A forward design method for the double-swing head configuration of a five-axis machine tool

Abstract

The present invention discloses a forward design method for a double-swing head configuration of a five-axis machine tool. A tool path is generated based on the workpiece to be processed, and a tool path posture set is extracted; the tool path posture set is Gaussian mapped in a Gaussian sphere to be represented by discrete points; the boundary points in the discrete points are identified and connected to form a posture continuous region; it is determined whether the vertex of the Gaussian sphere belongs to the posture continuous region, and the angle between the first rotating shaft and the second rotating shaft and the angle between the second rotating shaft and the tool axis are used as the axis angle, and the feasible domain of the axis angle is calculated through the posture continuous region; then the relationship between the axis angle and the two translation vectors is set to achieve the design of zero rotation radius of the double-swing head of the machine tool and the elimination of nonlinear errors. The present invention proceeds from the processing requirements of complex curved workpieces, and forward designs the feasible domain of the axis angle and the translation vector relationship of the double-swing head configuration of the five-axis machine tool, which has the advantages of precise and achievable curved surface processing tool path posture, elimination of nonlinear errors, and avoidance of translation axis compensation.

Description

Technical Field

[0001] The invention relates to a double-swing head design method, in particular to a forward design method for a double-swing head configuration of a five-axis machine tool. Background Art

[0002] High-precision, high-end five-axis machine tools, as industrial mother machines, are the foundation of the equipment manufacturing industry. Many high-precision workpieces are processed on double-swing head five-axis machine tools, where the design of the double-swing head is paramount. In traditional swing head designs, nonlinear errors cannot be eliminated due to the rotation radius, becoming a major factor affecting machining accuracy. In double-swing head machines, the rotation radius of the second rotating axis changes dynamically with the second rotating axis, resulting in poor and uneven surface finish. The highest precision in curved surface machining is affected by the structure, presenting an insurmountable bottleneck.

[0003] At present, the precision requirements for surface machining are getting higher and higher. However, traditional double-swing head surface machining requires complex post-processing procedures to reduce nonlinear errors due to the nonlinear displacement caused by the rotation radius, and the nonlinear errors cannot be completely eliminated. It is difficult to further improve the machining accuracy, and a lot of costs need to be spent on trajectory planning and interpolation.

[0004] Traditional swing head machine tool designs have various shortcomings including:

[0005] (1) There is a rotation radius, and from the perspective of mechanical structure, nonlinear error cannot be eliminated.

[0006] (2) To compensate for the nonlinear error due to the rotation radius, a large amount of cost is required in the post-processing procedure, and the steps are complicated.

[0007] (3) The rotation radius of the first axis will change with the rotation of the second rotating axis, and the nonlinear error will also change nonlinearly, resulting in uneven and uncontrollable accuracy distribution.

[0008] (4) Previous machine tool designs were unable to be personalized for the required working conditions, and were often designed based on intuition, resulting in insufficient performance or redundancy. Summary of the Invention

[0009] The purpose of the present invention is to overcome the shortcomings of the existing technology and propose a double-swing head forward design and development scheme that can achieve zero nonlinear error and personalized design based on the positive correlation between nonlinear error and rotation radius.

[0010] In order to achieve the above object, the technical solution adopted by the present invention is:

[0011] The forward design method of the double-swing head configuration of a five-axis machine tool of the present invention includes:

[0012] Step (1): Generate a tool path according to the workpiece to be processed, extract the posture part of the tool path, and form a tool path posture set;

[0013] Step (2): Gaussian mapping is performed on the tool path posture set, so that the tool path posture is represented by discrete points in the Gaussian sphere.

