CN114570807B - Six-axis bending device and method based on mandrel rotation - Google Patents

Six-axis bending device and method based on mandrel rotation Download PDF

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CN114570807B
CN114570807B CN202210089991.XA CN202210089991A CN114570807B CN 114570807 B CN114570807 B CN 114570807B CN 202210089991 A CN202210089991 A CN 202210089991A CN 114570807 B CN114570807 B CN 114570807B
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bending
mandrel
axis
bending die
core rod
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CN114570807A (en
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程诚
张任思绪
郭训忠
陶杰
刘春梅
杨秋成
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Nanjing University of Aeronautics and Astronautics
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Nanjing University of Aeronautics and Astronautics
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    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B21—MECHANICAL METAL-WORKING WITHOUT ESSENTIALLY REMOVING MATERIAL; PUNCHING METAL
    • B21D—WORKING OR PROCESSING OF SHEET METAL OR METAL TUBES, RODS OR PROFILES WITHOUT ESSENTIALLY REMOVING MATERIAL; PUNCHING METAL
    • B21D9/00—Bending tubes using mandrels or the like
    • B21D9/01—Bending tubes using mandrels or the like the mandrel being flexible and engaging the entire tube length
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/10—Geometric CAD
    • G06F30/17—Mechanical parametric or variational design
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/20—Design optimisation, verification or simulation
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02P—CLIMATE CHANGE MITIGATION TECHNOLOGIES IN THE PRODUCTION OR PROCESSING OF GOODS
    • Y02P40/00—Technologies relating to the processing of minerals
    • Y02P40/50—Glass production, e.g. reusing waste heat during processing or shaping
    • Y02P40/57—Improving the yield, e-g- reduction of reject rates

Abstract

The invention discloses a six-axis bending device and method based on mandrel rotation. The method is characterized in that a mandril rotating in a single direction is established, the mandril is applied to a scene of bending a space track pipe by three-dimensional free bending six-axis equipment, and a geometric parameter model between a space position parameter and a deflection parameter of a bending die deflection device and an angle parameter of the mandril rotating along the axial direction is established. The pipe bending forming device has the advantages that the inner wall can be supported in the pipe bending forming process, the wrinkling tendency of a thin-wall pipe can be effectively reduced, the section deformation of the pipe is inhibited, the wall thickness is prevented from being excessively reduced, and the forming quality and the service performance of the pipe can be ensured. The universal mandrel can effectively solve the problem that the universal mandrel cannot support the pipe under the condition of small bending radius in the bending forming process; the core rod can be bent to rotate to the required bending direction along the axis direction through an algorithm, and the problem that the core rod bent in a single direction is single in bending direction can be effectively solved.

Description

Six-axis bending device and method based on mandrel rotation
Technical Field
The invention belongs to a six-axis bending device and method based on mandrel rotation, and belongs to the field of plastic working forming.
Background
The three-dimensional free bending system of the complex component can realize high-precision die-free forming of pipes, profiles and wires under various bending radius conditions, forms great challenges for the traditional metal bending forming technology, and is an important technical innovation recognized in the field of plastic forming. Compared with the original three-dimensional free bending three-axis machine, the three-dimensional free bending six-axis machine has two more axes and has larger degree of freedom. The six-shaft free pipe bender can realize X, Y and Z movements, and also can realize the rotation angle delta of the bending die around the self axis and the rotation angle gamma of the bending die around the self axis, and can realize the axis twisting and bending in the bending process.
The six-shaft machine equipment can realize three-dimensional free forming of the space continuous variable-curvature component, and the bending die of the six-shaft machine has higher degree of freedom, so that the six-shaft machine equipment has higher advantage in forming a pipe with a small bending radius. When the thin-wall pipe is formed, the forming quality control of the pipe is a prominent difficult problem, and when the selection of process parameters and the structural design of a die are unreasonable, the thickness of the outer side wall of the bending section is greatly reduced, and the inner side of the bending section is easy to wrinkle. Therefore, when the pipe has a serious cross-sectional distortion, a mandrel needs to be disposed between the bending die and the guide mechanism to reduce the cross-sectional distortion and the wall thickness reduction of the pipe in the bending deformation zone. For large-caliber thin-walled tubes and blanks with special-shaped sections, the auxiliary forming by utilizing a core rod is also usually required.
