Abstract:
A control device for a machine tool for machining a workpiece while moving a rotating tool relative to the workpiece, the device being provided with: an input information-reading unit for reading input information, which comprises a path along the contour of the workpiece or the tool path of a first rotating tool that follows the external form of the workpiece; and a path-setting unit for converting the input information read by the input information-reading unit to generate a tool path for performing the machining using the end cutting edge of a second rotating tool.

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
       [0001]    This application is a U.S. National Phase patent application of International Patent Application No. PCT/JP2012/078197, filed on Oct. 31, 2012, which is hereby incorporated by reference in the present disclosure in its entirety. 
     
    
     FIELD OF THE INVENTION 
       [0002]    The present invention relates to a control device of a machine tool and a machine tool. 
       BACKGROUND OF THE INVENTION 
       [0003]    Machine tools which perform machining such as cutting by moving a tool relative to a workpiece are known in conventional art. In such machine tools, numerical control machine tools are known which specify a path of a tool by coordinates of predetermined axes or the like and perform machining by automatically moving the tool with respect to a workpiece. Such a numerical control machine tool can perform machining on a desired tool path and at a desired velocity by describing machine coordinates or moving velocity of a tool on a machining program. 
         [0004]    Patent Literature 1 discloses a curved surface cutting method in which a machining surface having a curved shape is obtained by using a milling tool such as a face milling cutter. This document discloses that the surface of an object to be machined is cut by using a milling tool whose rotation locus of cutting edge is circular and by moving the milling tool in a predetermined tool feeding direction in a state in which the rotation axis of the milling tool is inclined with respect to the normal line of a machining surface. 
         [0005]    Patent Literature 2 discloses a milling method which performs machining, by progressively bringing a milling tool close to a finished portion from a bulk material, while always removing the cut material, and a method of forming a track for the milling tool. This document discloses that a milling tool is guided along a continuous track whose cross-sectional shape is a spiral from the external contour of a bulk member to a contour portion of a finished member to change the shape of the member progressively. 
       CITATIONS LIST 
       [0000]    
       
         Patent Literature 1: Japanese Laid-Open Patent Application No. 2003-145334 
         Patent Literature 2: Japanese Laid-Open Patent Application No. 2000-263309 
       
     
       SUMMARY OF THE INVENTION 
       [0008]    It is known that when the width of a region where a workpiece is machined is small in a method of machining a workpiece, a side cutting edge of a rotary tool is used to machine the workpiece. For example, it is known that a side face of a plate member is machined by allowing a side cutting edge of a rod-like rotary tool such as an end mill to abut on a workpiece. 
         [0009]    However, in such a machining method, an end mill having a large tool diameter needs to be used to lessen the cusp height of a machining surface to perform high-precision machining. An end mill having a large tool diameter causes a problem that a large-sized machine tool is needed since the diameter of a tool to be used is large, and also causes a problem that machining time is prolonged. 
         [0010]    A high cutting speed is required for creating a highly accurate machining surface. However, when an end mill is rotated at a high speed, a spindle shaft of the end mill swings or vibrates, which may negatively affect the machining surface. It is also desired that an end mill which employs a special material such as diamond is used for performing high-precision machining such as mirror finishing. 
         [0011]    As mentioned above, high-precision machining such as mirror finishing has a problem that a large-sized end mill needs to be used or an end mill made of a special material needs to be used. 
         [0012]    A control device of a machine tool according to the present invention is a control device of a machine tool which machines a workpiece while a rotary tool is moved relative to a workpiece, comprising an input information reading unit which reads input information including a path passing through the contour of the workpiece or a tool path of a first rotary tool along the outline of the workpiece and a path setting unit which converts input information read by the input information reading unit to create a tool path along which machining is performed by using an end cutting edge of a second rotary tool. 
         [0013]    According to the above-described invention, the input information reading unit can be configured to read the input information including a tool path along which machining is performed by using the side cutting edge of the first rotary tool, and the path setting unit converts the input information, and generates a tool path in which machining is performed by using the end cutting edge of the second rotary tool whose diameter is larger than that of the first rotary tool. 
         [0014]    According to the above-described invention, the path setting unit can generate a tool path in which machining is performed by inclining the second rotary tool relative to the workpiece so that the bottom face of the second rotary tool is inclined with respect to a machining surface of the workpiece. 
         [0015]    According to the above-described invention, the input information reading unit can read a first machining program as the input information including a tool path of the first rotary tool, and the path setting unit outputs a second machining program including a tool path in which machining is performed by using an end cutting edge of the second rotary tool. 
         [0016]    A machine tool of the present invention comprises the above control device of the machine tool and a moving device which moves the second rotary tool relative to a workpiece in accordance with a tool path set by the path setting unit. 
         [0017]    According to the present invention, a control device of a machine tool in which machining precision of a machining surface is improved and the machine tool can be provided. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0018]      FIG. 1  is a schematic side view of a numerical control machine tool. 
           [0019]      FIG. 2  is an enlarged schematic cross-sectional view of a workpiece and a milling cutter. 
           [0020]      FIG. 3  is a bottom view of a milling cutter. 
           [0021]      FIG. 4  is a plan view of a workpiece. 
           [0022]      FIG. 5  is a side view of a workpiece. 
           [0023]      FIG. 6  is a schematic side view of a portion of a turning base which turns a table of a machine tool. 
           [0024]      FIG. 7  is a schematic view illustrating a first process of a method of machining a workpiece. 
           [0025]      FIG. 8  is a schematic view illustrating a second process of a method of machining a workpiece. 
           [0026]      FIG. 9  is a schematic view illustrating a third process of a method of machining a workpiece. 
           [0027]      FIG. 10  is a schematic view illustrating a fourth process of a method of machining a workpiece. 
           [0028]      FIG. 11  is a schematic view illustrating a fifth process of a method of machining a workpiece. 
           [0029]      FIG. 12  is a schematic view illustrating a sixth process of a method of machining a workpiece. 
           [0030]      FIG. 13  is a schematic view illustrating a seventh process of a method of machining a workpiece. 
           [0031]      FIG. 14  is a schematic view illustrating a method of machining a workpiece of comparative example. 
           [0032]      FIG. 15  is a schematic view of a machining system. 
           [0033]      FIG. 16  is a schematic view illustrating a path passing through the contour of a workpiece to be created in a numerical data reading unit. 
           [0034]      FIG. 17  is an enlarged schematic cross-sectional view of a portion where a milling cutter and a workpiece are in contact with each other. 
           [0035]      FIG. 18  is a view illustrating variables to be used for calculating a tool path of a milling cutter. 
           [0036]      FIG. 19  is a schematic perspective view of another machine tool. 
       