[0014] Step (3): Identify the boundary points of all discrete points in the Gaussian sphere, connect the boundary points to form a posture continuous region and extract the boundary curve of the posture continuous region;

[0015] Step (4): Determine whether the vertex of the Gaussian sphere belongs to the posture continuous area, take the angle α1 between the first rotating shaft and the second rotating shaft of the double swing head and the angle α2 between the second rotating shaft and the tool axis as the axis angle, and calculate the feasible domain of the two axis angles through the boundary curve;

[0016] Step (5): Set the axis angle α1 and the translation vector v1 from the first rotating axis center O1 to the second rotating axis center O2, and from the second rotating axis center O2 to the tool end P T The relationship between the translation vector v2 is established, and the relationship between the axis angle α1 and the two translation vectors and the feasible domain of the two axis angles are combined to construct the double swing head of the machine tool and manufacture it.

[0017] The double-swing head of the machine tool includes a first rotating shaft, a second rotating shaft and a tool shaft, wherein the second rotating shaft and the tool shaft are integrally arranged rotatably around the first rotating shaft, and the tool shaft is rotatably arranged around the second rotating shaft, and a tool for processing a product is mounted on the tool shaft;

[0018] The tool shaft is connected to the rotating part of the second rotating shaft through a connecting rod or a bracket, the fixed part of the second rotating shaft is connected to the rotating part of the first rotating shaft through a connecting rod or a bracket, and the fixed part of the first rotating shaft remains fixed.

[0019] The tool path posture set is a set of all posture vectors on the machining path, and the posture vector is a unit direction vector representing the tool axis direction in the machine tool coordinate system during the machining process.

[0020] In the step (1), after Gaussian mapping, each tool path posture is represented by a discrete point in the Gaussian sphere, and thus each tool path posture is represented by a plurality of discrete points in the Gaussian sphere.

[0021] When the posture continuous region contains Gaussian sphere vertices, step (4) is specifically as follows:

[0022] (4.1A) The angle α1 between the first rotating shaft and the second rotating shaft of the double swing head and the angle α2 between the second rotating shaft and the tool axis are both used as the interaxial angle, and the two interaxial angles are set to be equal;

[0023] (4.2A) The polar angle of the point with the largest polar angle in the boundary curve of step (3) is extracted as the maximum polar angle θ of the posture continuous area. S ;

[0024] (4.3A) According to the maximum polar angle θ of the attitude continuous area S , set the feasible region of the two axis angles according to the following formula:

[0025]

[0026] Among them, θ S Indicates the maximum polar angle of the attitude continuous area when the attitude continuous area contains the vertex of the Gaussian sphere;

[0027] When the posture continuous region does not contain the Gaussian sphere vertex, the step (4) is specifically as follows:

[0028] (4.1B) The polar angle of the point with the largest polar angle in the boundary curve of step (3) is extracted as the maximum polar angle θ of the posture continuous area max , extract the polar angle of the point with the smallest polar angle in the boundary curve of step (3) as the minimum polar angle θ of the posture continuous area min ;

[0029] (4.2B) According to the maximum polar angle θ of the posture continuous area max , minimum polar angle θ min , set the feasible region of the two axis angles according to the following formula:

[0030] When α1≥α2:

[0031]

[0032] θ max -α2≤α1≤θ min +α2

[0033] When α2≥α1:

[0034]

[0035] θ max -α1≤α2≤θ min +α1

[0036] Among them, θ max ,θ min They respectively represent the maximum polar angle and the minimum polar angle of the posture continuous area when the posture continuous area does not contain the vertex of the Gaussian sphere.

[0037] The step (5) is specifically as follows:

[0038] First, establish a first coordinate system with the center O1 of the first rotating shaft as the origin and the direction of the first rotating shaft axis toward the tool as the z-axis. Establish a translation vector v1 in the first coordinate system, pointing from the center O1 of the first rotating shaft to the center O2 of the second rotating shaft. v1 = (x1, y1, z1), where x1, y1, and z1 represent the components of the translation vector v1 in the x, y, and z-axis directions in the first coordinate system, respectively.

