CN106980751B - A kind of inverse kinematic method of the six axis automation drilling counter boring lathe containing double C axis - Google Patents
A kind of inverse kinematic method of the six axis automation drilling counter boring lathe containing double C axis Download PDFInfo
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Abstract
The invention discloses a kind of, and six axis containing double C axis automate the inverse kinematic method of drilling counter boring lathe, include the following steps: that (1) in six axis automation drilling counter boring lathe, establishes equipment basis coordinates system, each kinematic axis subcoordinate system and tool coordinate system；Coordinate system definition figure is drawn, each subcoordinate system and the change in coordinate axis direction of equipment basis coordinates system are consistent.(2) kinematics analysis is made to six axis automation drilling counter boring lathe, establishes direct kinematics model.(3) object pose and direct kinematics model that drilling counter boring lathe is automated according to six axis, establish the equation group of articulation amount；It is proposed a kind of inverse kinematic strategy of articulation amount split cavity oscillator, analytic method is combined with numerical method solves each articulation amount, to obtain its inverse kinematics model, the positive and negative solution of kinematics that six axis are automated with drilling counter boring lathe may be implemented in this method, guarantee the accuracy of machine tool motion control, to realize oval nest automation processing.
Description
Technical Field
The invention relates to the field of aircraft assembly technology and equipment, in particular to a kinematics inverse solution method of a six-axis automatic hole-making and dimple-sinking machine tool with double C axes.
Background
With the increasing design level of modern military aircrafts, the stealth performance of the aircrafts is continuously pursued, and the integral wing is widely applied. In the assembly of the integral wing, the oval-head earless supporting plate nut is used for realizing the unilateral fixation between the wing wall plate and the wing framework. Before using the special fastener, an assembling hole (an elliptic socket for short) similar to an ellipse is needed to be processed on the wing framework.
The traditional elliptical pit processing method adopts a manual processing tool, and depends on the technical level of workers to control the pit shape and pit depth of the elliptical pit, so that the processing steps are complicated, the efficiency is low, the stability of the processing quality is difficult to guarantee, and the assembly quality and reliability of the integral wing are greatly reduced. Therefore, the six-axis automatic hole-making dimple machine tool is designed and researched to improve the processing efficiency and quality of the elliptical dimple, ensure the assembly quality and reliability of the integral wing and make a contribution to the development of the military aircraft assembly technology.
The six-axis automatic hole-making countersink machine tool adopts a double-C-axis structural form, and has X, Y, Z, C in total1、A、C2Six motion axes. In general, inverse kinematics methods include analytical methods and numerical methods. The analytical method has high calculation speed and high precision, but is only suitable for motion axes which are vertical to each other and intersect at one point; the numerical method has wide application range, but the calculation speed and the calculation precision are limited. The single method is not suitable for the six-axis automatic hole-making and dimple-sinking machine tool. At the same time, due to the double C-axis knotThe structure form is easy to generate mutual influence in inverse kinematics solution, and the condition of inaccurate solution is easy to cause during solution; and the strokes of the three rotating shafts are relatively large, and the condition of periodic multiple solutions is easy to occur during solving. For example: the kinematic model of the six-axis automatic hole-making dimple-sinking machine tool is analyzed to find that at least two groups of rotation quantities can meet the machining requirement of the elliptical dimple, namely [ theta ]5,θ6,θ7]And [ theta ]5±π,-θ6,θ7±π]。
Aiming at a six-axis automatic hole-making and dimple-sinking machine tool with double C-axis, the calculation speed, the calculation precision and the stability of the inverse kinematics are comprehensively considered, and a practical and effective inverse kinematics solution algorithm is urgently needed to be provided for the motion control of the machine tool so as to realize the automatic machining of the elliptical dimple.
Disclosure of Invention
The invention provides a kinematics inverse solution method of a six-axis automatic hole-making and dimple-sinking machine tool with double C-axes, aiming at overcoming the defects of the prior art, and the kinematics inverse solution method can realize the kinematics inverse solution of the six-axis automatic hole-making and dimple-sinking machine tool, ensure the accuracy of machine tool motion control and realize the automatic processing of elliptical dimples.
