WO2017113416A1 - 加工轨迹平滑转接的方法及加工装置 - Google Patents

加工轨迹平滑转接的方法及加工装置 Download PDF

Info

Publication number
WO2017113416A1
WO2017113416A1 PCT/CN2015/100346 CN2015100346W WO2017113416A1 WO 2017113416 A1 WO2017113416 A1 WO 2017113416A1 CN 2015100346 W CN2015100346 W CN 2015100346W WO 2017113416 A1 WO2017113416 A1 WO 2017113416A1
Authority
WO
WIPO (PCT)
Prior art keywords
segment
trajectory
transition
track
point
Prior art date
Application number
PCT/CN2015/100346
Other languages
English (en)
French (fr)
Inventor
陈晓颖
Original Assignee
深圳配天智能技术研究院有限公司
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by 深圳配天智能技术研究院有限公司 filed Critical 深圳配天智能技术研究院有限公司
Priority to PCT/CN2015/100346 priority Critical patent/WO2017113416A1/zh
Priority to CN201580079812.2A priority patent/CN107615194B/zh
Publication of WO2017113416A1 publication Critical patent/WO2017113416A1/zh

Links

Images

Classifications

    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
    • G05B19/00—Programme-control systems
    • G05B19/02—Programme-control systems electric
    • G05B19/18—Numerical control [NC], i.e. automatically operating machines, in particular machine tools, e.g. in a manufacturing environment, so as to execute positioning, movement or co-ordinated operations by means of programme data in numerical form
    • G05B19/19—Numerical control [NC], i.e. automatically operating machines, in particular machine tools, e.g. in a manufacturing environment, so as to execute positioning, movement or co-ordinated operations by means of programme data in numerical form characterised by positioning or contouring control systems, e.g. to control position from one programmed point to another or to control movement along a programmed continuous path