[0039] Then, a second coordinate system is established with the center O2 of the second rotating shaft as the origin and the direction of the second rotating shaft axis toward the tool as the z-axis. In the second coordinate system, a coordinate system is established with the second rotating shaft center O2 pointing to the tool end P. T The translation vector v2, v2 = (x2, y2, z2), x2, y2, z2 respectively represent the components of the translation vector v2 in the x, y, and z axis directions in the second coordinate system;

[0040] Then, the relationship between the two translation vectors and the axis angle α1 is established, as shown in the following formula:

[0041] x1=0

[0042] z2 sinα1=-y1

[0043] Finally, combining the relationship between the axis angle α1 and the two translation vectors and the feasible domain of the two axis angles, the machine tool double swing head is forward constructed and manufactured.

[0044] The beneficial effects of the present invention are:

[0045] By using the present invention, the feasible domain of the two inter-axis angles can be quickly and effectively calculated from the specific workpiece tool path, providing a forward design basis and avoiding blind attempts and insufficient performance or excessive redundancy caused by workspace mismatch.

[0046] Compared with the traditional machine tool swing head design, the forward design method of the double swing head configuration based on the zero rotation radius theory can eliminate nonlinear errors, and especially includes the inverse solution of the feasible domain. Since it can eliminate nonlinear errors, it further avoids the complex post-processing procedures for compensating nonlinear errors, greatly improving production efficiency.

[0047] The zero-radius design of this invention completely eliminates nonlinear errors, significantly improving surface machining accuracy and surface quality. Suitable for ultra-high-precision surface machining, it eliminates nonlinear errors during trajectory interpolation while avoiding complex post-processing procedures. BRIEF DESCRIPTION OF THE DRAWINGS

[0048] The present invention will be further described below with reference to the accompanying drawings and examples;

[0049] Figure 1 is a general flow chart of the method of the present invention;

[0050] Figure 2 Schematic diagram of the double-swing head configuration of the method of the present invention;

[0051] Figure 3 This is a topological diagram of the double-swing head configuration of the method of the present invention;

[0052] Figure 4 Schematic diagram of triangulation of the tool path region not containing vertices in the method of the present invention;

[0053] Figure 5 A schematic diagram of triangulation of the tool path region including vertices in the method of the present invention;

[0054] Figure 6 A two-dimensional schematic diagram of the inter-axis angle configuration and the posture reachable space of the present invention;

[0055] Figure 7 A three-dimensional schematic diagram of the inter-axis angle configuration and the posture reachable space of the present invention;

[0056] Figure 8 It is a schematic diagram of the feasible region of the inter-axis angle under the specific structure of the present invention. DETAILED DESCRIPTION

[0057] The present invention is further described in detail below with reference to the accompanying drawings and examples.

[0058] According to Figure 1 The steps shown can finally be designed Figure 2 and Figure 3 The feasible domain of key parameters such as the two inter-axis angles and the translation vector in the double swing head structure shown in the figure, the specific process of the present invention is as follows:

[0059] The overall flow chart of the method of the present invention is as follows Figure 1 As shown, the method includes the following steps:

[0060] Step (1): Generate the tool path of the workpiece to be processed by computer-aided manufacturing software. The tool path consists of multiple tool positions. Each tool position is represented by (x, y, z, i, j, k), which includes two parts of information: the spatial position coordinates of the tool end in the machine tool coordinate system (x, y, z), and the tool posture vector (i, j, k). The posture vector represents the direction of the tool axis and is a unit vector that satisfies i. 2 +j 2 +k 2 =1, extract the posture part of each tool position in the tool path to form a tool path posture set N is the number of tool positions; each tool path posture is represented in vector form;

[0061] Step (2): Gaussian mapping is performed on the tool path posture set, that is, the posture vector of each tool position point is moved to the coordinate origin so that it is mapped to a Gaussian sphere. This coordinate system is the machine tool coordinate system used by the tool path. After Gaussian mapping, the tool path posture is represented by discrete points in the Gaussian sphere.

