JP5076854B2 - Device for measuring the width of two faces of regular polygons with even angles - Google Patents

Description

The present invention relates to a device for measuring the width of an even-numbered regular polygon.

As a regular polygon , for example, in the case of a regular octagon, there are four dihedral widths.
When measuring a plurality of dihedral widths of regular polygons of even angles such as regular hexagons, regular tetragons, regular decagons, etc. in addition to regular octagons , first of the regular polygons of even angles The dihedral width dimension between one side and the opposite side is measured by a detector, and then the two-sided width between the side adjacent to one side of the even polygon and the opposite side The dimensions are measured by a detector.
For example, in the case of a regular octagonal shape, the regular octagonal shape is rotated 45 degrees to convert the surface, and the dihedral width dimension is measured for each surface conversion.
Conventionally, in order to perform surface conversion of the positive polyhedra of even angle, a positive polyhedra even-angle releasably clamped by the chuck device to a required this chucking apparatus by the rotation control device for a motor as a driving source angle It turned and changed the surface.
An apparatus for measuring the dihedral width dimension of an even-numbered regular polygon is disclosed in Patent Document 1, for example.
JP-A-6-2013365

By the way, in the prior art, in order to change the surface of an even-numbered regular polygon, a chuck device, a rotation control device, etc. are required, the structure becomes complicated and the whole device becomes large and expensive. It was.
The purpose of this invention, the view of the problems, the surface transformation of the two-surface width of the positive polyhedra even-angle can be performed with a simple structure, second positive polyhedra even-angle and the cost can be reduced It is to provide a surface width measuring device.

In order to solve the above-mentioned problem, the even- width regular polygon double-sided width measuring apparatus according to claim 1 of the present invention is an even-numbered regular polygon that measures the dihedral width of an even-numbered regular polygon. The two-sided width measuring device of
The table surface of the fixed table has a flat surface on which the regular polygon can be arranged with one surface facing downward, and a two-surface width dimension between the lower surface of the regular polygon and the upper surface on the opposite side by a detector. The lower measurement position flat surface where is measured,
An upper conversion position flat surface which forms a flat surface adjacent to the measurement position flat surface on one side with a slight conversion step surface and on which the adjacent surface adjacent to the lower surface of the regular polygon can be arranged is stepped. Formed,
On one side of the fixed table, the lower part of the adjacent surface adjacent to the lower surface of the regular polygon arranged on the flat surface of the measurement position is rotated by contacting the upper edge of the conversion step surface, and the normal table is rotated. A conversion cylinder having a lateral cylinder rod for arranging the adjacent surface of the polygonal body as the next lower surface on the conversion position flat surface is disposed,
On the other side of the fixed table, the regular polygon arranged on the conversion position flat surface is slid to the measurement position flat surface, and the next lower surface of the regular polygon is arranged on the measurement position flat surface. A return cylinder having a horizontally oriented cylinder rod is provided.

According to the above-described configuration, the regular polygon of an even number of angles is arranged on the flat surface of the measurement position of the table surface of the fixed table with the one surface thereof facing downward, and the detector is provided between the lower surface of the regular polygon and the upper surface on the opposite side. The dihedral width dimension is measured.
Thereafter, the cylinder rod of the conversion cylinder is pushed out, and after the tip of the cylinder rod comes into contact with one side of the regular polygon, the cylinder rod is continuously pushed out to adjoin the lower surface of the regular polygon. The regular polygon is rotated toward the upper conversion position flat surface in a state in which the lower part of the regular polygon is in contact with the upper edge of the conversion step surface. Accordingly, the regular polygon is arranged on the flat surface of the conversion position with the adjacent surface as the lower surface.
Thereafter, the cylinder of the cylinder rod for returning is pushed out, after the leading end of the cylinder rod is in contact with the other side of the positive polyhedra, by extrusion of the subsequent cylinder rod, until the positive polyhedra measuring position flat surface planing Is done. As a result, the regular polygon is arranged on the measurement surface flat surface in a state where the surface is converted, the next dihedral width dimension of the regular polygon is measured by the detector, and the above operation is repeated. , All the dihedral width dimensions of the regular polygon are measured.
As described above, on the table surface of the fixed table, the measurement position flat surface and the conversion position flat surface are formed in a step shape with the conversion step surface, and the conversion cylinder and the return cylinder are provided on both sides of the fixed table. With the simple structure of disposing, it is possible to reliably perform the surface conversion of the two-sided width of the regular polygon, which is highly effective in reducing the cost.

