JPH11188677A - Method and device for attaching/detaching sheet to/from robot hand, and method and device for slidable contact with plate surface by the sheet - Google Patents

Abstract

PROBLEM TO BE SOLVED: To facilitate attachment/detachment of a sheet by attaching/detaching the sheet to/from a robot hand to wipe a dot-like raised part adhered to a coated surface when a chemical is coated on a glass plate by an opening/closing lever to be opened/closed through the engagement with an auxiliary attachment/ detachment member. SOLUTION: A pair of glass plates G are transferred to a pair of support rods 2, 2 by lowering a shuttle conveyor stopped at the prescribed position, and adsorbed and fixed by adsorptive pads 12, 12. A dot-like raised part with a chemical coated on a coating surface of the glass plates G is wiped by a sheet 3 fitted to a head plate 62 on a robot hand 61 of a multi-articulated robot through a sheet attaching/detaching means 30. The sheet 3 cut to the fixed size is supplied onto a movable plate 51 from a sheet feeding means 20, and the sheet 3 on the movable plate 51 is moved to an attachment/detachment station by a traversing means 50. An opening/closing lever 31 is opened/closed by being abutted on an auxiliary attachment/detachment member 41 to attach/ detach the sheet 3.

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to removing and attaching a sheet material for removing dirt on a plate-like body surface, removing a coating film, removing water droplets, a chemical solution, or sliding and polishing the surface to and from a robot hand, and mounting the sheet. The present invention relates to a method and an apparatus for slidingly contacting the surface of a plate-like body with a robot hand.

[0002]

2. Description of the Related Art Conventionally, various methods and apparatuses have been known for removing dirt and water droplets adhering to the surface of a plate, removing a coating film, and polishing the surface of the plate.

For example, when wiping off attached dirt and water droplets, a device in which the surface of the plate-like body is manually slid with a sheet material or a cloth, or a device in which a jig or the like for wiping work is devised is devised. It is used simply.

[0004] For example, Japanese Utility Model Publication No. 58-55985,
In Japanese Utility Model Application Laid-Open No. 56-146468, a wax member having a coating member such as a polishing sheet on the front surface, a large-diameter locking band at the center, and a small-diameter locking band at both ends is provided on the back surface. There is disclosed a rubbing tool used for application of an agent or other chemicals, polishing, wiping, brushing of the surface of an object, or massage of the face or body.

[0005] Alternatively, a dirt or a coating film on a plate is washed by passing it through a washing machine for spraying hot water or the like, and then dried with warm air or the like, or a head provided with a cloth, an abrasive sheet, a brush, or the like. Rotate to bring the surface of the plate into sliding contact,
There is a method of removing or polishing dirt or a coating film.

[0006]

In the case where a plate-like body such as a glass plate is coated with a chemical solution which is relatively quick-drying and solidified, if a small spot-like droplet adheres to the coating surface, the spot-like little rises. In order to smooth the raised portion, it is necessary to wipe off the raised portion.

[0007] Japanese Utility Model Publication No. 58-55985, Japanese Utility Model Publication No. 5
The thing described in 6-146468 discloses that wax, coating, wiping, and the like are manually performed using a rubbing tool,
There is a problem that the workability is poor due to manual operation, and dirt or the like adheres to the sliding surface as the number of use of the rubbing tool increases, and the wiping effect is reduced.

[0008] Further, in a method in which the surface of the plate is slid by washing with warm water or the like or by rotating a head on which a brush is mounted, the swelling on the coating surface is not only completed, but the surface of the plate is not stopped. However, there is a problem that it is not possible to remove only a spot-like raised portion.

[0009]