[0062] Step (3): Use triangulation method to identify the boundary points of all discrete points in the Gaussian sphere, connect the boundary points to form the posture continuous region D{Q} and extract the boundary curve B of the posture continuous region a , that is, find the boundary B in the node-edge-face-topology a ,B a is a polymorphism in the Gaussian sphere, defined as B a ={p1,p2…p m}(m is the number of polygon nodes, where p i =(x i ,y i ,z i ) are three-dimensional Cartesian coordinates. The triangulation method is Delaunay triangulation.

[0063] B a Convert to spherical coordinates. Select spherical coordinate system The spherical coordinate system is consistent with the machine tool coordinate system, where r is the radius of the sphere (the distance from the coordinate origin to the point), θ is the polar angle (the angle between the point and the positive direction of the z-axis, ranging from [0,π]), is the azimuth (the rotation angle of the point on the xy plane relative to the positive direction of the x-axis, ranging from [0, 2π)), the Gaussian sphere is the unit sphere, r = 1. For each point p_i, the corresponding spherical coordinates (θ i ,φ i ):

[0064] θ i =arccos(z i ),φ i =arctan 2(y i ,x i )

[0065] The polygon B can then be represented as:

[0066] B a ={(θ1,φ1),(θ2,φ2),…,(θ m ,φ m )};

[0067] Step (4): Determine whether the vertex (0,0,1) of the Gaussian sphere belongs to the posture continuous region D{Q}, that is, determine the condition (0,0,1)∈D{Q}, and take the angle α1 between the first rotating shaft and the second rotating shaft of the double swing head and the angle α2 between the second rotating shaft and the tool axis as the axis angle, and pass the boundary curve B a , combined with the relationship between the axis angle and the posture reachable space and the relationship between the posture reachable space and the tool path posture set, the feasible domain of the two axis angles is calculated. The posture reachable space refers to the set of all postures that the tool can reach in the machine tool coordinate system, such as Figure 7 As shown in Figure 2, the posture reachable space can be clearly represented as a distribution area of ​​Gaussian sum after Gaussian mapping;

[0068] Step (5): Set the axis angle α1 and the translation vector v1 from the first rotating axis center O1 to the second rotating axis center O2, and from the second rotating axis center O2 to the tool end P T The relationship between the translation vector v2 is established, and the relationship between the axis angle α1 and the two translation vectors and the feasible domain of the two axis angles are combined to construct the double swing head of the machine tool and manufacture it.

[0069] The forward design method refers to the forward design of the feasible design range of the inter-axis angles α1 and α2 and the relationship between the translation vectors v1 and v2 based on the requirements of satisfying the kinematic posture accessibility of the double-swing head configuration and eliminating nonlinear errors.

[0070] The key design parameters and contents of the double-swing head configuration are: the feasible design range of the axis angle α1 between the first rotating axis and the second rotating axis, the axis angle α2 between the second rotating axis and the tool axis, and the relationship between the axis angle α1 and the translation vectors v1 and v2.

[0071] The kinematic posture accessibility of the double-swing head configuration refers to the ability of the posture accessibility space to cover the tool path posture set of the workpiece to be processed. The feasible design range determined by the forward design method can ensure the kinematic posture accessibility of the double-swing head configuration.

[0072] like Figure 2 As shown, the double swing head of the machine tool includes a first rotating shaft, a second rotating shaft and a tool shaft. The second rotating shaft and the tool shaft are integrally arranged rotatably around the first rotating shaft. The tool shaft is rotatably arranged around the second rotating shaft. A tool for processing a product is mounted on the tool shaft.

[0073] The tool shaft is connected to the rotating portion of the second rotating shaft through a connecting rod or a bracket, and the fixed portion of the second rotating shaft is connected to the rotating portion of the first rotating shaft through a connecting rod or a bracket, and the fixed portion of the first rotating shaft remains fixed.

[0074] The tool path posture set is the set of all posture vectors on the machining path. The posture vector is the three-dimensional rotation angle of the tool expressed in the machine tool coordinate system during the machining process.