The principle of the universal rotating mandrel which is popular in the market at present is that the middle ball body is used as a movable joint to be linked to play a role in universal rotation, but when the bending radius is too small, the adjacent mandrel balls are easy to generate an interference phenomenon. Therefore, the invention adopts the core rod which can only be bent in one direction, and the thickness of the core ball is relatively low at the inner side of the core ball in the bending direction, so that the interference of the core ball can be relatively effectively avoided when the pipe with small bending radius is formed, but the actual forming requirement of a six-shaft machine cannot be met because the core rod can be formed in one direction. The present invention therefore contemplates a method of rotating a mandrel in conjunction with a six-axis bending die.
Disclosure of Invention
The invention provides a six-axis bending device and a method based on core rod rotation, aiming at the defect that a unidirectional bendable core rod can only be bent towards one direction, which comprises the following steps:
in order to achieve the purpose, the invention provides the following technical scheme:
the utility model provides a six bending apparatus based on plug is rotatory, includes the guiding mechanism who is used for carrying out crooked bending die and is used for carrying out the guide to shaping tubular product, guiding mechanism sets up on the fixing base, it is equipped with a Z to the slip table to slide on the fixing base, Z is equipped with the tubular product pushing mechanism who is used for promoting shaping tubular product to pass the bending die to being equipped with on the slip table, Z is used for driving its gliding Z to the sliding shaft to the slip table connection, Z is used for driving its pivoted Z axle propulsion motor to the sliding shaft connection, and then promotes shaping tubular product and impels along Z to the sliding shaft.
The pipe bending machine is characterized by further comprising a core rod capable of being bent in one direction, wherein the core rod penetrates through the pipe pushing mechanism and the inside of a formed pipe and extends to a pipe plastic deformation zone from the center of the bending die to the front end of the guide mechanism, the core rod is driven by a core rod push rod to move forwards along the formed pipe, the core rod push rod is controlled by a core rod push rod rotating motor to rotate around the axis of the Z shaft, and the core rod push rod is arranged in the pipe through the pipe pushing mechanism;
according to the bending direction required by the formed pipe, the mandrel push rod rotating motor drives the mandrel push rod to rotate, so that the bending direction of the mandrel rotates by an angle beta along the Y-axis positive direction from the initial bending direction, and the bending direction of the mandrel is consistent with the bending direction of the pipe;
because the thickness of the core ball is relatively lower at the inner side of the core ball in the bendable direction, the core ball can be relatively effectively prevented from interfering when the pipe with small bending radius is formed;
the core rod is composed of three core balls and a core ball handle, different core balls are connected with chain pieces at two ends of the plug pin through core ball connecting shafts, the core balls can rotate around the plug pin and the connecting shafts, and the thickness of each core ball in the bendable direction is thinner, so that the unidirectional bendable core rod can ensure that the bending radius is smaller in the bending process.
As a further scheme of the invention: the mandrel push rod is directly connected with a rotating central shaft of a mandrel push rod rotating motor through a bolt, and the rotating angle along the axis can be precisely adjusted through the motor.