DISCLOSURE OF THE INVENTION The present invention is intended to solve the above-mentioned problems, that is, a method in which a plate-like body such as a glass plate is coated with a chemical solution which dries relatively quickly and solidifies and then adheres to the coating surface. Cuts to a fixed size with sheet material supply means, with the aim of wiping and removing the slightly raised spots of slight spot-like droplets, and automatically attaching and detaching the wiping sheet material to and from the robot hand. The sheet material is supplied onto the movable plate, and the opening / closing lever is opened by opening and closing the opening / closing lever by opening and closing the liftable opening / closing auxiliary member to the opening / closing lever of the pair of sheet material attaching / detaching means provided on the opposite side surface of the robot hand. Release the attachment, push down the sheet material together with the movable plate with the robot hand, bend both ends of the sheet material in a U-shape with the fixed plate located near both ends of the movable plate, lower the attachment / detachment auxiliary member, and open and close the open / close lever. Close At the same time, a sheet material attaching / detaching method in which both ends of the sheet material are fixed and the sheet material is attached to the hand, and a robot that can be driven in the X, Y, Z, and θ axes by the attaching / detaching method of the sheet material The sheet material attached to the hand is brought into sliding contact with the surface of the plate-like body fixedly positioned at a predetermined position, and the plate-like body is subjected to dirt, water droplets, coating film removal, polishing, or the like, or The sheet material attached to the hand is pressed against a cloth immersed in a wiping liquid to impregnate the sheet material, and the sheet material is slid into contact with the surface of the plate material fixed at a predetermined position to form a plate-like material. Sliding contact method of plate-shaped surface to remove dirt and coating film,
In a device for attaching and detaching a sheet material to and from a hand that slides on a plate-like surface, a sheet material supply unit that supplies a sheet material cut to a fixed size onto a movable plate, and moves the sheet material on the movable plate to a detachment station. A movable plate moving means to be moved; a sheet material attaching / detaching means comprising a pair of opening / closing levers for constantly pressing the side of the wiping head against the opposite side surface of the robot hand; and an opening / closing lever by bringing an attaching / detaching auxiliary member into contact with the opening / closing lever. A sheet material attachment / detachment device configured to attach / detach a sheet material to / from a hand, the attachment / detachment assisting device to be opened, a fixing unit for adsorbing and fixing a plate-like body at a predetermined position, and the sheet material attachment / detachment device. Sliding contact of a plate-shaped surface comprising: a robot hand equipped with a sheet material; and a robot capable of driving the hand freely in X, Y, Z, and θ axes and sliding freely along the surface of the plate-shaped body. apparatus To provide.

[0010]

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS As shown in FIG. 1, a glass plate G or the like is supported, and a glass plate G is conveyed at a pitch feed by repeating forward and backward movement after repeating a predetermined distance, and not shown. As the shuttle conveyor and the shuttle conveyor stopped at a predetermined position descend, the glass plate G is moved to the pair of support rods 2,
A transfer fixing means 10 is provided, which is composed of suction pads 12 and 12 which are transferred onto and fixed by suction.

An articulated robot is provided in the vicinity of the transfer fixing means 10, and a robot head 61 at the end of the arm of the robot is provided with a rectangular head plate 62 via an attaching member. A sheet material attaching / detaching means 30 for detachably attaching the sheet material 3 is provided.

The sheet material attaching / detaching means 30 is attached to two opposite sides of the head plate 62 of the robot hand 61.
A pair of open / close levers 31, 31,... In the shape of a letter are pivotally mounted near the center of each of the open / close levers.
A rotatable abutting roll 3 is provided on one end side of 31.
, Provided on the other end side, the opposing open / close levers 31, 31,... Are connected by springs 33, 33 and are in tension with each other. The spring 33,
With the pulling force of 33, the pressing members 34, 34 at the ends of the opening / closing lever on the side of the springs 33, 33 are pressed against both ends of the sheet material 3 contacting the lower surface and both side surfaces of the head plate 62. The material 3 is fixed to the head plate 62.

The pressing members 34, 34,... Of the opening / closing levers 31, 31,... Always press the side surface of the head plate 62, that is, the mounted sheet material 3 by the springs 33, 33. By pressing the rolls 32, 32,... From below, the opening / closing levers 31, 31 are opened, the pressing force of the pressing members 34, 34,. It is released from the plate 62, falls into the collection hopper 4, and is collected.

An air nozzle (not shown) is provided in the vicinity of the head plate 62, and the release speed of the sheet material 3 can be increased by blowing air to the sheet material 3 as needed when the sheet material 3 is released.

Further, in the vicinity of the transport fixing means 10, a sheet material supply means 20 for supplying the sheet material 3 cut to a fixed size on the movable plate 51 to the articulated robot 60 side, There are provided table traversing means 50 for moving the sheet material 3 to the attaching / detaching station, and attaching / detaching auxiliary means 40 for opening and closing the opening / closing lever 31 by bringing the attaching / detaching auxiliary member 41 into contact with the opening / closing lever 31.

