KR101791073B1 - Post processing system using angle head spindle - Google Patents

Abstract

... 수학식 (1)

... 수학식 (2)The present invention relates to a post processor for 5-axis machining, wherein the 5-axis machining tool for 5-axis machining includes angle head spindles and the 5-axis machining post processor when the angle head spindle includes the tool head, (NC) data is represented by the following equation (1), and? _I is represented by the following equation (2): NC (numerical control) The present invention relates to a post processor for 5-axis machining. The post processor for 5-axis machining with an angle head can increase the accuracy and convenience of an NC program for machining a complicated inner surface.

... Equation (1)

&Quot; (2) "

Description

BACKGROUND OF THE INVENTION 1. Field of the Invention [0001] The present invention relates to a post processor for 5-axis machining using an angle head spindle,

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a post processor for 5-axis machining using an angle head spindle, and more particularly, to a post processor for 5-axis machining using an angle head spindle capable of increasing the accuracy and convenience of an NC program for machining a complicated inner surface .

The 5-axis machining can combine the two linear feed axes with three linear feed axes to implement various types of tool attitude vectors. The tool attitude vector at the arbitrary machining point determines only one effective tool attitude according to the tool attitude and the travel path plan to optimize the interference avoidance and the machining efficiency according to the structure of the infinite or the five axis air structure and the machining shape.

In this case, the 5-axis air structure is considered first, and the 5-axis air is divided into two types according to the shape of the pylons, namely, a table tilting and table rotation type, HT-TR (Head tilting, table rotation type and HT-HR type.

At this time, the workpiece is mounted on the table, the spindle is mounted on the head, the rotation which is rotating within an arbitrary angle limit is referred to as tilting, and the rotation which rotates infinitely is referred to as rotation.

Most of the 5-axis machining is realized by selecting the most suitable mechanism for the machining characteristics of the workpiece.

However, when an inclined shape is machined at an arbitrary angle on the inner surface of the part or the inner surface of the cylinder, the normal vector of the shape to be machined and the tool axis vector do not coincide with each other.

For example, a type most suitable for pocketing in the shape of a cylinder inclined with respect to the central axis of the cylinder is the HT-HR type, but when the inner diameter of the cylinder is small and the depth is deep, insertion of the head is impossible. Can not.

Especially, when a complicated inner shape machining such as an inner oil pocket groove of a hydrostatic bearing is required, it is impossible to perform a 5-axis grinding. Therefore, a gross cutter is used or the material itself is divided and then reworked.

However, these techniques have problems in that the manufacturing cost of the tool is increased, the cost of fixture is increased due to multiple setup, and the precision is lowered. To solve this problem, the inner construction vector is rotated at a desired angle, Angle head spindle (hereinafter, referred to as an angle head) capable of performing effective 5-axis machining is developed and variously applied.

In general, the angle head has a spindle of a machine tool in a vertical direction in order to perform a cutting operation in a machine tool such as a machining center or a boring machine. However, when the workpiece has to be machined horizontally, And is mounted on a spindle.

More specifically, an angle head which can be effectively used for a workpiece inner surface difficult to be machined by 5-axis machining or a shape deviating from a tilting limit can be obtained by rotating the main spindle through a bevel gear mechanism inside the angle head, And the like.

At present, the main processing part applying the angle head is an inner surface machining part of various shapes including an inner surface shape of an aircraft part, an engine block of an automobile or a ship, a brake monoblock pocket shape, and an oil pocket shape of a hydrostatic bearing.

At this time, the key issue for realizing 5-axis machining using angle head is post-processing. In 5-axis machining, post-processing refers to a task of converting a given tool posture and tool position vector, CL (Cutter location) data, into NC (numerical control) data corresponding to the mechanism of the machining center, Up to now, there have been few studies on post-processing post-processing using angle head.

On the other hand, the 5-axis air with the angle head has more complexity in the implementation of post-processing, while providing easier access and greater freedom to the inner shape that is difficult to process.

Therefore, it is necessary to clarify the geometrical relationship between the given 5-axis air mechanism and the angle head, and to post-process without interference and collision.

Korean Patent No. 10-1415974

SUMMARY OF THE INVENTION The present invention has been made in view of the above problems, and an object of the present invention is to provide an angle head spindle capable of increasing the accuracy and convenience of an NC program for complicated inner surface machining by developing a post processor for effectively 5-axis machining a cylindrical inner surface shape using an angle head spindle To provide a post processor for 5-axis machining.