Definitions

  • the invention relates to a method and a processing device for smooth processing of processing tracks.
  • the contour of the workpiece is usually made up of straight lines and arcs.
  • the machining motion of the CNC machine tool or the robot on the workpiece includes linear trajectory motion and circular trajectory motion. Taking into account the actual acceleration and deceleration of the motor during the movement, it will limit the maximum acceleration and deceleration during the trajectory movement, as well as the maximum jerk, to ensure that at any point of the trajectory, the acceleration and deceleration and jerk do not exceed the limit. value. At the intersection of the motion trajectory, because the direction of the trajectory changes, it is necessary to reduce the speed to zero or to a very low value to meet the above requirements.
  • the speed of the transition can be greatly increased. Improve, which can improve processing efficiency.
  • a smooth transition of two motion trajectories is usually implemented by using an arc.
  • the arc transfer can better solve the problem of inconsistent speed direction at the junction, due to the transfer arc and the front and rear rails The curvature of the traces is not equal, and the centripetal acceleration on the transition arc still causes a sudden change in acceleration at the time of the transfer.
  • the radius of the first arc motion track O 1 is R 1
  • the radius of the second arc motion track Q 2 is R 2
  • the radius of the transfer arc O is R, which is transferred at the track.
  • the speed at speed When maintaining a constant speed, a centripetal acceleration is generated on the arc, and the centripetal acceleration generated on the first circular arc trajectory O 1 is The centripetal acceleration on the second circular motion track Q 2 is The centripetal acceleration on the transfer arc O is Since the curvature of each arc track is not continuous, even if the speed and direction are kept constant before and after the transfer, there will be a sudden change in the centripetal acceleration (in an interpolation cycle). Mutation to a r , or mutation from a r to ), resulting in a discontinuity in the final acceleration. Therefore, the method of smooth switching with an arc still cannot satisfy the condition that the acceleration at the transfer point is continuous.
  • the technical problem to be solved by the present invention is to provide a method and a processing device for smoothly transferring a processing track, which can make the speed and acceleration at the transit point of the processing track continuous, and can avoid the situation that the speed is reduced to zero during the transfer process. Improve processing efficiency.
  • a technical solution adopted by the present invention is to provide a method for smoothly switching a processing track, comprising: acquiring data of a first track segment AB and data of a second track segment BC, the first track The segment AB and the second track segment BC intersect to form a corner; and data of the transition track segment MF connected between the first track segment AB and the second track segment BC is acquired according to the acquired data, wherein the transition track The segment MF is continuous with the curvature of the transition of the first track segment AB and the second track segment BC, respectively, and the slope is continuous; the data of the transition track segment MF is used as the processing path data of the corner for processing.
  • the method for realizing the transition of the transition trajectory segment MF with the curvature of the transition of the first trajectory segment AB and the second trajectory segment BC and the slope is continuous includes: the transition trajectory segment MF includes a first gyro curve Track segment MN, transition arc track segment NE and second a convoluted curve track segment EF, wherein the first convoluted curve track segment MN is connected between the first track segment AB and the transition arc track segment NE, and the first convoluted curve segment segment MN is respectively
  • the first trajectory segment AB and the transition circular trajectory segment NE have continuous curvature and continuous slope
  • the second gyroscopic curved trajectory segment EF is connected to the second trajectory segment BC and the transitional circular trajectory
  • the segments NE, and the second convoluted curve segment EF is continuous with the curvature of the transition of the second track segment BC and the transition arc track segment NE, respectively, and the slope is continuous.
  • the first trajectory segment AB and the second trajectory segment BC are both arcs
  • the step of acquiring the data of the first trajectory segment AB and the data of the second trajectory segment BC includes: acquiring the first trajectory The coordinates (x o1 , y o1 ) of the center O 1 of the segment AB and the radius R 1 , the coordinates (x o2 , y o2 ) of the center O 2 of the second track segment BC, and the radius R 2 , the transition arc a coordinate (x o , y o ) of the center O of the trajectory segment NE and a radius R; the data of the transition trajectory segment MF connected between the first trajectory segment AB and the second trajectory segment BC is acquired based on the acquired data
  • the step includes: setting a point M as a starting point of the first convoluted curve segment MN, and a point N being an end point of the first convoluted curve segment MN, and calculating the first convoluted curve according to the following equation group (1)
  • the step of acquiring the coordinates (x o , y o ) and the radius R of the center O of the transition arc track segment NE includes: obtaining a maximum bow height error e, and determining the transition circle according to the maximum bow height error e
  • the coordinates (x o , y o ) and the radius R of the center O of the arc track segment NE includes: obtaining a maximum bow height error e, and determining the transition circle according to the maximum bow height error e.
  • the first track segment AB is a straight line
  • the second track segment BC is an arc
  • the step of acquiring the data of the first track segment AB and the data of the second track segment BC includes: acquiring the first The slope k AB and the constant b of the track segment AB, the coordinates (x o2 , y o2 ) of the center O 2 of the second track segment BC, and the radius R 2 , the coordinates of the center O of the transition circular track segment NE ( x o , y o ) and radius R;
