KR101812519B1 - Elevator for Egg Stacking - Google Patents

Abstract

 A support frame, a pedestal supporting one end portion of the support frame so as to be movable up and down, and a pedestal supporting member for supporting the pedestal above the pedestal base so as to maintain the work height during the laminating operation and solidly laminate, A mounting sensor for detecting whether or not an egg plate is mounted at a predetermined height above a horizontal rotating table; a moving platform for moving the platform vertically; and a mounting sensor for detecting the mounting of the egg plate, And a controller for transmitting a control signal for driving the up-and-down exercise device in accordance with a detection signal of the on-board sensor, wherein the elevator includes an elevator for elevating the egg, Lt; / RTI >

Description

[0001] Elevator for Egg Stacking [

The present invention relates to an elevator for stacking eggs, and more particularly, to an elevator for stacking eggs, and more particularly, to an elevator for stacking eggs, The present invention relates to an elevator for stacking eggs.

Generally, an egg plate used for loading a plurality of eggs is mainly used in an egg plate formed by stacking five eggs and six rows in an egg plate. The egg plate is used most frequently, and a variety of eggs such as 5 rows × 2 rows, 5 rows × 3 rows, Egg plates that can load eggs in quantity are often used.

The egg plate has a structure in which collapsing does not occur when eggs are stacked with layers at several stages without the eggs colliding with each other as the eggs are stacked.

Eggs produced in poultry houses are stacked on the egg board at the time of shipment and many layers of stacking work are carried out. In this way, stacking the eggs one by one is a very difficult task.

In other words, as the egg board loaded with the eggs is transported by the conveyor in the process of shipping the eggs, the operator moves the egg board one by one to the nearby bed, etc. and stacks them on the 5th and 10th floors. And the work height is continuously increased as the number of layers of the egg plate is increased, so that there is a problem that the body such as the legs, the waist, and the arms of the worker is overloaded.

Open Patent Publication No. 1994-0025898 discloses a stacking apparatus for an egg plate which is capable of continuous operation until a predetermined number of egg plates containing eggs are stacked and stacked when the eggs are sorted by size into an egg plate .

However, in the laminating apparatus for the egg plate disclosed in Japanese Laid-Open Patent Publication No. 1994-0025898, the operator has to manually press the foot switch every time to lower the seat, so that the operation is troublesome.

It is difficult to change the number of layers of the egg plate, and it is difficult to lower the plate at an accurate height corresponding to the height of the work according to the increase of the number of layers.

In addition, in order to maintain a solid laminate structure of the egg plate, the egg plate must be rotated by 90 degrees for each layer, and the worker has to rotate the egg plate one by one.

SUMMARY OF THE INVENTION Accordingly, the present invention has been made to solve the above problems occurring in the prior art, and it is an object of the present invention to provide a method and apparatus for automatically stacking eggs, And an object of the present invention is to provide an elevator for egg stacking capable of always maintaining a working height.

Another object of the present invention is to provide an elevator for stacking eggs, which is easy to work and can improve a working speed because the egg is automatically rotated by 90 ° every time the eggs are stacked.

The elevator for egg stacking proposed by the present invention comprises a support frame, a platform on which the one end portion of the support frame is supported so as to be vertically movable, a horizontal swivel base horizontally rotatable above the platform, A vertical movement device installed to move the platform vertically and to lower the platform by a predetermined height when the mounting sensor detects the mounting of the egg plate; And a controller for transmitting a control signal for driving the up-and-down movement device and the horizontal rotation device according to a detection signal of the on-board detection sensor.

The up-and-down movement device includes a drive motor for driving forward or reverse rotation, an up-down drive mechanism for converting the forward rotation and the reverse rotation drive of the drive motor into a vertical movement, And a detection sensor.

The up-and-down driving mechanism includes a driving wheel rotatably installed at an upper end portion or a lower end portion of the platform and rotated by receiving a rotational force of the driving motor, And a track member which is wound on the driving wheel and the driven wheel, orbits, and is connected to the platform.

The up-and-down movement device may further include a top-end sensor for detecting a top end position of the platform, and may further include an elevation driving switch for driving the driving motor in a reverse direction to raise the platform manually .

The horizontal rotation device rotates the horizontal swivel by 90 ° as the mounting detection sensor senses the mounting of the egg plate.