A bending method of a six-axis bending device based on mandrel rotation comprises the following steps:
the first step is as follows: knowing the rotation angle of the core rod, the distance A between the guide mechanism and the bending die and the eccentricity U, the rotation angles alpha and theta of the bending die around the X direction and the Y direction can be deduced, and the angle transformation gamma of the bending die in the space can be obtained;
the second step is that: the initial bending direction of the core rod is defined as Y-axis positive direction, namely
Figure GDA0004090123470000031
Direction, obviouslyThe initial bendable direction of the mandrel is rotated to ^ 5 when the mandrel can be bent>
Figure GDA0004090123470000032
The direction is known, and the rotation angle beta of the core rod at the moment is not less than the angle BDF;
the third step: according to the distance A between the guide mechanism and the bending die and the component theta of the deflection angle of the bending die on the YOZ plane, the method can deduce
Figure GDA0004090123470000033
Recombination BF = U x The linear distance from the center of the bending die to the front end of the guide mechanism can be deduced,
Figure GDA0004090123470000034
the fourth step: according to the rotation angle beta = ≈ BDF of the core rod, the following can be deduced:
Figure GDA0004090123470000035
the fifth step: according to the spatial position relationship and the established mathematical model geometric relationship, the offset distances of the bending mode in the X-axis direction and the Y-axis direction can be expressed as follows:
Figure GDA0004090123470000036
Figure GDA0004090123470000037
Figure GDA0004090123470000038
and a sixth step: the component α of the bending mode deflection angle in the XOZ plane can be expressed as:
Figure GDA0004090123470000039
Figure GDA00040901234700000310
the deflection angle of the bending die along the axial direction is as follows: />
Figure GDA00040901234700000311
The seventh step: after the bending section is bent, the position of the bending die returns to the point D, and the core rod rotates by an angle beta along the axial direction to enable the bending direction to face the positive direction of the Y axis;
wherein: the parameters include: distance A from the front end of the guide mechanism of the six-shaft machine to the bending die, and displacement U of the X-direction bending die x Displacement U of Y-direction bending die y (ii) a The deflection parameters of the bending die deflection device comprise: the deflection angle gamma of the bending die along the axis direction of the bending die, the decomposition angle alpha of the deflection angle of the bending die to the Z-X plane, and the decomposition angle theta of the deflection angle of the bending die to the Z-Y plane; and the angle parameters of the mandrel rotating along the axial direction comprise: the rotation angle beta of the core rod along the axial direction thereof;
OD＝A；OE＝BD＝FA＝U y ；OC＝AD＝U x ；∠DOA＝α；∠DOB＝θ；∠FOA＝γ；
o point spatial coordinates (0, 0); e point space coordinates (0, U) y ,0)；
D point space coordinates (0, A); spatial coordinates of point B (0, U) y A); c point space coordinate (U) x ,0,0)；
Simultaneous F point space coordinate (U) x ,U y A); spatial coordinates of point A (U) x ,0,A)：
Figure GDA0004090123470000041
Has the advantages that:
1. by using the unidirectional bendable core rod, the invention effectively solves the problems that the thickness of the outer side wall of the bending section is greatly reduced, the inner side is easy to wrinkle, the cross section of the pipe is seriously distorted, and the forming quality of the pipe is difficult to ensure when the three-dimensional free bending six-shaft machine equipment is used for forming the pipe with the small bending space and the continuously variable curvature. The effect of reducing bending defects is achieved, and the forming quality under the condition is improved.
2. According to the process algorithm provided by the invention, the unidirectional bendable core rod is matched with the deflection of the bending die of the six-axis machine and is rotated to the pipe forming direction along the axis direction of the unidirectional bendable core rod, so that the unidirectional bendable core rod is effectively prevented from being single in forming direction and cannot meet the requirement of forming a continuous variable-curvature component in space by three-dimensional free bending six-axis machine equipment.
3. The process analytic algorithm provided by the invention is simple and feasible, has high production efficiency, and has important engineering application value and obvious economic benefit in actual production.
Drawings
FIG. 1 is a schematic view of a mathematical geometric model of a mandrel according to the present invention;
FIG. 2 is a schematic structural view of the present invention;
FIG. 3-1 is a front view of a mandrel of the present invention;
FIG. 3-2 is a top view of a mandrel of the present invention;
FIGS. 3-3 are cross-sectional views of the mandrel of the present invention;
FIG. 4 is a schematic view of an example formed tube;
wherein: the bending die comprises a bending die 1, a one-way bendable mandrel 2, a guide mechanism 3, a Z-axis pushing motor 4, a Z-direction sliding shaft 5, a formed tube 6, a tube pushing mechanism 7, a Z-direction sliding table 8, a mandrel push rod 9 and a mandrel push rod rotating motor 10.
Detailed Description
The invention is described in detail below with reference to a specific example of two consecutive bending arcs of a six-axis machine.
