CN110501117A - The rigid body for verifying solid moment of inertia perpendicular axis theorem is accurately positioned three-line pendulum - Google Patents
The rigid body for verifying solid moment of inertia perpendicular axis theorem is accurately positioned three-line pendulum Download PDFInfo
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- CN110501117A CN110501117A CN201910793392.4A CN201910793392A CN110501117A CN 110501117 A CN110501117 A CN 110501117A CN 201910793392 A CN201910793392 A CN 201910793392A CN 110501117 A CN110501117 A CN 110501117A
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01M—TESTING STATIC OR DYNAMIC BALANCE OF MACHINES OR STRUCTURES; TESTING OF STRUCTURES OR APPARATUS, NOT OTHERWISE PROVIDED FOR
- G01M1/00—Testing static or dynamic balance of machines or structures
- G01M1/10—Determining the moment of inertia
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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
- G09B23/06—Models for scientific, medical, or mathematical purposes, e.g. full-sized devices for demonstration purposes for physics
- G09B23/08—Models for scientific, medical, or mathematical purposes, e.g. full-sized devices for demonstration purposes for physics for statics or dynamics
- G09B23/10—Models for scientific, medical, or mathematical purposes, e.g. full-sized devices for demonstration purposes for physics for statics or dynamics of solid bodies
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Abstract
The invention discloses a kind of rigid bodies for verifying solid moment of inertia perpendicular axis theorem to be accurately positioned three-line pendulum, including pedestal, the upright bar being fixed on pedestal, it is fixed on the cross bar of upright bar upper end, upper disk, lower wall and three suspension wires between upper disk and lower wall, it further include the perpendicular axis theorem test block being placed on lower wall, perpendicular axis theorem test block is that there are two the thin plate-like objects of adjacent and orthogonal plane for periphery setting, alignment pin is correspondingly arranged in two planes of perpendicular axis theorem test block, lower wall is provided centrally with and the first pin shaft or the second pin shaft matches and axis is vertical with lower wall dowel hole;The configuration of the present invention is simple, easy to operate, rigid body registration conveniently do verifying solid moment of inertia perpendicular axis theorem, and the adjustable applicable various sizes of rigid body to be measured of three suspension wires, the volume and occupied space of three-line pendulum can be effectively reduced, to reduce cost.
Description
Technical field
The invention belongs to experiment of machanics instrument technical field more particularly to a kind of verifying solid moment of inertia perpendicular axis theorems
Rigid body be accurately positioned three-line pendulum.
Background technique
Three-line pendulum is in collegial physical examination for the common experiment of machanics instrument of Measuring Moment of Inertia Using, including branch
Frame, upper disk, lower wall and three suspension wires between upper disk and lower wall, wherein lower wall is used to place rigid body to be measured, using putting
The variation of rigid body front and back three-line pendulum rotation period to be measured and quality is set to measure the rotary inertia of object under test.
In current collegial physical examination, the verification test of the parallel-axis theorem of solid moment of inertia is generally all done, still
But the verification test of the perpendicular axis theorem of solid moment of inertia is not done, therefore, needs a kind of easy to operate and rigid body registration
Verifying solid moment of inertia perpendicular axis theorem rigid body be accurately positioned three-line pendulum test apparatus.
In addition, the size of rigid body to be measured is that the spatial dimension determined by three suspension wires limits on three-line pendulum, it is existing at present
The distance of three fixed points to lower disk center of the three-line pendulum suspension wire in technology be it is fixed, so the maximum ruler of rigid body to be measured
Very little is also fixed, therefore when the size of rigid body to be measured is beyond spatial dimension determined by three suspension wires, between meeting and suspension wire
Interfere, thus can not carry out using with measurement, cause test can not carry out;It can certainly be by the way that three-line pendulum be designed
It is larger to solve problem above, but the volume that will cause three-line pendulum in this way, which increases, occupied space increases, cost increases asks
Topic.
Summary of the invention
Technical problem to be solved by the invention is to provide a kind of structures to be simple and convenient to operate, rigid body registration is tested
Demonstrate,prove solid moment of inertia perpendicular axis theorem rigid body be accurately positioned three-line pendulum, and three suspension wires it is adjustable it is applicable it is various sizes of to
Rigid body is surveyed, the volume and occupied space of three-line pendulum can be effectively reduced, to reduce cost.
