Patent Publication Number: US-2010111632-A1

Title: Method and apparatus for non-rotary machining

Description:
FIELD OF THE INVENTION 
     This invention relates generally to methods and tools for machining parts and, more particularly, to machines that are capable of performing profiling operations. 
     BACKGROUND 
     Machining operations fall into two large categories: Hole-making and profiling. Hole-making includes drilling, tapping, and counterboring. Profiling is the removal of material from a workpiece by means of cutting to produce a specified shape and surface finish. Both lathes and mills can perform profiling operations. Generally, lathes produce parts at faster material removal rates and with finer surface finishes than mills. However, the profiling operation of a lathe is restricted to a two-dimensional work envelope which limits the parts it can produce to those with circular cross-sections. A mill can profile within a three-dimensional work envelope, which permits the production of parts with a greater range of shapes, although at a slower material removal rate and with a rougher finish than a lathe. The present invention combines the advantages of the lathe and the mill in profiling operations without their limitations by producing parts with an unrestricted range of shapes with very fine surface finishes at high rates of material removal. 
     The profiling operations of lathes and mills are limited because they rely upon rotary motion to cut away material from the workpiece. Rotary motion creates a sufficiently high surface footage to remove material. Those skilled in the art will recognize that surface footage is the linear rate of movement of the cutting edge of the tool calculated by multiplying the revolutions per minute of the workpiece or tool by its circumference. However, rotary motion imposes symmetry about the axis of rotation upon either the shape of the part to be produced or the cutting tool used. In the case of the lathe, the workpiece rotates and the cutting tool does not. It is the need to rotate the workpiece that restricts the lathe to a two-dimensional work envelope and so limits the parts a lathe can profile to those with circular cross-sections, i.e., axial symmetry. In the case of the mill, the cutting tool rotates and the workpiece does not. This permits a three-dimensional work envelope and so the profiling of parts within a wide range of complex surfaces, i.e., non-symmetrical shapes, including those with non-uniform rational B-spline (NURBS) surfaces which are also known as Bezier curves. However, the need to rotate the cutting tool, which imposes axial symmetry upon it, limits the shape and surface finish that a mill can produce on a workpiece and the material removal rate at which it can do so. Moreover, the rough surface finish left by milling often necessitates a secondary grinding operation or polishing by hand to create a finer finish on a part, therefore adding time and expense to its production. 
     Machine tools that profile by means of non-rotary methods exist in prior art, including planers, shapers, broaching machines and, most recently, U.S. Patent Publication No. U.S. 62003/0103829 to Suzuki et al. which is herein incorporated by reference. However, none of these machine tools are capable of producing the unrestricted range of shapes provided by the present invention. This is because the profiling operations of all of these machine tools are restricted to one-dimensional cutting paths within a two-dimensional work envelope. For example, the Suzuki invention discloses a method of cutting long, straight rails made of hardened steel. In this method a static, i.e., non-rotating, cutting tool is fixtured at a starting point within a two-dimensional work envelope to cut the workpiece along a linear one-dimensional path. To cut along a different one-dimensional path, the tool must be re-fixtured at a different starting point within the work envelope. Like all other methods of non-rotary machining in the prior art, this device is constrained to a one-dimensional cutting path within a two-dimensional work envelope. Lacking three-dimensional motion within a three-dimensional work envelope, none of these non-rotary methods of machining can produce anything more than simple shapes on a workpiece and so have only highly specialized and severely limited applications. 
     Therefore, the need exists to provide a method and apparatus for profiling operations with three-dimensional non-rotary machining characteristics that overcome the shortcomings of all present machine tools and machining methods in order to produce substantially fine finishes and complex shapes at rapid material removal rates without the expense of secondary operations and manual labor. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The present invention will now be described with reference to the accompanying drawings wherein like reference numerals in the following written description correspond to like elements in the several drawings identified below. 
         FIG. 1  is a perspective view of a prior art machined part that can be produced by the non-rotary machining method of the present invention. 
         FIG. 2  is part view of the part depicted in  FIG. 1  as machined by prior art milling techniques. 
         FIG. 3  is a partial view of the part depicted in  FIG. 1  as machined by the present invention. 
         FIG. 4  is a front view of a non-rotary cutting tool used in accordance with an embodiment of the present invention to machine the part as depicted in  FIG. 3 . 
         FIG. 5  is a side view of the tool depicted in  FIG. 4 . 
         FIG. 6  is an elevation view of a prior art tool used in accordance with a prior art mill to machine the part as depicted in  FIG. 2 . 
         FIG. 7  is a bottom view of the tool depicted in  FIG. 6 . 
         FIG. 8  is a bottom view of the prior art tool depicted in  FIGS. 6 and 7  as used to machine a part. 
         FIG. 9  is a front view of a non-rotary cutting tool used in accordance with various embodiments of the present invention. 
         FIG. 10  is a side view of the tool depicted in  FIG. 9 . 
         FIG. 11  illustrates perspective views of different insertable cutting edges for the tool depicted in  FIGS. 9 and 10 . 
         FIG. 12  is a front view of an axially asymmetric non-rotary cutting tool used in accordance with various embodiments of the present invention. 
         FIG. 13  is a side view of the tool depicted in  FIG. 12 . 
         FIG. 14  is an elevation view of the tool depicted in  FIGS. 9 and 10  being used to machine a part in accordance with one aspect of the present invention. 
         FIG. 15  is a perspective view of a part machined in accordance with the “3-axis” embodiment of the present invention. 
         FIG. 16  is a perspective view of another part machined in accordance with the “4-axis” embodiment of the present invention. 
         FIG. 17  is a perspective view of a non-rotary machining apparatus in accordance with the “3-axis” and “4-axis” embodiments of the present invention. 
         FIG. 18  is a flow chart of the non-rotary machining method of the present invention machining the part depicted in  FIG. 15  in accordance with the “3-axis” embodiment of the present invention. 
         FIG. 19  is a flow chart of the non-rotary machining method of the present invention machining the part depicted in  FIG. 16  in accordance with the “4-axis” embodiment of the present invention. 
         FIG. 20  is a flow chart of the non-rotary machining method of the present invention machining a complex surface, such as a NURBS surface, in accordance with a “5-axis” or “7-axis” embodiment of the present invention. 
     