Referring to fig. 2, the bending apparatus includes a bending die 1, a mandrel 2 capable of bending in one direction, a guide mechanism 3, a Z-axis propulsion motor 4, a Z-direction slide shaft 5, a formed tube 6, a tube propulsion mechanism 7, a Z-direction slide table 8, a mandrel push rod 9, and a mandrel push rod rotation motor 10. The one-way bendable core rod 2 is driven by the core rod push rod 9 to move forwards along the pipe and rotate around the Z axis. The mandrel push rod 9 is controlled to rotate around the axis of the Z axis by a mandrel push rod rotating motor 10. The mandrel pusher 9 is inserted into the tube by means of the tube advancing mechanism 7. The pipe pushing mechanism 7 is connected to the Z-direction sliding table 8 through bolts. The Z-direction sliding table 8 controls the pushing of the forming pipe 6 along the Z-direction sliding shaft 5 through the Z-axis pushing motor 4.
The one-way bendable core rod is connected with the external thread at the front end of the core rod push rod through the internal thread of the core ball handle, and the core rod is pushed to the position from the front end of the guide mechanism to the center of the bending die through the core rod push rod. Before bending, the bendable direction of the unidirectional bendable core rod needs to be rotated to the Y-axis positive homing.
The tail end of the one-way bendable core rod 2 is connected with the front end of a core rod push rod 9 penetrating through the tube pushing mechanism 7 and arranged in the tube, and the position of the one-way bendable core rod is positioned in a tube plastic deformation area from the center of the bending die 1 to the front end of the guide mechanism 3. The bending die moves from an initial position D (the eccentricity of the initial position is 0, the initial elevation angle is 0) along the X axial direction and the Y axial direction respectively x And U y To point F of space. According to the bending direction required by the pipe 6, the mandrel push rod rotating motor 10 drives the mandrel push rod 9 to rotate, so that the bending direction of the mandrel 2 is rotated by a angle beta along the Y-axis positive direction from the initial bending direction, and the bending direction of the mandrel is consistent with the bending direction of the pipe.
Specifically, the analysis steps of the matching process of the core rod and the bending die for bending the arc segment with continuously variable curvature on the three-dimensional free bending six-axis machine equipment by using the one-way bendable core rod are as follows:
the first step is as follows: the formed pipe 6 passes through the bending die 1 and the guide mechanism 3, the tail end of the pipe is connected with the pipe pushing mechanism 7, then the core rod 2 is pushed to the position from the front end of the guide mechanism 3 to the center of the bending die 1 through the core rod push rod 9 as shown in figure 2, and the bendable direction of the core rod 2 which can be bent in the single direction is rotated to the Y-axis positive homing.
The second step is that: the tube advancing mechanism 7 advances the tube 6 forward along the Z-axis at a constant speed to form a straight segment as shown at 4-1 in fig. 4.
The third step: the pipe material propelling mechanism 7 continues to propel the pipe material 6 forward along the Z axis at a constant speed, and simultaneously the bending die moves towards the X direction and the Y direction respectively
Figure GDA0004090123470000061
Distance, one-way bendable core rod 2-wayThe core rod push rod rotating motor 10 drives the core rod push rod 9 to rotate by an angle beta along the Z-axis direction 1 At the same time, the bending die deflects an angle gamma along the axis of the bending die in accordance with the rotation of the unidirectional bendable core rod 2 1 . Wherein the core rod 2 which can be bent in one direction rotates a angle beta along the Z-axis direction 1 Angle of deflection gamma with respect to bending die 1 The coordination relationship is as follows:
knowing the rotation angle of the core rod, the distance A =60mm between the guide mechanism and the bending die and the eccentricity
Figure GDA0004090123470000062
Figure GDA0004090123470000063
The rotation angle of the core rod at this time can be known
Figure GDA0004090123470000064
According to the distance A between the guide mechanism and the bending die and the component theta of the deflection angle of the bending die on the YOZ plane 1 Can deduce
Figure GDA0004090123470000065
Recombined and combined>
Figure GDA0004090123470000066
The linear distance from the center of the bending die to the front end of the guide mechanism can be deduced,
Figure GDA0004090123470000067
according to the spatial position relationship and the established mathematical model geometric relationship, the offset distances of the bending mode in the X-axis direction and the Y-axis direction can be expressed as follows:
Figure GDA0004090123470000068
Figure GDA0004090123470000069
/>
Figure GDA00040901234700000610
component alpha of bending mode deflection angle in XOZ plane 1 Can be expressed as:
Figure GDA0004090123470000071
the deflection angle of the bending die along the axial direction is:
Figure GDA0004090123470000072
the first bend segment is formed as shown at 4-2 in figure 4.