In order to solve the above technical problems, the technical scheme is that verifying the rigid of solid moment of inertia perpendicular axis theorem
Body be accurately positioned three-line pendulum, including pedestal, the upright bar being fixed on the pedestal, the cross bar for being fixed on the upright bar upper end, on
Disk, lower wall and three suspension wires between the upper disk and the lower wall, further include the vertical axis being placed on the lower wall
Theorem test block, the perpendicular axis theorem test block are that there are two the laminal objects of adjacent and orthogonal plane for periphery setting
Body is correspondingly arranged on the first pin shaft and the second pin shaft, first pin shaft in two planes of the perpendicular axis theorem test block
Axis mass center vertical and also with the perpendicular axis theorem test block with a wherein plane for the perpendicular axis theorem test block
Intersection, the axis of second pin shaft are vertical with another plane of the perpendicular axis theorem test block and also fixed with the vertical axis
Manage the mass center intersection of test block;
Being provided centrally with of the lower wall matches with first pin shaft or second pin shaft and axis and the lower wall
Vertical dowel hole;It is described to hang down after first pin shaft or second pin shaft are coupled with the dowel hole respectively
The projection of the mass center of the mass center of d-axis theorem test block and the lower wall in the horizontal plane is overlapped.
The surface of the perpendicular axis theorem test block is provided with for positioning the vertical axis as a preferred technical solution,
The hollow out witness marker of the mass center of theorem test block.
It as a preferred technical solution, further include being placed on the lower wall for covering the perpendicular axis theorem test block
Drop windage cover, the drop windage cover is the arc cover being centrosymmetric.
Mounting hole there are three being uniformly arranged on the outer peripheral surface of the lower wall as a preferred technical solution, three peaces
The center line for filling hole intersecting with any on the axial line of the lower wall, respectively corresponds to be equipped in three mounting holes and stretch
Contracting bar, the lower end of the suspension wire are fixedly connected on the outer end of the telescopic rod.
The cross bar includes the fixed rack being fixedly connected with the upright bar, the fixation as a preferred technical solution,
Movable rail is slidably fitted in sliding rail, the upper disk is fixedly mounted on the outer end of the movable rail.
By adopting the above-described technical solution, the rigid body of verifying solid moment of inertia perpendicular axis theorem is accurately positioned three lines
Pendulum including pedestal, the upright bar being fixed on the pedestal, the cross bar for being fixed on the upright bar upper end, upper disk, lower wall and is set to institute
Three suspension wires between disk and the lower wall are stated, further include the perpendicular axis theorem test block being placed on the lower wall, it is described
Perpendicular axis theorem test block is periphery setting there are two the thin plate-like object of adjacent and orthogonal plane, and the vertical axis is fixed
Manage and be correspondingly arranged on the first pin shaft and the second pin shaft in two planes of test block, the axis of first pin shaft with it is described vertical
A wherein plane for theorem of principal axes test block is vertical and also intersects with the mass center of the perpendicular axis theorem test block, second pin shaft
Axis is vertical with another plane of the perpendicular axis theorem test block and mass center phase also with the perpendicular axis theorem test block
It hands over;
Being provided centrally with of the lower wall matches with first pin shaft or second pin shaft and axis and the lower wall
Vertical dowel hole;It is described to hang down after first pin shaft or second pin shaft are coupled with the dowel hole respectively
The projection of the mass center of the mass center of d-axis theorem test block and the lower wall in the horizontal plane is overlapped;The beneficial effects of the present invention are:
One, since alignment pin and the corresponding matching of dowel hole are arranged, so that the perpendicular axis theorem test block can be with
It is supported and positions, the perpendicular axis theorem test block on the one hand can be supported and install, when on the other hand installing and under described
It is positioned between disk, accurate positioning, meets the test condition of rigid unit normal theorem of principal axes, verifying rigid unit normal theorem of principal axes can be done
Experiment, and during making test, operate simpler convenience, and verification test is more accurate;
Two, the telescopic rod can be protruding along the mounting hole, in the prior art do not have regulatory function phase
Than the space that three suspension wires of the invention are formed is adjustable, and applicable various sizes of rigid body to be measured can effectively reduce the body of three-line pendulum
Long-pending and occupied space increases the convenience used to reduce cost;
Three, the drop windage cover is covered on outside the perpendicular axis theorem test block and the test block support frame, it is described
Drop windage cover can effectively reduce the windage of the perpendicular axis theorem test block, improve the accuracy of test measurement;
Four, the configuration of the present invention is simple, easy to operate, rigid body registration, conveniently do verifying solid moment of inertia vertical axis
Theorem, and the adjustable applicable various sizes of rigid body to be measured of suspension wire, can effectively reduce the volume and occupied space of three-line pendulum, from
And reduce cost.
