CN106023732A - Space rotary transformation device - Google Patents
Space rotary transformation device Download PDFInfo
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- CN106023732A CN106023732A CN201610596208.3A CN201610596208A CN106023732A CN 106023732 A CN106023732 A CN 106023732A CN 201610596208 A CN201610596208 A CN 201610596208A CN 106023732 A CN106023732 A CN 106023732A
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- ectosphere
- interior
- ball
- omni
- space
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- G—PHYSICS
- G09—EDUCATION; CRYPTOGRAPHY; DISPLAY; ADVERTISING; SEALS
- G09B—EDUCATIONAL OR DEMONSTRATION APPLIANCES; APPLIANCES FOR TEACHING, OR COMMUNICATING WITH, THE BLIND, DEAF OR MUTE; MODELS; PLANETARIA; GLOBES; MAPS; DIAGRAMS
- G09B23/00—Models for scientific, medical, or mathematical purposes, e.g. full-sized devices for demonstration purposes
- G09B23/02—Models for scientific, medical, or mathematical purposes, e.g. full-sized devices for demonstration purposes for mathematics
- G09B23/04—Models for scientific, medical, or mathematical purposes, e.g. full-sized devices for demonstration purposes for mathematics for geometry, trigonometry, projection or perspective
Abstract
The invention discloses a space rotary transformation device. The space rotary transformation device comprises an outer ball and an inner ball which are concentric, and is characterized by further comprising an outer ball supporting mechanism, an inner ball supporting mechanism, an outer ball manual rotation mechanism, an outer ball autorotation mechanism, an inner ball attitude keeping mechanism and an inner and outer ball three-dimensional space positioning mechanism, wherein the outer ball manual rotation mechanism drives an outer omnidirectional wheel through a hand wheel so as to accomplish rotary transformation of the outer ball around a fixed coordinate system, the outer ball autorotation mechanism drives an inner omnidirectional wheel through a motor so as to accomplish rotary transformation of the outer ball around an outer ball follow-up coordinate system, and calculation for an equivalent rotating axis, an equivalent rotating angle and the like is accomplished through the two types of coordinate transformation. The space rotary transformation device can visually demonstrate the space rotary coordinate transformation process, and can verifies related principles of space coordinate transformation by using measured data and a transformation formula.
Description
Technical field
The present invention relates to teaching appliance and experimental facilities, be specially a kind of Space Rotating converting means.
Background technology
Rotation transformation is a kind of important conversion in euclidean geometry, and rotation transformation device is to become with Space Rotating
A kind of device demonstrated designed based on changing correlation theory.
In mechanical speciality, the course such as Fundamentals of Robot Techniques there are the related Sections such as spatial alternation, religion
Teacher is when explaining these contents, it is common that draws 3 d space coordinate on blackboard and explains, this teaching
Mode needs student to have stronger space imagining ability, increases student and understands that Space Rotating conversion is relevant and know
The difficulty known.
Summary of the invention
For solving a difficult problem for existing teaching, the present invention proposes a kind of Space Rotating converting means.
Space Rotating converting means of the present invention, its technical scheme includes concentric ectosphere and interior ball, and institute is different
Be also to include ectosphere supporting mechanism, interior ball supporting mechanism, outer player's rotating mechanism, ectosphere rotation motivation
Structure, interior ball attitude maintaining body and interior ectosphere three-dimensional fix mechanism, wherein:
1, described ectosphere supporting mechanism includes the outer buphthalmos wheels being supported in ectosphere lower external face.
2, described interior ball supporting mechanism is included on ectosphere inner surface layout and is supported on interior outer surface of ball
Interior buphthalmos wheels.
3, described outer player's rotating mechanism include being arranged in drive to frictionally outside ectosphere ectosphere rotating around X,
Three outer omni-directional wheels that Y, Z axis rotate, each outer omni-directional wheel is driven by coaxial mounted handwheel, each handwheel
Respectively by respective graduated disc record rotational angle.
4, described ectosphere autorotation mechanism drive to frictionally in including being arranged in ectosphere ectosphere rotating around X,
Three interior omni-directional wheels that Y, Z axis rotate, the motor that each interior omni-directional wheel is installed by an axle head drives and by separately
The encoder record rotational angle that one axle head is installed.
5, described interior ball attitude maintaining body is included on interior ball bottom interior surface and difference on lateral interior surfaces
The Magnet arranged, with each Magnet corresponding to arranging the electric magnet attracted each other with corresponding Magnet outside ectosphere.