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
       [0037]    With reference to  FIGS. 1 to 19 , a control device of a machine tool and the machine tool are described. Examples of the machine tool include a vertical machining center whose spindle shaft extends in the vertical direction. In the following embodiments, a first rotary tool is an end mill, and a second rotary tool is a milling cutter. Herein, a side face of a plate member is machined by using an end cutting edge of a milling cutter. 
         [0038]      FIG. 1  is a schematic view of a numerical control machine tool. A milling cutter  20  serving as a rotary tool for machining is attached to a machine tool  10 . A workpiece  1  serving as an object to be machined is fixed on a table  14 . 
         [0039]    The machine tool  10  comprises a bed  12 , which is placed on the floor of a factory or the like and a column  13 , which is fixed on the bed  12 . The machine tool  10  includes a moving device which moves the milling cutter  20  and the workpiece  1  relative to each other. 
         [0040]    A X-axis guide rail  25  is arranged on the top surface of the bed  12 . The X-axis guide rail  25  extends in the X-axis direction (right and left direction in  FIG. 1 ). A saddle  15  is engaged with the X-axis guide rail  25 . The saddle  15  is formed so as to move in the X-axis direction along the X-axis guide rail  25 . A turning base  16  which is a swiveling device is mounted on the saddle  15 . The turning base  16  supports a table swiveling base  17  via a turning shaft  16   a . The turning shaft  16   a  extends in the Y-axis direction. The turning base  16  is formed so as to turn the table swiveling base  17  around the turning shaft  16   a  as indicated by an arrow  101 . The table  14  is fixed to the table swiveling base  17 . 
         [0041]    A numerical control rotary table  18  for rotating the workpiece  1  around a C-axis is arranged on the top surface of the table  14 . The workpiece  1  is fixed to the rotary table  18  via a holding member  19  for holding the workpiece. 
         [0042]    A moving device is driven, and thus the table  14  moves in the X-axis direction together with the saddle  15  and the turning base  16 . The workpiece  1  thus moves in the X-axis direction. The table swiveling base  17  turns, and thus the orientation of the workpiece  1  with respect to the milling cutter  20  can be changed. Further, the rotary table  18  is driven, and thus the workpiece  1  can be turned around the C-axis. 
         [0043]    A Y-axis guide rail  26  which extends in the Y-axis direction (a direction vertical to the paper surface in  FIG. 1 ) is arranged on the column  13 . A headstock  27  is engaged with the Y-axis guide rail  26 . The headstock  27  is formed so as to move in the Y-axis direction along the Y-axis guide rail  26 . 
         [0044]    A Z-axis guide rail  29  which extends in the Z-axis direction (up and down direction in  FIG. 1 ) is mounted on the headstock  27 . A spindle head  30  is mounted on the Z-axis guide rail  29 . The spindle head  30  is formed so as to move in the Z-axis direction along the Z-axis guide rail  29 . 
         [0045]    A spindle shaft  31  is rotatably supported by the spindle head  30 . The milling cutter  20  is mounted on the spindle shaft  31 . A motor for rotating the milling cutter  20  is connected to the spindle shaft  31 . The motor is driven, and thus the milling cutter  20  rotates around the central axis of the spindle shaft  31  as the rotation axis. 
         [0046]    The moving device is driven, and thus the headstock  27  moves in the Y-axis direction with respect to the column  13 . The milling cutter  20  thus moves in the Y-axis direction. Further, the moving device is driven, and thus the spindle head  30  moves in the Z-axis direction with respect to the headstock  27 . The milling cutter  20  thus moves in the Z-axis direction. 
         [0047]    As mentioned above, the moving device includes a plurality of moving axes, which are an X-axis, a Y-axis and a Z-axis as linear feed axes, and a C-axis as a rotational feed axis. The milling cutter  20  can be moved linearly relative to the workpiece  1  supported by the table  14 . Further, the rotary table  18  is driven, and thus the milling cutter  20  can be rotationally moved relative to the workpiece  1 . 
         [0048]      FIG. 2  illustrates a schematic cross-sectional view of the milling cutter  20  and the workpiece  1 .  FIG. 3  illustrates a schematic bottom view of the milling cutter  20 . With reference to  FIGS. 2 and 3 , the milling cutter  20  includes a body portion  22  and a cutting portion  23  which cuts the workpiece  1 . The body portion  22  of the milling cutter  20  is formed in a columnar shape. The cutting portion  23  is arranged along the circumferential direction of a bottom face  22   a  of the body portion  22 . A plurality of cutting portions  23  are arranged apart from each other. The cutting portion  23  is referred to as “a chip” and is replaceable. 
         [0049]    The milling cutter  20  rotates around a rotation axis  24  as a rotation center. The body portion  22  rotates, and thus the cutting portion  23  rotates in a direction indicated by an arrow  103 . With reference to  FIG. 2 , the rotating milling cutter  20  is arranged to be in contact with the surface of the workpiece  1 . The surface of the workpiece  1  is a machining surface. The cutting portion  23  is in contact with the workpiece  1 . The milling cutter  20  moves relative to the workpiece  1  as indicated by an arrow  102  while rotating, and thus the surface of the workpiece  1  can be machined. 
         [0050]    In an example illustrated in  FIG. 2 , the milling cutter  20  is arranged so that the rotation axis  24  is inclined with respect to the normal line direction of the surface of the workpiece  1 . In other words, the bottom face  22   a  of the body portion  22  is inclined with respect to the surface of the workpiece  1 . The cutting portion  23  on the front side in the advancing direction as indicated by the arrow  102  moves detached from the surface of the workpiece  1 . The cutting portion  23  arranged on the back side in the advancing direction performs cutting in contact with the surface of the workpiece  1 . The milling cutter  20  thus performs cutting process by using a heel portion. 
         [0051]      FIG. 4  illustrates a schematic plan view of a machined workpiece  1 .  FIG. 5  illustrates a side view of a machined workpiece  1 . The workpiece  1  is a plate member. The workpiece  1  includes side faces  1   a ,  1   b ,  1   c , and  1   d , and maximum area surface  1   e  whose area is the largest. Each of the side faces  1   a ,  1   b ,  1   c , and  1   d  is formed to have a area which is smaller than the maximum area surface  1   e  of the workpiece  1 . In cutting process, the side faces  1   a ,  1   b ,  1   c , and  1   d  of the workpiece  1  are machined. In this example, the side faces are mirror finished. 
         [0052]    With reference to  FIG. 2 , the milling cutter  20  is arranged so that the side face  1   a  and the bottom face  22   a  of the body portion  22  are opposed to each other in order to machine the side faces  1   a ,  1   b ,  1   c , and  1   d  of the workpiece  1 . The side faces  1   a ,  1   b ,  1   c , and  1   d  of the workpiece  1  can be machined by moving the milling cutter  20  relative to the workpiece  1 . 
         [0053]      FIG. 6  is a schematic view illustrating a state of a machine tool when the side faces  1   a ,  1   b ,  1   c , and  1   d  of the workpiece  1  are machined. The workpiece  1  needs to be arranged so that the side faces  1   a ,  1   b ,  1   c , and  1   d  are opposed to the milling cutter  20 . For this purpose, the turning base  16  is driven to turn the table swiveling base  17  by 90° as indicated by the arrow  101 . At least one side face of the side faces  1   a ,  1   b ,  1   c , and  1   d  of the workpiece  1  can be arranged upside. 