The horizontal rotation device includes a driving motor for driving rotation, a horizontal rotation shaft rotated by driving of the driving motor and integrally connected to the horizontal rotation unit, and an angle detection sensor installed to sense the position of the horizontal rotation unit .

The drive motor is configured to be capable of forward rotation or reverse rotation drive.

The horizontal rotary device may further include a plurality of support holes for supporting and supporting the horizontal rotation table at a predetermined height from the platform.

The horizontal rotating device may further include a rotation driving switch for rotating the driving motor so as to manually rotate the horizontal rotating table.

Wherein the controller senses the mounting of the egg plate on the mounting sensor and rotates the driving motor of the up-and-down movement device in the forward direction to lower the platform, and when detecting the position of the platform by the down- Stopping the descent of the platform by stopping the rotation of the motor and repeating the descending and stopping operations of the platform so that the platform is rotated in the reverse direction to raise the platform to the uppermost position when the number of times of descent satisfies the set value.

As the controller senses the mounting of the egg plate on the mounting sensor, the controller rotates the driving motor of the horizontal rotating unit to rotate the horizontal rotating unit. When the angle detecting sensor senses the position of the horizontal rotating unit, The rotation of the horizontal rotation axis is stopped by stopping the driving of the motor, and when the rotation of the horizontal rotation axis is stopped and then rotated again, the rotation direction of the driving motor is controlled so as to rotate in the direction opposite to the rotation direction immediately before.

According to the elevator for stacking eggs according to the embodiment of the present invention, since the platform is automatically lowered each time the elevator is mounted so that the elevation of the elevator does not increase due to the increase in the number of laminated layers, This is possible.

According to the elevator for stacking eggs according to the embodiment of the present invention, since the egg plate with the eggs is detected, the egg plate is automatically lowered, the height is lowered to the correct height, and the number of stacks can be adjusted. And it is possible to improve the workability.

Further, according to the elevator for stacking eggs according to the embodiment of the present invention, each stacked egg plate is rotated 90 ° in the direction opposite to the direction of previous rotation every time when one egg plate is mounted, so that the stacked structure of the egg plate is maintained It is possible to do.

1 is a perspective view showing an elevator for stacking eggs according to a first embodiment of the present invention.
2 is a side view showing an elevator for stacking eggs according to a first embodiment of the present invention.
3 is a block diagram showing an elevator for stacking eggs according to a first embodiment of the present invention.
4 is a side sectional view showing an elevator for stacking eggs according to the first embodiment of the present invention.
5 is a front view showing an elevator for stacking eggs according to the first embodiment of the present invention.
6 is a side sectional view showing a supporting frame and a platform in an elevator for stacking eggs according to the first embodiment of the present invention.
7 is a plan sectional view showing a supporting frame and a platform in an elevator for stacking eggs according to the first embodiment of the present invention.
FIG. 8 is a side view showing a sensor for detecting a falling edge in the elevator for stacking eggs according to the first embodiment of the present invention. FIG.
FIG. 9 is a side view showing the portion to be detected in the elevator for stacking eggs according to the first embodiment of the present invention. FIG.
10 is a side sectional view showing a horizontal rotary device in an elevator for stacking eggs according to a first embodiment of the present invention.
11 is a partial plan view showing a horizontal rotary device in an elevator for stacking eggs according to the first embodiment of the present invention.
12 is an operational state diagram showing a horizontal rotary device in an elevator for stacking eggs according to the first embodiment of the present invention.
13 is a front view of the operating state of the elevator for stacking eggs according to the first embodiment of the present invention, in which the egg plate is mounted as one layer.
14 is an operating state side view showing a state in which the egg plate is mounted as two layers in the elevator for stacking eggs according to the first embodiment of the present invention.
15 is a front view of the operating state of the elevator for stacking eggs according to the first embodiment of the present invention, in which the egg plate is mounted in 10 layers.
16 is an operating state side view showing a state in which the egg plate is mounted in 10 layers in the elevator for stacking eggs according to the first embodiment of the present invention.
17 is a flowchart showing an operation process of the elevator for stacking eggs according to the first embodiment of the present invention.

Next, a preferred embodiment of the elevator for stacking eggs according to the present invention will be described in detail with reference to the drawings.

In the following description, the same reference numerals are used for the same technical elements, and detailed descriptions for avoiding redundant description are omitted.