6, described interior ectosphere three-dimensional fix mechanism is included on ectosphere inner surface and pacifies with orthogonal space position
Three laser beam emitting heads towards interior ball of dress, with each laser beam emitting head position corresponding on interior outer surface of ball
It is respectively mounted laser pick-off head.
For realizing the rotational stability of ectosphere, the position of three interior omni-directional wheels corresponds respectively to three Ge Wai omnidirectionals
The position of wheel.
The preferred arrangement scheme of omni-directional wheel is, it is forward and backward that three outer omni-directional wheels are arranged in same level
Position and left or right position, this horizontal plane is in the biggest ball path position of ectosphere.
For preferred arrangement, the external magnet that can make sidepiece is relative with the outer omni-directional wheel of left or right position and puts.
For realizing stable support, described outer buphthalmos wheels at least include eight buphthalmos wheels and the inner ring of outer ring
Four buphthalmos wheels；Described interior buphthalmos wheels at least include 12 buphthalmos wheels that space is uniform.
Designing routinely, three laser beam emitting heads are arranged on the episphere of ectosphere, corresponding, and three
Individual laser pick-off head is arranged on the episphere of interior ball.
Further design is, on the middle vertical (crossing the vertical plane in the center of circle) within described interior ball
Being provided with cross sleeve pipe, the internal magnet bottom interior ball is located at the bottom of vertical tube in cross sleeve pipe and by vertical tube
Interior spring compression, the internal magnet of interior ball sidepiece is located at the one end of transverse tube in cross sleeve pipe and by transverse tube
Interior spring compression.
Beneficial effects of the present invention:
1, Space Rotating converting means of the present invention student can be allowed to see intuitively space coordinates is in rotational transform
During various states, and clarifying space rotation of the coordinate system conversion correlation theory formula.
2, the present invention is available around fixed coordinate system conversion and completes equivalence around the servo-actuated coordinate system transformation of ectosphere
The teaching demonstration that rotating shaft converts with effective rotation.
Accompanying drawing explanation
Fig. 1 is the perspective view of one embodiment of the present invention.
Fig. 2 be Fig. 1 embodiment top view.
Fig. 3 is ectosphere supporting mechanism and the perspective view of outer player's rotating mechanism in Fig. 1.
Fig. 4 is the top view of Fig. 3.
Fig. 5 is that the perspective view of Fig. 1, Fig. 2 China and foreign countries revolutions motivation structure (comprises ectosphere three-dimensional
Space orientation mechanism).
Fig. 6 is that in Fig. 1, Fig. 2, the axonometric chart of interior ball attitude maintaining body (comprises interior ball three dimensions fixed
Position mechanism).
Figure number identifies: 1, ectosphere；2, interior ball；3, outer omni-directional wheel；4, handwheel；5, motor；6、
Encoder；7, Magnet；8, electric magnet；9, laser beam emitting head；10, laser pick-off head；11, interior entirely
To wheel；12, outer buphthalmos wheels；13, interior buphthalmos wheels；14, cross sleeve pipe；15, spring；16、
Base plate；17, support.
Detailed description of the invention
Technical scheme is described further by illustrated embodiment below in conjunction with the accompanying drawings.
Space Rotating converting means of the present invention includes ectosphere 1 and interior ball 2, the lower external of described ectosphere 1
Face is supported by the outer buphthalmos wheels 12 on horizonal base plate 16 can realize all-direction rotation, and described outer buphthalmos is taken turns
Group 12 is made up of four buphthalmos wheels of the eight of outer ring buphthalmos wheels and inner ring；Described ectosphere 1 forward and backward,
It is respectively equipped with four supports 17 on left and right base plate 16, forward and backward, right support 17 passes through wheel carrier
Being respectively mounted three outer omni-directional wheels 3 contacted with the outer surface of ectosphere 1, each outer omni-directional wheel 3 is in identical
Horizontal plane on, this horizontal plane by the centre of sphere of ectosphere 1, rear outer omni-directional wheel 3 be horizontally disposed with and by
The handwheel 4 of concentric zones graduated disc drives, and outer omni-directional wheel 3 front, right is vertically arranged and is carved by concentric zones respectively
The handwheel 4 of scale drives, and left socle 17 arranges electric magnet 8, this electric magnet 8 height and outer omni-directional wheel
3 highly consistent, another electric magnet 8 is located on the base plate 16 bottom ectosphere 1, is positioned at the four of inner ring
Individual buphthalmos wheel center, as shown in Figure 1, Figure 2, Figure 3, Figure 4.