    
    
     DESCRIPTION OF PREFERRED EMBODIMENT 
     Comparison with the Prior Art. The present invention is distinguished from current machining methods and apparatuses for profiling operations by: [1] A non-rotating cutting tool that is unconstrained by axial symmetry and [2] driven along a one-, two-, or three-dimensional cutting path [3] within a three-dimensional work envelope [4] to remove material from a non-rotating workpiece. No other method or apparatus for machining possesses all of these characteristics. As a consequence of these characteristics the present invention can machine: [1] Parts with an unrestricted range of shapes from simple to complex, symmetrical and asymmetrical, [2] including those with thin cross-sections, [3] with fine surface finishes [4] at high rates of material removal. No other method or apparatus for machining can produce these results on a single machine tool in a single profiling operation. The comparison of these characteristics and capabilities between the present invention and prior art are illustrated in Table 1 below. 
     
       
         
           
               
             
               
                 TABLE 1 
               
             
            
               
                   
               
               
                 COMPARISON OF CURRENT MACHINING METHODS TO NON-ROTARY MACHINING METHOD 
               
            
           
           
               
               
               
               
               
               
               
               
               
               
            
               
                 Machining 
                 1-D Tool 
                 2-D Tool 
                 3-D Tool 
                 2-D Work 
                 3-D Work 
                 Complex 
                 Thin Cross- 
                 Fine 
                 Rapid Material 
               
               
                 Method 
                 Path 
                 Path 
                 Path 
                 Envelope 
                 Envelope 
                 Shapes 
                 Sections 
                 Finish 
                 Removal 
               
               
                   