Starting to form a second bending section, the pipe pushing mechanism 7 continues to push the pipe 6 forward along the Z axis at a constant speed, and simultaneously the bending die moves to the X direction and the Y direction respectively
Figure GDA0004090123470000073
The core rod 2 which can be bent in one direction drives the core rod push rod 9 to rotate by an angle beta along the Z-axis direction through the core rod push rod rotating motor 10 2 At the same time, the bending die is matched with the rotation of the core rod 2 which can be bent in one direction to deflect an angle gamma along the axis of the bending die 2 . Wherein the core rod 2 which can be bent in one direction rotates a angle beta along the Z-axis direction 2 Angle of deflection gamma with respect to bending die 2 The coordination relationship is as follows:
knowing the rotation angle of the mandrel, the guide to bending die distance A =60mm and the eccentricity
Figure GDA0004090123470000074
Figure GDA0004090123470000075
At the moment, the core rod and the Y axis deflect at a positive angle beta 3 The bending die being referenced to an initial positionThe time deflection angle is gamma 3 ；
The positive deflection angle of the core rod and the Y axis at the moment can be known
Figure GDA0004090123470000076
According to the distance A between the guide mechanism and the bending die and the component theta of the deflection angle of the bending die on the YOZ plane 2 Can derive
Figure GDA0004090123470000077
Recombined and combined>
Figure GDA0004090123470000078
The linear distance from the center of the bending die to the front end of the guide mechanism can be deduced,
Figure GDA0004090123470000079
according to the spatial position relationship and the established mathematical model geometric relationship, the offset distances of the bending mode in the X-axis direction and the Y-axis direction can be expressed as follows:
Figure GDA00040901234700000710
Figure GDA00040901234700000711
Figure GDA0004090123470000081
component alpha of bending mode deflection angle in XOZ plane 2 Can be expressed as:
Figure GDA0004090123470000082
/>
the deflection angle of the bending die along the axial direction is as follows:
Figure GDA0004090123470000083
at the moment, the core rod 2 which can be bent in one direction rotates by a rotating angle beta along the axis direction of the Z axis 2 ＝β 3 -β 1 = -90 degrees and bending mode deflection angle gamma 2 ＝γ 3 -γ 1 =3.47 °. The second bend segment is formed as shown at 4-3 in figure 4.
The final shape of the continuously varying curvature arc segment is shown in fig. 4.
It will be understood that modifications and variations can be made by persons skilled in the art in light of the above teachings and all such modifications and variations are intended to be included within the scope of the invention as defined in the appended claims.

Claims (3)

1. The utility model provides a six-axis bending device based on mandrel rotation, is including being used for carrying out crooked bending die (1) and being used for carrying out guiding mechanism (3) to shaping tubular product (6), guiding mechanism (3) set up on the fixing base, it is equipped with one Z to slip table (8) to slide on the fixing base, Z is equipped with tubular product pushing mechanism (7) that are used for promoting shaping tubular product (6) to pass bending die (1) to slip table (8), Z is connected to slip table (8) and is used for driving its gliding Z to sliding shaft (5), Z is connected to sliding shaft (5) and is used for driving its pivoted Z axle propulsion motor (4), and then promotes shaping tubular product (6) and impels to sliding shaft (5) along Z;
the bending die is characterized by further comprising a mandrel (2) capable of being bent in a one-way mode, wherein the mandrel (2) penetrates into a tube propelling mechanism (7) and a formed tube (6) and extends to a tube plastic deformation zone from the center of the bending die (1) to the front end of the guide mechanism (3), the mandrel (2) is driven by a mandrel push rod (9) to move forwards along the formed tube (6), the mandrel push rod (9) is controlled by a mandrel push rod rotating motor (10) to rotate around the axis of a Z axis, and the mandrel push rod (9) is arranged in the tube through the tube propelling mechanism (7);
according to the bending direction required by the formed pipe (6), the core rod push rod rotating motor (10) drives the core rod push rod (9) to rotate, so that the bending direction of the core rod (2) rotates by a angle beta along the Y-axis positive direction from the initial bending direction, and the bending direction of the core rod (2) is consistent with the pipe bending direction;
because the thickness of the core ball is relatively lower at the inner side of the core ball in the bendable direction, the core ball can be relatively effectively prevented from interfering when the pipe with small bending radius is formed;
the core rod (2) is composed of three core balls and a core ball handle, different core balls are connected with chain pieces at two ends of the plug pin through core ball connecting shafts, the core balls can rotate around the plug pin and the connecting shafts, and the thickness of each core ball in the bendable direction is thinner, so that the unidirectional bendable core rod can ensure that the bending process has smaller bending radius.