Described interior ball 2 is positioned and concentric with ectosphere 1 by the interior buphthalmos wheels 13 arranged on ectosphere 1 inner surface,
Described interior buphthalmos wheels 13 are made up of 12 buphthalmos wheels uniform on the inner surface of ectosphere 1；Described interior ball
2 with in the space of ectosphere 1 by wheel carrier further respectively have three contact with the inner surface of ectosphere 1 interior entirely
To wheel 11, three interior omni-directional wheels 11 are pointed to forward and backward, right outer omni-directional wheel 3, each interior omni-directional wheel respectively
One axle head of 11 installs motor 5, and another axle head installs encoder 6, as shown in Figure 1, Figure 2, Figure 5.
Middle vertical plane within described interior ball 2 is (with electric magnet 8 composition on support 17 and on base plate 16
Vertical coplanar) be provided with cross sleeve pipe 14, if the bottom of described cross sleeve pipe 14 vertical tube equipped with
The Magnet 7 of dry lamination, described Magnet 7 is pressed on the inner surface of interior ball 2 also by the spring 15 in vertical tube
Relative with the electric magnet 8 on base plate 16, the left part of cross sleeve pipe 14 transverse tube is equipped with the magnetic of some laminations
Ferrum 7, described Magnet 7 be pressed on the inner surface of interior ball 2 by the spring 15 in transverse tube and with support 17
On electric magnet 8 relative；The inner surface of described ectosphere 1 episphere is provided with three swashing towards interior ball 2
Light emission head 9, the beam direction of three laser beam emitting heads 9 forms orthogonal space, with three Laser emission
The position of 9 is corresponding, is respectively equipped with three laser pick-ofves 10 on the outer surface of interior ball 2 episphere,
Space orientation and the reset of ectosphere 1 and interior ball 2 is realized, as shown in Figure 1, Figure 2, Fig. 6 by 3 para-positions
Shown in.
The demonstration mode of the present invention:
1, fixed coordinate system (X, Y, Z) as shown in Figure 1 is set up.
Rotation hand wheel 4 drives omni-directional wheel 3 outside the right side to rotate, and drives ectosphere 1 to rotate, record handwheel 4
Graduated disc corner, is multiplied by the radius ratio of outer omni-directional wheel 3 and ectosphere 1, i.e. can be converted into ectosphere 1 around
The corner α of fixed coordinate system X-axis；Before rotation hand wheel 4 drives, outer omni-directional wheel 3 rotates, and drives ectosphere 1
Rotate, the graduated disc corner of record handwheel 4, be multiplied by the radius ratio of outer omni-directional wheel 3 and ectosphere 1,
I.e. can be converted into the ectosphere 1 corner β around fixed coordinate system Y-axis；Outer omni-directional wheel 3 after rotation hand wheel 4 driving
Rotate, and drive ectosphere 1 to rotate, the graduated disc corner of record handwheel 4, is multiplied by outer omni-directional wheel 3
With the radius ratio of ectosphere 1, i.e. can be converted into the ectosphere 1 corner γ around fixed coordinate system Z axis.
So far, complete once around the rotation transformation of X-axis-Y-axis-Z axis of fixed coordinate system, by formula
After RPY (α, beta, gamma)=Rot (Z, γ) Rot (Y, β) Rot (X, α) (1) can calculate ectosphere 1 rotation
Attitude matrix, and verified by ectosphere 1 attitude；To other rotation sequences around fixed coordinate system
Rank transformation, can change outer omni-directional wheel 3 successively and rotate order, such as: around the rotation of Y-axis-X-axis-Z axis sequence
Conversion, outer omni-directional wheel 3, right outer omni-directional wheel 3 and rear outer omni-directional wheel 3 before can rotating successively.