The objects of the present invention are not limited to the above-mentioned objects, and other objects not mentioned can be clearly understood by those skilled in the art from the following description.

According to an aspect of the present invention, there is provided a post processor for 5-axis machining,

Wherein the 5-axis machining unit for 5-axis machining includes an angle head spindle,

The post processor for 5-axis machining in the case of including the angle head spindle converts the CL (Cutter location) data, which is a given tool posture and tool position vector, into numerical control (NC) data suitable for the mechanism of the machining apparatus,

Wherein the numerical control (NC) data is represented by the following equation (1), and? _I is represented by the following equation (2).

... 수학식 (1)

... Equation (1)

(In the above equation (1), θ _j is the rotation angle, θ _i is the tilt angle, and P _NC is the position vector of the NC data.)

... 수학식 (2)

&Quot; (2) "

(2), the subscripts i, j and k of K _ij mean the rotation center axes x, y and z, respectively, and u _i , u _j and u _k are the tool posture vector components of the CL data, α is the initial angle of inclination of the angle head, and K _ij is the AB type mechanism.)

Further, the present invention provides a post processor for 5-axis machining, wherein the θ _j in the equation (1) is expressed by the following equation (3).

... 수학식 (3)

... (3)

(3), the subscripts i, j and k of K _ij mean the rotation center axes x, y and z, respectively, and u _i , u _j and u _k are the tool posture vector components of the CL data, K _ij is an AB type mechanism.)

Further, the present invention provides a post processor for 5-axis machining, wherein P _NC in the case of the HT-HR type is expressed by Equation (4).

... 수학식 (4)

... (4)

(The subscript i, j, k of the K _ij in equation (4) refers to the respective central axis of rotation x, y, z, and P _CL is a position vector of the CL _{data, T 1 = T (t i} , t _j , t _k ), and K _ij is the AB type mechanism.

Further, the present invention provides a post processor for 5-axis machining, wherein P _NC in the case of HT-TR type is expressed by Equation (5).

... 수학식 (5)

... (5)

(The subscript i, j, k of the K _ij in equation (5) refers to the respective central axis of rotation x, y, z, and P _CL is the position of the CL data _{vector, T 1 = T (t i} , t _j , t _k ), T ₂ = R _j (-θ _j ), and K _ij is the AB type mechanism.

Further, the present invention provides a post processor for 5-axis machining, wherein the P _NC in the case of the TT-TR type is the equation (6).

... 수학식 (6)

... (6)

(Where the subscript i, j, k of K _ij in the equation (6) means the rotation center axis x, y, z respectively, P _CL is the position vector of CL data and T ₂ = R _{j j} ), T ₃ = R _i (-θ _i ), and K _ij is the AB type mechanism.

Further, the present invention provides a post processor for 5-axis machining, wherein the P _NC in the case of the TT-TR-AC type is represented by equation (7).

... 수학식 (7)

... (7)

(The subscript i, j, k of the K _ij from equation (7) indicates the respective central axis of rotation x, y, z, and P _CL is a position vector of the CL _{data, T 1 = T (t i} , t _j , t _k ), T ₂ = R _j (-θ _j ), T ₃ = R _i (-θ _i ), and K _ij is the AB type mechanism.

In the present invention as described above, it is possible to increase the accuracy and convenience of the NC program for the inner surface machining of a complicated shape through the post processor for 5-axis machining with the angle head.

In the present invention, it is possible to suggest an inverse mechanism for a five-axis air mechanism equipped with an angle head, and a theoretical basis for development of an accurate post process such as a gauge length reflection to solve a problem of a control of a tool line point, In addition to the E-POST developed in the company, the angle head 5-axis machining mechanism module can be mounted.

The effects according to the present invention are not limited by the contents exemplified above, and more various effects are included in the specification.

FIG. 1 is a front view showing an inner diameter machining angle head according to an embodiment of the present invention, FIG. 2 is a plan view showing an inner diameter machining angle head according to an embodiment of the present invention, and FIG. 3 is a cross- .
4 is a conceptual view showing a 5-axis machining using an angle head according to the present invention.
5 is a conceptual view showing the type of machining of the angle head in accordance with the rotation feed.
FIG. 6 is a schematic view for explaining a 5-axis processing machine according to a method in which rotation is added to a communication axis.
7 is a view showing five mechanisms of a five-axis machining apparatus.
8 is a view for explaining the gauge length protruding from the center axis of the angle head to the tool tip.
9 is a view showing an example of implementing a post processor for 5-axis machining.
FIG. 10 is a view showing an angle head 5-axis machining machine simulation for a specimen, and FIG. 11 is a diagram showing an actual machining result.