         [0054]    When the side faces  1   a ,  1   b ,  1   c , and  1   d  of the workpiece  1  are machined, four side faces  1   a ,  1   b ,  1   c , and  1   d  are successively machined. Next, a method of machining the workpiece  1  will be described. 
         [0055]      FIG. 7  is a schematic view of a first process of a method of machining the workpiece  1 . In the subsequent  FIGS. 7 to 13 , relative movement of milling cutter  20  with respect to the workpiece  1  is illustrated. The milling cutter  20  shown by a alternate long and short dash line represents the milling cutter  20  arranged in the previous process. In this example, cutting is started from the side face  1   a  having the smallest area among the side faces  1   a ,  1   b ,  1   c , and  1   d . In the machining method, which is not limited to the above-mentioned embodiment, cutting may be started from the side faces  1   b  and  1   d  having the large area. 
         [0056]    In the first process, the milling cutter  20  is arranged on a side of the side face  1   a  of the workpiece  1 . In this case, the milling cutter  20  is arranged at a position where the side face  1   a  is cut, by moving the milling cutter  20  in the Y-axis direction. The milling cutter  20  is moved toward the side face  1   a . In this example, the milling cutter  20  is moved relative to the workpiece  1  from a position in front of the position where machining is to be started. In other words, air cutting is performed. 
         [0057]      FIG. 8  is a schematic view of a second process of a method of machining the workpiece  1 . The side face  1   a  is started to be machined by the milling cutter  20 . The side face  1   a  of the workpiece  1  is cut by moving the milling cutter  20  along the side face  1   a  of the workpiece  1  as indicated by an arrow  111 . Machining is performed to the corner of the workpiece  1 . 
         [0058]      FIG. 9  is a schematic view of a third process of a method of machining the workpiece  1 . After finishing machining to the end portion of the side face  1   a , the workpiece  1  is rotated around the C-axis in order to form a corner portion having a curved shape. The workpiece  1  is rotated around a rotation axis  2  as indicated by an arrow  112 . A corner portion having a curved shape can be formed by cutting the workpiece  1  while rotating the workpiece  1  relative to the milling cutter  20 . 
         [0059]      FIG. 10  is a schematic view of a fourth process of a method of machining the workpiece  1 .  FIG. 10  illustrates a state in which the formation of the first corner portion of the workpiece  1  is finished. The workpiece  1  is rotated with respect to the milling cutter  20  until a corner portion of the workpiece  1  is formed. The bottom face  22   a  of the body portion  22  of the milling cutter  20  is opposed to the side face  1   b  of the workpiece  1 . 
         [0060]      FIG. 11  is a schematic view of a fifth process of a method of machining the workpiece  1 . Next, the side face  1   b  is machined by moving the milling cutter  20  along the side face  1   b  as indicated by an arrow  113 . In a similar manner, the side faces  1   c  and  1   d  can be formed by combining a linear movement and a rotation movement of the milling cutter  20  with respect to the workpiece  1 . 
         [0061]      FIG. 12  is a schematic view of a sixth process of a method of machining the workpiece  1 .  FIG. 12  illustrates a state in which the milling cutter  20  moves around all the side faces of the workpiece  1  and returns to the end portion of the side face  1   a . In such a manner, the side faces  1   a ,  1   b ,  1   c , and  1   d  of the workpiece  1  can be cut successively. 
         [0062]      FIG. 13  is a schematic view of a seventh process of a method of machining the workpiece  1 . After machining the side faces  1   a ,  1   b ,  1   c , and  1   d , machining is again performed along the side face  1   a . As indicated by an arrow  114 , the milling cutter  20  is moved along the side face  1   a . At this time, a linear movement is continued over the position where machining of the side face  1   a  is finished. In other words, the milling cutter  20  is moved to keep a distance from the workpiece  1 . Such an operation prevents machining precision of the side face  1   a  from deteriorating. 
         [0063]    As mentioned above, high-precision machining of the side faces  1   a ,  1   b ,  1   c , and  1   d  of the workpiece  1  can be performed by using the milling cutter  20 . For example, the side faces  1   a ,  1   b ,  1   c , and  1   d  can be mirror finished. 
         [0064]    As comparative example, a method of machining a side face of a plate member by using an end mill as a first rotary tool will now be described. In comparative example, machining is performed by using a side cutting edge of a rotary tool. Here, the side cutting edge of a rotary tool represents a cutting edge on a plane extending in a direction parallel to the rotation axis of the rotary tool. The end cutting edge of the rotary tool represents a cutting edge on an end face extending in a direction perpendicular to the rotation axis of the rotary tool. 
         [0065]      FIG. 14  illustrates a schematic view of a machining method of comparative example. In the machining method of comparative example, the side faces  1   a ,  1   b ,  1   c , and  1   d  of the workpiece  1  is machined by using an end mill  41  as a first rotary tool. The end mill  41  is arranged so that the axis direction of the end mill  41  is parallel to the side faces  1   a ,  1   b ,  1   c , and  1   d . With reference to  FIG. 1 , in place of the milling cutter  20 , the end mill  41  can be mounted on the machine tool  10 . The turning base  16  is controlled so that the side faces  1   a ,  1   b ,  1   c , and  1   d  of the workpiece  1  are parallel to the axis direction of the end mill  41 . Thereafter, the workpiece  1  can be machined by moving the end mill  41  along a side face of the workpiece  1 . 
         [0066]    With reference to  FIG. 14 , a tool tip point  41   a  which is the rotation center of the end mill  41  moves along the outline of the workpiece  1  during machining of the end mill  41 . The side face  1   a  of the workpiece  1  is machined with a side cutting edge of the end mill  41  by moving the end mill  41  as indicated by an arrow  115  and an arrow  116 . In a similar manner, the side faces  1   b ,  1   c , and  1   d  are machined by moving the end mill  41  along the side faces  1   b ,  1   c , and  1   d  as indicated by arrows  117 ,  118 , and  119 . Machining of the side faces  1   a ,  1   b ,  1   c , and  1   d  of the workpiece  1  is completed by further moving the end mill  41  as indicated by arrows  116  and  120 . 
         [0067]    When machining is performed by using a side cutting edge of the end mill  41  in such a manner as in comparative example, the radius of gyration of a portion in contact with a machining surface is equal to the radius of the end mill  41 . This reduces the radius of gyration of a portion to be cut. In order to lessen the cusp height of the machining surface, the tool diameter of the end mill  41  needs to be increased, and the size of the machine tool needs to be large. When an end mill is rotated at a high speed, a spindle shaft of the end mill swings or vibrates, which may negatively affect the machining surface. 
         [0068]    By machining with an end cutting edge of a milling cutter in such a manner as in the present embodiment, the radius of gyration when a cutting portion rotates is made to be large. With reference to  FIG. 3 , since the milling cutter  20  rotates as indicated by the arrow  103 , the radius of gyration of a cutting portion of the milling cutter  20  is a cutting edge radius Rt, which is larger than the radius of gyration of an end mill. The machining speed of the cutting portion  23  can be made high, and a high accuracy surface machining can be easily performed. Since the radius of curvature of a cutting surface of the end cutting edge  23   a  is large, the machining precision is improved compared with the case in which machining is performed by an end mill or the like. 