               
               
                 Non-Rotary 
                 X 
                 X 
                 X 
                 X 
                 X 
                 X 
                 X 
                 X 
                 X 
               
               
                 Machining 
               
               
                 Milling 
                 X 
                 X 
                 X 
                 X 
                 X 
                 X 
               
               
                 Turning 
                 X 
                 X 
                   
                 X 
                   
                   
                 X 
                 X 
                 X 
               
               
                 Shaping 
                 X 
                   
                   
                 X 
                   
                   
                   
                   
                 X 
               
               
                 Planing 
                 X 
                   
                   
                 X 
                   
                   
                   
                   
                 X 
               
               
                 Broaching 
                 X 
                   
                   
                 X 
               
               
                 Suzuki 
                 X 
                   
                   
                 X 
               
               
                 Publication 
               
               
                   
               
            
           
         
       
     
     The present invention is most directly compared to the profiling operations of mills, because it mostly obsoletes the need for such. The primary utility a mill will retain is hole-making within a three-dimensional work envelope. The reason for this obsolescence is that the non-rotary machining method of the present invention can execute any profiling operation that a mill can: [1] Without any restriction of the shape required for the part [2] with a finer lathe-like surface finish, thus eliminating or reducing the need for grinding or polishing, [3] at material removal rates generally five to forty times faster. These advantages are a direct consequence of the present invention employing a static (i.e., non-rotating) cutting tool instead of a rotating one. This difference is well demonstrated by the significantly increased material removal rates of the present invention, as will be fully described later. Furthermore, an apparatus embodying this method will generally be less expensive, less complex, and sturdier than a comparable mill. 
     Unrestricted Range of Shapes. Despite their significant disadvantages mills are presently used to machine parts with complex shapes, such as large die sets used in the automotive industry to form car roofs, hoods, and fenders or smaller precision components like impellers or the like. For example,  FIG. 1  illustrates a perspective view of a prior art impeller  100  that can be produced by the non-rotary machining center and methods of the present invention. The area depicted by “II” indicates a close-up as shown in  FIG. 2  while the area “III” indicates that shown in the  FIG. 3 . Those skilled in the art recognize that amongst existing machine tools, mills are the least restricted in the shapes they can produce in a profiling operation. However, the need to rotate the cutting tool imposes the constraint of axial symmetry upon it. That, in turn, restricts to the shape of the tool the range of shapes that a mill can cut into a workpiece. 
     As specifically seen in  FIG. 2  and  FIG. 3  the differences in the type of cut using prior art milling techniques and the non-rotary machining method of the present invention are clearly illustrated.  FIG. 2  illustrates a close-up of the type of cut as used with prior art milling techniques that create a radius between edges while  FIG. 3  uses present machining methods to create an orthogonal edge. With regard to  FIG. 3 , an example of the process creates an orthogonal interior corner formed by the intersection of two curved surfaces. This type of surface cannot be produced using prior art milling techniques. Both FIGS.  2  and  3  illustrate an impeller  100  utilizing a series of vanes  102 , that extend outwardly from a concave surface  104 . As shown in  FIG. 3 , the intersection of a vane  102  and the surface  104  creates a sharp inside corner  106 . 