The technical scheme of the invention is as follows: a kinematic inverse solution method of a six-axis automatic hole-making and socket-boring machine tool with double C-axes comprises the following steps:
(1) in a six-axis automatic hole-making and socket-boring machine tool, establishing an equipment base coordinate system, a sub-coordinate system of each motion axis and a cutter coordinate system, and drawing a coordinate system definition diagram to ensure that the directions of the coordinate axes of each sub-coordinate system and the equipment base coordinate system are kept consistent;
(2) performing kinematic analysis on a six-axis automatic hole making and dimple forming machine tool, and establishing a forward kinematic model;
(3) and establishing an equation set of joint quantities according to the target pose and the forward kinematics model of the six-axis automatic hole-making dimple machine tool, and solving each joint quantity by utilizing a kinematics inverse solution strategy of joint quantity separation solving so as to obtain the inverse kinematics model of the joint quantity.
The specific steps of the step (1) are as follows:
(1.1) defining each coordinate system in the six-axis automatic hole-making and socket-boring machine tool: base coordinate system O0Axis of motion X, Y, Z, C1、A、C2Corresponding sub-coordinate system O1、O2、O3、O4、O5、O6And a tool coordinate system O7；
And (1.2) drawing a coordinate system definition diagram of the six-axis automatic hole-making and socket-boring machine tool, wherein the coordinate axis direction of each sub-coordinate system is consistent with the coordinate axis direction of the equipment base coordinate system.
The specific steps of the step (2) are as follows:
(2.1) performing kinematic analysis on a six-axis automatic hole-making and dimple-sinking machine tool, and respectively calculating homogeneous transformation matrixes of all motion axes:
wherein, T01Is from a coordinate system O0To the coordinate system O1Of the ideal homogeneous transformation matrix, T12Is from a coordinate system O1To the coordinate system O2Of the ideal homogeneous transformation matrix, T23Is from a coordinate system O2To the coordinate system O3Of the ideal homogeneous transformation matrix, T34Is from a coordinate system O3To the coordinate system O4Ideal homogeneity ofTransformation matrix, T45Is from a coordinate system O4To the coordinate system O5Of the ideal homogeneous transformation matrix, T56Is from a coordinate system O,5To the coordinate system O6Of the ideal homogeneous transformation matrix, T67Is from a coordinate system O6To the coordinate system O7An ideal homogeneous transformation matrix; d1,d2,d3,θ4,θ5,θ6Respectively, six-shaft automatic hole-making spot facing machine X, Y, Z, C1、A、C2The joint amount of the shaft; x is the number of7,y7,z7The displacement offset from the last motion axis coordinate system to the cutter coordinate system in the x, y and z directions;
(2.2) establishing a forward kinematics model of the six-axis automatic hole-making and dimple-sinking machine tool:
wherein, T07Is from the base coordinate system O0To the tool coordinate system O7The ideal homogeneous transformation matrix is a forward kinematic model of the six-axis automatic hole-making and spot-facing machine tool and represents the theoretical pose of the tail end of the six-axis automatic hole-making and spot-facing machine tool, R (q) is a tool coordinate system attitude matrix of 3 multiplied by 3, and P (q) is a tool coordinate system position matrix of 3 multiplied by 1. In the attitude matrix, [ r ]11,r21,r31]TIs the attitude vector of the X-axis of the tool coordinate system, [ r ]12,r22,r32]TIs the attitude vector of the Y-axis of the tool coordinate system, [ r ]13,r23,r33]TIs the pose vector of the Z-axis of the tool coordinate system.
Analyzing the forward kinematics model in the step (2.2), wherein the translational shaft joint quantity only affects the tail end position of the machine tool, and the rotary shaft joint quantity affects both the tail end position and the tail end posture of the machine tool; in the attitude matrix, the attitude vector [ r ] of the Z axis of the tool coordinate system13,r23,r33]TAmount of articulation with only the axis of rotation theta4,θ5Related to theta6Independent, X-axis and Y-axis attitude vectors [ r ] of the tool coordinate system11,r21,r31]TAnd [ r12,r22,r32]TAnd θ4,θ5,θ6All are related.