Width across flats measuring device of the positive polyhedra even-angle according to claim 2 is the width across flats measuring device of the positive polyhedra even-angle according to claim 1,
The height of the central axis of the cylinder rod of the conversion cylinder is set to a position higher than the height of the central axis of the regular polygon of the even angle arranged on the measurement position flat surface,
A structure in which a lower portion of an adjacent surface adjacent to a lower surface of the regular polygon is brought into contact with an upper edge of the conversion step surface and rotated while pressing one side portion of the regular polygon by a cylinder rod tip of the conversion cylinder. It is characterized by that.

According to the above configuration, the tip of the cylinder rod of the conversion cylinder is pressed against a position higher than the height of the central axis of the regular polygon, and the regular polygon of the even angle is rapidly rotated toward the flat surface of the conversion position. This is effective in improving the measurement speed of the width across flats.

Width across flats measuring device of the positive polyhedra according to claim 3 is the width across flats measuring device of the positive polyhedra even-angle according to claim 1 or 2,
The pressing force of the cylinder rod of the return cylinder is set larger than the pressing force of the cylinder rod of the conversion cylinder,
When sliding an even-numbered regular polygon on the flat surface of the conversion position to the flat surface of the measurement position, the return is made with the tip surface of the cylinder rod of the conversion cylinder in contact with one side of the regular polygon. After pushing out the cylinder rod of the cylinder for conversion and after the tip of the cylinder rod of the return cylinder comes into contact with the other side of the regular polygon, the regular polygon is moved to the measurement position while pushing back the cylinder rod of the conversion cylinder. It is characterized by being configured to slide to a flat surface.

According to the above construction, when to slide a positive polyhedra of the even angle on conversion position the flat surface to the original measuring position flat plane, the between the cylinder rod end of the cylinder of the cylinder rod end and converting cylinder back With the regular polygon held (clamped), it can be slid to the flat surface of the measurement position. Accordingly, it is possible to prevent a problem that the regular polygon is unexpectedly rotated on the stepped surface for conversion, and it is possible to accurately measure each two-surface width dimension of the regular polygon.

  The best mode for carrying out the present invention will be described in accordance with an embodiment.

[Example 1]
A first embodiment of the present invention will be described with reference to the drawings.
FIG. 1 is a perspective view showing an even-numbered regular polygon. FIG. 2 is a perspective view showing a two-sided width measuring apparatus for an even-numbered regular polygon according to Embodiment 1 of the present invention. Figure 3 is a side view showing a state of measuring the two surface width dimension and symmetry dimensions of positive polyhedra even-angle by two surface width measuring device of the positive polyhedra even number angle. FIG. 4 is an explanatory diagram showing a state where regular polygons having even angles are arranged on the measurement position flat surface of the fixed table. FIG. 5 is an explanatory diagram showing a state in which an even-numbered regular polygon on the measurement position flat surface is installed on the conversion position flat surface while being rotated by the conversion cylinder. FIG. 6 is an explanatory diagram showing a state in which an even-numbered regular polygon on the conversion position flat surface is returned to the measurement position flat surface. FIG. 7 is an explanatory view showing a state in which an even-numbered regular polygon is returned on the measurement position flat surface.

As shown in FIG. 1, an even-numbered regular polygon 1 (hereinafter also simply referred to as a regular polygon) , which is an object to be measured, includes a circular head 2 and a regular polygon (a regular octagonal column in the figure) 3. Are integrally formed adjacent to each other on the same center line.
As shown in FIG. 2, the two-surface width measuring device for measuring the two-surface width dimension between one surface of the regular polygon 1 and the opposite surface is a fixed table 10, a conversion cylinder 21, and a return device. A cylinder 31, a support column 40, a first detector 42, an elevating member 50, and a second detector 61 are provided.
As shown in FIG. 2 to FIG. 4, the lower measurement position that forms a flat surface on the table surface (upper surface) of the fixed table 10 on which the regular polygon portion 3 of the regular polygon 1 can be arranged with one surface facing downward. A flat surface 11 is formed.
Further, as shown in FIG. 4, on the table surface (upper surface) of the fixed table 10, a conversion step having a slight height (for example, a height of about 0.3 mm to 2 mm) on one side of the measurement position flat surface 11. An upper conversion position flat surface 12 forming a flat surface on which the adjacent surface adjacent to the surface 13 and adjacent to the lower surface of the regular polygon portion 3 of the regular polygon 1 can be installed is formed in a step shape.