BRIEF DESCRIPTION OF THE DRAWINGS The advantages and features of the present invention and the manner of achieving them will become apparent with reference to the embodiments described in detail below with reference to the accompanying drawings. The present invention may, however, be embodied in many different forms and should not be construed as being limited to the embodiments set forth herein. Rather, these embodiments are provided so that this disclosure will be thorough and complete, and will fully convey the scope of the invention to those skilled in the art. Is provided to fully convey the scope of the invention to those skilled in the art, and the invention is only defined by the scope of the claims.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS Reference will now be made in detail to the preferred embodiments of the present invention, examples of which are illustrated in the accompanying drawings. &Quot; and / or "include each and every combination of one or more of the mentioned items. ≪ RTI ID = 0.0 >

Although the first, second, etc. are used to describe various components, it goes without saying that these components are not limited by these terms. These terms are used only to distinguish one component from another. Therefore, it goes without saying that the first component mentioned below may be the second component within the technical scope of the present invention.

The terminology used herein is for the purpose of illustrating embodiments and is not intended to be limiting of the present invention. In the present specification, the singular form includes plural forms unless otherwise specified in the specification. The terms " comprises "and / or" comprising "used in the specification do not exclude the presence or addition of one or more other elements in addition to the stated element.

Unless defined otherwise, all terms (including technical and scientific terms) used herein may be used in a sense commonly understood by one of ordinary skill in the art to which this invention belongs. Also, commonly used predefined terms are not ideally or excessively interpreted unless explicitly defined otherwise.

The terms spatially relative, "below", "beneath", "lower", "above", "upper" And can be used to easily describe a correlation between an element and other elements. Spatially relative terms should be understood in terms of the directions shown in the drawings, including the different directions of components at the time of use or operation. For example, when inverting an element shown in the figures, an element described as "below" or "beneath" of another element may be placed "above" another element . Thus, the exemplary term "below" can include both downward and upward directions. The components can also be oriented in different directions, so that spatially relative terms can be interpreted according to orientation.

Hereinafter, preferred embodiments of the present invention will be described in detail with reference to the accompanying drawings.

FIG. 1 is a front view showing an inner diameter machining angle head according to an embodiment of the present invention, FIG. 2 is a plan view showing an inner diameter machining angle head according to an embodiment of the present invention, and FIG. 3 is a cross- .

1 to 3, an inner diameter machining angle head according to an embodiment of the present invention includes a housing 1 as a center, a tool shank portion 2 connected to a machine tool spindle, a main shaft (3), a bevel gear (4) for converting the direction of the rotational force, a gear body (14) constituted by combining bevel gears, an angle spindle shaft (7) for turning and rotating the tool, And a tool 15 for machining the workpiece.

At this time, the tool 15 may be an endmill, but does not limit the termination of the tool in the present invention.

The angle head is formed by forming a conical tool shank portion 2 on the upper side of the housing 1 so as to be rotatably protruded in the housing 1. The protruded tool shank portion 2 is mounted on a spindle of a machine tool .

A main shaft 3 supported by bearings is connected to the lower portion of the tool shank 2. The bevel gear 4 is coupled to the main shaft 3 and the bevel gear 4 is coupled to the main shaft 3. [ The rotation direction of the driving force transmitted from the main shaft 3 can be changed to 90 degrees by being connected to the bevel gear provided on the direction conversion shaft 5 which intersects the main shaft 3 in the 90 ° direction.

The driving force converted by the bevel gear 4 of the direction changing shaft 5 into a rotational direction of 90 degrees is transmitted to the spur gear 6 provided on one side of the direction changing shaft 5 in parallel with the main shaft 3 The spur gears 6, 60, 62, 64, and 66 are formed in a multi-step manner so that the driving force can be transmitted to the spur gear 60, which is disposed at the lower end of the angle head, To the spindle shaft 7 and the driving force transmitted to the angle spindle shaft 7 may be configured to rotate in the horizontal direction in the vertical direction of the machine tool spindle.