       FIG. 4  is a front view of a non-rotary cutting tool used in accordance with an embodiment of the present invention used to machine the part as depicted in  FIG. 3 .  FIG. 5  is a side view of the tool depicted in  FIG. 4 . Because the machining method of the present invention employs a non-rotating cutting tool  200 , axial symmetry is not a requirement for the tool. Therefore, the tool  200  does not need to be relieved in all directions to clear the curved surfaces  102   104  of the impeller  100 . The tool  200  needs only to be relieved on the posterior side  206  that is perpendicular to the direction of its cutting path. Therefore, the tool&#39;s cutting edge  202  can feature a sharp corner  204  which can be continuously re-oriented along the path of the corner  106 , by means of the present invention, to machine it as specified. For this reason, the present invention, unlike a mill, is unrestricted in the shapes it can cut in a profiling operation. 
       FIG. 6  is an elevation view of a prior art tool used in accordance with a prior art mill to machine the part as depicted in  FIG. 2 .  FIG. 7  is a bottom view of the tool depicted in  FIG. 6 . In order to cut the side of the vane  102  and the concave curve of the surface  104  to specification, a mill must use an axially symmetrical cutting tool like that shown in  FIG. 6 . As seen in  FIGS. 6 and 7 , the tool  300  includes a spherical nose  302  and cutting edge  304 . The tool  300  is relieved in all directions to clear the curved surfaces  102 ,  104  specified for the impeller  100 .  FIG. 2  illustrates the prior art techniques where the vanes  102  and the concave surface  104  of the milled impeller  100  are to specification. Instead of the sharp inside corner  106  as seen in  FIG. 3 , at their intersection is a large radius  108  conforming to the spherical nose  302  of the mill&#39;s rotating cutting tool. 
     Finer Surface Finishes. Even when a mill can profile a shape to its specified dimensions, it will leave a rough or scalloped edge. As noted above, prior art  FIG. 8  illustrates the cutting tool  300  as frequently used by a mill in profiling operations. The tool  300  includes a number of cutting edges  304 , called flutes, which cut material away from the workpiece  306  as the tool  300  rotates. Because the flutes  304  are spaced apart from each other, material is not cut away constantly from the workpiece  306 . Instead, the material is only cut away during the time when one of the four flutes  304  is in contact with the workpiece  306 . Consequently, the removal of material by the rotating tool  300  is not consistent as it moves through the workpiece  306 . The result is an uneven surface marked by a series of scallops  308 . If these scallops  308  are excessive or otherwise unwanted, it is necessary to grind or manually polish the workpiece  306  after completion of the profiling operation on the mill to produce a sufficiently fine finish on the completed part. 
       FIG. 9  is a front view of a non-rotary cutting tool used in accordance with various embodiments of the present invention while  FIG. 10  is a side view of the tool depicted in  FIG. 9 . Unlike the flutes  304  of a mill&#39;s rotating cutting tool  300 ,  FIGS. 9-10  illustrate the non-rotating tool  400  with a cutting edge  404  that, when employed by the present invention in a profiling operation, is in constant, stable contact with the workpiece  500  as depicted in  FIG. 14 . As a result, there are no scallops left on the cut surface of the workpiece  500 . For this reason, the present invention produces a much finer surface finish in a profiling operation than a mill does, thus eliminating or reducing the need for subsequent grinding or polishing. 
     Faster material removal rates.  FIG. 11  illustrates perspective views of different insertable cutting edges for the tool depicted in  FIGS. 9 and 10 . Alternatively to that shown in  FIGS. 9-10 , the non-rotating cutting tool  400  may include a cutting edge  404  that is either inserted into or integral to the tool body  402 . It should be evident to those skilled in the art that the cutting edge  404  is illustrated as a “circular edge” that may be altered to a sharp point, square face  408  or other geometries such as shown in  FIG. 11  to machine the desired shape and surface finish on a workpiece. 
       FIG. 12  illustrates a front view of an axially asymmetric non-rotary cutting tool used in accordance with various embodiments of the present invention.  FIG. 13  is a side view of the tool depicted in  FIG. 13 . The tool body  412  can be of any shape necessary to support the cutting edge  404  while providing relief for it to machine deep or other spatially constrained features into a workpiece. An example of this tool body is illustrated in  FIGS. 12-13 . Often a non-rotating cutting tool  400  such as that depicted in  FIGS. 9-10  will be the same as, or similar to, cutting tools used for turning. This is due to the fact that the non-rotary machining method of the present invention does not restrict the operation of the tool as does turning to a two-dimensional cutting path within a two-dimensional work envelope. Therefore, a non-rotating cutting tool can possess cutting edges, tool body shapes, and asymmetrical features not found in turning tools to machine complex shapes not possible with turning. 