The specific steps of the step (3) are as follows:
(3.1) according to the normal direction of the surface of the workpiece and the requirement of the drilling position, expressing the terminal target pose of the six-axis automatic drilling and dimpling machine tool as follows:
wherein, TdIs a matrix of target poses, P, of the machine tool coordinate systemdIs a target position matrix, R, of the tool coordinate systemdIs a target attitude matrix of the tool coordinate system, [ u ]x,uy,uz]TIs the target attitude vector of the X-axis of the tool coordinate system, [ v ]x,vy,vz]TIs the target attitude vector of the Y-axis of the tool coordinate system, [ w ]x,wy,wz]TIs the target attitude vector of the Z axis of the tool coordinate system, [ o ]x,oy,oz]TIs the target position vector.
(3.2) enabling the theoretical pose of the tail end of the six-axis automatic hole-making and spot-facing machine tool to be equal to the target pose state, and expressing the theoretical pose with a formula as follows:
T07＝Td
(3.3) establishing an equation set of the joint quantity according to the equality of the corresponding elements of the matrix, wherein the equation set comprises the following steps:
wherein, equation ox、oy、、ozCalled the machine tool end position constraint equation, equation wx、wy、、wzCalled tool axis direction constraint equation, equation vx、vy、、vzCalled the constraint equation of the major axis direction of the elliptical fossa; solving the equation set in the inverse kinematics solution process to obtain the expression of each joint quantity;
and (3.4) solving the joint quantity by using a kinematic inverse solution strategy for joint quantity separation solving.
The kinematics inverse solution strategy for joint quantity separation solution comprises separation solution of rotation quantity and translation quantity, and the separation solution of the rotation quantity corresponds to the kinematics inverse solution process of the six-axis automatic hole-making and dimple-sinking machine tool, and is represented as the solution sequence of each joint quantity of the machine tool. The specific process is as follows:
firstly, solving a rotating shaft C by adopting an L-M nonlinear optimization method according to a tool axis direction constraint equation1Joint quantity theta of shaft4And the joint quantity theta of the A axis5The objective function of the process is:
J(q)＝Jori(q)＝Ewx 2+Ewy 2+Ewz 2
wherein,
Ewx＝sinθ4sinθ5-wx
Ewy＝-cosθ4sinθ5-wy
Ewz＝cosθ5-wz
then, based on the obtained theta4、θ5And the constraint equation of the long axis direction of the elliptical fossa is solved by adopting an analytic method2Joint quantity theta of shaft6The expression is:
θ6＝arccos(vz/sinθ5)
finally, according to the obtained theta4、θ5、θ6And the constraint equation of the end position of the machine tool, and solving the joint quantity d of the translation shaft by adopting an analytic method1,d2,d3(ii) a The expression is as follows:
d1＝ox-x7(cosθ4cosθ6-sinθ4cosθ5sinθ6)
-y7(-cosθ4sinθ6-sinθ4cosθ5cosθ6)-z7sinθ4sinθ5
d2＝oy-x7(sinθ4cosθ6+cosθ4cosθ5sinθ6)
-y7(-sinθ4sinθ6+cosθ4cosθ5cosθ6)+z7cosθ4sinθ5
d3＝oz-x7sinθ5sinθ6-y7sinθ5cosθ6-z7cosθ5
therefore, inverse kinematics of the six-axis automatic hole-making and socket-boring machine tool with double C-axes is realized, and a reverse kinematics model of the six-axis automatic hole-making and socket-boring machine tool with double C-axes is obtained.
In the step (3.2), in order to obtain the joint quantity q through inverse kinematics, the theoretical pose of the tail end of the six-axis automatic hole-making countersinking machine tool needs to reach a target pose state, namely T07＝Td。
In step (3.3), the main factors influencing the hole-making quality are the position of the hole and the axial direction of the hole, corresponding to the attitude of the end position of the machine tool and the feeding direction of the spindle, i.e., [ o ]x,oy,oz]TAnd [ wx,wy,wz]TWhen the dimple direction is required, the method should also be usedTaking into account the attitude vector associated therewith, i.e. [ v ]x,vy,vz]TTherefore, the equation set of the joint quantity is established according to the equality of the matrix corresponding elements.
In the step (3.4), the inverse kinematics solution strategy for the joint quantity separation solution is provided by analyzing the characteristics of the forward kinematics model of the six-axis automatic hole-making and dimple-drilling machine tool and comprehensively considering the calculation precision, calculation speed and stability of the equation set solution.