In this case, in order to allow the angle head to be installed on the machine tool spindle, the angle head must be fixed. To this end, a spindle fixing device 9 is installed on the upper part of the fixed body 13 assembled to the housing 1 .

The spindle fixing device 9 is installed in a portion protruding from one side of the housing 1 and is provided with a nozzle 10 elastically supported by a spring 12 and a nozzle 10 is mounted on one side of the spindle of the machine tool So as to prevent the housing 1 from rotating along the tool shank 2 while resiliently contacting.

In addition, when the nozzle 10 is operated up and down by the spring 12, the pin 11 is installed in a direction orthogonal to the nozzle 11 so that it can operate up and down like a nozzle. When the nozzle 10 is lowered in contact with the spindle of the machine tool, the pin 11 is also lowered and deviates from the pin mounting cutout of the housing 1, so that the rotation force of the spindle of the machine 1 is transmitted to the housing 1, The collet 8 and the tool 15 assembled on the angle spindle shaft 7 are rotated and the work is performed.

Hereinafter, the application of the angle head according to the present invention will be described in more detail.

4 is a conceptual view showing a 5-axis machining using an angle head according to the present invention.

Referring to FIG. 4, in the normal machining, as shown in FIG. 4A, the normal vector n of the side surface run and the axis vector u of the spindle are inconsistent, and machining becomes impossible.

4B, the normal vector is coincided with the co-ordinate vector by using the angle head. In this case, the side face machining as shown in FIG. 4C and the inner face machining as shown in FIG. It is possible.

5 is a conceptual view showing the type of machining of the angle head in accordance with the rotation feed.

5A shows a three-axis linear cutting example in which rotational feed is not required due to groove machining in the vertical direction, FIG. 5B shows a case in which only a rotational feed by rotation is added in the groove machining in the radial direction, FIG. 5C is a conceptual view of machining a chamfered portion of the inner surface, and corresponds to a 5-axis machining because two tilting and rotation rotations are required at the same time.

Therefore, it is necessary to combine and apply appropriate 5-axis ball and angle head according to the given shape.

On the other hand, the post processing means that, for example, in the 5-axis machining process, the CL (Cutter location) data composed of the position vector r _u and the posture vector u of the tool is divided into a position vector r _u and a tilt angle? (Numerical Control) data composed of rotation angles Φ.

The 5-axis machine shows different types of mechanisms depending on how the rotation is added to the table and the spindle, so that even if the same CL data is output, different NC data are output.

Therefore, we must define the inverse problem for the mechanism to obtain the desired output value correctly.

Especially, the mechanism of 5-axis air with added angle head becomes more complicated, and technical considerations such as compensating for the protruded tool length when controlling the tool line end point are added.

Accordingly, in order to extend the versatility of various types of 5-axis machining mechanisms and to maximize the user's convenience, in addition to the post processor for 5-axis machining, a 5-axis machining mechanism with an angle head (hereinafter referred to as an angle head mechanism Respectively.

FIG. 6 is a schematic view for explaining a 5-axis processing machine according to a method in which rotation is added to a communication axis.

Referring to FIG. 6, the 5-axis machine is divided into three types according to the manner in which rotation is added to the table and the spindle. The HT-HR type (FIG. 6A) used mainly in a large workpiece or a three- The HT-TR type (FIG. 6B) used for turn-mill combined machining and the TT-TR type used for 5-axis machining of small precision workpieces (FIG. 6C).

The general definition is as follows.

(a) HT-HR (Head Tilting and Head Rotating configuration): Head (= spindle) -tilting with two rotations on the head

(b) HT-TR (Head Tilting and Table Rotating configuration): Table / spindle-tilting with one rotation each on the table and spindle

(c) TT-TR (Table Tilting and Table Rotating configuration): Table-tilting with two rotations on the table

More specifically, the five-axis machining apparatus has three types of mechanisms. First, the two rotary transfer shafts for rotating and tilting are mounted on the main shaft (Head Tilting - Head Rotation, hereinafter referred to as HT-HR) (Table Tilting - Table Rotation, hereinafter referred to as TT-TR), and finally a rotary table and a rotary tool axis which can be tilted (Head Tilting-Table Rotation, hereinafter referred to as HT-TR).

In addition, the above-mentioned three mechanisms are divided into AB, AC, and BC types according to the combination of the rotation angle that rotates infinitely and the tilting angle that performs finite rotation, so that nine mechanisms are derived, If you define each type of milling, there are total 18 kinds.