       FIG. 14  illustrates a non-rotating cutting tool  400  removing material from a workpiece  500  in accordance with an embodiment of the present invention. Once in contact with the workpiece  500  the cutting edge  404  of the tool  400  is continuously engaged in a uniform cutting motion that removes material with a constant force. This is in sharp contrast to the variable force of the rotating cutting tool  300  used by a mill in a profiling operation, as depicted in  FIG. 8 . In that instance each flute  304  of the tool  300  rotates towards the workpiece  306  and swings from no engagement to full engagement to no engagement again. The variation in force is the result in the change of the chip load of the tool  300  as the mass of material that the flute  304  is removing increases from zero to full chip load to zero again. Furthermore, the force of a rotating cutting tool  300  also varies because its acceleration decreases from maximum surface footage at its outside diameter to zero at its centerline, so that the nature of its cutting motion ranges from shearing at the maximum radial extent of the flute  310  to tearing along most the flute&#39;s edge  312  to scraping along its bottom  314  to pushing through material at its center  316 . 
     The difference between the two types of cutting motions is that a rotating cutting tool  300  leaves a series of scallops  308  from side-cutting on the surface of the workpiece  306  and a rough finish from bottom-cutting, whereas a non-rotating cutting tool  400  leaves a smooth finish on the workpiece  500 . This is because the variable force of a rotating cutting tool  300  has the effect of mostly tearing material away from the workpiece  306  rather than shearing it as does a non-rotating cutting tool  400  from the workpiece  500 . Additionally, by shearing material with constant force to remove it rather than tearing it away with variable force, the non-rotary machining method can produce parts with thinner cross-sections more precisely, more quickly, and with less scrap than is possible with milling. Also, shearing instead of tearing keeps the heat from the friction of the cutting motion in the chip rather than the cutting tool  400  or the workpiece  500 , which improves tool life and reduces defects and distortions in the finished part, especially those with complex shapes or thin cross-sections. Less obvious is that the variable force of a rotating cutting tool  300  introduces a much larger element of chaos into the cutting motion than does the constant force of a non-rotating cutting tool  400 . This disorder, often manifesting itself as chatter, increases the unpredictably of a profiling operation on a mill compared to the present invention and therefore significantly restricts the range, performance, and productivity of mills even for simple operations. The constancy of force in the cutting motion of a non-rotating cutting tool  400  along a three-dimensional path through a three-dimensional work envelope is the essence of the present invention which cannot be replicated by any machining method or apparatus of prior art. 
     The stable, constant cutting force that the present invention applies through a non-rotating cutting tool ensures that energy is not drawn away from the task of material removal in the form of chaotic motion such as chatter. Therefore, constancy of the cutting force is critical to increasing the material removal rate of the present invention in comparison to milling. Even more fundamental to the present invention&#39;s significantly faster material removal rates is that, unlike a mill, none of the cutting force it delivers is diverted to the rotation of the cutting tool. Because the rate of material removal is the result of the depth of cut multiplied by the width of cut multiplied by the linear rate of the cutting tool&#39;s motion through the workpiece, commonly called the “feed rate,” the rotation of the cutting tool is not a direct factor. Consequently, any cutting force that must be diverted to rotation of the tool, commonly called the “cutting speed” or “surface footage”, reduces the force available to increase the feed rate and, in turn, increases the material removal rate. Table 2 compares the non-rotary method of the present invention to milling for four common machining operations using the best practices for each to illustrate the greater material removal rates of the present invention by factors of 12, 23, 33, and even 200. For this and the other reasons stated above, the present invention can remove material from a workpiece in profiling operations at rates generally 5 to 40 times faster than a mill. 
     
