Tool path generation method and apparatus

The present invention relates to a tool path generation method and apparatus for generating a tool path at the time of machining a workpiece.

As this type of a tool path generation method, in general, smoothing treatment which approximates a broken line obtained by connecting a plurality of machining points by a curve so as to generate a smooth tool path is known. If such smoothing treatment is carried out across-the-board at all of the machining path including parts with shapes of large bend angles, the error in shape from the desired machined shape increases and thus, the machined shape may be conversely degraded. Considering this point, for example, Patent Literature 1 describes a method of comparing a bend angle of a broken line with a predetermined threshold value and validating (turning on) or invalidating (turning off) the smoothing treatment in accordance with their relative magnitudes.

In this regard, machining point data is generally prepared by utilizing a CAD/CAM system etc. For this reason, even if a curvature of a machined surface is constant, the lengths of the broken line segments (block lengths) vary and the bend angles also vary. Therefore, if the method, like the one described in the above Patent Literature 1, of turning the smoothing treatment on and off at a specific bend angle is used, there will be portions where the smoothing treatment is turned on and portions where it is turned off regardless of the curvature of the machined surface being constant and therefore, it is difficult to obtain a smooth machined surface.

Patent Literature 1

Japanese Unexamined Patent Publication No. 2009-199483

The present invention is a tool path generation method for generating a tool path at a time of machining a workpiece, including a bend angle calculation step of calculating a bend angle at each connecting point of a broken line which is obtained by successively connecting a predetermined plurality of machining points by line segments, an approximation curve derivation step of deriving an approximation curve closer to the connecting point the larger the bend angle calculated by the bend angle calculation step, and a tool path generation step of generating the tool path by a new broken line along the approximation curve derived by the curve derivation step.

Further, the present invention is a tool path generation apparatus for generating a tool path at a time of machining a workpiece, including a bend angle calculation unit calculating a bend angle at each connecting point of a broken line which is obtained by successively connecting a predetermined plurality of machining points by line segments, an approximation curve derivation unit deriving an approximation curve closer to the connecting point the larger the bend angle calculated by the bend angle calculation unit, and a tool path generation unit generating the tool path by a new broken line along the approximation curve derived by the approximation curve derivation unit.

FIG. 1 is a view which shows the general configuration of the entire machine tool which has a tool path generation apparatus according to an embodiment of the present invention.

FIG. 2A to FIG. 2C are views which show transitions in the generation of a tool path.

FIG. 3A and FIG. 3B are views which explain problem points in the case of smoothing treatment such as in FIG. 2C .

FIG. 4 is a view which explains other problem points in the case of smoothing treatment such as in FIG. 2C .

FIG. 5 is a block diagram which shows the configuration of a control device of FIG. 1 .

FIG. 6 is a view which explains processing in the bend angle calculation unit of FIG. 5 .

FIG. 7 is a view which explains processing in a route insertion unit, approximation curve calculation unit, and data extraction unit of FIG. 5 , in the case where machining points are comprised of 2D data.

FIG. 8 is a view which shows a characteristic feature of the imaginary block length which is stored in a characteristic storage unit of FIG. 5 .

FIG. 9 is a view which explains a calculation formula of an approximation curve.

FIG. 10 is a view which explains processing in a route insertion unit, approximation curve calculation unit, and data extraction unit of FIG. 5 , in the case where machining points are comprised of 3D data.

FIG. 11 is a view which explains the advantageous effects according to the present invention.

Hereinafter, referring to FIG. 1 to FIG. 11 , embodiments of a tool path generation apparatus according to present invention will be explained. FIG. 1 is a view which shows a general configuration of the entire machine tool which has the tool path generation apparatus according to an embodiment of the present invention and shows a vertical machining center as an example.

A column 2 is erected on a bed 1 . At the column 2 , a spindle head 3 is supported movably in the up-down direction (Z-axis direction) via a linear feed mechanism. At the spindle head 3 , a tool 4 is attached facing downward via the spindle. The tool 4 is, for example, an end mill and is driven to rotate by a spindle motor inside of the spindle head 3 . On the bed 1 , a saddle 5 is supported movably in the horizontal direction (Y-axis direction) via a linear feed mechanism. On the saddle 5 , a table 6 is supported movably in the horizontal direction (X-axis direction) perpendicular to the Y-axis direction. Each of the linear feed mechanisms is, for example, comprised of a ball screw and a servo motor which drives rotation of the ball screw. Due to the above configuration, the tool 4 and the workpiece W move relative to each other in the three perpendicular axis directions (X-, Y-, and Z-directions) whereby the workpiece W is worked.