         [0069]    Further, since the workpiece  1  is in contact with an end cutting edge of the milling cutter  20 , a swing or a vibration of the main axis of the milling cutter  20  can be suppressed. A negative influence on a machining surface due to a swing or a vibration of the main axis can be suppressed. Further, mirror finishing can be performed by a milling cutter without using a tool made of a valuable material such as diamond. 
         [0070]    In the machining method, the milling cutter  20  is arranged so that the rotation axis  24  thereof is inclined with respect to the normal line direction of a machining surface of the workpiece  1 . In other words, machining is performed in a state in which the bottom face of the milling cutter  20  is inclined with respect to the machining surface of the workpiece  1 . By employing this configuration, a high-precision machining can be performed. For example, mirror finishing can be easily performed. In the above-mentioned embodiment, cutting process is performed with a heel portion of the milling cutter  20 . However, the present invention is not limited to the embodiment, and machining may be performed by using a front end in the advancing direction of the milling cutter  20 . In other words, machining may be performed by using a toe portion of the milling cutter  20 . 
         [0071]    In many cases of machining, the end mill  41  of comparative example is selected as a tool for machining a side face of the plate workpiece  1 . In a CAM apparatus or the like, a tool path in a case of using the end mill  41  is output. A control device  55  of the machine tool  10  reads input information including a tool path of the end mill  41  along the outline of the workpiece  1 . Next, the read input information is converted and a tool path for machining the side faces  1   a ,  1   b ,  1   c , and  1   d  of the workpiece  1  by using an end cutting edge of the milling cutter  20  is generated. 
         [0072]      FIG. 15  illustrates a schematic view of a machining system comprising a machine tool  10  and a device for generating input numerical data  54  for inputting to the machine tool  10 . The shape of the workpiece  1  is designed by a CAD (computer aided design) apparatus  51 . The CAD apparatus  51  provides a CAM (computer aided manufacturing) apparatus  53  with shape data  52  of the workpiece  1 . 
         [0073]    In the CAM apparatus  53 , the input numerical data  54  as input information to be input to the control device  55  of the machine tool  10  is generated based on the shape data  52 . The input numerical data  54  is numerical data when a side face of the workpiece  1  is machined by using a side cutting edge of the end mill  41  as the first rotary tool. The input numerical data  54  includes data representing a path of a tool tip point when the end mill  41  is used. The tool tip point of the end mill  41  is a point of rotation center of the bottom face. The input numerical data  54  includes coordinate values of the X-axis, Y-axis and Z-axis. 
         [0074]    The numerical control machine tool  10  includes the control device  55 . The control device  55  includes an arithmetic processing unit. The arithmetic processing unit includes a microprocessor (CPU) performing arithmetic processing and the like, a ROM (Read Only Memory) and a RAM (Random Access Memory) as storage devices, and other peripheral circuits. 
         [0075]    The control device  55  generates output numerical data  62  using input numerical data  54 . The control device  55  includes a numerical data reading unit  56  which functions as an input information reading unit and a path setting unit  60 . The numerical data reading unit  56  has a function of reading the input numerical data  54 . The numerical data reading unit  56  reads the input numerical data  54 . The numerical data reading unit  56  outputs a coordinate value sequence. The coordinate value sequence includes the coordinate values of the X-axis, Y-axis and Z-axis and the rotational angle of the C-axis. 
         [0076]    The path setting unit  60  generates output numerical data  62  based on the read input numerical data  54 . The path setting unit  60  sets a tool path for machining by using an end cutting edge of the milling cutter  20 . The path setting unit  60  sets a tool path of the milling cutter  20  based on the inclination angle or the like of the milling cutter  20  with respect to the workpiece  1 . The output numerical data  62  includes numerical data for moving the milling cutter  20  relative to the workpiece  1 . In other words, the output numerical data  62  includes a command for a moving device when the milling cutter  20  is used. 
         [0077]    The output numerical data  62  which is output from the path setting unit  60  can be set by, for example, the coordinate values of X-axis, Y-axis and Z-axis of the tool tip point of the milling cutter  20 , and a relative angle between the workpiece  1  and the milling cutter  20  on the C-axis. 
         [0078]    The output numerical data  62  is input to a numerical control unit  63 . The numerical control unit  63  drives each-axis servomotor  64  of the moving device based on the output numerical data  62 . The each-axis servomotor  64  includes an X-axis servomotor, a Y-axis servomotor, a Z-axis servomotor, a C-axis servomotor, and the like. This enables a relative movement between the workpiece  1  and the milling cutter  20 . 
         [0079]    Next, a control for generating a tool path for performing machining by using an end cutting edge of the milling cutter  20  in the path setting unit  60  will be described. 
         [0080]    A tool path when the end mill  41  of comparative example as illustrated in  FIG. 14  is used is set in the input numerical data  54 . The path setting unit  60  converts the tool path into a path which passes the contour of the workpiece  1  by using the tool path when the end mill  41  is used. 
         [0081]      FIG. 16  is a schematic view illustrating a path which passes the contour of the workpiece  1 . An arrow  121  indicates that a tool enters a workpiece. Arrows  122  to  129  indicate paths passing through the side faces  1   a ,  1   b ,  1   c , and  1   d  of the workpiece  1 . Further, arrows  122  and  130  indicate that a tool is detached from the workpiece. A shape surrounded by the arrows  122  to  129  is equal to the contour of the machined workpiece  1 . For example, the arrow  122  corresponds to the side face  1   a  of the workpiece  1 , and the arrow  124  corresponds to the side face  1   b.    
         [0082]    A path which passes the contour of the workpiece  1  can be calculated by, for example, the tool path of the end mill  41  as illustrated in  FIG. 14  is moved inside by the radius of the end mill  41 . In other words, an operation which offsets by a length corresponding to the radius of the end mill  41  is performed. 
         [0083]    Next, a tool path for performing machining with an end cutting edge of the milling cutter  20  is generated based on a path which passes the contour of the workpiece  1 . The following example is illustrated by using a workpiece coordinate system whose origin is the position of the center of mass of the maximum area surface  1   e  of the workpiece  1 , and may be illustrated by using a machine coordinate system. 
         [0084]    A vector Pn which is a point sequence representing a path which passes the contour of the workpiece  1  is represented by the following expression (1). The point sequence can be represented by the coordinate of the X-axis and the coordinate of the Y-axis. A variable n represents the number of point included in a path. In this example, N points for calculating the tool path are set. 
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                                 x 
                               