[0075] In step (1), after Gaussian mapping, each tool path posture vector is represented by a discrete point in the Gaussian sphere, and thus each tool path posture is represented by several discrete points in the Gaussian sphere.

[0076] When the posture continuous region contains the vertices of the Gaussian sphere, such as Figure 5 As shown, step (4) is specifically as follows:

[0077] (4.1A) The angle α1 between the first rotating shaft and the second rotating shaft of the double swing head and the angle α2 between the second rotating shaft and the tool axis are both used as the interaxial angle, and the two interaxial angles are set to be equal;

[0078] (4.2A) The polar angle of the point with the largest polar angle in the boundary curve of step (3) is taken as the maximum polar angle θ of the posture continuous region when the posture continuous region contains the vertex of the Gaussian sphere. S ; The spherical coordinate system where the polar angle is located and the axis direction and origin of the machine tool coordinate system where the posture vector is located are the same.

[0079] (4.3A) According to the maximum polar angle θ of the attitude continuous area S , combining the relationship between the axis angle and the pose reachable space and the relationship between the pose reachable space and the tool path pose set, the feasible region of the two axis angles is set according to the following formula:

[0080]

[0081] Among them, θ S is the maximum polar angle of the attitude continuous area when the attitude continuous area contains the vertex of the Gaussian sphere;

[0082] In the above formula The space Ω is reached according to the posture T The relationship between the continuous posture region D{Q} and the maximum polar angle θ of the continuous posture region is obtained S Relationship; specifically:

[0083] The posture reachable space is expressed as:

[0084]

[0085] The relationship between the posture reachable space and the posture continuous area is:

[0086] When the posture continuous region does not contain the Gaussian sphere vertex, Figure 4 As shown, step (4) is specifically as follows:

[0087] (4.1B) In step (3), the boundary curve B a The polar angle of the point with the largest polar angle is extracted as the maximum polar angle θ of the posture continuous region when the posture continuous region does not contain the Gaussian sphere vertex max , extract the polar angle of the point with the smallest polar angle in the boundary curve of step (3) as the minimum polar angle θ of the posture continuous area min ;

[0088] Extract the maximum polar angle, defined as θ max ; Extract the minimum polar angle, defined as θ min ;

[0089] Extract the maximum azimuth angle, defined as φ max ; Extract the minimum azimuth, defined as φ min ;

[0090] The final posture continuous area range is:

[0091]

[0092] (4.2B) According to the maximum polar angle θ of the posture continuous area max , minimum polar angle θ min , combining the relationship between the axis angle and the pose reachable space and the relationship between the pose reachable space and the tool path pose set, the feasible domain of the two axis angles is set according to the following formula:

[0093] When α1≥α2:

[0094]

[0095] θ max -α2≤α1≤θ min +α2

[0096] Among them, when hour, The two ends of are equal, that is

[0097]

[0098] The schematic diagram of the feasible region of the axis angle is as follows Figure 8 As shown,

[0099]

[0100] When α2≥α1:

[0101]

[0102] θ max -α1≤α2≤θ min +α1

[0103] when When α2 is feasible, The two ends of are equal, that is

[0104] Among them, θ max ,θ min They respectively represent the maximum polar angle and the minimum polar angle of the posture continuous area when the posture continuous area does not contain the vertex of the Gaussian sphere.

[0105] like Figure 6 and Figure 7 As shown in the figure, the relationship between the reachable space of the tool axis posture and the inter-axis angle configuration is as follows: At this time, the polar angle range of the reachable space of the posture is:

[0106] Ω T Polar angle range: (|α1-α2|,(α1+α2))

[0107] According to the conditions The feasible region of the two axis angles can be obtained.