The spindle motor and the servo motors are controlled in accordance with a machining program by a control device 10 . In the machining program, a path of movement of the tool 4 is set as a tool path in advance. The tool 4 moves relative to the workpiece 4 along this tool path.

The machining program is prepared by utilizing a known CAD/CAM system. That is, the CAD data corresponding to the machined shape of the workpiece W is used as the basis to prepare CAM data consisting of a set of fine linear commands. This CAM data is comprised of a tremendous volume of point group data, so data is thinned from the CAD data in accordance with predetermined rules to give an amount of data suitable for a machining program. Due to this, a machining program is prepared.

FIG. 2A is a view which shows an example of a tool path according to the thus prepared machining program. A comparatively rough broken line is used to show the tool path PA 1 . The machining program is given coordinate data of end points of the broken line segments (called “machining command points”, “block end points”, or simply “machining points”) in a block format. The block end points are successively connected to give the tool path PA 1 of FIG. 2A . Below, in a broken line comprised of consecutive line segments ( FIG. 2A , L 1 and L 2 ), the angle θ formed by the line segment L 2 with the extension of the line segment L 1 when it is extended toward L 2 is defined as a “bend angle”.

If the tool 4 is moved along the tool path PA 1 comprised of the comparatively rough broken line which is shown in FIG. 2A , it is not possible to obtain a smooth machined surface of the workpiece W. Therefore, a predetermined curve approximation formula is used to calculate an approximation curve for each machining point, and the approximation curve is used as the basis to correct the tool path, which is referred as so-called “smoothing treatment”.

FIG. 2B is a view which shows an example of a tool path after the smoothing treatment. After the smoothing treatment, the tool path PA 2 is given by a large number of points of coordinate data along the approximation curve, and the smoothing treatment results in a smooth curve. For this reason, a smooth machined surface is obtained. On the other hand, at a machining point P 1 with a large bend angle, the tool path PA 2 greatly deviates from the targeted workpiece shape (dotted line) and therefore the desired shape of the workpiece cannot be obtained. To avoid this problem, it may be considered to not carry out the smoothing treatment across-the-board for all of the machining points, but to invalidate the smoothing treatment when a bend angle θ is large,

FIG. 2C is a view which shows an example of a tool path PA 3 which is obtained by invalidating the smoothing treatment when a bend angle θ at a machining point is larger than a threshold value θa. If validating (turning on) and invalidating (turning off) the smoothing treatment in accordance with bend angles θ in this way, it is possible to suppress shape error of the workpiece W at a machining point P 1 with a large bend angle θ.

However, machining point data is prepared by utilizing a CAD/CAM system. Therefore, even if the curvature of a machined surface SF 1 is constant such as when machining a cylindrical shape, the lengths of the broken line segments (block lengths ΔL) will differ and the bend angles θ will also differ as shown in FIG. 3A . For this reason, when carrying out smoothing treatment, there will be a region A where the smoothing treatment is partially turned off as shown in FIG. 3B , so it will be difficult to obtain a smooth machined surface.

Furthermore, differences in machining points, as shown in FIG. 4 , also occur among adjoining tool paths (dotted line region A). Differences also occur in the bend angles θ. For this reason, when a threshold value θa is set near the bend angles θ of the machining points in this region A, there will be a tool path where the smoothing treatment is turned on and a tool path where it is turned off and therefore, it will not be possible to obtain a smooth machined surface in whole. In order to solve the above such problem, in the present embodiment, the tool path is generated in the following way.

FIG. 5 is a block diagram which shows the configuration of the control device 10 . The control device 10 has a tool path generation device 20 which generates a tool path at the time of machining a workpiece and a numerical control device 30 which uses the NC data set by the machining program as the basis to control the motors of the machine tool so that the tool 4 moves relative to the workpiece W along this tool path.

The tool path generation device 20 is comprised of a processing system which has a CPU, ROM, RAM, and other peripheral circuits etc. It has a program reading unit 21 , a bend angle calculation unit 22 , a route insertion unit 23 , a characteristic storage unit 24 , an approximation curve calculation unit 25 , and a data extraction unit 26 .