The sheet material supply means 20 is mounted on a rotatable shaft of a sheet material 3 ′ wound in a roll shape, and a plurality of feed rolls 21, 21,... For guiding the sheet material 3 ′ to a cutter 22. And a cutter 22 for rotating the eccentric shaft by driving a motor (not shown) to cut the sheet material 3 ′ into a predetermined size.

The sheet material 3 cut to a predetermined size by the sheet material supply means 20 is placed on a movable plate 51, and the sheet material 3 is in a state of waiting for mounting on the robot hand 61. The table traversing means 50 includes a traversing cylinder 53 that traverses the movable plate 51 by a constant stroke, and a movable plate 51.
The movable plate 51 includes a movable plate return spring 54 provided at a lower portion of the movable plate 51 for returning the pressed movable plate 51 to its original height, and fixed plates 52 provided before and after the movable plate 51 in the transverse direction.

When the sheet material 3 cut to a fixed size is to be mounted on the robot hand 61, the movable plate 51 traverses to the loading / unloading station position by the operation of the traversing cylinder 53 of the table traversing means 50 and the lower portion of the loading / unloading station. Of the robot hand 6 is closed.
When the used sheet material 3 attached to 1 is discarded, the movable plate returns to the cutter 22 side, and the collection hopper 4 of the collection box (not shown) provided at the lower part of the attachment / detachment station is exposed to the surface. Become.

Further, the attachment / detachment assisting means 40 is provided with an attachment / detachment assisting member 41 which is located at the attachment / detachment station position and can be moved up and down by an elevating cylinder 42, and moves the head plate 62 of the robot hand 61 between the attachment / detachment assisting members 41. When inserted, the opening / closing lever 3 of the sheet material attaching / detaching means 40
The contact rolls 32, 32,... Abut on the attachment / detachment auxiliary member 41, and the opening / closing levers 31, 31,.

The opening / closing operation of the opening / closing levers 31, 31,...
Is pressed down, or the robot hand 61 is positioned near the upper part of the attachment / detachment assisting member 41 and the opening / closing assisting member 41 is opened / closed by moving it up and down.

That is, when the used sheet material 3 already mounted is discarded, as shown in FIG. 2, the head plate 61 of the robot hand 61 is loosely inserted into the attachment / detachment auxiliary member 41 of the attachment / detachment station, and the opening / closing lever is opened. The robot hand 61 is lowered by a predetermined distance to open the 31, 31 to open the open / close levers 31, 31, and the discarded sheet material 3 is collected in the collection hopper 4.

When the newly supplied sheet material 3 is mounted, as shown in FIG. 3, the table is set so that the movable plate 51 and the fixed plates 52, 52, etc. are located at the lower position of the loading / unloading station. 55, the robot hand 61 is loosely inserted into the attachment / detachment assisting member 41 at the ascending position, and the opening / closing levers 31, 31,... The sheet material 3 is pushed down to move the movable plate 51 and the head plate 62.
The both ends of the sheet material 3 sandwiched between are bent upward by the fixing plates 52, 52. When the attachment / detachment auxiliary member 41 is lowered, the opening / closing levers 31, 31,... Are changed from the open state to the closed state by the spring 33, and both ends of the sheet material 3 are pressed and fixed.

The robot 60 has a robot hand 61 at the end of its arm.
It can be driven freely along the axis, the Z axis, and the θ axis. For this reason, even if a plate-shaped body such as a glass plate is curved, the robot hand 61 to which the new sheet material 3 is attached is reciprocated at least once or more while slightly ascending and descending along the curved surface shape. The entire upper surface of the body is moved while sliding the sheet material 3 on the body, so that dirt, water droplets, coating film removal, polishing, etc. of the plate-like body can be performed.

Alternatively, the hand 61 of the robot 60
The sheet material 3 mounted on the sheet material 3 is pressed against a cloth dipped in a wiping liquid such as alcohol to impregnate the sheet material 3, and the sheet material 3 is slid on the surface of the plate-shaped body G fixed at a predetermined position. The plate G may be contacted to remove dirt or a coating film.