[0108] Step (5) is specifically as follows: Figure 3 As shown,

[0109] First, a first coordinate system is established with the center O1 of the first rotating axis as the origin and the direction of the axis of the first rotating axis toward the tool as the z-axis. In the first coordinate system, a translation vector v1 is established from the center O1 of the first rotating axis to the center O2 of the second rotating axis, v1 = (x1, y1, z1), x1, y1, z1 respectively represent the components of the translation vector v1 in the x, y, z axis directions in the first coordinate system; the first coordinate system and the second coordinate system are both rectangular coordinate systems.

[0110] Then, a second coordinate system is established with the center O2 of the second rotating shaft as the origin and the direction of the second rotating shaft axis toward the tool as the z-axis. In the second coordinate system, a coordinate system is established with the second rotating shaft center O2 pointing to the tool end P. T The translation vector v2, v2 = (x2, y2, z2), x2, y2, z2 respectively represent the components of the translation vector v2 in the x, y, and z axis directions in the second coordinate system;

[0111] The first coordinate system is consistent with the machine tool coordinate system in the direction of the coordinate axis. The x-axis directions of the first and second coordinate systems are both perpendicular to the plane where v1 and v2 are located and point outward. The y-axis direction is determined according to the right-hand rule.

[0112] According to the zero rotation radius theory, the intersection of the two rotating shafts and the tool end P T For the same point, we can get

[0113]

[0114] This is the necessary and sufficient condition for the tool end point to be on the axis of the second rotation axis. Then the origin O2 of the second rotation axis coordinate system points to the tool end P T The translation vector v2 is expressed as v2 = (0, z2 sinα1, z2 cosα1) in the first coordinate system, pointing from O1 to P T The translation vector In the first coordinate system, it is expressed as

[0115]

[0116] Then, the relationship between the two translation vectors and the axis angle α1 is established, as shown in the following formula:

[0117]

[0118] Finally, combining the relationship between the axis angle α1 and the two translation vectors and the feasible domain of the two axis angles, the machine tool double swing head is forward constructed and manufactured.

[0119] Finally, the actual setting of the axis angle α1 satisfies the following relationship as the relationship between the axis angle α1 and the two translation vectors:

[0120] z2 sinα1=-y1

[0121] It can realize zero rotation radius of the double swing head of the machine tool, that is, the intersection of the axes of the two rotating shafts and the end point of the tool P T Where y1 represents the component of the translation vector v1 in the y-axis direction from the center of the first rotating shaft O1 to the center of the second rotating shaft O2 in the first coordinate system, and z2 represents the component of the translation vector v1 in the y-axis direction from the center of the second rotating shaft O2 to the tool end P in the second coordinate system. T The component of the translation vector v2 in the z-axis direction. The requirement for eliminating nonlinear errors is achieved through the design of zero rotation radius, which means that the axes of the first rotating shaft and the second rotating shaft form an intersection and coincide with the end of the tool.