The program reading unit 21 successively reads the block end point data of the machining program which is prepared by the CAD/CAM system, i.e., the 3D coordinate data of the machining points (machining point data).

The bend angle calculation unit 22 successively calculates the bend angle θ of each machining point, based on the machining point data read by the program reading unit 21 . For example as shown in FIG. 6 , if the machining point data of the three points P 0 , P 1 , and P 2 are read, the bend angle θ 1 at P 1 is calculated, if the machining point data of P 3 is read, the bend angle θ 2 at P 2 is calculated, and if the machining point data of P 4 is read, the bend angle θ 3 at P 3 is calculated. It is also possible to read all of the machining point data, then calculate the bend angles θ at the machining points all together.

The route insertion unit 23 inserts a route (imaginary block R) along the imaginary axis α which perpendicularly intersects each of the X-axis, Y-axis, and Z-axis at the machining points used for calculation of the bend angles θ. After that, the route insertion unit 23 , the approximation curve calculation unit 25 , and the data extraction unit 26 carry out the smoothing treatment by using the concept of the imaginary block R to generate a new tool path. Here, in order to facilitate the explanation of the imaginary block R, first, the explanation will be given assuming that the machining points are given by 2D coordinate data.

FIG. 7 is a conceptual view of an imaginary block R in the case where the machining points are given by 2D coordinate data. In the figure, the machining points P 1 , P 2 , and P 3 are respectively set on an XY plane (upper figure), while the X- and Y-components of the points are respectively P 1 (x 1 , y 1 ), P 2 (x 2 , y 2 ), and P 3 (x 3 , y 3 ). P 1 and P 2 are connected by the line segment L 1 , and P 2 and P 3 are connected by the line segment L 2 , whereby a broken line is formed. The curve PA 5 in the figure is a tool path which is obtained by approximation of the machining points P 1 , P 2 , and P 3 by a curve on the XY plane.

When such machining points P 1 , P 2 , and P 3 are given by only the XY components, the axis perpendicular to each of the X-axis and Y-axis is the Z-axis. The imaginary axis α is equal to the Z-axis. Therefore, if inserting the imaginary block R at the machining point P 2 which has the bend angle θ 2 , i.e., between the line segments L 1 and L 2 , toward the Z-axis direction, the line segment L 2 is shifted in the Z-axis direction, and a new broken line which successively connects the end points P 1 and P 2 of the line segment L 1 and the end points P 2 ′ and P 3 ′ of the line segment L 2 after shifting is obtained. At this time, the length of the inserted imaginary block R (imaginary block length ΔR) is determined by a characteristic feature of the imaginary block length ΔR which is stored in the characteristic storage unit 24 .

FIG. 8 is a view which shows the feature f(θ) of the imaginary block length ΔR which is stored in the characteristic storage unit 24 . In the figure, the imaginary block length ΔR increases in a S-shape along with an increase of the bend angle θ. That is, in a region A with a small bend angle θ (0≦θ≦θα), ΔR is substantially 0, while in a region B with a bend angle θ larger than a predetermined value θα (θα<θ≦θβ), ΔR increases by a comparatively large ratio along with an increase of the bend angle θ, and in a region C with a bend angle θ over a predetermined value θβ (θβ<θ), ΔR is substantially constant (=ΔRmax). The imaginary block length ΔR which corresponds to the bend angle θ 2 at the machining point P 2 of FIG. 7 is the maximum ΔRmax.

If expressing the α coordinate component at the machining point P 2 by α 2 (=−ΔRmax), the X, Y, and α components of the points P 1 , P 2 , P 2 ′, and P 3 ′ which constitute the new broken line become respectively P 1 (x 1 , y 1 , 0), P 2 (x 2 , y 2 , 0), P 2 ′ (x 2 , y 2 , α 2 ), and P 3 ′ (x 3 , y 3 , α 2 ). The approximation curve calculation unit 25 of FIG. 5 calculates the approximation curve L 4 of these four points ( FIG. 7 ).

The approximation curve L 4 is, for example, calculated by a 3D Bezier curve. A “Bezier curve” is an approximation curve P(t) of the four points Q 0 , Q 1 , Q 2 , and Q 3 such as shown in FIG. 9 . The calculation formula is expressed by the following formula (I).