                             
                           
                         
                         
                           
                             
                               P 
                               
                                 n 
                                 y 
                               
                             
                           
                         
                       
                       ] 
                     
                      
                     
                       ( 
                       
                         1 
                         ≤ 
                         n 
                         ≤ 
                         N 
                       
                       ) 
                     
                   
                 
               
               
                 
                   ( 
                   1 
                   ) 
                 
               
             
           
         
       
     
         [0085]    A vector Qn which is a command value of an output of the path setting unit  60  is represented by the following expression (2). The command value of the output of the path setting unit  60  can be set by the coordinate of the Y-axis, the coordinate of the Z-axis, and the rotational angle around the C-axis. The tool path setting unit  60  outputs a vector Qn as a command value of the expression (2) by using the point sequence of the expression (1). 
         [0000]    
       
         
           
             
               
                 
                   [ 
                   
                     Mathematical 
                      
                     
                         
                     
                      
                     2 
                   
                   ] 
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   
                     
                       Q 
                       n 
                     
                     → 
                   
                   = 
                   
                     
                       [ 
                       
                         
                           
                             
                               Q 
                               
                                 n 
                                 y 
                               
                             
                           
                         
                         
                           
                             
                               
                                 
                                   
                                     Q 
                                     
                                       n 
                                       z 
                                     
                                   
                                 
                               
                               
                                 
                                   
                                     Q 
                                     
                                       n 
                                       c 
                                     
                                   
                                 
                               
                             
                           
                         
                       
                       ] 
                     
                      
                     
                       ( 
                       
                         1 
                         ≤ 
                         n 
                         ≤ 
                         N 
                       
                       ) 
                     
                   
                 
               
               
                 
                   ( 
                   2 
                   ) 
                 
               
             
           
         
       
     
         [0086]      FIG. 17  is an enlarged cross-sectional view of the milling cutter  20  and the workpiece  1  for describing variables for calculating a tool path of the milling cutter  20 .  FIG. 17  is an enlarged schematic cross-sectional view of a portion where the workpiece  1  is in contact with the milling cutter  20 . For ease of understanding,  FIG. 17  illustrates a milling cutter so that the radius of curvature of an end cutting edge  23   a  is smaller than that of the actual milling cutter, and so that a lead angle θ is larger than the actual lead angle. 
         [0087]    The cutting portion  23  includes the end cutting edge  23   a . The bottom face of the milling cutter  20  is opposed to a machining surface of the workpiece  1 . The end cutting edge  23   a  is formed so that the cross-sectional shape is an arc. The end cutting edge  23   a  includes a vertex  23   b . A tool corner radius Rc is the radius of curvature at the end cutting edge  23   a  of the cutting portion  23 . A point Bc is the center point of the tool corner radius Rc. The vertex  23   b  is a point which crosses the end cutting edge  23   a  when a line parallel to the rotation axis  24  passing the point Bc is drawn. 
         [0088]    The lead angle θ is an inclination angle of the milling cutter with respect to a machining surface of the workpiece  1 . For example, the lead angle θ is an angle formed by the bottom face  22   a  of the body portion  22  and the machining surface of the workpiece  1 . Alternatively, the lead angle θ is an angle formed by the normal line direction of a machining surface of the workpiece  1  and the rotation axis  24 . Examples of the lead angle θ include a small angle not larger than 1°. In this example, 0.05° is adopted for the lead angle θ. 
         [0089]    A tool tip point Tc is set on the bottom face of the body portion  22 . The tool tip point of the milling cutter  20  in the present invention is a point where the rotation axis  24  of the milling cutter  20  and the bottom face of the milling cutter  20  are crossed with each other. The cutting edge radius Rt is a distance between the tool tip point Tc and the vertex  23   b  in the diameter direction of the milling cutter  20 . A point of contact D is a point where the cutting portion  23  is in contact with the workpiece  1 . In this example, since the lead angle θ is small and the tool corner radius Rc is large, it may be approximated that the point of contact D and the vertex  23   b  are located at the same position. 
         [0090]      FIG. 18  is an explanatory drawing for calculating a tool path when the milling cutter  20  is used. An advancing direction at a vector Pn which is the n-th point of P is calculated. A vector ΔPn representing a movement from the n-th point P to the (n+1)-th point P is calculated by the following expression (3). A moving distance Ln from the n-th point P to the (n+1)-th point P is calculated by the following expression (4). 
         [0000]      [Mathematical 3] 
         [0000]      {right arrow over (Δ P   n )}={right arrow over ( P   n+1 )}−{right arrow over ( P   n )}(1≦ n≦N− 1)  (3)
 
         [0000]        L   n =|  Δ P   n   |(1≦ n≦N− 1)  (4)
 
         [0091]    Next, as a normalized advancing direction when moving from the n-th point P to the (n+1)-th point P, a vector U 1   n  is calculated by the expression (5). Further, a vector U 1   n-1  which is an advancing direction when moving from the (n−1)-th point P to the n-th point P is determined. Thereafter, an advancing direction U 2   n  in which points before and after the n-th point P are averaged is determined by the expression (6). 
         [0000]    
       