7 is a view showing five mechanisms of a five-axis machining apparatus.

That is, FIG. 7 shows the five most widely used mechanisms among the various combinations of the five-axis machining apparatuses described above. In order to add versatility to the present invention, the unit vector of the tool posture axis , And then maps the part coordinate system to the machine coordinate system using the rotation angle and the tilting angle.

The tilt angle and the rotation angle of these equipments can be obtained from the inverse mechanism solution as shown in the following equations (1) and (2).

`... 수학식 (1)

`... (1)

... 수학식 (2)

&Quot; (2) "

At this time, in the case of an angle head spindle, an initial tilt angle? By a bevel gear or the like is added when the tilt angle is derived, and can be obtained as shown in the following equation (3).

... 수학식 (3)

... (3)

Here, subscripts i, j, k of K _ij mean the rotation center axes x, y, z, respectively.

That is, K _ij denotes an AB type, K _ik denotes an AC type, and K _jk denotes a BC type mechanism.

U _i , u _j , and u _k are the tool posture vector components of the CL data, and θ _i is the tilt angle that is the finite rotation angle, α is the initial inclination angle of the angle head, and θ _j is the rotation angle that is the infinite rotation angle.

When the tilt angle and the rotation angle are obtained as described above, the position vector of the CL data can be converted into the position vector of the NC data using the following equations (4), (5) and (6) As a result, the final NC data can be obtained by the following equation (8).

In the present invention, the TT-TR type device, which is an example of the mechanism of mounting the angle head, has a structure in which a moving transformation matrix T ₁ = T (t _i , t _j , t _k ) shall be added.

In case of TT-TR-AC type, an error occurs when controlling the tool lead point. Therefore, the movement transformation should be additionally performed considering the offset amount t _j .

8 is a view for explaining the gauge length protruding from the center axis of the angle head to the tool tip.

T _j means g / l which is the gage length protruding from the center axis of the angle head to the tool tip as shown in FIG.

... 수학식 (4)

... (4)

... 수학식 (5)

... (5)

... 수학식 (6)

... (6)

... 수학식 (7)

... (7)

... 수학식 (8)

... (8)

And in the equation (4) to _{(8), T 1 = T} (t i, t j, t k), T 2 = R j (-θ j), T 3 = R i (-θ i), P _NC is a position vector of NC data, and P _CL is a position vector of CL data.

[0001] The present invention relates to a post processor for 5-axis machining using an angle head spindle, and is capable of performing NC (Numerical control) for each machine mechanism by giving given CL (Cutter location) data through position data mapped to a rotation angle, a tilting angle, The NC data is expressed by Equation (8). &Quot; (8) "

That is, the present invention relates to a post processor for 5-axis machining, wherein the 5-axis machining for 5-axis machining includes angle head spindles and the 5-axis machining post processor including the angle head spindles has a given tool posture and tool position vector The NC (Numerical control) data is converted into NC (Numerical control) data corresponding to the mechanism of the corresponding machine, and the NC (Numerical control) data is expressed by Equation (8).

In this case, in the equation (8), the rotation angle that is θ _j , that is, the infinite rotation angle is equal to the equation (2), and the tilt angle that is θ _i , In equation (3), α corresponds to the initial angle of inclination of the angle head.

In the equation (8), P _NC in the case of HT-HR type is expressed by equation (4), P _NC in case of HT-TR type is represented by equation (5) P _NC corresponds to equation (6), and, P _NC of TT-TR-AC when the type corresponds to the equation (7).

The parameters in the present invention are summarized in Table 1 below.

9 is a view showing an example of implementing a post processor for 5-axis machining.

Referring to FIG. 9, a 5-axis post processor as shown in FIG. 9 is implemented using a Visual Basic 6.0 program based on the proposed algorithm. The angled head mechanism is selected and the corresponding mechanism is selected in the main tab. G / L Input), enter the machine limit command for the straight line and the rotary axis, enter the setup value for the origin offset command, and the environment setting for running the post processor is completed do.

Once the configuration is complete, you can input the CL data you want to convert (Data Input command) and then perform the desired post processing by selecting the data format you want to output from the NC translator dialog box.

The right upper side of FIG. 9 is the CL data input screen and the lower right side shows the NC data output screen.

Hereinafter, simulation and 5-axis machining according to the present invention will be described.

FIG. 10 is a view showing an angle head 5-axis machining machine simulation for a specimen, and FIG. 11 is a diagram showing an actual machining result.