       
         
           
               
             
               
                 TABLE 2 
               
             
            
               
                   
               
               
                 COMPARISON OF MATERIAL REMOVAL RATES FOR 41xx SERIES ALLOY STEEL WORKPIECE 
               
            
           
           
               
               
               
               
               
               
               
               
               
            
               
                   
                 Machining 
                   
                 Depth of 
                 Width of 
                 Cutting Speed 
                 Feed Rate 
                 Material Removal 
                 Non-Rotary/Milling 
               
               
                 Operation 
                 Method 
                 Cutting Tool 
                 Cut (mm) 
                 Cut (mm) 
                 (m/min.) 
                 (m/min.) 
                 Rate (c.c./min.) 
                 Comparison 
               
               
                   
               
            
           
           
               
               
               
               
               
               
               
               
               
            
               
                 surfacing 
                 milling per 
                 110 mm dia. carbide 
                 0.25 
                 100 
                 150 
                 2.0 
                 50.0 
                 12 
               
               
                   
                 prior art 
                 inserted surface mill 
               
               
                   
                 non-rotary per 
                 20 mm dia. carbide 
                 6.5 
                 1.5 
                 n/a 
                 60 
                 582 
               
               
                   
                 present invention 
                 inserted cutter 
               
               
                 side milling 
                 milling per 
                 20 mm dia. carbide 
                 10 
                 18 
                 45 
                 0.18 
                 32.4 
                 23 
               
               
                   
                 prior art 
                 end mill 
               
               
                   
                 non-rotary per 
                 10 mm wide carbide 
                 3.3 
                 7.5 
                 n/a 
                 30 
                 743 
               
               
                   
                 present invention 
                 inserted cutter 
               
               
                 rough 
                 milling per 
                 20 mm carbide 
                 3.3 
                 4 
                 300 
                 1.5 
                 19.8 
                 33 
               
               
                 contouring 
                 prior art 
                 inserted ball- 
               
               
                   
                   
                 nose end mill 
               
               
                   
                 non-rotary per 
                 20 mm dia. carbide 
                 6.5 
                 3.3 
                 n/a 
                 30 
                 644 
               
               
                   
                 present invention 
                 inserted cutter 
               
               
                 finish 
                 milling per 
                 3 mm dia. carbide 
                 0.6 
                 0.25 
                 120 
                 1.0 
                 0.15 
                 200 
               
               
                 contouring 
                 prior art 
                 ball-nose end mill 
               
               
                   
                 non-rotary per 
                 3 mm dia. carbide 
                 1.0 
                 0.25 
                 n/a 
                 120 
                 30 
               
               
                   
                 present invention 
                 inserted cutter 
               
               
                   
               
            
           
         
       
     