In this way, the sheet material 3 is impregnated with an appropriate amount of alcohol, and
If a sliding contact is made along the surface of the glass plate G, even if a spot-like surplus film on the coating film applied and dried and solidified on the upper surface side of the glass plate G occurs,
By performing the sliding contact wiping with the sheet material impregnated with the alcohol liquid, the surplus film having irregularities is flattened and does not adversely affect other coating films.

Further, X, X
If the locus of the position and angle of the robot hand 61 is registered and stored in a controller (not shown) while moving in the Y, Z, and θ axis directions, the operation is automatically repeated every time the plate-shaped body G is carried in. be able to.

Furthermore, if the shapes of various plate-like bodies are registered in advance in a controller (not shown), it is possible to quickly respond to changes in the type of product to be produced.

[0028]

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS A detailed description will be given below of a sheet material 3 to be attached to and detached from a robot hand 61, a method of sliding a sheet surface G by the sheet material 3 and a sliding device 1 according to the present invention with reference to the drawings.

First, as shown in FIG.
When the glass sheet G is carried in at a pitch feed by a shuttle conveyor (not shown) 0 and stopped at a predetermined position near the center of the sliding contact device 1, the shuttle conveyor descends,
The glass plate is transferred onto the support rod 2. An elastic rubber material also serving as a cushioning material is adhered to the support rod 2 at several places to prevent scratches caused by contact with the glass plate G. In this state, the glass plate G is suction-fixed by the suction pads 12 sucked from below the glass plate G by a vacuum source (not shown).

In the vicinity of the outside of the transport fixing means 10, X, Y,
An articulated robot 60 that can be driven on the Z and θ axes is provided, and the upper curved surface of the glass plate G is slid by the sheet material 3 attached to the robot hand 61 at the tip of the robot 60 so as to match the shape of the glass plate G. In contact therewith, the surface of the glass plate G is flattened by wiping off excess film portions after coating.

The wiping sheet material 3 is a sheet made of a hygroscopic acrylic nonwoven fabric. The sheet material 3 is impregnated with isopropyl alcohol, and is an excess film of a coating film on the surface of the glass plate G. The protruding portions were wiped off to make the entire surface flat and uniform.

Now, the sheet material 3 ′ wound into a roll by the sheet material supply means 20 is cut into a fixed size by the cutter 22 and supplied onto the movable plate 51 on the table 55.
The table 55 traverses by a certain stroke by the operation of the traverse cylinder 53 of the table traversing means 50, and the sheet material 3
Is moved to the attaching / detaching station. At the upper position of the attachment / detachment station, an attachment / detachment assisting member 41 having a rectangular frame is provided, and the robot hand 61 of the robot 60 is inserted into the attachment / detachment assisting member 41 from above, and as shown in FIG. The contact rolls 32 of the sheet material attaching / detaching means 30 provided on the hand 61 are provided.
The opening / closing lever 31, which is pressed against the sheet material 3 against the head plate 62 by fixing the opening / closing lever 31,
31,... Are opened. At the same time, as shown in FIG.
After the both ends of the sheet material 3 are bent upward by the fixed plates 52, 52 at both ends of the movable plate 51, the attachment / detachment auxiliary member 41 is lowered by the backward movement of the lifting / lowering cylinder 42. Open / close levers 31, 3 in the open state
Are closed by the tensile force of the springs 33 of the sheet material fixing means 30, and the opening and closing levers 31, 31,.
Are pressed against the end of the head plate 62 to fix the sheet 3.

Robot hand 61 with sheet material 3 attached
Rises, the movable plate 51 is returned to the original height by the movable plate return spring 54. When the robot hand 61 further separates from the attachment / detachment assisting member 41, the attachment / detachment assisting member is raised by the operation of the elevating cylinder 42, and the table 55 is moved back to the cutter 22 side by the reciprocation of the traversing cylinder 53 of the table traversing means 50. .

Robot hand 61 with sheet material 3 mounted
Moves to the upper part of the immersion tank 5 adjacent to the table, presses the sheet material 3 against the cloth impregnated with the alcohol liquid in the immersion tank 5, soaks the alcohol in the sheet material 3, and is already on standby. The curved glass plate G is slid from one end to the other end along a curved surface to remove a convex portion of the coating film and flatten it. The number of times of sliding contact is not limited to one, and may be performed a plurality of times as necessary.