         
           
             
               
                 
                   [ 
                   
                     Mathematical 
                      
                     
                         
                     
                      
                     4 
                   
                   ] 
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   
                     
                       U 
                       
                         1 
                         n 
                       
                     
                     → 
                   
                   = 
                   
                     
                       
                         
                           Δ 
                            
                           
                               
                           
                            
                           
                             P 
                             n 
                           
                         
                         → 
                       
                       
                          
                         
                           
                             Δ 
                              
                             
                                 
                             
                              
                             
                               P 
                               n 
                             
                           
                           → 
                         
                          
                       
                     
                     = 
                     
                       
                         
                           
                             Δ 
                              
                             
                                 
                             
                              
                             
                               P 
                               n 
                             
                           
                           → 
                         
                         
                           L 
                           n 
                         
                       
                        
                       
                         ( 
                         
                           1 
                           ≤ 
                           n 
                           ≤ 
                           
                             N 
                             - 
                             1 
                           
                         
                         ) 
                       
                     
                   
                 
               
               
                 
                   ( 
                   5 
                   ) 
                 
               
             
             
               
                 
                   
                     
                       U 
                       
                         2 
                         n 
                       
                     
                     → 
                   
                   = 
                   
                     
                       
                         
                           
                             U 
                             
                               1 
                               
                                 n 
                                 - 
                                 1 
                               
                             
                           
                           → 
                         
                         + 
                         
                           
                             U 
                             
                               1 
                               n 
                             
                           
                           → 
                         
                       
                       
                          
                         
                           
                             
                               U 
                               
                                 1 
                                 
                                   n 
                                   - 
                                   1 
                                 
                               
                             
                             → 
                           
                           + 
                           
                             
                               U 
                               
                                 1 
                                 n 
                               
                             
                             → 
                           
                         
                          
                       
                     
                      
                     
                       ( 
                       
                         2 
                         ≤ 
                         n 
                         ≤ 
                         
                           N 
                           - 
                           1 
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   ( 
                   6 
                   ) 
                 
               
             
           
         
       
     
         [0092]    Although in the above-mentioned example, advancing directions before and after the n-th point P are taken into consideration in order to accurately calculate the advancing direction of the n-th point, advancing directions before and after the n-th point P need not be taken into account at a straight portion immediately before entering a curved portion. In other words, only a straight movement portion immediately before the curved portion may be taken into consideration. When entering a straight portion from a curved portion, only a straight movement portion can be taken into consideration in a similar manner to the above. As illustrated in  FIG. 18 , it is set that the moving distance of the point P on the straight movement portion is large and the moving distance of the point P on the curved portion is small. In this example, a length threshold T is set and an advancing direction U 3   n  can be determined by the following expression (7) based on moving distances before and after the point P and the length threshold T. The length threshold T can be set based on a moving distance on the straight portion and a moving distance on the curved portion. 
         [0000]    
       
         
           
             
               
                 
                   
                       
                   
                    
                   
                     [ 
                     
                       Mathematical 
                        
                       
                           
                       
                        
                       5 
                     
                     ] 
                   
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   
                     
                       U 
                       
                         3 
                         D 
                       
                     
                     → 
                   
                   = 
                   
                     { 
                     
                       
                         
                           
                             
                               U 
                               
                                 1 
                                 
                                   n 
                                   - 
                                   1 
                                 
                               
                             
                             → 
                           
                         
                         
                           
                             ( 
                             
                               
                                 
                                   L 
                                   
                                     n 
                                     - 
                                     1 
                                   
                                 
                                 &gt; 
                                 T 
                               
                               , 
                               
                                 
                                   L 
                                   n 
                                 
                                 ≤ 
                                 T 
                               
                             
                             ) 
                           
                         
                         
                           
                               
                           
                         
                       
                       
                         
                           
                             
                               U 
                               
                                 1 
                                 n 
                               
                             
                             → 
                           
                         
                         
                           
                             ( 
                             
                               
                                 
                                   L 
                                   
                                     n 
                                     - 
                                     1 
                                   
                                 
                                 ≤ 
                                 T 
                               
                               , 
                               
                                 
                                   L 
                                   n 
                                 
                                 &gt; 
                                 T 
                               
                             
                             ) 
                           
                         
                         
                           
                             ( 
                             
                               2 
                               ≤ 
                               n 
                               ≤ 
                               
                                 N 
                                 - 
                                 1 
                               
                             
                             ) 
                           
                         
                       
                       
                         
                           
                             
                               U 
                               
                                 2 
                                 n 
                               
                             
                             → 
                           
                         
                         
                           
                             ( 
                             
                               Region 
                                
                               
                                   
                               
                                
                               other 
                                
                               
                                   
                               
                                
                               than 
                                
                               
                                   
                               
                                
                               the 
                                
                               
                                   
                               
                                
                               above 
                                
                               
                                   
                               
                                
                               region 
                             
                             ) 
                           
                         
                         
                           
                               
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   7 
                   ) 
                 
               
             
           
         
       
     
         [0093]    Next, since the first point (n=0) and the last point (n=N) are not calculated in the expression (7), advancing directions on the first point and the last point are set. Normalized advancing directions at all points are represented by a vector Vn of the following expression (8). 
         [0000]    
       
         
           
             
               
                 
                   [ 
                   
                     Mathematical 
                      
                     
                         
                     
                      
                     6 
                   
                   ] 
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   
                     
                       V 
                       n 
                     
                     → 
                   
                   = 
                   
                     { 
                     
                       
                         
                           
                             
                               U 
                               
                                 1 
                                 n 
                               
                             
                             → 
                           
                         
                         
                           
                             ( 
                             
                               n 
                               = 
                               1 
                             
                             ) 
                           
                         
                       
                       
                         
                           
                             
                               U 
                               
                                 3 
                                 n 
                               
                             
                             → 
                           
                         
                         
                           
                             ( 
                             
                               2 
                               ≤ 
                               n 
                               ≤ 
                               
                                 N 
                                 - 
                                 1 
                               
                             
                             ) 
                           
                         
                       
                       
                         
                           
                             
                               U 
                               
                                 1 
                                 
                                   n 
                                   - 
                                   1 
                                 
                               
                             
                             → 
                           
                         
                         
                           
                             ( 
                             
                               n 
                               = 
                               N 
                             
                             ) 
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   8 
                   ) 
                 
               
             
           
         
       
     