When 2, assuming initial, ectosphere 1 overlaps with the earth fixed coordinate system with moving coordinate system, uses motor 5
In after driving, omni-directional wheel 11 (corresponding with rear outer omni-directional wheel 3) rotates, and drives ectosphere 1 to rotate, and utilizes
The angle value that encoder 6 gathers is multiplied by interior omni-directional wheel 11 and the radius ratio of ectosphere 1, i.e. can be converted into ectosphere
1 around the corner γ of moving coordinate system Z axis；Omni-directional wheel 11 (front outer omni-directional wheel 3 in before using motor 5 to drive
Corresponding) rotate, and drive ectosphere 1 to rotate, the angle value utilizing encoder 6 to gather is multiplied by interior omni-directional wheel
11 with the radius ratio of ectosphere 1, i.e. can be converted into the ectosphere 1 corner β around moving coordinate system Y-axis；Use electricity
In machine 5 drives the right side, omni-directional wheel 11 (right outer omni-directional wheel 3 is corresponding) rotates, and drives ectosphere 1 to rotate, profit
The angle value gathered with encoder 6 is multiplied by the radius ratio of interior omni-directional wheel 11 and ectosphere 1, outside i.e. can be converted into
Ball 1 is around the corner α of moving coordinate system X-axis, so far, complete once around ectosphere 1 with moving coordinate system Z axis-Y
The rotational transform of axle-X-axis；By formula Euler (γ, β, α)=Rot (Z, γ) Rot (Y, β) Rot (X, α)
(2) the postrotational attitude matrix of ectosphere 1 can be calculated, verified by ectosphere 1 attitude.If
Motor 5 driving order can be changed successively, such as moving around other rotation sequence transformations of servo-actuated coordinate axes
The rotational transform of coordinate axes Y-X-Z sequence, interior omni-directional wheel 11, right interior omni-directional wheel 11 before can driving successively
With rear interior omni-directional wheel 11.
3, completing above two rotational transform, contrast two times result is identical, i.e. can verify that around fixing axle
The order rotated is contrary with the order rotated around servo axis, and when solid fixed-axis rotation, rotational transform matrix is from the right side
To premultiplication, when servo axis rotates, rotational transform matrix is taken advantage of from left to right, because of the angle correspondent equal rotated,
Therefore obtained transformation results is identical.
When 4, assuming initial, ectosphere 1 overlaps with the earth fixed coordinate system with moving coordinate system, now ectosphere 1
Position and attitude be defined as 1} system, arbitrarily rotates three handwheels 4 and drives the outer omni-directional wheel 3 of correspondence to rotate respectively,
Make ectosphere 1 have an arbitrary initial attitude, write down each handwheel 4 rotational angle, according in the 1st mode
Formula calculate ectosphere 1 initial attitude matrix, and now will be defined as { 0} system by ectosphere 1 position and attitude.Root
The rotational transform matrix calculated according to the 1st mode, its inverse matrix be 0} be tied to the rotational transform matrix of 1} system,
In this matrix the 3rd list show the unit vector on the Z axis of 1} system the component on three coordinate axess of 0} system,
Define this vector k=[kx ky kz]T.The Z axis assuming fixed coordinate system is an Equivalent Axis K, passes through
Control outer omni-directional wheel 3 make coordinate system the 0} system relative equivalent i.e. Z axis of rotating shaft K rotates θ angle, and now outside
Ball 1 attitude is defined as that { 2} system, { 0} is tied to that { the rotational transform matrix of 2} system is
In formula, s θ=sin θ, c θ=cos θ, vers θ=(1-cos θ).
Ectosphere 1 attitude also can rotate obtain by controlling three interior omni-directional wheels 11, in conjunction with formula (2) and
(3), calculating three rotational angles according to Inverse Kinematics Solution, backward drives interior omni-directional wheel 11 so that ectosphere
1 attitude returns to { 0} system；Again by driving three outer omni-directional wheels 3 or three interior omni-directional wheels 11 all can make
Time ectosphere 1 returns to initial 1} system, thus demonstrate and verify the relevant reason such as Equivalent Axis, effective rotation
Opinion.
Claims (7)
1. Space Rotating converting means, including concentric ectosphere (1) and interior ball (2), its feature exists
In also including ectosphere supporting mechanism, interior ball supporting mechanism, outer player's rotating mechanism, ectosphere rotation motivation
Structure, interior ball attitude maintaining body and interior ectosphere three-dimensional fix mechanism, wherein:
1., described ectosphere supporting mechanism includes the outer buphthalmos being supported in ectosphere (1) lower external face
Wheels (12)；
2. in, described interior ball supporting mechanism is included on ectosphere (1) inner surface layout and is supported in
Interior buphthalmos wheels (13) on ball (2) outer surface；
3. outside, described outer player's rotating mechanism includes that being arranged in ectosphere (1) drives the most to frictionally
Three outer omni-directional wheels (3) that ball (1) rotates rotating around X, Y, Z axis, each outer omni-directional wheel (3)
Being driven by coaxial mounted handwheel (4), each handwheel (4) is rotated by respective graduated disc record respectively
Angle；
4. outside, described ectosphere autorotation mechanism drives in including being arranged in ectosphere (1) to frictionally
Three interior omni-directional wheels (11) that ball (1) rotates rotating around X, Y, Z axis, each interior omni-directional wheel (11)
Encoder (6) the record rotation that the motor (5) installed by an axle head drives and installed by another axle head
Angle；
5., described interior ball attitude maintaining body is included on interior ball (2) bottom interior surface and in sidepiece
The Magnet (7) being respectively provided with on surface, is arranged with right outward corresponding to ectosphere (1) with each Magnet (7)
Answer the electric magnet (8) that Magnet (7) attracts each other；
6., described interior ectosphere three-dimensional fix mechanism is included on ectosphere (1) inner surface with space
Three laser beam emitting heads towards interior ball (2) (9) that quadrature position is installed, with each laser beam emitting head
(9) position is respectively mounted laser pick-off head (10) corresponding on interior ball (2) outer surface.