Sheet material 3 mounted on robot hand 61
When the sliding contact of the upper surface of the predetermined number of glass plates G is completed, the glass plate G is replaced with a new one. However, the number can be freely set and may be determined as needed.

When it is necessary to replace the wiping sheet material 3, the robot hand 61 mounted with the sheet material 3 moves to the upper position of the attaching / detaching station, and as shown in FIG. The contact rolls 32, 32,... Of the sheet material attaching / detaching means 30 provided in the robot hand 61 are inserted from above into the attaching / detaching auxiliary member 41 framed in a square.
2 is brought into contact with the attachment / detachment assisting member 41, and as shown in FIG. 2B, the opening / closing levers 31, 31,... The fixing of the material 3 is released. The sheet material 3 falls naturally and is collected in the collection box through the collection hopper 4 provided below the attachment / detachment station. However, if necessary, high-pressure air is blown out by an air nozzle attached near the robot hand 61. Accordingly, the detachment of the sheet material 3 from the head plate 62 can be accelerated.

The robot hand 61 having removed the sheet material 3 to be discarded rises, waits at the upper position of the loading / unloading station, and waits for the supply of a new sheet material 3. The glass plate G, which has been slid and wiped, releases the suction by the suction pad 12, is lifted by a shuttle conveyor (not shown) of the transport fixing means 10, and is again carried out by pitch feed to the next step. At the same time, the next glass plate G is pitch-fed from the previous process.
Is carried in.

The wiping liquid is immersed in a cloth or the like in an isopropyl alcohol immersion tank 5 to make contact with the wiping sheet material 3 not through the alcohol liquid tank but through a cloth impregnated with alcohol. Therefore, the amount of alcohol impregnating the sheet material 3 becomes an appropriate amount.

In the present invention, isopropyl alcohol is used as the wiping liquid. However, the wiping liquid is determined by the chemical of the film applied to the surface of the glass plate G, and is not limited to isopropyl alcohol.

An elastic rubber plate was adhered to the lower surface of the head plate 62 of the robot hand 61, and a belt material having irregularities was adhered. This is to prevent scratches or the like from being generated on the surface of the glass plate G when the surface of the glass plate G is brought into sliding contact with the sheet material 3 and to increase the pressing force per unit area at the time of sliding contact. .

Although the preferred embodiment has been described above, the present invention is not limited to this, and various applications can be considered. Although the robot 60 has been described as an articulated robot, it may be a portal robot, and may be X, Y, Z, θ.
It is not limited to this as long as it can be driven by a shaft.

The head plate 62 of the robot hand 61 is not limited to a flat plate, but may have a convex arc shape. In this case, the movable plate 51 may have a concave shape that matches the arc shape of the head plate 62.

Further, the opening / closing levers 31, 31,...
The opening / closing levers 31, 31,... May be opened and closed by an air cylinder or a small motor instead of the springs 33, 33, which pull each other.

Alternatively, the sheet material 3 is prepared by cutting a rolled sheet material into a predetermined size and supplying it. However, the sheet material 3 is taken out one by one from the already cut and stacked sheet material 3 and supplied. You may do it. Further, the material of the sheet material 3 is not limited to the acrylic nonwoven fabric, but may be made of a cloth such as flannel, cotton, or paper such as Kimwipe.

The attachment / detachment assisting member 41 of the attachment / detachment assisting means 40 has a rectangular frame shape.
The contact rolls 32, 32, are not limited to a rectangular frame shape but may be a pair of horizontal frame shapes as long as they press the contact rolls 32, 32,. Is also good.

Further, the lifting / lowering cylinder 42 of the attachment / detachment assisting means 40 and the traversing cylinder 53 of the table traversing means 50
May be driven by a motor instead of an air cylinder.

Alternatively, the supporting rods 2, 2 of the glass plate G
Is not rod-shaped, but can support the glass plate G,
It may be supported at several points by a rod-shaped member or the like.
The glass plate G may be a flat plate or a curved plate. The glass plate may be a single plate such as a tempered glass plate, a semi-tempered glass plate, a raw plate, or a plurality of tempered glass plates or a combination of tempered glass and raw plate glass.
The target is an intermediate film such as VB or EVA, or a laminated glass bonded by resin injection.