         [0094]    Next, a vector On as an offset vector from the point of contact D of the cutting portion to the tool tip point Tc is calculated. The vector On is represented by the following expression (9). 
         [0000]    
       
         
           
             
               
                 
                   [ 
                   
                     Mathematical 
                      
                     
                         
                     
                      
                     7 
                   
                   ] 
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   
                     
                       O 
                       n 
                     
                     → 
                   
                   = 
                   
                     
                       [ 
                       
                         
                           
                             
                               
                                 
                                   V 
                                   
                                     n 
                                     x 
                                   
                                 
                                 · 
                                 
                                   B 
                                   x 
                                 
                               
                               - 
                               
                                 
                                   V 
                                   
                                     n 
                                     y 
                                   
                                 
                                 · 
                                 
                                   B 
                                   y 
                                 
                               
                             
                           
                         
                         
                           
                             
                               
                                 
                                   V 
                                   
                                     n 
                                     x 
                                   
                                 
                                 · 
                                 
                                   B 
                                   y 
                                 
                               
                               + 
                               
                                 
                                   V 
                                   
                                     n 
                                     y 
                                   
                                 
                                 · 
                                 
                                   B 
                                   x 
                                 
                               
                             
                           
                         
                       
                       ] 
                     
                      
                     
                       ( 
                       
                         1 
                         ≤ 
                         n 
                         ≤ 
                         N 
                       
                       ) 
                     
                   
                 
               
               
                 
                   ( 
                   9 
                   ) 
                 
               
             
           
         
       
     
         [0095]    The variable Bx and variable By are calculated from the following expression (10). The variable Dr represents the rotation direction of the workpiece  1 . For example, when the rotation direction of the workpiece  1  is clockwise, the variable Dr is set to 1, and when the rotation direction of the workpiece  1  is counterclockwise, the variable Dr is set to (−1). The variable Bx and the variable By are the same value regardless of the position of the point P. For this reason, the variables may be calculated in advance, and quoted every time each of the advancing directions of a plurality of points P is calculated. 
         [0000]    
       
         
           
             
               
                 
                   [ 
                   
                     Mathematical 
                      
                     
                         
                     
                      
                     8 
                   
                   ] 
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   
                     B 
                     → 
                   
                   = 
                   
                     
                       [ 
                       
                         
                           
                             
                               B 
                               x 
                             
                           
                         
                         
                           
                             
                               B 
                               y 
                             
                           
                         
                       
                       ] 
                     
                     = 
                     
                       
                         
                           R 
                           c 
                         
                         · 
                         
                           [ 
                           
                             
                               
                                 
                                   
                                     sin 
                                      
                                     
                                         
                                     
                                      
                                     θ 
                                   
                                    
                                   
                                       
                                   
                                 
                               
                             
                             
                               
                                 
                                   1 
                                   - 
                                   
                                     cos 
                                      
                                     
                                         
                                     
                                      
                                     θ 
                                   
                                 
                               
                             
                           
                           ] 
                         
                       
                       + 
                       
                         
                           R 
                           i 
                         
                         · 
                         
                           D 
                           r 
                         
                         · 
                         
                           [ 
                           
                             
                               
                                 
                                   cos 
                                    
                                   
                                       
                                   
                                    
                                   θ 
                                 
                               
                             
                             
                               
                                 
                                   sin 
                                    
                                   
                                       
                                   
                                    
                                   θ 
                                 
                               
                             
                           
                           ] 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   10 
                   ) 
                 
               
             
           
         
       
     
         [0096]    Next, a vector Qn as a command value is calculated by the expression (11) based on a vector Vn which is the advancing direction of the point P and an vector On as a offset vector. 
         [0000]    
       
         
           
             
               
                 
                   [ 
                   
                     Mathematical 
                      
                     
                         
                     
                      
                     9 
                   
                   ] 
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   
                     
                       Q 
                       n 
                     
                     → 
                   
                   = 
                   
                     [ 
                     
                       
                         
                           
                             
                               P 
                               
                                 n 
                                 x 
                               
                             
                             + 
                             
                               O 
                               
                                 n 
                                 x 
                               
                             
                           
                         
                       
                       
                         
                           
                             
                               P 
                               
                                 n 
                                 y 
                               
                             
                             + 
                             
                               O 
                               
                                 n 
                                 y 
                               
                             
                           
                         
                       
                       
                         
                           
                             
                               atan 
                                
                               
                                   
                               
                                
                               2 
                                
                               
                                 ( 
                                 
                                   
                                     
                                       V 
                                       
                                         n 
                                         y 
                                       
                                     
                                     · 
                                     
                                       D 
                                       r 
                                     
                                   
                                   , 
                                   
                                     
                                       V 
                                       
                                         n 
                                         x 
                                       
                                     
                                     · 
                                     
                                       D 
                                       r 
                                     
                                   
                                 
                                 ) 
                               
                             
                             + 
                             
                               θ 
                               · 
                               
                                 D 
                                 r 
                               
                             
                           
                         
                       
                     
                     ] 
                   
                 
               
               
                 
                   ( 
                   11 
                   ) 
                 
               
             
           
         
       
     
         [0097]    In the expression (11), the mathematical function (a tan 2) is a function which calculates the arc tangent (inverse tangent) of a numerical value. The mathematical function (a tan 2) is represented by the expression (12). 
         [0000]    
       
         
           
             
               
                 
                   [ 
                   
                     Mathematical 
                      
                     
                         
                     
                      
                     10 
                   
                   ] 
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   
                     atan 
                      
                     
                         
                     
                      
                     2 
                      
                     
                       ( 
                       
                         y 
                         , 
                         x 
                       
                       ) 
                     
                   
                   = 
                   
                     { 
                     
                       
                         
                           
                             
                               tan 
                               
                                 - 
                                 1 
                               
                             
                              
                             
                               y 
                               x 
                             
                           
                         
                         
                           
                             ( 
                             
                               x 
                               &gt; 
                               0 
                             
                             ) 
                           
                         
                       
                       
                         
                           
                             
                               
                                 
                                   tan 
                                   
                                     - 
                                     1 
                                   
                                 
                                  
                                 
                                   ( 
                                   
                                     y 
                                     x 
                                   
                                   ) 
                                 
                               
                               + 
                               π 
                             
                             , 
                           
                         
                         
                           
                             ( 
                             
                               
                                 y 
                                 ≥ 
                                 0 
                               
                               , 
                               
                                 x 
                                 &lt; 
                                 0 
                               
                             
                             ) 
                           
                         
                       
                       
                         
                           
                             