Space Rotating converting means the most according to claim 1, it is characterised in that: in three
The position of omni-directional wheel (11) corresponds respectively to the position of three outer omni-directional wheels (3).
Space Rotating converting means the most according to claim 2, it is characterised in that: outside three
Forward and backward position that omni-directional wheel (3) is arranged in same level and left or right position, this horizontal plane
It is in the biggest ball path position of ectosphere (1).
Space Rotating converting means the most according to claim 3, it is characterised in that: sidepiece
External magnet (8) is relative with the outer omni-directional wheel (3) of left or right position and puts.
5. according to the Space Rotating converting means described in any one in Claims 1 to 4, its feature
It is: described outer buphthalmos wheels (12) include eight buphthalmos wheels of outer ring and four buphthalmos wheels of inner ring；
Described interior buphthalmos wheels (13) include 12 buphthalmos wheels that space is uniform.
6. according to the Space Rotating converting means described in any one in Claims 1 to 4, its feature
It is: three laser beam emitting heads (9) are arranged on the episphere of ectosphere (1), corresponding,
Three laser pick-off heads (10) are arranged on the episphere of interior ball (2).
7. according to the Space Rotating converting means described in any one in Claims 1 to 4, its feature
It is: the middle vertical that described interior ball (2) is internal is provided with cross sleeve pipe (14), interior ball (2)
The internal magnet (7) of bottom is located at the bottom of vertical tube in cross sleeve pipe (14) and by the bullet in vertical tube
Spring (15) compresses, and horizontal stroke is located in cross sleeve pipe (14) by the internal magnet (7) of interior ball (2) sidepiece
The one end of pipe is also compressed by the spring (15) in transverse tube.
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| Application Number | Priority Date | Filing Date | Title |
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| CN201610596208.3A CN106023732B (en) | 2016-07-25 | 2016-07-25 | Space Rotating converting means |
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|---|---|---|---|
| CN201610596208.3A CN106023732B (en) | 2016-07-25 | 2016-07-25 | Space Rotating converting means |
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| CN106023732B CN106023732B (en) | 2018-07-17 |
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Cited By (5)
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| CN107137062A (en) * | 2017-06-29 | 2017-09-08 | 桂林电子科技大学 | The device and method of ability is known by the test mankind sense of equilibrium |
| CN107229345A (en) * | 2017-07-21 | 2017-10-03 | 河北科技大学 | Projection algorithm in two axle gyro ceremony motion storehouses |
| CN107305750A (en) * | 2017-07-21 | 2017-10-31 | 河北建研节能设备有限公司 | The two spherical storehouses of axle gyro ceremony fantasy sport |
| CN107356251A (en) * | 2017-07-21 | 2017-11-17 | 河北科技大学 | Method for testing motion in two axle gyro ceremony motion storehouses |
| CN107357319A (en) * | 2017-07-21 | 2017-11-17 | 河北科技大学 | Motion control method in two axle gyro ceremony motion storehouses |
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| CN107357319A (en) * | 2017-07-21 | 2017-11-17 | 河北科技大学 | Motion control method in two axle gyro ceremony motion storehouses |
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| CN106023732B (en) | 2018-07-17 |
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Application publication date: 20161012 Assignee: Cenxi Hengchuang Network Technology Co.,Ltd. Assignor: GUILIN University OF ELECTRONIC TECHNOLOGY Contract record no.: X2022450000246 Denomination of invention: Space rotation conversion device Granted publication date: 20180717 License type: Common License Record date: 20221206 |
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