  In the first embodiment, as shown in FIGS. 2 and 3, one surface of the regular polygon portion 3 of the regular polygon 1 is disposed on the measurement position flat surface 11 on the front side of the table surface of the fixed table 10. A front table surface 16 having a front step surface 15 is formed so that the circular head 2 of the regular polygon 1 does not hit the table surface.

As shown in FIGS. 2 and 4, the first bracket 20 and the second bracket 30 are erected on both sides of the measurement position flat surface 11 and the conversion position flat surface 12 of the fixed table 10 so as to face each other. Yes.
A conversion cylinder 21 made of an air cylinder is horizontally attached to the outer surface of the first bracket 20 located on the measurement position flat surface 11 side. The tip of the cylinder rod 22 of the conversion cylinder 21 passes through the first bracket 20 and protrudes from the inner surface of the first bracket 20.
In the first embodiment, the height of the central axis of the cylinder rod 22 of the conversion cylinder 21 is set at a position higher than the height of the central axis of the regular polygon 1 arranged on the measurement position flat surface 11. Yes. Then, one side portion of the regular polygon portion 3 of the regular polygon 1 (in the first embodiment, a portion closer to the upper portion of one lateral surface of the regular polygon portion 3) is pressed by the tip of the cylinder rod 22 of the conversion cylinder 21. However, the lower part of the adjacent surface adjacent to the lower surface of the regular polygon part 3 is brought into contact with the upper edge of the conversion step surface 13 and rotated.

A return cylinder 31 made of an air cylinder is horizontally attached to the outer surface of the second bracket 30 located on the conversion position flat surface 12 side. The tip of the cylinder rod 32 of the return cylinder 31 passes through the second bracket 30 and protrudes from the inner surface of the second bracket 30.
In the first embodiment, the height of the central axis of the cylinder rod 32 of the return cylinder 31 is set to a height position substantially the same as the height of the central axis of the regular polygon 1 arranged on the conversion position flat surface 12. Has been. Then, the other side of the regular polygon 3 of the regular polygon 1 (substantially the central portion of the other lateral surface of the regular polygon 3 in this embodiment 1) is pressed by the tip of the cylinder rod 32 of the return cylinder 31. However, the regular polygon 1 arranged on the conversion position flat surface 12 is slid to the original measurement position flat surface 11.

  The pressing force of the cylinder rod 32 of the return cylinder 31 is set to be larger than the pressing force of the cylinder rod 22 of the conversion cylinder 21. When the regular polygon 1 on the conversion position flat surface 12 is slid to the measurement position flat surface 11, the tip of the cylinder rod 32 of the conversion cylinder 31 is one side of the regular polygon 3 of the regular polygon 1. The cylinder rod 32 of the return cylinder 31 is pushed out while being in contact with the cylinder, and the regular polygon part 3 of the regular polygon 1 is held (clamped) between the tip of the cylinder rod 32 and the tip of the cylinder rod 22 of the conversion cylinder 21. ) While sliding the regular polygon 1 to the measurement position flat surface 11.

  Further, in the first embodiment, in the state where the cylinder rod 32 of the return cylinder 31 is disposed at the retracted end position, as shown in FIG. 5, the measurement position flat surface 11 is obtained by pushing the cylinder rod 22 of the conversion cylinder 21. The backward end position of the cylinder rod 32 of the return cylinder 31 is set so that the regular polygon 1 is not excessively rotated when the regular polygon 1 is rotated up to the conversion position flat surface 12. Has been. That is, when the regular polygon 1 is excessively rotated, a part of the regular polygon 3 of the regular polygon 1 hits the tip of the cylinder rod 32 at the retracted end position of the return cylinder 31 and the regular polygon 1 The rotation is prevented.