Detailed description of the invention
The following drawings are only intended to schematically illustrate and explain the present invention, not delimit the scope of the invention.Wherein:
Fig. 1 is the structural schematic diagram of the embodiment of the present invention;
Fig. 2 is the main view of the embodiment of the present invention;
Fig. 3 is the side view of the embodiment of the present invention;
Fig. 4 is the top view of the embodiment of the present invention;
Fig. 5 is the structural schematic diagram after installation drop windage cover of the embodiment of the present invention;
Fig. 6 is the structural schematic diagram of perpendicular axis theorem test block of the embodiment of the present invention;
Fig. 7 is the structural schematic diagram before telescopic rod of the embodiment of the present invention stretches out in mounting hole;
Fig. 8 is the structural schematic diagram after telescopic rod of the embodiment of the present invention stretches out in mounting hole;
In figure: 1- pedestal;2- upright bar;3- cross bar;31- fixed rack;32- movable rail;The upper disk of 4-;5- lower wall;51- is fixed
Position pin hole;52- mounting hole;53- telescopic rod;6- suspension wire;7- perpendicular axis theorem test block;The first pin shaft of 71-;The second pin shaft of 72-;
73- hollow out witness marker;74- plane;Windage cover drops in 8-.
Specific embodiment
With reference to the accompanying drawings and examples, the present invention is further explained.In the following detailed description, only pass through explanation
Mode describes certain exemplary embodiments of the invention.Undoubtedly, those skilled in the art will recognize, In
In the case where without departing from the spirit and scope of the present invention, described embodiment can be repaired with a variety of different modes
Just.Therefore, attached drawing and description are regarded as illustrative in nature, and are not intended to limit the scope of the claims.
Embodiment one:
As shown in Figures 1 to 4, the rigid body for verifying solid moment of inertia perpendicular axis theorem is accurately positioned three-line pendulum, including bottom
It seat 1, the upright bar 2 be fixed on the pedestal 1, the cross bar 3 for being fixed on 2 upper end of upright bar, upper disk 4, lower wall 5 and is set to described
Three suspension wires 6 between upper disk 4 and the lower wall 5, the pedestal 1 has supporting role, as the installation base body of the present embodiment,
The upper disk 4 is parallel with the lower wall 5 to be correspondingly arranged, and the upper disk 4 can be rotated relative to the cross bar 3, described for driving
Lower wall 5 rotates, wherein three suspension wires 6 are evenly arranged, and the upper disk 4 is connect with the lower wall 5, when the upper disk 4 rotates
When, it drives the lower wall 5 to rotate by suspension wire 6, realizes the rotation of rigid body to be measured, tested for realizing the measurement of rotary inertia;
It further include the perpendicular axis theorem test block 7 being placed on the lower wall 5, the perpendicular axis theorem test block 7 is provided with for periphery
The thin plate-like object of two adjacent and orthogonal planes, it is corresponding in two planes 74 of the perpendicular axis theorem test block 7
It is provided with alignment pin, for the plane 74 referring to Fig. 6, the alignment pin includes the first pin shaft 71 and the second pin shaft 72, described
The axis of first pin shaft 71 is vertical with a wherein plane for the perpendicular axis theorem test block 7 and also surveys with the perpendicular axis theorem
The mass center of test specimen 7 intersects, and the axis of second pin shaft 72 is vertical with another plane of the perpendicular axis theorem test block 7 and goes back
Intersect with the mass center of the perpendicular axis theorem test block 7;The lower wall 5 is provided centrally with and first pin shaft 71 or described
The dowel hole 51 that second pin shaft 72 matches and axis is vertical with the lower wall 5;First pin shaft 71 or second pin shaft
After 72 are coupled with the dowel hole 51 respectively, the mass center of the perpendicular axis theorem test block 7 and the mass center of the lower wall 5
Projection in the horizontal plane is overlapped.