Compared with the prior art, the invention has the advantages that:
(1) aiming at a six-axis automatic hole-making and dimple-sinking machine tool with double C-axes, a kinematics inverse solution strategy for joint quantity separation solution is provided, a translation axis and a rotation axis are separated and solved, and the rotation axis is separated and solved, so that the accuracy and the stability of the kinematics inverse solution process are ensured;
(2) aiming at the structural characteristics of a six-axis automatic hole-making and dimple-sinking machine tool with double C-axes, a kinematics inverse solution method combining an analytical method and a numerical method is adopted, the calculation speed and the calculation precision in the kinematics inverse solution process are ensured to the greatest extent, and the robustness of the kinematics inverse solution method is improved;
(3) the kinematics positive and negative solution of the six-axis automatic hole-making dimple machine tool is realized, the foundation is laid for the motion control of the machine tool, the automatic processing of the elliptical dimple is realized, and the automation degree of the aircraft assembly is improved.
Drawings
FIG. 1 is a coordinate system definition diagram of a six-axis automated spot facing machine;
FIG. 2 is a kinematic reverse-solving flow chart of a six-axis automatic hole-making and socket-sinking machine tool.
Detailed Description
In order to more specifically describe the present invention, the following detailed description is provided for the technical solution of the present invention with reference to the accompanying drawings and the specific embodiments.
As shown in fig. 1, a six-axis automatic hole-making and socket-boring machine tool adopts a double-C-axis structural form, and defines a base coordinate system, a coordinate system of each motion axis and a coordinate system of a cutter of the machine tool;
as shown in FIG. 2, the kinematic inverse solution flow chart of the six-axis automatic hole-making countersinking machine tool comprises the steps of the kinematic inverse solution process and corresponding algorithms.
As shown in fig. 1, the inverse kinematics solution method of the six-axis automatic hole-making and socket-boring machine tool including two C-axes of the embodiment includes the following steps:
step 1: in a six-axis automatic hole-making and socket-boring machine tool, establishing an equipment base coordinate system, a coordinate system of each motion axis and a cutter coordinate system; drawing a coordinate system definition diagram to make the coordinate axis directions of each sub coordinate system consistent with the coordinate axis directions of the equipment base coordinate system. The method comprises the following steps:
step 1.1: defining each coordinate system in the six-axis automatic hole-making and socket-sinking machine tool: base coordinate system O0Axis of motion X, Y, Z, C1、A、C2Sub-coordinate system O corresponding to axis1、O2、O3、O4、O5、O6And a tool coordinate system O7；
Step 1.2: drawing a coordinate system definition diagram of the six-axis automatic hole-making and socket-sinking machine tool, wherein the coordinate axis direction of each sub-coordinate system is consistent with the coordinate axis direction of the equipment base coordinate system as shown in figure 2.
Step 2: and (4) performing kinematic analysis on the six-axis automatic hole making and dimple forming machine tool, and establishing a forward kinematic model. The method comprises the following steps:
step 2.1: performing kinematic analysis on a six-axis automatic hole-making dimple machine tool, and respectively calculating homogeneous transformation matrixes of all motion axes:
wherein, T01Is from a coordinate system O0To the coordinate system O1Of the ideal homogeneous transformation matrix, T12Is from a coordinate system O1To the coordinate system O2Of the ideal homogeneous transformation matrix, T23Is from a coordinate system O2To the coordinate system O3Of the ideal homogeneous transformation matrix, T34Is from a coordinate system O3To the coordinate system O4Of the ideal homogeneous transformation matrix, T45Is from a coordinate system O4To the coordinate system O5Of the ideal homogeneous transformation matrix, T56Is from a coordinate system O,5To the coordinate system O6Of the ideal homogeneous transformation matrix, T67Is from a coordinate system O6To the coordinate system O7An ideal homogeneous transformation matrix; d1,d2,d3,θ4,θ5,θ6Respectively, six-shaft automatic hole-making spot facing machine X, Y, Z, C1、A、C2The joint amount of the shaft; x is the number of7,y7,z7The displacement offset from the last motion axis coordinate system to the cutter coordinate system in the x, y and z directions;
step 2.2: establishing a forward kinematics model of a six-axis automatic hole-making dimple machine tool:
wherein, T07Is from the base coordinate system O0To the tool coordinate system O7The homogeneous transformation matrix is a forward kinematics model of the six-axis automatic hole-making dimple machine tool. R (q) is a 3 × 3 tool coordinate system attitude matrix, and P (q) is a 3 × 1 tool coordinate system position matrix. In the attitude matrix, [ r ]11,r21,r31]TIs the attitude vector of the X-axis of the tool coordinate system, [ r ]12,r22,r32]TIs the attitude vector of the Y-axis of the tool coordinate system, [ r ]13,r23,r33]TIs the pose vector of the Z-axis of the tool coordinate system.