As shown in FIG. 2, a support column 40 is erected vertically on the back side of the fixed table 10, and the first detector mounting portion 41 is in a lateral direction at a substantially intermediate height position of the support column 40. It is fixed to the overhang. And the 1st detector 42 which measures the dihedral width dimension A of the regular polygon part 3 of the regular polygon 1 is attached to the 1st detector attachment part 41 with the movable detection part 43 facing upwards. Yes.
In addition, on the front side of the support column 40, an air cylinder or the like is used as a drive source (not shown), and an elevating member 50 is assembled to be movable up and down by a vertical slide mechanism (not shown). An extension part 51 is extended upward from the first part, and a tip of the extension part 51 is opposed to the upper part of the movable detection part 43 of the first detector 42 so as to be detachable. The surface width detected portion 52 protrudes horizontally.
As shown in FIGS. 2 and 3, the lower part of the elevating member 50 is in contact with the upper surface of the regular polygonal portion 3 of the regular polygon 1 arranged on the measurement position flat surface 11 so as to be able to contact and separate. A shaft-like stopper member 55 that restricts the descent of the elevating member 50 protrudes in a hanging shape.

Further, on the front side of the elevating member 50, a second detector mounting portion 60 is projected at a position facing the upper side of the circular head 2 of the regular polygon 1 arranged on the measurement position flat surface 11. The second detector mounting portion 60 has a symmetry dimension of the circular head 2 of the regular polygon 1 (from the upper surface of the regular polygon 3 of the regular polygon 1 arranged on the measurement position flat surface 11). A second detector 61 for measuring the distance dimension (B) from the outer peripheral surface of the upper end of the circular head 2 is mounted with the movable detector 62 facing downward (see FIG. 3).
That is, in the first embodiment, the dihedral width dimension A is measured based on the vertical displacement amount of the detection unit 43 of the first detector 42 and the vertical direction of the detection unit 62 of the second detector 61 is measured. The symmetry dimension B is measured based on the amount of displacement.
The drive sources such as the conversion cylinder 21, the return cylinder 31 and the air cylinder of the elevating member 50 are controlled by a control device (not shown) based on a set program.

The even- width regular polygonal two-sided width measuring apparatus according to the first embodiment is configured as described above.
Therefore, when measuring each dihedral width dimension A of the regular polygon portion 3 of the even-numbered regular polygon 1 and each symmetry dimension B of the circular head 2, first, the measurement position flat surface of the fixed table 10 is measured. 11 is arranged with one surface of the regular polygon part 3 of the regular polygon 1 facing downward.
Next, the elevating member 50 is lowered, and when the lower end of the stopper member 55 comes into contact with the upper surface of the regular polygonal portion 3, the elevating member 50 is stopped from descending (see FIGS. 3 and 4).
At this time, the two-surface-width detected portion 52 that moves down integrally with the elevating member 50 comes into contact with the upper end of the movable detecting portion 43 of the first detector 42, and the detecting portion 43 is displaced in the vertical direction. A dihedral width dimension A between the lower surface of the regular polygon 3 of the polygon 1 and the upper surface on the opposite side is measured.
Further, when the lower end of the stopper member 55 comes into contact with the upper surface of the regular polygon portion 3 and the descending of the elevating member 50 is stopped, the movable detection portion 62 of the second detector 61 is the circular head of the regular polygon 1. 2 is displaced in the vertical direction by hitting the upper end of the outer peripheral surface, and the symmetry dimension B of the circular head 2 of the regular polygon 1 is measured based on the amount of displacement.

  For example, electrical signals based on the vertical displacements of the detectors 43 and 62 of the first and second detectors 42 and 61 are respectively sent to a control device (not shown). One dihedral width dimension A of the polygonal portion 3 and the symmetry dimension B of the circular head 2 are respectively measured, and the dihedral width dimension A and the symmetry dimension B are displayed on a display device (not shown). Is displayed. When the dihedral width dimension A and the symmetry dimension B are each within the allowable range, the process proceeds to the surface conversion step described below, and either one or both of the dihedral width dimension A and the symmetry dimension B is permitted. When the value is exceeded, it is desirable to notify by operating (turning on) a notification means such as a buzzer or a lamp, and to stop the apparatus.