The present invention can be applied not only to a glass plate but also to various panel materials.

[0049]

According to the present invention, a small spot-like droplet adhering to an application surface after coating a plate-like body such as a glass plate with a chemical solution having a relatively fast drying and solidifying rate by a simple structure is applied. It is possible to wipe off a slightly raised portion.

Further, the present invention can be applied to the removal of dirt and water droplets attached to the plate-like surface, and the excess coating film on the plate-like surface can be wiped uniformly and quickly without wiping unevenness. Further, the sheet material for wiping can be automatically attached to and detached from the robot hand, and the wiping sheet material can be automatically attached and removed.

Even if the plate is not only a flat shape but also a curved glass plate, the entire surface of the plate follows the curved surface of the plate and is uniformly wiped without uneven wiping. Can be wiped automatically at high speed.

Further, since the used sheet material is discarded and automatically replaced with a clean sheet material, it is possible to always wipe with a clean sheet material.

[Brief description of the drawings]

FIG. 1 is an overall perspective view of a method and an apparatus for slidingly contacting a sheet material according to the present invention.

FIGS. 2A and 2B are cross-sectional views illustrating removal of a sheet material of the present invention from a robot hand.

FIGS. 3A and 3B are cross-sectional views illustrating mounting of the sheet material of the present invention on a robot hand.

[Explanation of symbols]

 G plate-like body 1 sliding contact device 2 support rod 3, 3 'sheet material 4 recovery hopper 5 immersion tank 10 transport fixing means 12 suction pad 20 sheet material supply means 21 feed roll 22 cutter 30 sheet material attaching / detaching means 31 opening / closing lever 32 Contact roll 33 Spring 34 Sheet material pressing member 40 Attaching and detaching assisting means 41 Attaching and detaching assisting member 42 Elevating cylinder 50 Table traversing means 51 Movable plate 52 Fixed plate 53 Traverse cylinder 54 Movable plate return spring 55 Table 60 Robot 61 Robot hand 62 Head plate

Claims (5)

[Claims] A sheet material cut to a fixed size by a sheet material supply means is supplied onto a movable plate, and is detachably mounted on an opening / closing lever of a pair of sheet material attachment / detachment means provided on opposite sides of a robot hand. The members are brought into contact, the opening / closing lever is opened, the mounting of the sheet material is released, and the sheet material is pushed down together with the movable plate by a robot hand, and both ends of the sheet material are U-shaped with fixed plates located near both ends of the movable plate. A method for attaching and detaching a sheet material, comprising: lowering an opening / closing lever by folding and lowering an opening / closing lever after bending, and fixing both ends of the sheet material to attach the sheet material to a hand. 2. A plate-like body in which a sheet material mounted on a hand of a robot that can be driven in X, Y, Z, and θ axes is positioned and fixed at a predetermined position by the method for attaching and detaching a sheet material according to claim 1. A method for sliding a plate-shaped surface, which is slid on the surface of the plate-shaped member to remove stains, water droplets, coating films, and polish on the plate-shaped body. 3. The sheet material mounted on the hand of the robot is pressed against a cloth immersed in a wiping liquid to impregnate the sheet material, and the sheet material is fixed to a predetermined position on the surface of a plate-like body. The method for slidingly contacting a plate-like surface according to claim 2, wherein the surface of the plate-like body is stained or the coating film is removed by sliding contact. 4. An apparatus for attaching and detaching a sheet material to and from a hand that slides on a plate-like surface, comprising: a sheet material supply means for supplying a sheet material cut to a fixed size onto a movable plate; Table traversing means for moving to the station;
Sheet material attaching / detaching means comprising a pair of opening / closing levers which constantly press the side of the wiping head against opposing side surfaces of the robot hand, and attaching / detaching assisting means for opening and closing the opening / closing lever by bringing the attaching / detaching auxiliary member into contact with the opening / closing lever. A sheet material attaching / detaching device, characterized in that a sheet material comprising: 5. A fixing means for adsorbing and fixing a plate-like body at a predetermined position, a hand of a robot to which a sheet material is attached by the sheet material attaching / detaching apparatus according to claim 4, and an X, Y hand. And a robot that can be driven freely along the axes of Z, θ and θ and that can slide freely along the surface of the plate-like body.