Claims

1. A forward design method for a five-axis machine tool with a double swing head configuration, characterized in that: The method comprises the following steps: Step (1): Generate a tool path according to the workpiece to be processed, extract the posture part of the tool path, and form a tool path posture set; Step (2): Gaussian mapping is performed on the tool path posture set, so that the tool path posture is represented by discrete points in the Gaussian sphere. Step (3): Identify the boundary points of all discrete points in the Gaussian sphere, connect the boundary points to form a posture continuous region and extract the boundary curve of the posture continuous region; Step (4): Determine whether the vertex of the Gaussian sphere belongs to the posture continuous area, take the angle α1 between the first rotating shaft and the second rotating shaft of the double swing head and the angle α2 between the second rotating shaft and the tool axis as the axis angle, and calculate the feasible domain of the two axis angles through the boundary curve; Step (5): Set the axis angle α1 and the translation vector v1 from the first rotating axis center O1 to the second rotating axis center O2, and from the second rotating axis center O2 to the tool end P T The relationship between the translation vector v2 and the axis angle α1 are combined with the relationship between the two translation vectors and the feasible domain of the two axis angles to construct the double swing head of the machine tool and manufacture it; When the posture continuous region contains Gaussian sphere vertices, step (4) is specifically as follows: (4.1A) The angle α1 between the first rotating shaft and the second rotating shaft of the double swing head and the angle α2 between the second rotating shaft and the tool axis are both used as the interaxial angle, and the two interaxial angles are set to be equal; (4.2A) The polar angle of the point with the largest polar angle in the boundary curve of step (3) is extracted as the maximum polar angle θ of the posture continuous area. S ; (4.3A) According to the maximum polar angle θ of the attitude continuous area S , set the feasible region of the two axis angles according to the following formula: Among them, θ S Indicates the maximum polar angle of the attitude continuous area when the attitude continuous area contains the vertex of the Gaussian sphere; When the posture continuous region does not contain the Gaussian sphere vertex, the step (4) is specifically as follows: (4.1B) The polar angle of the point with the largest polar angle in the boundary curve of step (3) is extracted as the maximum polar angle θ of the posture continuous area max , extract the polar angle of the point with the smallest polar angle in the boundary curve of step (3) as the minimum polar angle θ of the posture continuous area min ; (4.2B) According to the maximum polar angle θ of the posture continuous area max , minimum polar angle θ min , set the feasible region of the two axis angles according to the following formula: When ɑ1≥α2: i max -α2≤α1≤θ min +a2 When α2≥α1: i max -α1≤α2≤θ min +a1 Among them, θ max ,θ min They represent the maximum polar angle and the minimum polar angle of the posture continuous area when the posture continuous area does not contain the vertex of the Gaussian sphere; The step (5) is specifically as follows: First, establish a first coordinate system with the center O1 of the first rotating shaft as the origin and the direction of the first rotating shaft axis toward the tool as the z-axis. Establish a translation vector v1 in the first coordinate system, pointing from the center O1 of the first rotating shaft to the center O2 of the second rotating shaft. v1 = (x1, y1, z1), where x1, y1, and z1 represent the components of the translation vector v1 in the x, y, and z-axis directions in the first coordinate system, respectively. Then, a second coordinate system is established with the center O2 of the second rotating shaft as the origin and the direction of the second rotating shaft axis toward the tool as the z-axis. In the second coordinate system, a coordinate system is established with the second rotating shaft center O2 pointing to the tool end P. T The translation vector v2, v2 = (x2, y2, z2), x2, y2, z2 respectively represent the components of the translation vector v2 in the x, y, and z axis directions in the second coordinate system; Then, the relationship between the two translation vectors and the axis angle α1 is established, as shown in the following formula: x1＝0 z2sinα1=-y1 Finally, combining the relationship between the axis angle α1 and the two translation vectors and the feasible domain of the two axis angles, the machine tool double swing head is forward constructed and manufactured.

2. The forward design method for a double-swing head configuration of a five-axis machine tool according to claim 1, characterized in that: The double-swing head of the machine tool includes a first rotating shaft, a second rotating shaft and a tool shaft, wherein the second rotating shaft and the tool shaft are integrally arranged rotatably around the first rotating shaft, and the tool shaft is rotatably arranged around the second rotating shaft, and a tool for processing a product is mounted on the tool shaft; The tool shaft is connected to the rotating part of the second rotating shaft through a connecting rod or a bracket, the fixed part of the second rotating shaft is connected to the rotating part of the first rotating shaft through a connecting rod or a bracket, and the fixed part of the first rotating shaft remains fixed.

3. The forward design method for a five-axis machine tool with a double-swing head configuration according to claim 1, characterized in that: The tool path posture set is a set of all posture vectors on the machining path, and the posture vector is a unit direction vector representing the tool axis direction in the machine tool coordinate system during the machining process.

4. The forward design method for a five-axis machine tool with a double-swing head configuration according to claim 1, characterized in that: In the step (1), after Gaussian mapping, each tool path posture is represented by a discrete point in the Gaussian sphere, and thus each tool path posture is represented by a plurality of discrete points in the Gaussian sphere.

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