As described above, when one dihedral width dimension A of the regular polygon portion 3 of the regular polygon 1 and the symmetry dimension B of one circular head 2 are measured, the elevating member 50 is lifted up originally. It is raised to the end position and waits.
At substantially the same time, the cylinder rod 22 of the conversion cylinder 21 is pushed out, and the tip of the cylinder rod 22 comes into contact with one side (one lateral surface) of the regular polygon 3 of the regular polygon 1. Thereafter, the lower side of the adjacent surface adjacent to the lower surface of the regular polygon part 3 is brought into contact with the upper edge of the conversion step surface 13 by the subsequent extrusion of the cylinder rod 22, so that the regular polygon 1 is the upper conversion position flat surface. 12 is turned (see FIG. 5).
Thereby, the adjacent surface of the regular polygon 3 of the regular polygon 1 is arranged on the conversion position flat surface 12. That is, the adjacent surface of the regular polygon part 3 is disposed on the replacement position flat surface 12 as a lower surface.

Thereafter, as shown in FIG. 6, the cylinder rod 32 of the return cylinder 31 is pushed out, and the tip of the cylinder rod 32 contacts the other side portion (the other lateral surface) of the regular polygon portion 3 of the regular polygon 1. After the contact, the regular polygon 1 is slid to the original measurement position flat surface 11 by the subsequent extrusion of the cylinder rod 32 and arranged on the measurement position flat surface 11, and each cylinder of the conversion cylinder 21 and the return cylinder 31. The rods 22, 32 are retracted.
Here, again, the elevating member 50 is lowered, and when the lower end of the stopper member 55 comes into contact with the upper surface of the regular polygonal portion 3, the elevating member 50 stops being lowered. At this time, the next two-surface width dimension A and the circle of the regular polygon part 3 of the regular polygon 1 based on the amount of displacement in the vertical direction of the detection parts 43 and 62 of the first and second detectors 42 and 61. The next symmetry dimension B of the head 2 is measured respectively.

By repeating the above-described operation, all the dihedral width dimensions A of the regular polygon part 3 of the regular polygon 1 and the symmetry dimension B of the circular head 2 are measured.
For example, when the regular polygon part 3 of the regular polygon 1 is a regular octagon, the symmetry dimension B of the circular head 2 is measured a total of 8 times.
In addition, when measuring only each dihedral width dimension A of the regular polygon part 3 of the regular polygon 1, when the regular polygon part 3 of the regular polygon 1 is a regular octagon, it measures four times in total.

  As described above, on the table surface (upper surface) of the fixed table 10, the measurement position flat surface 11 and the conversion position flat surface 12 are formed in a step shape with the conversion step surface 13 and converted into both side portions of the fixed table 10. By the simple structure of disposing the cylinder 21 for return and the cylinder 31 for return, the surface conversion of each two-sided width of the regular polygon part 3 of the regular polygon 1 can be performed reliably, which is effective in reducing the cost. large.

  In the first embodiment, the tip of the cylinder rod 22 of the conversion cylinder 21 is pressed against a position higher than the height of the central axis of the regular polygon 1 so that the regular polygon 1 faces the conversion position flat surface 12. It can be quickly rotated, and has a great effect on improving the measurement speed of each two-surface width dimension A of the regular polygon portion 3 of the regular polygon 1 and the symmetry dimension B of the circular head 2.

  In the first embodiment, when the regular polygon 1 on the conversion position flat surface 12 is slid to the original measurement position flat surface 11, the tip of the cylinder rod 32 of the return cylinder 31 and the cylinder rod of the conversion cylinder 21 are used. In the state where the regular polygonal part 3 of the regular polygon 1 is held (clamped) between the 22 tips, it can be slid to the original measurement position flat surface 11. Thereby, the trouble that the regular polygon 1 rotates unexpectedly on the step surface 13 for conversion can be prevented, and the two-surface width dimension A of the regular polygon 3 of the regular polygon 1 or the circular head 2 can be prevented. The symmetry dimension B can be accurately measured.

In addition, this invention is not limited to the said Example 1, In the range which does not deviate from the summary of this invention, it can also be implemented with a various form.
For example, in the first embodiment, the regular polygon 1 having an even number of angles includes the circular head 2 and the regular polygon 3, and the two-surface width dimension A of the regular polygon 3 is Although the case where the symmetry dimension B is measured has been illustrated, the present invention can be implemented even when each dihedral width dimension of an even-numbered regular polygon having no circular head 2 is measured.
In addition to regular octagonal shapes , regular polygons of even angles include regular hexagonal shapes, regular tetragonal shapes, regular decagonal shapes, and the like.
In the first embodiment, the dihedral width dimension A is measured based on the vertical displacement of the detection unit 43 of the first detector 42, and the vertical direction of the detection unit 62 of the second detector 61 is measured. Although the case where the symmetry dimension B is measured based on the displacement amount is illustrated, this is also the case when the two-surface width dimension A and the symmetry dimension B are measured using another detector, for example, an optical detector. The invention can be implemented.