Analyzing the model, the joint quantity of the translation shaft only affects the tail end position of the machine tool, and the joint quantity of the rotation shaft not only affects the tail end position of the machine tool but also affects the tail end posture of the machine tool; in the attitude matrix, the attitude vector [ r ] of the Z axis of the tool coordinate system13,r23,r33]TAmount of articulation with only the axis of rotation theta4,θ5Related to theta6Independent, X-axis and Y-axis attitude vectors [ r ] of the tool coordinate system11,r21,r31]TAnd [ r12,r22,r32]TAnd θ4,θ5,θ6All are related.
And step 3: establishing an equation set of joint quantity according to a target pose and a forward kinematics model of the six-axis automatic hole-making dimple machine tool; a kinematic inverse solution strategy for joint mass separation solution is provided, and each joint mass is solved by combining an analytical method and a numerical method to obtain a reverse kinematic model of the joint mass. The method specifically comprises the following steps:
step 3.1: according to the requirements of the normal direction of the surface of the workpiece, the hole-making position and the like, the terminal target pose of the six-axis automatic hole-making and dimple-making machine tool can be expressed as follows:
wherein, TdIs a matrix of target poses, P, of the machine tool coordinate systemdIs a target position matrix, R, of the tool coordinate systemdIs a target attitude matrix of the tool coordinate system, [ u ]x,uy,uz]TIs the target attitude vector of the X-axis of the tool coordinate system, [ v ]x,vy,vz]TIs the target attitude vector of the Y-axis of the tool coordinate system, [ w ]x,wy,wz]TIs the target attitude vector of the Z axis of the tool coordinate system, [ o ]x,oy,oz]TIs the target position vector.
Step 3.2: in order to solve the joint quantity q through inverse kinematics, the theoretical pose of the tail end of the six-axis automatic hole-making and counter boring machine tool needs to reach a target pose state, namely:
T07＝Td
step 3.3: since the main factors affecting the quality of hole making are the position of the hole and the axial direction of the hole, the attitude corresponding to the end position of the machine tool and the feed direction of the spindle, i.e., [ o ]x,oy,oz]TAnd [ wx,wy,wz]T. When the dimple direction is required, the related attitude vector, namely [ v ] should be consideredx,vy,vz]T. Therefore, from the equality of the matrix corresponding elements, a system of equations for the joint quantities is established as follows:
wherein, equation ox、oy、、ozCalled the machine tool end position constraint equation, equation wx、wy、、wzCalled tool axis direction constraint equation, equation vx、vy、、vzCalled the constraint equation of the major axis direction of the elliptical fossa; solving the equation set in the inverse kinematics solution process to obtain the expression of each joint quantity;
step 3.4: through analyzing the characteristics of a forward kinematics model of the six-axis automatic hole-making countersinking machine tool and comprehensively considering the calculation precision, the calculation speed and the stability of the equation set solution, a kinematics inverse solution strategy for joint quantity separation solution is provided. This strategy includes two aspects: 1) solving the separation of the rotation amount and the translation amount; 2) the separation between the rotation amounts is solved.