In the present embodiment, in order to which the test for being able to achieve perpendicular axis theorem measures, the perpendicular axis theorem is theoretically required
Test block 7 does not have thickness, but since the rigid body of any physical presence all has thickness, it is impossible to there is the rigid of zero thickness
Body, and if thickness is excessive, perpendicular axis theorem will be cannot get, therefore thin plate-like object described in the present embodiment is very thin thickness
Thin plate rigid body, the thin plate-like object with a thickness of 2mm-10mm, the length of a plane is 100-150mm, another plane
Length be 160mm-200mm;There are two adjacent and orthogonal plane 74, two planes for the periphery tool of the thin plate-like object
74 setting can be used for measuring Jx and Jy, more convenient the thin plate-like object can be placed on the lower wall 5, be made
It is simple and convenient to obtain test process.
When test, the perpendicular axis theorem test block 7 is placed on the lower wall 5 first, it, will be described in placement process
The alignment pin of perpendicular axis theorem test block 7 is inserted into the dowel hole 51, then by rotating the upper disk 4, so that
The lower wall 5, the perpendicular axis theorem test block 7 being placed on the lower wall 5 rotation, to be surveyed to measure perpendicular axis theorem
The rotary inertia of test specimen 7;Since alignment pin and the corresponding matching of dowel hole 51 are arranged, so that the perpendicular axis theorem is tested
Part 7 can be supported and position, and the perpendicular axis theorem test block 7 on the one hand can be supported and install, when on the other hand installing
It is positioned between the lower wall 5, accurate positioning, so that operating simpler convenience, and verification test is more during test
It is accurate to add.
Referring to Fig. 6, the surface of the perpendicular axis theorem test block 7 is provided with for positioning the perpendicular axis theorem test block
The hollow out witness marker 73 of 7 mass center.In the present embodiment, the hollow out witness marker 73 is the circular hole of hollow out, certainly may be used
Think that other have the mark for facilitating mark mass center, such as there is cross intersection at the center of hollow out circular hole or irregularly-shaped hole
Bar, the center of cross crossbar are mass center, and such mode can be used for facilitating the position of mark mass center.Horizontal positioned
When the perpendicular axis theorem test block 7 measures rotary inertia, the hollow out witness marker 73 is aligned with the dowel hole, i.e.,
It can be convenient the center for the mass center of the perpendicular axis theorem test block 7 being directed at the lower wall 5, so that test process is simpler
It is convenient.
When the perpendicular axis theorem test block 7 is when upright, biggish air drag can be generated, is tested in order to prevent
Influence of the windage to the thin plate-like object in the process, therefore three-line pendulum further includes being placed on the lower wall 5 for covering institute
The drop windage cover 8 for stating perpendicular axis theorem test block 7, referring to Fig. 5, the drop windage cover 8 is the arc cover being centrosymmetric, institute
Stating drop windage cover 8 is transparent cover, can be used for facilitating the motion conditions of observation internal part.When test, by the drop windage
Cover 8 covers on outside the perpendicular axis theorem test block 7, and the drop windage cover 8 can effectively reduce the perpendicular axis theorem test
The windage of part 7 improves the accuracy of test measurement.
The perpendicular axis theorem test block 7 is made of heavy material, is made for example, by using metal materials such as iron, lead,
It can better lecture experiment effect.
The checking test method of perpendicular axis theorem:
Perpendicular axis theorem (being also perpendicular axis theorem) is a physics theorem, can be used to calculate the rotation of a plate sheet
Inertia.Think deeply a rectangular coordinate system in space, two of them reference axis is parallel to this thin slice;If it is known that this thin slice is relative to this
The rotary inertia of two reference axis, then perpendicular axis theorem can be used to calculate thin slice used relative to the rotation of third reference axis
Amount.Rectangular coordinate system in space is established to a thin slice, is located at this thin slice in xoy plane.Enable Jx, Jy, Jz difference thin slice phase thus
For the rotary inertia of x, y, z axis, then there is Jz=Jx+Jy.