It is a perspective view which shows the regular polygon of an even angle | corner . It is a perspective view which shows the two-plane width | variety measuring apparatus of the regular polygon of an even number angle | corner which concerns on Example 1 of this invention. It is a side view which shows the state which measures the dihedral width dimension and symmetry dimension of the regular polygon of an even number angle similarly with the dihedral width measuring apparatus of the regular polygon of an even number angle . It is explanatory drawing which shows the state by which the regular polygon of an even-numbered angle | corner is similarly arrange | positioned on the measurement position flat surface of a fixed table. It is explanatory drawing which shows the state which installs on the conversion position flat surface similarly, rotating the regular polygon of an even angle | corner on a measurement position flat surface with the cylinder for conversion. It is explanatory drawing which shows the state which returns the regular polygon of an even-numbered angle similarly on a conversion position flat surface on a measurement position flat surface. It is explanatory drawing which shows the state where the regular polygon of an even number angle was similarly returned on the measurement position flat surface.

1 Regular polygon of even number 3 3 Regular polygon part 10 Fixed table 11 Measurement position flat surface 12 Conversion position flat surface 13 Conversion step surface 21 Conversion cylinder 22 Cylinder rod 31 Return cylinder 32 Cylinder rod 42 First detector 43 Detection unit

Claims (3)

A device for measuring the width across flats of an even-numbered regular polygon, which measures the width across flats of an even-numbered regular polygon,
The table surface of the fixed table has a flat surface on which the regular polygon can be arranged with one surface facing downward, and a two-surface width dimension between the lower surface of the regular polygon and the upper surface on the opposite side by a detector. The lower measurement position flat surface where is measured,
An upper conversion position flat surface which forms a flat surface adjacent to the measurement position flat surface on one side with a slight conversion step surface and on which the adjacent surface adjacent to the lower surface of the regular polygon can be arranged is stepped. Formed,
On one side of the fixed table, the lower part of the adjacent surface adjacent to the lower surface of the regular polygon arranged on the flat surface of the measurement position is rotated by contacting the upper edge of the conversion step surface, and the normal table is rotated. A conversion cylinder having a lateral cylinder rod for arranging the adjacent surface of the polygonal body as the next lower surface on the conversion position flat surface is disposed,
On the other side of the fixed table, the regular polygon arranged on the conversion position flat surface is slid to the measurement position flat surface, and the next lower surface of the regular polygon is arranged on the measurement position flat surface. A two-sided width measuring device for a regular polygon having an even number of angles , wherein a return cylinder having a sideways cylinder rod is disposed. The device for measuring the width across flats of an even-numbered regular polygon according to claim 1,
The height of the central axis of the cylinder rod of the conversion cylinder is set to a position higher than the height of the central axis of the regular polygon of the even angle arranged on the measurement position flat surface,
A structure in which a lower portion of an adjacent surface adjacent to a lower surface of the regular polygon is brought into contact with an upper edge of the conversion step surface and rotated while pressing one side portion of the regular polygon by a cylinder rod tip of the conversion cylinder. A two-sided width measuring device for a regular polygon having an even number of angles . A two-sided width measuring apparatus for an even-numbered regular polygon according to claim 1 or 2,
The pressing force of the cylinder rod of the return cylinder is set larger than the pressing force of the cylinder rod of the conversion cylinder,
When sliding an even-numbered regular polygon on the flat surface of the conversion position to the flat surface of the measurement position, the return is made with the tip surface of the cylinder rod of the conversion cylinder in contact with one side of the regular polygon. After pushing out the cylinder rod of the cylinder for conversion and after the tip of the cylinder rod of the return cylinder comes into contact with the other side of the regular polygon, the regular polygon is moved to the measurement position while pushing back the cylinder rod of the conversion cylinder. A device for measuring the width across two sides of a regular polygon having an even number of angles, wherein the device is configured to slide to a flat surface.

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