       FIG. 17  is a perspective view of a non-rotary machining apparatus in accordance with the “3-axis” and “4-axis” embodiments of the present invention. The apparatus employing the non-rotary machining method of the present invention can be embodied in a variety of configurations. In contrast to that shown in  FIG. 17 , these embodiments are comparable to those of computer numerical controlled mills (known in the trade as “machining centers”), except that the present invention does not use a spindle to rotate a cutting tool. Instead, as seen in  FIG. 9 , a non-rotary cutting tool is used in accordance with various embodiments of the present invention. In this illustration a tool holder  610  replaces the spindle into which a non-rotating cutting tool  400  is affixed. The simplest embodiment of the present invention is a “3-axis” machine  600 , which can drive the cutting tool along any one of the three linear axes  502   504   506 , or any combination of them (under certain circumstances), that together define the machine&#39;s three-dimensional work envelope.  FIG. 15  illustrates a workpiece where a “3-axis” machine is sufficient to machine the circular cavity  508  into the workpiece  500  by means of the process flowcharted in  FIG. 18  described hereinafter. Yet another basic embodiment is a “4-axis” machine  600 , which has all of the three-axis linear motion of the “3-axis” machine plus a “rotary axis”  510  to continuously re-orient the cutting tool&#39;s face  404  in any direction to maintain its perpendicularity to a level two-dimensional cutting path. Maintaining perpendicularity optimizes the performance of the cutting tool and thus maximizes the range of shapes the machine can cut. The mechanism for this fourth axis  510  can be either a rotary tool holder  610  to which the cutting tool  400  is attached or a rotary table  612  to which the workpiece  500  is attached. By either means, a “4-axis” machine is sufficient to machine the curved circular cavity  512  into the workpiece  500  illustrated in  FIG. 16  by means of the process flowcharted in  FIG. 19  described hereinafter. 
       FIG. 18  is a flow chart of the non-rotary machining method of the present invention machining the part depicted in  FIG. 15  in accordance with the “3-axis” embodiment of the present invention. The non-rotary machining method  700  includes the steps of setting up the machine for operation  701 . A cutting tool is fixtured in a tool holder  703  and a workpiece is fixtured on a table  705 . Tool and cutting path data is then loaded into the machine&#39;s controller  707  and a cycle start is initiated to execute operation  709 . The tool then moves toward the workpiece to the start point of the first cutting path  711  and then removes material from the workpiece along a 1-dimensional cutting path without rotation  713 . At the end point of the cutting path the tool moves to a relief point above the workpiece  715  and a determination is made if the operation is completed  717 . If not, the operation continues with the cutting tool moving to the start point of the next cutting path  711 . If the operation is completed, the cutting tool returns to the cycle start position  719  and the operation ends  721 . 
       FIG. 19  is a flow chart of the non-rotary machining method of the present invention machining the part depicted in  FIG. 16  in accordance with the “4-axis” embodiment of the present invention. The method  800  includes the steps of setting up the machine for operation  801  where the cutting tool is fixtured in a tool holder  803 . A workpiece is then fixed on the table  805  and the tool and cutting path data is loaded into the controller  807 . Cycle start is initiated  809  and the cutting tool moves toward the workpiece to the start part of the first cutting path  811 . The cutting tool then removes material from the workpiece along a level 2-dimensional cutting path without rotation while tool holder continuously re-orients the tool to maintain the perpendicularity of the face of the cutting edge to the cutting path  813 . At the end point of the cutting path the tool moves to a relief point above the workpiece  815 . A determination is then made if the operation is completed  817 . If not, the cutting tool moves to the start point of the next cutting path  811 . If the operation is completed, then the cutting tool returns to the cycle start position  819  and the operation ends  821 . 
     Still more complex embodiments are the “5-axis” and the “7-axis” machines. These embodiments have all of the three-axis linear and fourth-axis rotary motions of the “4-axis” machine plus additional rotary or tilt axes to orient the cutting tool&#39;s face in any direction to maintain its perpendicularity to any three-dimensional cutting path. These machines are unrestricted in the shapes and surfaces they can produce, including NURBS surfaces, by means of the process flowcharted in  FIG. 20 . 
       FIG. 20  is a flow chart of the non-rotary machining method in accordance with a “5-axis” or “7-axis” embodiment of the present invention. The process  900  includes the step of setting up the machine for operation  901  and fixturing the cutting tool in a tool holder  903 . The workpiece is fixtured on the table  905  and the tool and cutting path is loaded into the controller  907 . Cycle start is initiated  909  and the cutting tool moves to the start point of the first cutting path  911 . The cutting tool then removes material from the workpiece along a 3-dimensional cutting path without rotation while the tool holder continuously re-orients and tilts the tool to maintain the perpendicularity of the face of the cutting edge to the cutting path  913 . A determination is made if the operation is completed  917 . If not completed, the cutting tool moves to the start point of the next cutting path  911  and the operation continues. If the operation is complete, the cutting tool returns to the cycle start position  919  and the operation ends  921 . Thus, the method of the present invention as describe in  FIGS. 18-20 , overcomes the limitations of lathes and mills in profiling operations by employing a non-rotary method of machining and eliminates milling for most profiling operations. 
     While the present invention has been described in terms of the preferred embodiments discussed in the above specification, it will be understood by one skilled in the art that the present invention is not limited to these particular preferred embodiments, but includes any and all such modifications that are within the spirit and scope of the present invention as defined in the appended claims.