Referring to FIG. 10, a tool path for a machining specimen is generated and CL data is outputted. After the developed post processor is converted into NC data, a machine simulation method is used to obtain accuracy of the converted NC data To perform simulation processing.

Simulation through machine simulation has the advantage of being able to grasp and correct various problems such as micro-machining, over-cutting, collision, interference and transfer limit that can occur during 5-axis machining. Mechanism modeling of the same shape has been carried out and it is possible to make safe machining by setting the connection, drive relationship and the feed limit of each feed axis mechanism.

Then, the NC data, which was verified through the cutting simulation results, was transmitted to the five-axis air bearing the angle head, and the machining result as shown in FIG. 11 was obtained.

As described above, in the present invention, it is possible to increase the accuracy and convenience of the NC program for the inner surface machining of a complicated shape through the post processor for 5-axis machining with the angle head.

More specifically, in the present invention, it is possible to suggest an inverse mechanism for a five-axis air mechanism equipped with an angle head, and to establish a theoretical basis for developing an accurate post process such as reflecting a gauge length In addition to the existing E-POST, an angle head 5-axis machining mechanism module can be installed.

Further, in the present invention, the accuracy of the post-presser developed by modeling a 5-axis TT-TR 5-axis air gap and modeling the inner oil pocket groove of the hydrostatic bearing after the angle head was mounted was verified.

One embodiment of the invention described above and shown in the drawings should not be construed as limiting the technical idea of the present invention. The scope of protection of the present invention is limited only by the matters described in the claims, and those skilled in the art will be able to modify the technical idea of the present invention in various forms. Accordingly, such improvements and modifications will fall within the scope of the present invention as long as they are obvious to those skilled in the art.

Claims (6)

In a postprocessor for 5-axis machining,
Wherein the 5-axis machining unit for 5-axis machining includes an angle head spindle,
The post processor for 5-axis machining in the case of including the angle head spindle converts the CL (Cutter location) data, which is a given tool posture and tool position vector, into numerical control (NC) data suitable for the mechanism of the machining apparatus,
The numerical control (NC) data is represented by the following equation (1), θ _i is the following equation (2), and P _NC in the case of the TT-TR- Post processor for shaft processing.

... Equation (1)
(In the above equation (1), θ _j is the rotation angle, θ _i is the tilt angle, and P _NC is the position vector of the NC data.)

&Quot; (2) "
(2), the subscripts i, j and k of K _ij mean the rotation center axes x, y and z, respectively, and u _i , u _j and u _k are the tool posture vector components of the CL data, α is the initial angle of inclination of the angle head, and K _ij is the AB type mechanism.)

... (7)
(The subscript i, j, k of the K _ij from equation (7) indicates the respective central axis of rotation x, y, z, and P _CL is a position vector of the CL _{data, T 1 = T (t i} , t _j , t _k ), T ₂ = R _j (-θ _j ), T ₃ = R _i (-θ _i ), and K _ij is the AB type mechanism. The method according to claim 1,
Wherein the θ _j in the equation (1) is the following equation (3).

... (3)
(3), the subscripts i, j and k of K _ij mean the rotation center axes x, y and z, respectively, and u _i , u _j and u _k are the tool posture vector components of the CL data, K _ij is an AB type mechanism.) The method according to claim 1,
And the P _NC in the case of the HT-HR type is the equation (4).

... (4)
(The subscript i, j, k of the K _ij in equation (4) refers to the respective central axis of rotation x, y, z, and P _CL is a position vector of the CL _{data, T 1 = T (t i} , t _j , t _k ), and K _ij is the AB type mechanism. The method according to claim 1,
And the P _NC in the case of the HT-TR type is the equation (5).

... (5)
(The subscript i, j, k of the K _ij in equation (5) refers to the respective central axis of rotation x, y, z, and P _CL is the position of the CL data _{vector, T 1 = T (t i} , t _j , t _k ), T ₂ = R _j (-θ _j ), and K _ij is the AB type mechanism. The method according to claim 1,
And the P _NC in the case of the TT-TR type is the equation (6).

... (6)
(Where the subscript i, j, k of K _ij in the equation (6) means the rotation center axis x, y, z respectively, P _CL is the position vector of CL data and T ₂ = R _{j j} ), T ₃ = R _i (-θ _i ), and K _ij is the AB type mechanism. delete

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