The embodiments described below are intended to illustrate the preferred embodiments of the present invention in an effective manner and should not be construed to limit the scope of the present invention.

1 to 5, the elevator for stacking eggs according to the first embodiment of the present invention includes a supporting frame 100, a platform 200, a horizontal swivel 300, a mounting detection sensor 400, a controller 410, a vertical movement device 500, and a horizontal rotation device 600.

The support frame 100 is installed at a predetermined height on the ground.

The platform (200) is supported on the support frame (100) at the rear end thereof and has a cantilever structure.

The platform 200 may have a substantially rectangular planar shape, and may have various flat shapes other than a rectangular shape.

6 and 7, the platform 200 includes a horizontal plate 201 horizontally installed on the ground, and a pair of vertically curved upper and lower portions formed on both sides of the horizontal plate 201 And a front vertical plate 203 formed by bending vertically downward from the opposite end edge of the horizontal plate 201 opposite to the support frame 100.

The lateral vertical plate 202 is formed so as to gradually increase in vertical width from the front side (the front vertical plate 203 side) to the rear side (the support frame 100 side).

The rear end of the platform 200 is supported by the support frame 100 so as to be vertically movable.

One end of the platform 200 is coupled to the support frame 100 using a linear motion guide 210 so as to be vertically slidable.

A pair of wheels 220 rotating in a rolling contact with the support frame 100 may be further installed at the rear end of the platform 200 when the platform 200 is moved up and down.

The wheels 220 can be installed at the rear ends of the pair of side vertical plates 202 of the platform 200.

The horizontal swivel (300) is horizontally rotatable above the platform (200).

The horizontal swivel (300) has a plate shape and is installed substantially horizontally on the ground.

On the horizontal swivel (300), an egg plate (2) on which an egg (1) is mounted is mounted.

The upper edge of the horizontal swivel 300 may be further provided with a rim for preventing slippage and separation of the egg plate 2.

The mounting detection sensor 400 senses whether or not the egg plate 2 is mounted on the horizontal swivel 300 at a predetermined height.

That is, whether or not the egg plate 2 is present in the predetermined sensing area on the horizontal swivel 300.

The mount detection sensor 400 is a photo sensor and is installed at an upper end portion of the support frame 100.

In addition to the photo sensor, the mount detection sensor 400 may include a sensor and a camera configured to detect whether an object exists in a predetermined sensing area.

The up-and-down exercise device 500 moves up and down the platform 200 and is installed to lower the platform 200 by a predetermined height when the placement sensor 400 senses the placement of the egg plate 2.

The up-and-down movement device 500 includes a drive motor 501 for forward rotation or reverse rotation drive, a vertical drive mechanism 510 for converting the forward rotation and reverse rotation drive of the drive motor 501 into vertical movement, A falling edge detecting sensor 520 installed to detect the falling position of the platform 200 at a predetermined interval and a rising edge detecting sensor 530 detecting the top edge of the platform 200. [

The drive motor 501 may be a servo motor.

The vertical movement mechanism 510 includes a driving wheel 512 rotatably installed at an upper end portion or a lower end portion of the platform 200 and rotated by receiving the rotational force of the driving motor 501, A driven wheel 514 which is rotatably installed on the opposite end of the driving wheel 512 of the driving wheel 100 and a driven wheel 514 which is wound around the driven wheel 512 and the driven wheel 514 to orbit, (516).

The driving wheel 512 and the driven wheel 514 may each be a sprocket wheel, and the raceway member 516 may be a chain.

It is also possible that two of the driving wheel 512 and the driven wheel 514 are provided on one axis and two of the raceway members 516 are also provided.

Although not shown in the drawings, the driving wheel 512 and the driven wheel 514 may be formed of a belt pulley or a roller, and the raceway member 516 may be formed of a belt, a rope or the like.

The raceway member 516 is connected to the platform 200 in a section between the upper wheel 512 and the lower wheel 514 during orbital motion and is installed to move the platform 200 up and down.

The falling edge detection sensor 520 may be an ultrasonic sensor, or may be an optical sensor, a limit switch, or the like.

As shown in FIGS. 8 and 9, on the support frame 10, a sensing unit 522 for sensing the position of the falling-edge detection sensor 520 is installed at a predetermined interval.