Verify the experimental procedure of perpendicular axis theorem:
Step 1: the first pin shaft 71 (or second pin shaft 72) of perpendicular axis theorem test block 7 is first inserted into the lower wall 5
In dowel hole 51, so that perpendicular axis theorem test block 7 is mounted on lower wall 5, the mass center of perpendicular axis theorem test block 7 is under
The center of disk 5 is aligned, and at this moment rotary shaft is parallel to 7 place plane of perpendicular axis theorem test block;
Step 2: then covering drop windage cover 8, the rotary inertia of 7 current location of perpendicular axis theorem test block is measured, this
Rotary inertia is set as Jx.
Step 3: the second pin shaft 72 (or first pin shaft 71) of perpendicular axis theorem test block 7 is inserted into the lower wall 5 again
In dowel hole 51, so that perpendicular axis theorem test block 7 is mounted on lower wall 5, the mass center of perpendicular axis theorem test block 7 is under
The center of disk 5 is aligned, and at this moment rotary shaft is parallel to 7 place plane of perpendicular axis theorem test block;
Step 4: then covering drop windage cover 8, the rotary inertia of 7 current location of perpendicular axis theorem test block is measured, this
Rotary inertia is set as Jy.
Step 5: perpendicular axis theorem test block 7 is removed from lower wall 5 again, then perpendicular axis theorem test block 7 is laid flat
On lower wall 5, the center of the mass center alignment lower wall 5 of perpendicular axis theorem test block 7, at this moment rotary shaft is surveyed perpendicular to perpendicular axis theorem
7 place plane of test specimen, then tests the rotary inertia of 7 current location of current vertical theorem of principal axes test block, this rotary inertia is
Jz。
Step 6: finally comparing the numerical value between Jz and Jx+Jy, if data are coincide preferably, so that it may determine vertical axis
Theorem is that correctly, the verification process of perpendicular axis theorem is completed.
Embodiment two:
Embodiment second is that further improved on the basis of example 1 to the lower wall 5 and the cross bar 3,
Therefore, details are not described herein for the part being the same as example 1, and only the lower wall 5 and the cross bar 3 are specifically described.
Referring to figs. 7 and 8, mounting hole 52 there are three being uniformly arranged on the outer peripheral surface of the lower wall 5, three mounting holes
52 center line intersecting with any on the axial line of the lower wall 5, respectively corresponds and is equipped in three mounting holes 52
Telescopic rod 53, the lower end of the suspension wire 6 are fixedly connected on the outer end of the telescopic rod 53, since the telescopic rod 53 can be in institute
Sliding in mounting hole 52 is stated, therefore, in use, the telescopic rod 53 can be manually adjusted relative to 5 outer peripheral surface of lower wall
Extended position, when the telescopic rod 53 is shorter relative to the extension elongation of 5 outer peripheral surface of lower wall, referring to Fig. 7, in this way, three
The space that root suspension wire 6 is formed is smaller, can be used for measuring size lesser test block, when the telescopic rod 53 is relative under described
When the extension elongation of 5 outer peripheral surface of disk is longer, it can be used for measuring scale in this way, the space that three suspension wires 6 are formed is larger referring to Fig. 8
Very little biggish test block, in adjustment process, it is ensured that the extension elongation of three telescopic rods 53 be it is identical, guarantee it is described under
Disk 5 is horizontal, for guaranteeing to measure accuracy.The telescopic rod 53 can be protruding along the mounting hole 52, with
It is compared in the prior art without regulatory function, the space that three example suspension wires 6 of this implementation are formed is adjustable, applicable various sizes of
Rigid body to be measured, can effectively reduce the volume and occupied space of three-line pendulum, to reduce cost, increase the convenience used.