P ( t )=(1− t ) 3 Q 0+3 t (1− t ) 2 Q 1+3 t 2 (1− t ) Q 2+ t 3 Q 3  (I)

The letter “t” corresponds to the path on the curve P(t) which starts from Q 0 . By entering the X-, Y-, Z-, and other coordinate components into Q 0 to Q 3 of the formula (I) and changing “t” over the entire length of 0 to P(t), the coordinate values of P(t) are found for each coordinate component.

Specifically, when finding the approximation curve L 4 of FIG. 7 , by entering the X-components x 1 , x 2 , x 2 , and x 3 of P 1 , P 2 , P 2 ′, and P 3 ′ into Q 0 to Q 4 and changing “t” by a predetermined pitch, the X-component of each point Pt is found for each predetermined pitch. Similarly, by entering the Y-components y 1 , y 2 , y 2 , and y 3 of P 1 , P 2 , P 2 ′, and P 3 ′ into Q 0 to Q 4 and changing “t” by a predetermined pitch, the Y-component of each point Pt is found for each predetermined pitch. Further, by entering the α-components 0, 0, α 2 , and α 2 of P 1 , P 2 , P 2 ′, and P 3 ′ into Q 0 to Q 4 and changing “t” by a predetermined pitch, the α-component of each point Pt is found for each predetermined pitch. By connecting the points Pt which are found in the above way, the approximation curve L 4 of FIG. 7 is obtained in the XYα space.

The data extraction unit 26 extracts the remaining components after removing the α-components from the approximation curve L 4 , i.e., the XY components of the points Pt. Due to this, as shown in FIG. 7 , it is possible to obtain a plurality of points Pt′ which are points projecting the points Pt on the XY plane. By successively connecting these Pt′, a new tool path PA 4 can be generated.

The thus generated tool path PA 4 has a smaller inside curve amount of the tool path (distance from machining point P 2 to tool path PA 4 ) compared with the tool path PAS which is obtained by simply approximating the machining points P 1 to P 3 by a curve ( FIG. 7 ) and is suppressed in strength of smoothing of the inside curve amount of the tool path. Here, the “strength of smoothing” is determined in accordance with the imaginary block length ΔR which is inserted at the machining point P 2 . The larger the bend angle θ is, the longer the imaginary block length ΔR becomes ( FIG. 8 ). For this reason, the larger the bend angle θ, the more the strength of the smoothing can be suppressed.

In the example of FIG. 7 , the bend angle θ is large and the block length ΔR is long, so the approximation curve L 4 passes on the imaginary block R and the inside curve amount becomes 0. However, when the bend angle θ is small, the approximation curve L 4 does not pass on the imaginary block R and the inside curve amount does not become 0. That is, in a region C where the bend angle θ is larger than θβ of FIG. 8 , the inside curve amount becomes 0 and a result similar to those when the smoothing treatment is turned off, shown in the machining point P 1 of FIG. 2C , is obtained. On the other hand, in the region A where the bend angle θ is smaller than θα of FIG. 8 , the inside curve amount is large and a result similar to those when the smoothing treatment is turned on, shown in the machining point P 1 of FIG. 2B , is obtained.

Next, as shown in FIG. 10 , the smoothing treatment when the machining points P 1 to P 3 are given by the XYZ coordinates will be explained. In this case, after the bend angle calculation unit 22 calculates the bend angle θ 2 at the machining point P 2 , the route insertion unit 23 inserts an imaginary block R along the imaginary axis α which is perpendicular to each of the XYZ axes, between the line segment L 1 and the line segment L 2 . Although the imaginary axis α is a conceptual axis which cannot actually be shown, it is shown for convenience sake in FIG. 10 . FIG. 10 shows the tool path PA 6 obtained by just smoothing treatment of the machining points P 1 to P 3 .

The imaginary block length ΔR is determined by the characteristic feature f(θ) of FIG. 8 . The approximation curve calculation unit 25 calculates the approximation curve L 5 of the points P 1 , P 2 , P 2 ′, and P 3 ′ after insertion of the imaginary block R by the above formula (I). That is, by entering the XYZα coordinate components of P 1 , P 2 , P 2 ′, and P 3 ′ into Q 0 to Q 3 of formula (I) and changing “t” over the entire length of 0 to P(t), the coordinate values of P(t) are determined for each coordinate component.