The sensing part 522 is formed of a groove or the like and is installed at a predetermined interval along the vertical direction of the support frame 100.

A plurality of the to-be-sensed portions 522 are installed with a spacing difference corresponding to the inter-layer height of the egg plate 2 on which the layers are stacked, and the to-be-sensed portions 522 located at the lowermost portion are spaced apart Respectively.

The interlayer height is, for example, one height of the egg plate 2.

The ascending end detecting sensor 530 is installed at the upper end of the supporting frame 100 and detects the position (height) of the platform 200 when the platform 200 is lifted.

The rising-edge detecting sensor 530 may be an ultrasonic sensor, an optical sensor, a limit switch, or the like.

The up-and-down movement device 500 may further include an elevation driving switch 550 for reversely rotating the driving motor 501 to manually elevate the platform 200.

The elevation drive switch 550 is installed at the upper end of the support frame 100.

The elevation drive switch 550 is installed to elevate the platform 200 regardless of the descending position of the platform 200.

The horizontal rotation device 600 horizontally rotates the horizontal rotation platform 300.

The horizontal rotary device 600 is installed to rotate the horizontal rotary table 300 by 90 ° once.

10 and 11, the horizontal rotating device 600 includes a driving motor 601 that rotates and drives the driving motor 601 to rotate integrally with the horizontal rotating bar 300 A plurality of support holes 620 for supporting and supporting the horizontal rotation table 300 at a predetermined height from the platform 200 and a plurality of support holes 620 for sensing the rotation angle And an angle detection sensor 630 installed to detect the angle of the vehicle.

The driving motor 601 is configured to be capable of forward rotation and reverse rotation.

The drive motor 601 may be a servo motor or the like.

The horizontal rotation shaft 610 is rotatably supported on the platform 200.

The driving motor 601 can rotate the horizontal rotary shaft 610 through gear transmission, chain transmission, belt transmission, or the like.

For example, the driving motor 601 rotates the rotating shaft 610 through the bevel gear 612.

The support hole 620 is formed to support a load applied to the horizontal swivel 300 and to maintain horizontal and minimize friction during rotation.

The support hole 620 is formed of a ball caster and is provided along the horizontal rotation axis 610.

The support hole 620 is installed at 3 to 5 positions along the outer end of the horizontal swivel 300.

The angle sensor 630 may be an ultrasonic sensor, and may be an optical sensor, a limit switch, or the like.

The angle sensor 630 is installed in the platform 200.

Sensing units 632 for sensing the position of the angle sensing sensor 630 are installed at the horizontal rotation axis 300 or the horizontal rotation axis 610 at predetermined intervals.

The object to be detected 632 may be a protrusion, a groove, or the like.

The sensing unit 632 is installed at intervals of 90 degrees along the circumference of the horizontal rotation axis 610.

The horizontal rotating device 600 may further include a rotation driving switch 650 for rotating the driving motor 650 to manually rotate the horizontal rotating table 300.

The rotation drive switch 650 is installed at the upper end of the support frame 100.

The rotation drive switch 650 can rotate the horizontal swivel 300 regardless of whether the egg plate 2 is mounted or not.

The controller 700 transmits a control signal for driving the up-and-down motion device 500 and the horizontal rotation device 600 according to a detection signal of the on-board detection sensor 400.

The controller 700 senses the mounting of the egg plate 2 on the mounting sensor 400 and rotates the driving motor 501 of the up-and-down moving device 500 to lower the platform 200 .

The controller 700 senses the position of the platform 200 in the lower stage detection sensor 520 and stops the rotation of the driving motor 501 to stop the descent of the platform 200.

In the controller 700, when the lowering and stopping operations of the platform 200 are repeated and the lowered number of times satisfies the set value, the controller 700 reversely rotates the driving motor 501 to raise the platform 200 to the uppermost position .

In addition, the controller 700 controls the horizontal swivel 300 to rotate in different directions (clockwise and counterclockwise) each time the mounting sensor 400 detects the mounting of the egg plate 2 It is also possible to control.

That is, as shown in FIG. 11, the controller 700 detects the mounting of the egg plate 2 on the mounting detection sensor 400 and rotates the driving motor 601 of the horizontal rotary device 600 The driving of the driving motor 601 is stopped by rotating the horizontal swivel 300 and detecting the position (angle) of the horizontal swivel 300 from the angle detection sensor 620, It is also possible to control the rotation direction of the driving motor 601 so as to rotate in the direction opposite to the immediately preceding rotation direction when the rotation of the horizontal rotation table 300 is stopped and then rotated again.