2. The mandrel-rotation-based six-axis bending device according to claim 1, wherein the mandrel (2) is connected with the external thread at the front end of the mandrel push rod (9) through the internal thread of the mandrel ball shank, the mandrel push rod (9) is directly connected with the rotation central shaft of the mandrel push rod rotation motor (10) through a bolt, and the rotation angle along the axis can be precisely adjusted through the motor.
3. A mandrel rotation-based bending method for a six-axis bending apparatus according to any one of claims 1 to 2, comprising the steps of:
the first step is as follows: knowing the rotation angle of the core rod, the distance A between the guide mechanism and the bending die and the eccentricity U, the rotation angles alpha and theta of the bending die around the X direction and the Y direction can be deduced, and the angle transformation gamma of the bending die in the space can be obtained;
the second step is that: the initial bending direction of the core rod is defined as Y-axis positive direction, namely
Figure FDA0004090123460000021
Direction, it is apparent that the initial bendable direction of the mandrel has been rotated into->
Figure FDA0004090123460000022
The direction is known, and the rotation angle beta of the core rod at the moment is not less than the angle BDF;
the third step: according toThe distance A between the guide mechanism and the bending die and the component theta of the deflection angle of the bending die on the YOZ plane can be deduced
Figure FDA0004090123460000023
Recombination BF = U x The linear distance from the center of the bending die to the front end of the guide mechanism can be deduced,
Figure FDA0004090123460000024
the fourth step: according to the rotation angle beta = ≈ BDF of the core rod, the following can be deduced:
Figure FDA0004090123460000025
the fifth step: according to the spatial position relationship and the established mathematical model geometric relationship, the offset distances of the bending mode in the X-axis direction and the Y-axis direction can be expressed as follows:
Figure FDA0004090123460000026
Figure FDA0004090123460000027
Figure FDA0004090123460000028
and a sixth step: the component α of the bending mode deflection angle in the XOZ plane can be expressed as:
Figure FDA0004090123460000029
Figure FDA00040901234600000210
the deflection angle of the bending die along the axial direction is:
Figure FDA00040901234600000211
the seventh step: after the bending section is bent, the position of the bending die returns to the point D, and the core rod rotates by an angle beta along the axial direction to enable the bending direction to face the positive direction of the Y axis;
wherein: the parameters include: distance A from the front end of the guide mechanism to the bending die, and displacement U of the bending die in the X direction x Displacement U of the bending die in the Y direction y (ii) a The deflection parameters of the bending die deflection device comprise: the deflection angle gamma of the bending die along the self axis direction, the decomposition angle alpha of the deflection angle of the bending die to the Z-X plane, and the decomposition angle theta of the deflection angle of the bending die to the Z-Y plane;
and the angle parameters of the mandrel rotating along the axial direction comprise: the rotation angle beta of the core rod along the axial direction thereof;
OD＝A；OE＝BD＝FA＝U y ；OC＝AD＝U x ；∠DOA＝α；∠DOB＝θ；∠FOA＝γ；
o point spatial coordinates (0, 0); e point space coordinates (0, U) y ,0)；
D point spatial coordinates (0, A); spatial coordinates of point B (0, U) y A); c point space coordinate (U) x ,0,0)；
Simultaneous F point space coordinate (U) x ,U y A); spatial coordinates of point A (U) x 0, A) gives:
Figure FDA0004090123460000031
/>
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CN112270079B (en) * 2020-10-22 2024-03-29 南京航空航天大学 Three-dimensional free bending active bending die movement pose analysis method
CN113059039A (en) * 2021-05-19 2021-07-02 南京航空航天大学 Method for avoiding interference by realizing three-dimensional free bending forming through bending die deflection
CN113787122B (en) * 2021-09-06 2023-02-24 南京航空航天大学 Flexible support core rod, support device and pipe bending robot forming control method

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