In the inverse kinematics solution process corresponding to the six-axis automatic hole-making and dimple-sinking machine tool, the solution sequence of each joint quantity of the machine tool is represented. The specific process is as follows:
firstly, solving a rotating shaft C by adopting an L-M nonlinear optimization method according to a tool axis direction constraint equation1Axis and A-axis joint angle, i.e. theta4And theta5(ii) a The objective function of the process is:
J(q)＝Jori(q)＝Ewx 2+Ewy 2+Ewz 2
wherein,
Ewx＝sinθ4sinθ5-wx
Ewy＝-cosθ4sinθ5-wy
Ewz＝cosθ5-wz
then, based on the obtained theta4、θ5And the constraint equation of the long axis direction of the elliptical fossa is solved by adopting an analytic method2Axial joint quantity, i.e. theta6(ii) a The expression is as follows:
θ6＝arccos(vz/sinθ5)
finally, according to the obtained theta4、θ5、θ6And a constraint equation of the end position of the machine tool, and solving the joint quantity of the translation shaft, namely d, by adopting an analytic method1,d2.d3(ii) a The expression is as follows:
d1＝ox-x7(cosθ4cosθ6-sinθ4cosθ5sinθ6)
-y7(-cosθ4sinθ6-sinθ4cosθ5cosθ6)-z7sinθ4sinθ5
d2＝oy-x7(sinθ4cosθ6+cosθ4cosθ5sinθ6)
-y7(-sinθ4sinθ6+cosθ4cosθ5cosθ6)+z7cosθ4sinθ5
d3＝oz-x7sinθ5sinθ6-y7sinθ5cosθ6-z7cosθ5
therefore, inverse kinematics solution of the six-axis automatic hole-making and socket-boring machine tool with double C-axes is realized.
The above-mentioned embodiments are intended to illustrate the technical solutions and advantages of the present invention, and it should be understood that the above-mentioned embodiments are only the most preferred embodiments of the present invention, and are not intended to limit the present invention, and any modifications, additions, equivalents, etc. made within the scope of the principles of the present invention should be included in the scope of the present invention.
Claims (2)
1. A kinematic inverse solution method of a six-axis automatic hole-making and socket-boring machine tool with double C-axes comprises the following steps:
(1) in a six-axis automatic hole-making and socket-boring machine tool, an equipment base coordinate system, a sub-coordinate system of each motion axis and a cutter coordinate system are established, a coordinate system definition diagram is drawn, and the directions of the coordinate axes of each sub-coordinate system and the equipment base coordinate system are kept consistent, and the method specifically comprises the following steps:
(1.1) defining each coordinate system in the six-axis automatic hole-making and socket-boring machine tool: base coordinate system O0Axis of motion X, Y, Z, C1、A、C2Corresponding sub-coordinate system O1、O2、O3、O4、O5、O6And a tool coordinate system O7；
(1.2) drawing a coordinate system definition diagram of the six-axis automatic hole-making and socket-boring machine tool, wherein the coordinate axis direction of each sub-coordinate system is consistent with the coordinate axis direction of the equipment base coordinate system;
(2) performing kinematic analysis on a six-axis automatic hole making and dimple forming machine tool, and establishing a forward kinematic model, which comprises the following specific steps:
(2.1) performing kinematic analysis on a six-axis automatic hole-making and dimple-sinking machine tool, and respectively calculating homogeneous transformation matrixes of all motion axes:
wherein, T01Is from a coordinate system O0To the coordinate system O1Of the ideal homogeneous transformation matrix, T12Is from a coordinate system O1To the coordinate system O2Of the ideal homogeneous transformation matrix, T23Is from a coordinate system O2To the coordinate system O3Of the ideal homogeneous transformation matrix, T34Is from a coordinate system O3To the coordinate system O4Of the ideal homogeneous transformation matrix, T45Is from a coordinate system O4To the coordinate system O5Of the ideal homogeneous transformation matrix, T56Is from a coordinate system O,5To the coordinate system O6Of the ideal homogeneous transformation matrix, T67Is from a coordinate system O6To the coordinate system O7An ideal homogeneous transformation matrix; d1,d2,d3,θ4,θ5,θ6Are respectively six-shaftDynamic hole-making dimpling machine tool X, Y, Z, C1、A、C2The joint amount of the shaft; x is the number of7,y7,z7The displacement offset from the last motion axis coordinate system to the cutter coordinate system in the x, y and z directions;
(2.2) establishing a forward kinematics model of the six-axis automatic hole-making and dimple-sinking machine tool:
wherein, T07Is from the base coordinate system O0To the tool coordinate system O7The homogeneous transformation matrix of (a) is a forward kinematics model of a six-axis automatic hole-making and dimple-making machine tool, R (q) is a tool coordinate system attitude matrix of 3 multiplied by 3, and P (q) is a tool coordinate system position matrix of 3 multiplied by 1; in the attitude matrix, [ r ]11,r21,r31]TIs the attitude vector of the X-axis of the tool coordinate system, [ r ]12,r22,r32]TIs the attitude vector of the Y-axis of the tool coordinate system, [ r ]13,r23,r33]TIs the attitude vector of the Z axis of the tool coordinate system;
(3) establishing an equation set of joint quantities according to a target pose and a forward kinematics model of a six-axis automatic hole-making dimple machine tool, and solving each joint quantity by utilizing a kinematics inverse solution strategy of joint quantity separation solving to obtain a reverse kinematics model thereof, wherein the method specifically comprises the following steps:
(3.1) according to the normal direction of the surface of the workpiece and the requirement of the drilling position, expressing the terminal target pose of the six-axis automatic drilling and dimpling machine tool as follows:
wherein, TdIs a matrix of target poses, P, of the machine tool coordinate systemdIs a target position matrix, R, of the tool coordinate systemdIs a target attitude matrix of the tool coordinate system, [ u ]x,uy,uz]TIs the object of the X-axis of the tool coordinate systemAttitude vector, [ v ]x,vy,vz]TIs the target attitude vector of the Y-axis of the tool coordinate system, [ w ]x,wy,wz]TIs the target attitude vector of the Z axis of the tool coordinate system, [ o ]x,oy,oz]TIs the target position vector;
(3.2) enabling the theoretical pose of the tail end of the six-axis automatic hole-making and spot-facing machine tool to be equal to the target pose state, and expressing the theoretical pose with a formula as follows:
T07＝Td
(3.3) establishing an equation set of the joint quantity according to the equality of the corresponding elements of the matrix, wherein the equation set comprises the following steps:
wherein, equation ox、oy、ozCalled the machine tool end position constraint equation, equation wx、wy、wzCalled tool axis direction constraint equation, equation vx、vy、vzCalled the constraint equation of the major axis direction of the elliptical fossa; solving the equation set in the inverse kinematics solution process to obtain the expression of each joint quantity;
and (3.4) solving the joint quantity by using a kinematic inverse solution strategy for joint quantity separation solving.
2. The inverse kinematics solution method of the double-C-axis six-axis automatic hole-making and socket-sinking machine tool is characterized in that the inverse kinematics solution strategy of the joint quantity separation solution comprises the separation solution of the rotation quantity and the translation quantity, and the separation solution between the rotation quantities is expressed as the solution sequence of each joint quantity of the machine tool in the inverse kinematics solution process of the six-axis automatic hole-making and socket-sinking machine tool; the specific process is as follows:
firstly, solving a rotating shaft C by adopting an L-M nonlinear optimization method according to a tool axis direction constraint equation1Joint quantity theta of shaft4And the joint quantity theta of the A axis5The objective function of the process is:
J(q)＝Jori(q)＝Ewx 2+Ewy 2+Ewz 2
wherein,
Ewx＝sinθ4sinθ5-wx
Ewy＝-cosθ4sinθ5-wy
Ewz＝cosθ5-wz
then, based on the obtained theta4、θ5And the constraint equation of the long axis direction of the elliptical fossa is solved by adopting an analytic method2Joint quantity theta of shaft6The expression is:
θ6＝arccos(vz/sinθ5)
finally, according to the obtained theta4、θ5、θ6And the constraint equation of the end position of the machine tool, and solving the joint quantity d of the translation shaft by adopting an analytic method1,d2,d3(ii) a The expression is as follows:
d1＝ox-x7(cosθ4cosθ6-sinθ4cosθ5sinθ6)-y7(-cosθ4sinθ6-sinθ4cosθ5cosθ6)-z7sinθ4sinθ5
d2＝oy-x7(sinθ4cosθ6+cosθ4cosθ5sinθ6)-y7(-sinθ4sinθ6+cosθ4cosθ5cosθ6)+z7cosθ4sinθ5
d3＝oz-x7sinθ5sinθ6-y7sinθ5cosθ6-z7cosθ5
therefore, inverse kinematics of the six-axis automatic hole-making and socket-boring machine tool with double C-axes is realized, and a reverse kinematics model of the six-axis automatic hole-making and socket-boring machine tool with double C-axes is obtained.
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