When the controller 700 is installed as described above, it is possible to rotate the horizontal swivel 300 in 90 ° increments each time the egg plate 2 is mounted on the horizontal swivel 300.

12, when one layer of the egg plate 2 is mounted, the horizontal swivel 300 is rotated 90 ° clockwise, and when the next layer is mounted, the horizontal swivel 300 is rotated 90 ° counterclockwise .

When the horizontal plate 300 is rotated by 90 degrees in the different direction every time the plate 2 is mounted, the plate 2 can be prevented from being weakened by the inertia action Do.

In other words, when the egg plate 2 starts rotating or the rotating egg plate 2 is stopped, inertia acts to cause twisting, tilting and the like. At this time, the egg plate 2 is continuously rotated by 90 degrees However, if the horizontal swivel 300 is rotated by 90 degrees in the other direction each time, the direction of action of the inertia changes each time, thereby minimizing the occurrence of twisting or tilting. It is possible to do.

Next, operation of the elevator for stacking eggs according to the first embodiment of the present invention will be described with reference to the drawings.

The number of layers to be stacked before the egg board 2 loaded with the egg 1 is stacked on the platform 200 is set and a set value is input to the controller 700 corresponding to the set stacking number.

After the operator inputs a set value to the controller 700 as described above and the operator places one egg plate 2 on which the egg 1 is loaded on the horizontal swivel 300, The upper and lower moving apparatus 500 and the horizontal rotating apparatus 600 are operated while the egg plate 2 is detected and the lowering of the platform 200 and the rotation of the horizontal rotating table 300 are performed by 90 °. )

When the mounting sensor 400 senses the mounting of the egg plate 2, the driving motor 501 rotates, and accordingly, the up and down movement mechanism 500 The wheel 512 and the driven wheel 514 and the raceway member 516 rotate while the platform 200 descends by the raceway member 516 and the descending stage detection sensor 520 is rotated by the plurality of detected portions 522 The driving motor 501 stops rotating and the descent of the platform 200 is stopped.

When the mounting sensor 400 detects the mounting of the egg plate 2, the driving motor 601 rotates, and the horizontal swivel 300 is moved in one direction The angle sensing sensor 530 senses the sensing part 532 and stops the rotation of the horizontal rotation table 300 while the driving motor 601 stops the rotation.

When the operator places the egg plate 2 on which the egg 1 is placed on the horizontal swivel 300 and stacks the egg plate 2 in two layers in the above state, As the egg plate 2 is detected again, the vertical movement device 500 and the horizontal rotation device 600 are operated again to further lower the platform 200 and rotate the horizontal rotation platform 300 by 90 degrees. 13 and 14)

The operation of the up-and-down movement device 500 when the egg plate 2 is mounted with the two-layer mounting sensor 400 as described above is the same as the operation of the up-and-down motion device 500, 522), the detailed description thereof will be omitted.

The operation of the horizontal rotary device 600 is the same as the operation of the horizontal rotary device 600 except that the angle detecting sensor 630 detects the first to sixth sensing units 632 The same process as the first process is performed, so that detailed description will be omitted.

The controller 700 controls the driving motor 601 of the horizontal rotary apparatus 600 so that the horizontal rotary table 300 is rotated in the opposite direction to the immediately preceding rotary direction every time the egg plates 2 are mounted one by one, .

In the controller 700, each time the egg plate 2 is mounted one by one, it is determined whether the falling number (falling number of times) of the platform 200 satisfies the set value. When the controller 700 satisfies the set value The driving motor 501 of the up-and-down exercise device 500 is rotated in the reverse direction so as to raise the platform 200 to the uppermost start position.

For example, when the egg plate 2 on which the eggs 1 are stacked is stacked in 10 layers, if the set value is input to the controller 700 so that the platform 200 is raised to the home position, the operator moves the tenth egg plate 2 When the elevating platform 200 is lowered and the descending stage detecting sensor 520 senses the position of the eleventh elevating platform, when the elevating platform 200 is stopped for the tenth time, the driving motor 501 of the up-and- As the elevating platform is raised, the elevating stage detecting sensor 540 senses the position of the platform 200 and stops the reverse rotation of the driving motor 501 Is completed. (See Figs. 15 to 17)

Meanwhile, the elevating platform 200 can raise the driving motor 501 by reversing the elevation driving switch 550 irrespective of the number of falling stages.

