trajectory orthogonal coordinate system according to the first embodiment of the present invention.

FIG. 9 is a diagram showing a time history of a rotational angular velocity according to the first embodiment of the present invention.

FIG. 10 is a diagram showing a configuration of a driving mechanism and a controller of a pseudo weightless state generating device according to a second embodiment of the present invention.

FIG. 11 is a diagram showing a configuration of a driving mechanism and a controller of a pseudo weightless state generating device according to a third embodiment of the present invention.

FIG. 12 is a diagram showing a periodic function related to t according to the third embodiment of the present invention.

FIG. 13 is a diagram showing a driving mechanism of a pseudo weightless state generating device according to a conventional example.

FIG. 14 is a diagram showing a control method of a pseudo weightless state generating device according to a conventional example.

FIG. 15 is a view showing displacements of an outer motor and an inner motor from a reference angle according to a conventional example.

[Explanation of symbols]

 a: trajectory generator 1 ... gantry 2 ... outer frame 3 ... inner frame 4 ... motor 5 ... motor 7 ... random number generator 11 ... stage 12 ... outer motor 13 ... inner motor 14 ... controller 15 ... outer motor speed command signal 16 ... Inner motor speed command signal 151 ... Outer motor speed command signal 161 ... Inner motor speed command signal 20 ... Controller 21 ... Outer motor angle detector 22 ... Inner motor angle detector 23,24 ... Integrator 25 ... Compensator 26 ... Drive mechanism 27 Controller 28 Trajectory calculator

Claims (3)

[Claims] 1. A trajectory generating apparatus for generating a trajectory of a point moving on a spherical surface, wherein the uniformity of the trajectory of the point can be mathematically proved, and the period at which the angular velocity changes continuously and the trajectory becomes uniform is determined. A trajectory generation device comprising a trajectory calculation unit that can arbitrarily set a rotation trajectory and arbitrarily set a rotational trajectory density. 2. A pseudo zero-gravity state generating device which determines the attitude of a stage by rotating an outer frame and an inner frame by driving an outer motor and an inner motor, each rotating shaft being provided to be orthogonal to each other, Outer motor angle detection means for detecting the rotation angle of the outer motor; inner motor angle detection means for detecting the rotation angle of the inner motor; and each detection result of the outer motor angle detection means and the inner motor angle detection means. Compensating means for compensating to match each angle command value of the outer motor and the inner motor, and outputting the same as each speed command signal to the outer motor and the inner motor. apparatus. 3. A pseudo weightless state generating apparatus according to claim 2, further comprising a calculating means for calculating each of said angle command values.