                               
                                 tan 
                                 
                                   - 
                                   1 
                                 
                               
                                
                               
                                 ( 
                                 
                                   y 
                                   x 
                                 
                                 ) 
                               
                             
                             - 
                             π 
                           
                         
                         
                           
                             ( 
                             
                               
                                 y 
                                 &lt; 
                                 0 
                               
                               , 
                               
                                 x 
                                 &lt; 
                                 0 
                               
                             
                             ) 
                           
                         
                       
                       
                         
                           
                             π 
                             2 
                           
                         
                         
                           
                             ( 
                             
                               
                                 y 
                                 &gt; 
                                 0 
                               
                               , 
                               
                                 x 
                                 = 
                                 0 
                               
                             
                             ) 
                           
                         
                       
                       
                         
                           
                             - 
                             
                               π 
                               2 
                             
                           
                         
                         
                           
                             ( 
                             
                               
                                 y 
                                 &lt; 
                                 0 
                               
                               , 
                               
                                 x 
                                 = 
                                 0 
                               
                             
                             ) 
                           
                         
                       
                       
                         
                           NaN 
                         
                         
                           
                             ( 
                             
                               
                                 x 
                                 = 
                                 0 
                               
                               , 
                               
                                 y 
                                 = 
                                 0 
                               
                             
                             ) 
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   12 
                   ) 
                 
               
             
           
         
       
     
         [0098]    The vector Qn which is a command value expresses the coordinate value of the Y-axis and the coordinate value of the Z-axis of the tool tip point Tc, and the rotational angle of the workpiece  1  around the C-axis. The command value can be calculated based on the relative position of the tool center Tc with respect to the point of contact D of the cutting portion  23  and the advancing direction of the point of contact D. As mentioned above, the path setting unit  60  can set the relative position of the milling cutter  20  with respect to the workpiece  1 . In other words, a tool path of the milling cutter  20  can be set. 
         [0099]    An effect of the machining method will be described in more detail. When machining is performed by using an end cutting edge of the milling cutter  20 , the radius of curvature of a portion where the workpiece  1  is machined is large. For example, the diameter of the end mill of comparative example is from 10 mm to 16 mm. In this case, the radius of curvature of a portion where the workpiece  1  is machined is from 5 mm to 8 mm. In contrast, the tool corner radius Rc which is the radius of curvature of the end cutting edge  23   a  of the cutting portion  23  of the milling cutter of the above-mentioned example is about 100 mm. As mentioned above, since the radius of curvature of a portion where the workpiece  1  is machined is large, high-precision machining can be performed. 
         [0100]    When machining is performed by using an end cutting edge of a milling cutter, the radius of gyration when a cutting portion rotates is large. The radius of gyration when a cutting portion rotates is equal to the cutting edge radius Rt. In the above-mentioned example, the cutting edge radius Rt is about 37 mm. In contrast, the radius of gyration of a portion of the end mill  41  for cutting is equal to the radius of the end mill  41 . For example, the radius of gyration of the end mill  41  is from 5 mm to 8 mm. As mentioned above, the radius of gyration of a portion of the milling cutter  20  for cutting may be larger than that of the end mill  41 . This can make the machining speed of a cutting portion with respect to the workpiece  1  high and enables high precision surface machining. 
         [0101]    In the above-mentioned embodiment, the control device  55  generates a tool path of the milling cutter  20  by using the input numerical data  54  generated by the CAM apparatus  53 . However, the present invention is not limited to the embodiment, and a tool path of the milling cutter  20  may be generated by reading the shape data of the workpiece  1  output from a CAD apparatus by the numerical data reading unit  56 . A path which passes the contour of the workpiece  1  can be generated based on the shape of the workpiece  1 . By this control, a high precision cutting process can be performed by inputting only information of the outline of a workpiece such as the contour of a workpiece and information of a cutting edge of a rotary tool. For example, high-precision machining can be performed by inputting the coordinate of the outline of a workpiece and the tool corner radius Rc and the cutting edge radius Rt of the cutting portion  23 . At this time, for a variable such as a lead angle, a pre-set value can be used. 
         [0102]    For the input information read by the input information reading unit, information including a tool path in which machining is performed by using a side cutting edge of a first rotary tool along the outline of a workpiece can be adopted. For example, the input information may be a first machining program including a tool path of the first rotary tool. In the input numerical data on which a tool path of a rotary tool is directly described, the relative position of the rotary tool with respect to the workpiece is represented by the coordinate values of the point sequence. In contrast, a machining program includes a macro code or the like in order for a user to read or create the program easily. The input information reading unit may read such a machining program. In a similar manner, a path setting unit may output a second machining program including a tool path in which machining is performed using an end cutting edge of a milling cutter as output information. 
         [0103]    With reference to  FIG. 1 , the machine tool  10  includes a turning base  16  and a table swiveling base  17  for changing the orientation of the workpiece  1 . However, the present invention is not limited to the embodiment, and any machine tool which can perform machining using an end cutting edge of a tool. 
         [0104]      FIG. 19  illustrates a schematic perspective view of another machine tool  10 . Another moving device of the machine tool  10  includes a rotary workpiece head  71 . The workpiece  1  is supported by a rotary workpiece head  71  via the holding member  72 . The rotary workpiece head  71  is driven, and thus the workpiece  1  can be rotated around the A-axis  73 . The milling cutter  20  is formed to rotate as indicated by an arrow  103 . The milling cutter  20  is formed to move in the Y-axis direction and the Z-axis direction. Also in such a machine tool, machining of a side face of the workpiece  1  in a similar manner to the above-mentioned embodiment can be performed. 
         [0105]    In the above-mentioned embodiment, the first rotary tool is an end mill, and the second rotary tool is a milling cutter. However, the present invention is not limited to the embodiment, and a rotary tool for machining while rotating around the rotation axis can be used. 
         [0106]    The above-described embodiments can be appropriately combined with each other. In the above-described drawings, the same reference numerals are attached to the same or corresponding portions. The above-described embodiments are merely examples and are in no way intended to limit the invention. Further, the above-described embodiments include modifications indicated in the scope of claims. 
       REFERENCE SIGNS LIST 
       [0000]    
       
           1  workpiece 
           1   a  to  1   d  side face 
           2  rotation axis 
           10  machine tool 
           20  milling cutter 
           22  body portion 
           22   a  bottom face 
           23  cutting portion 
           23   a  end cutting edge 
           24  rotation axis 
           41  end mill 
           54  input numerical data 
           55  control device 
           56  numerical data reading unit 
           60  path setting unit 
           62  output numerical data 
           71  rotary workpiece head