The egg plate (2) stacked in 10 layers on the platform (200) is unloaded by the operator and the laminating operation is completed once.

1: Egg 2: Egg plate
100: support frame 200: platform
300: Horizontal swivel 400: Mounting detection device
500: Up and down movement device 501: Drive motor
510: Up and down driving mechanism 520:
540: rising edge detection sensor 550: elevation driving switch
600: Horizontal rotating device 601: Driving motor
610: Horizontal rotating shaft 620:
630: Angle detection sensor 650: rotation drive switch
700: controller

Claims (12)

A support frame 100,
A pedestal 200 having one end supported by the support frame 100 so as to be vertically movable,
A horizontal swivel 300 mounted horizontally above the platform 200,
A mounting detection sensor 400 for detecting the presence or absence of the mounting of the egg plate 2 on the horizontal swivel 300,
A vertical movement device 500 installed to lower the platform 200 by a predetermined height when the platform 200 is moved up and down and the mounting sensor 400 detects the mounting of the egg plate 2,
A horizontal rotation device 600 for rotating the horizontal swivel 300 by 90 degrees as the mounting detection sensor 400 senses the mounting of the egg plate 2,
And a controller (700) for transmitting a control signal for driving the up-and-down motion device (500) and the horizontal rotation device (600) according to a detection signal of the on-
The up-and-down movement device 500 includes a drive motor 501 that is driven to rotate forward or backward, an up-and-down drive mechanism 510 that converts forward and reverse rotation of the drive motor 501 into up and down movements, A falling edge detection sensor 520 installed to detect the position of the platform 200 at predetermined intervals, and a lower edge detection sensor 520 installed at a predetermined interval along the vertical direction of the support frame 100, A lift sensor 530 for sensing the uppermost position of the platform 200 and a drive motor 501 for manually lifting the platform 200 The controller 700 detects the mounting of the egg plate 2 in the mounting sensor 400 and rotates the driving motor 501 in the normal direction The elevating platform 200 is lowered, and the lower stage detecting sensor 520 As the position of the platform 200 is sensed, the rotation of the driving motor 501 is stopped to stop the descent of the platform 200, and the descent and the stop operation of the platform 200 are repeated, The controller controls the driving motor 501 to rotate in the reverse direction to raise the platform 200 to the uppermost position,
The up-and-down driving mechanism 510 includes a driving wheel 512 rotatably installed at an upper end portion or a lower end portion of the platform 200 and rotated by receiving the rotational force of the driving motor 501, A driven wheel 514 which is rotatably installed on the opposite end of the driving wheel 512 of the driving wheel 100 and a driven wheel 514 which is wound on the driving wheel 512 and the driven wheel 514 and orbital motion, And a track member (516)
The horizontal rotating device 600 includes a driving motor 601 driven for forward or reverse rotation and a horizontal rotating shaft 610 rotated by driving of the driving motor 601 and integrally connected to the horizontal rotating table 300. [ An angle sensing sensor 630 installed to sense the position of the horizontal swivel 300 and a rotation driving switch 650 for rotationally driving the driving motor 601 to rotate the horizontal swivel 300 manually, The controller 700 rotates the driving motor 601 in a different direction each time the mounting sensor 400 senses the mounting of the egg plate 2 to rotate the horizontal rotating table 300 The driving of the driving motor 601 is stopped to stop the rotation of the horizontal rotation unit 300 and the rotation of the horizontal rotation unit 300 is stopped by sensing the position of the horizontal rotation unit 300 by the angle detection sensor 630, When the rotation is stopped and then rotated again, And controls the rotating direction of the driving motor (601) so as to rotate the driving motor (601) in a direction opposite to the rotating direction. delete delete delete delete delete delete delete delete delete delete The method according to claim 1,
The horizontal rotary apparatus 600 further includes a plurality of support holes 620 for supporting the horizontal rotation table 300 at a predetermined height from the platform 200,
Wherein the support hole (620) is formed of a ball wheel and is spaced apart along a circumference at a position spaced a certain distance from the center of rotation.

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