When the extension elongation of the telescopic rod 53 is longer, the telescopic rod 53 or tested rigid body are stood with described in order to prevent
It causes to interfere between bar 2, therefore further the cross bar 3 is designed.Referring to fig. 4, the cross bar 3 includes standing with described
The fixed rack 31 that bar 2 is fixedly connected is slidably fitted with movable rail 32, the fixed peace of upper disk 4 in the fixed rack 31
Mounted in the outer end of the movable rail 32, the movable rail 32 can be slided along the fixed rack 31, when described flexible
When the extension elongation of bar 53 is longer, while the movable rail 32 is adjusted, so that the movable rail 32 is relative to the fixation
Sliding rail 31 moves out, i.e., so that the upper disk 4 is moved away from 2 direction of upright bar, in this way, the lower wall 5 is also by band
It is dynamic to be moved far from the upright bar 2, it is possible to prevente effectively from causing to interfere between the telescopic rod 53 and the upright bar 2.
The configuration of the present invention is simple, easy to operate, rigid body registration, conveniently to do verifying solid moment of inertia vertical axis fixed
Reason, and the adjustable applicable various sizes of rigid body to be measured of suspension wire, can effectively reduce the volume and occupied space of three-line pendulum, thus
Reduce cost.
The above shows and describes the basic principle, main features and advantages of the invention.The technology of the industry
Personnel are it should be appreciated that the present invention is not limited to the above embodiments, and the above embodiments and description only describe this
The principle of invention, without departing from the spirit and scope of the present invention, various changes and improvements may be made to the invention, these changes
Change and improvement all fall within the protetion scope of the claimed invention.The claimed scope of the invention by appended claims and its
Equivalent thereof.
Claims (5)
1. the rigid body for verifying solid moment of inertia perpendicular axis theorem is accurately positioned three-line pendulum, including pedestal, is fixed on the pedestal
On upright bar, cross bar, upper disk, lower wall and three between the upper disk and the lower wall of being fixed on the upright bar upper end
Suspension wire, it is characterised in that: further include the perpendicular axis theorem test block being placed on the lower wall, the perpendicular axis theorem test block
It is periphery setting there are two the thin plate-like object of adjacent and orthogonal plane, two of the perpendicular axis theorem test block are flat
Its of the first pin shaft and the second pin shaft, the axis of first pin shaft and the perpendicular axis theorem test block are correspondingly arranged on face
In a plane it is vertical and also intersect with the mass center of the perpendicular axis theorem test block, the axis of second pin shaft with it is described vertical
Another plane of theorem of principal axes test block is vertical and also intersects with the mass center of the perpendicular axis theorem test block;
Being provided centrally with of the lower wall matches with first pin shaft or second pin shaft and axis is vertical with the lower wall
Dowel hole;After first pin shaft or second pin shaft are coupled with the dowel hole respectively, the vertical axis
The projection of the mass center of the mass center of theorem test block and the lower wall in the horizontal plane is overlapped.
2. the rigid body of verifying solid moment of inertia perpendicular axis theorem is accurately positioned three-line pendulum, feature as described in claim 1
Be: the surface of the perpendicular axis theorem test block is provided with the hollow out of the mass center for positioning the perpendicular axis theorem test block
Witness marker.
3. the rigid body of verifying solid moment of inertia perpendicular axis theorem is accurately positioned three-line pendulum, feature as described in claim 1
It is: further includes being placed on the lower wall for covering the drop windage cover of the perpendicular axis theorem test block, the drop windage
Cover is the arc cover being centrosymmetric.
4. the rigid body of the verifying solid moment of inertia perpendicular axis theorem as described in claims 1 to 3 any claim is accurately fixed
Position three-line pendulum, it is characterised in that: be uniformly arranged on the outer peripheral surface of the lower wall there are three mounting hole, in three mounting holes
Heart line intersecting with any on the axial line of the lower wall, respectively corresponds in three mounting holes and is equipped with telescopic rod, institute
The lower end for stating suspension wire is fixedly connected on the outer end of the telescopic rod.
5. the rigid body of verifying solid moment of inertia perpendicular axis theorem is accurately positioned three-line pendulum, feature as claimed in claim 4
Be: the cross bar includes the fixed rack being fixedly connected with the upright bar, and movable cunning is slidably fitted in the fixed rack
Rail, the upper disk are fixedly mounted on the outer end of the movable rail.
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