The data extraction unit 26 extracts the components remaining after removal of the α-components from the approximation curve L 5 , i.e., the XYZ components of the points Pt. Due to this, as shown in FIG. 10 , it is possible to obtain points Pt′ corresponding to Pt in the XYZ 3D space. By successively connecting these Pt′, a new tool path PA 7 can be generated.

The thus generated tool path PA 7 has a smaller inward curve amount of the tool path compared with the tool path obtained by just smoothing treatment of the machining points P 1 to P 3 and is suppressed in strength of smoothing.

The point group data obtained by the data extraction unit 26 is output to a not shown program rewriting unit, and the block data of the machining program is rewritten along the tool path PA 7 . Based on this machining program, the numerical control device 30 controls the drive of the motors. Due to this, the workpiece W is machined along the tool path PA 7 .

The operation of the tool path generation method of according to the present embodiment is summarized as follows:

First, the program reading unit 21 reads the machining program which is generated by the CAD/CAM system, while the bend angle calculation unit 22 calculates the bend angle θ of the broken line which is obtained by successively connecting the block end points of the machining program (bend angle calculation step).

Next, an approximation curve L 5 closer to the connecting point P 2 the larger the calculated bend angle θ (for example, θ 2 ) is derived (curve derivation step), and a tool path PA 7 is generated along the approximation curve L 5 (tool path generation step).

In this case, the route insertion unit 23 inserts an imaginary block R, which is parallel to the imaginary axis α perpendicular to the X-axis, Y-axis, and Z-axis and which has an imaginary block length ΔR which corresponds to the bend angle θ 2 , at the connecting point P 2 . Due to this, the machining points P 2 and P 3 respectively move in parallel along the imaginary axis α by the imaginary block length ΔR whereby the imaginary points P 2 ′ and P 3 ′ are set. Next, the approximation curve calculation unit 25 calculates the approximation curve L 5 of the four points P 1 , P 2 , P 2 ′, and P 3 ′, and the data extraction unit 26 extracts the XYZ components of the approximation curve L 5 and thus, the new tool path PA 7 is generated by the point group data of the 3D space.

By generating the tool path PA 7 in this way, it is possible to change the strength of the smoothing in accordance with the bend angle θ 2 and possible to optimize the inward curve amount of the tool path according to the smoothing treatment. That is, imaginary block length ΔR corresponds to the strength of the smoothing. When the bend angle θ is large, the inward curve amount is small (smoothing becomes weak), while when the bend angle θ is small, the inward curve amount is large (smoothing becomes large). For this reason, even when the positions of the machining points differ on the same tool path or between adjoining tool paths and the bend angles θ differ, it is possible to smoothly machine the workpiece W and obtain the precise workpiece shape.

FIG. 11 is a view which shows a characteristic feature f 1 (broken line) of the smoothing strength in the case of turning the smoothing treatment on and off in accordance with the relative magnitude of a bend angle θ and threshold value θa, and a characteristic feature f 2 (solid line) of the smoothing strength in the case of carrying out the smoothing treatment according to the present embodiment. As explained above, the smoothing strength corresponds to the inward curve amount of the connecting point.

According to the characteristic feature f 1 , for example, when the bend angles of adjoining machining points P 1 and P 2 are θ 1 and θ 2 , at the machining point P 1 , the smoothing treatment is turned on (smoothing strength maximum), while at the machining point P 2 , the smoothing treatment is turned off (smoothing strength 0). For this reason, despite the bend angle θ not changing that much, the smoothing strength rapidly changes and obtaining a smooth machined surface becomes difficult. As opposed to this, according to the characteristic feature f 2 , if the bend angles are θ 1 and θ 2 , the change in smoothing strength is small and a smooth machined surface can be obtained.

According to the present embodiment, the following functions and effects can be exhibited:

(1) The bend angles θ at the connecting points of the broken line obtained by successively connecting a plurality of machining points are calculated, an approximation curve L 5 ( FIG. 10 ) closer to the connecting points the larger the bend angles θ is derived, and a tool path PA 7 is generated along the approximation curve L 5 . Due to this, it is possible to suppress error of the machined shape of the workpiece W and obtain a smooth machined surface even if the bend angles θ differ. (2) An imaginary block R which is perpendicular to the XYZ axes and has a length corresponding to the bend angle θ is inserted, and an approximation curve L 5 of the broken line after insertion of the imaginary block is calculated. Therefore, an approximation curve L 5 closer to the connecting points the larger the bend angles θ can be easily derived. (3) The point group data which is obtained by extraction of the XYZ components from the approximation curve L 5 is used as the basis to generate the tool path PA 7 , so it is possible to easily generate the tool path PA 7 of a 3D space from the approximation curve L 5 which uses the imaginary block R. In this case, the imaginary axis α perpendicularly intersects each of the XYZ axes, so even if removing the components of the imaginary axis α, there is no effect on the other XYZ coordinate components. (4) The characteristic feature f(θ) of the imaginary block length ΔR is divided into substantially three regions A to C ( FIG. 8 ). At the region A with a small bend angle θ and the region C with a large one, the imaginary block length ΔR is made substantially constant, while at the intermediately region B where the bend angle θ is θα to θβ, the imaginary block length ΔR is made to gradually become longer along with an increase of the bend angle θ. Due to this, it is possible to change the rate of change of the smoothing strength in accordance with the magnitude of the bend angle θ and possible to obtain excellent smoothing corresponding to the differences in positions of the machining points compared with the case of changing the smoothing strength by a constant rate of change corresponding to the bend angle θ.

The feature of the present invention is changing the strength of smoothing in accordance with the bend angle θ. As long as carrying out a smoothing treatment closer to the connecting point the larger the bend angle θ and using a new broken line after the smoothing treatment to generate the tool path PA 5 , the approximation curve derivation step and the tool path generation step as a smoothing treatment step may be configured in any way. That is, it is also possible to generate a tool path closer to the connecting point the larger the bend angle θ without inserting the imaginary block R.

In the above embodiment, in a broken line obtained by successively connecting three successive machining points (first machining point P 1 , second machining point P 2 , and third machining point P 3 ) by line segments, the larger the bend angle θ at the middle machining point P 2 , the greater the amount of movement along the imaginary axis α perpendicular to the XYZ axes is made by moving in parallel the machining points P 2 and P 3 along the imaginary axis α in the same direction to set imaginary points (first imaginary point P 2 ′ and second imaginary point P 3 ′), and an approximation curve L 5 of these points P 1 , P 2 , P 2 ′, and P 3 ′ is calculated. However, as long as deriving an approximation curve closer to the connecting point the larger the bend angle θ, the approximation curve derivation step may be configured in any way.

In the above embodiment, the program reading unit 21 reads the machining program prepared by the CAD/CAM system and the bend angle calculation unit 22 calculates the bend angles θ at the individual connecting points. However, it is possible to prepare the initial machining program without going through a CAD/CAM system. The configuration of the bend angle calculation unit is not limited to this. The route insertion unit 23 inserts the imaginary axis α at a connecting point and the approximation curve calculation unit 25 approximates the curve by a Bezier curve to find the approximation curve L 5 . However, it is also possible to approximate a curve by a B spline curve or NURBS curve or other curve so as to find the approximation curve L 5 . The configuration of the approximation curve derivation unit is not limited to the one which is explained above. The data extraction unit 26 extracts the XYZ components of the approximation curve L 5 to generate the tool path PA 7 . However, it is also possible to thin a predetermined number of data after extraction of the XYZ components, in order to generate the tool path. The configuration of the tool path generation unit is not limited to the one explained above.

In the above embodiment, the control device 10 provided at the machine tool is provided with the tool path generation apparatus 20 and the numerical control device 30 . However, the numerical control device 20 may also be provided with the tool path generation apparatus 30 . Further, it is also possible to provide the tool path generation apparatus 20 separate from the control device 10 . In the above embodiment, although the tool path generation apparatus 10 is applied to a machining center, the tool path generation apparatus of the present invention can be similarly applied to another machine tool which requires generation of a tool path at the time of machining a workpiece.

According to the present invention, smoothing treatment closer to the connecting point the larger the bend angle at the connecting point is carried out and a tool path is generated by the new broken line after the smoothing treatment. Therefore, it is possible to suppress error of the machined shape of the workpiece and obtain a smooth machined surface even if there are differences in the bend angles.

10 control device

20 tool path generation apparatus

21 program reading unit

22 bend angle calculation unit

23 route insertion unit

24 characteristic storage unit

25 approximation curve calculation unit

26 data extraction unit

30 numerical control device

L 4 , L 5 approximation curve

PA 1 to PA 7 tool path