  • the step of acquiring data of the transition trajectory segment MF connected between the first trajectory segment AB and the second trajectory segment BC according to the acquired data comprises: setting the point M to The starting point of the first convoluted curve segment MN, the point N is the end point of the first convoluted curve segment MN, and the curve length s 1 and the ratio of the first convoluted curve segment MN are calculated according to the following equation group (3)
  • a processing device for realizing a smooth connection of a processing track comprising: a first acquiring module, configured to acquire data of the first track segment AB and a second track segment BC data, the first trajectory segment AB and the second trajectory segment BC intersect to form a corner; the second obtaining module is configured to acquire the connection between the first trajectory segment AB and the second trajectory segment according to the acquired data
  • the control module is used for The data of the transition trajectory MF is used as the processing path data of the corner for processing.
  • the transition track segment MF includes a first convoluted curve segment MN, a transition arc track segment NE, and a second convoluted curve segment segment EF, wherein the first convoluted curve segment segment MN is connected to the first segment segment Between AB and the transitional arc track segment NE, and the first convoluted curve segment MN is continuous with the curvature of the transition of the first track segment AB and the transition arc track segment NE, respectively, and the slope is continuous
  • the second convoluted curve segment EF is connected between the second track segment BC and the transition arc track segment NE, and the second convoluted curve segment segment EF and the second track segment BC are respectively
  • the transition of the transition arc track segment NE is continuous and the slope is continuous.
  • the first trajectory segment AB and the second trajectory segment BC are both arcs, and the point M is the starting point of the first gyroscopic trajectory segment MN, and the point N is the first gyroscopic trajectory segment MN
  • the first obtaining module is configured to acquire the first track segment AB
  • the second acquisition module is configured to calculate the curve length s 1 and the proportional coefficient of the first convoluted curve segment MN according to the following equation group (1) c 1 , the inclination
  • the second obtaining module is configured to calculate a curve length s 2 and a proportional coefficient c 2 of the second convoluted curve segment EF, a tilt angle ⁇ 2 of the straight line OE, and a tilt of the straight line O 2 F according to the following equation group (2) Angle ⁇ 2 :
  • the first obtaining module is configured to obtain a maximum bow height error e, and determine a coordinate (x o , y o ) and a radius R of a center O of the transition circular track segment NE according to the maximum bow height error e. .
  • the first trajectory segment AB is a straight line
  • the second trajectory segment BC is an arc
  • the point M is the starting point of the first gyroscopic trajectory segment MN
  • the point N is the first gyroscopic curve segment
  • the first acquiring module is configured to acquire the first track segment
  • the second obtaining module is configured to calculate a curve length s 2 and a proportional coefficient c 2 of the second convoluted curve segment EF, a tilt angle ⁇ 2 of the straight line O 2 F, and a tilt of the straight line OE according to the following equation group (4) Angle ⁇ 2 :
  • the present invention passes the first A transition trajectory segment MF is added between the trajectory segment AB and the second trajectory segment BC, wherein the transition trajectory segment MF is continuous with the slope of the transition of the first trajectory segment AB and the second trajectory segment BC, respectively, and the curvature is continuous, thereby smoothing
  • the speed of the transfer can be greatly increased, the speed of the transfer can be kept substantially the same, and the acceleration before and after the transfer can be kept consistent, so that the speed of the transfer can be prevented from falling to zero, which is beneficial to the situation.
  • FIG. 1 is a schematic view showing a processing path of a circular motion track to a circular motion track in the prior art
  • FIG. 2 is a schematic diagram of a smooth transition between a circular arc motion trajectory and a circular arc motion trajectory using a transition arc;
  • FIG. 3 is a flow chart of an embodiment of a method for smooth processing transfer of a processing track according to the present invention
  • FIG. 4 is a schematic diagram of a transition path segment MF transition between a first trajectory segment AB and a second trajectory segment BC in an embodiment of the method for smoothing the trajectory of the trajectory according to the present invention
  • FIG. 5 is a schematic diagram of a curve combination of a transition track segment MF in an embodiment of a method for smooth processing of a processing track according to the present invention
  • FIG. 6 is a schematic diagram showing the principle of determining the center and radius of the transitional arc track segment NE in an embodiment of the method for smoothing the processing track of the present invention
  • FIG. 7 is a schematic diagram showing the principle of determining a curve equation of a first convoluted curve segment MN in an embodiment of a method for smooth processing of a processing track according to the present invention
  • FIG. 8 is a schematic diagram showing the principle of determining a curve equation of a second convoluted curve segment EF in an embodiment of the method for smoothing the processing track of the present invention
  • FIG. 9 is a schematic diagram showing the principle of determining a curve equation of a first convoluted curve segment MN in another embodiment of the method for smoothing the processing track of the present invention.
  • FIG. 10 is a schematic structural view of an embodiment of a processing apparatus for smoothing a processing track according to the present invention.
  • the method for smoothing the trajectory of the present invention is applicable to continuous processing including, but not limited to, a numerically controlled machining system and a robot.
  • the method for realizing the smooth transition of the machining path of the numerical control machining system includes the following steps:
  • Step S301 Acquire data of the first track segment AB and the second track segment BC, and the first track segment AB and the second track segment BC intersect to form a corner.
  • the first track segment AB and the second track segment BC are two consecutive processing paths, and the two processing paths intersect to form a corner B.
  • the processing direction is from the first track segment AB to the second track segment BC, that is, the second track segment BC is the next segment of the processing path.
  • the data of the first track segment AB and the data of the second track segment BC are contour data about the workpiece to be machined, that is, the machining path data of the workpiece to be machined.
  • the contour data of the workpiece to be processed may be stored in the storage area in advance to acquire data of the first track segment AB and the second track segment BC from the storage area, or may be the first track segment AB and the first to obtain the instant input.
  • the data of the two track segments BC may be stored in the storage area in advance to acquire data of the first track segment AB and the second track segment BC from the storage area, or may be the first track segment AB and the first to obtain the instant input.
  • Step S302 Acquire data of the transition trajectory segment MF connected between the first trajectory segment AB and the second trajectory segment BC according to the acquired data of the first trajectory segment AB and the second trajectory segment BC, wherein the transition trajectory segment MF The curvature of the transition between the first track segment AB and the second track segment BC is continuous and the slope is continuous.
  • the transition point of the transition track segment MF and the first track segment AB is the point M
  • the transition point of the transition track segment MF and the second track segment BC is the point F
  • the curvature at F is continuous and the slope is continuous.
  • the continuous curvature means that the curvatures of the two curves are consistent at the transition
  • the continuous slope means that the two curves have the same tangent at the transition, ie the slopes are consistent. Therefore, in the present embodiment, the transition trajectory segment MF and the first trajectory segment AB have the same slope and curvature at the position of the transit point M, and the position of the transition trajectory segment MF and the second trajectory segment BC at the transit point F Have the same slope and curvature.
  • Step S303 The data of the transition trajectory segment MF is used as the processing path data of the corner for processing.
  • the transition trajectory segment MF and the first trajectory segment AB at the transition point
  • the position of the point M has the same slope and curvature
  • the transition track segment MF has the same slope and curvature as the position of the second track segment BC at the point F of the transition, thereby transitioning from the first track segment AB to the transition track segment MF
  • the velocity and acceleration at the transition can be made continuous, that is, consistent, without reducing the speed to zero, so that the processing efficiency can be greatly improved.
  • the transition trajectory segment MF can be implemented by using a gyroscopic curve with continuously varying curvature, for example, a single gyroscopic curve or a combination of multiple gyroscopic curves to realize the transition point.
  • the curvature is continuous and the slope is continuous; of course, the transition trajectory MF can also be realized by a combination of arcs of different curvatures to achieve continuous curvature and continuous slope at the transition.
  • the convolution curve is a kind of spiral, and its curve is defined as: the curvature and the length are linear, and the formula is expressed as:
  • k represents the curvature of any point on the convolution curve (eg, H point)
  • k a represents the curvature at the beginning of the convolution curve
  • c is the proportional coefficient
  • s represents the length of the curve from the start of the convolution curve to the arbitrary point (H point).
  • the tangent angle at the starting point of the convolution curve is ⁇ a , according to the definition of curvature It can be seen that the tangent angle is the integral of the curvature, so the tangent tilt angle at any point on the convolution curve is:
  • the transition trajectory segment MF adopts a combination of a convoluted curve + an arc + a convoluted curve to achieve continuous curvature and continuous slope at the transition.
  • the transition trajectory segment MF includes a first convoluted curve segment MN, a transition arc segment segment NE, and a second convoluted curve segment segment EF.
  • the first convoluted curve track segment MN is connected between the first track segment AB and the transition arc track segment NE.
  • the transition of the first convoluted curve segment MN and the first track segment AB is the point M
  • the transition of the first convoluted curve segment MN and the transition arc segment segment NE is the point N.
  • first recursive curve segment MN and the first trajectory segment AB at the point M are continuous in curvature and continuous in slope, and the curvature of the first convoluted curve segment MN and the transition arc segment segment NE at the point N is continuous and the slope is continuous.
  • the second convoluted curve track segment EF is connected between the second track segment BC and the transition arc track segment NE.
  • the transition of the second convoluted curve segment EF and the second track segment BC is point F
  • the transition of the second convoluted curve segment segment EF and the transition arc segment segment NE is point E.
  • the second recursive curve trajectory segment EF and the second trajectory segment BC have continuous curvature and continuous slope
  • the curvature of the second convoluted curve segment EF and the transitional arc segment segment NE are continuous and the slope is continuous.
  • the first track segment AB and the second track segment BC are both arcs, as shown in FIG.
  • Obtaining the data of the first track segment AB and the data of the second track segment BC includes: acquiring the coordinates (x o1 , y o1 ) of the center O 1 of the first track segment AB and the radius R 1 and the second track segment BC The coordinates (x o2 , y o2 ) of the center O 2 and the radius R 2 , the coordinates (x o , y o ) of the center O of the transition arc track segment NE, and the radius R.
  • first track segment AB may be determined according to the contour of the workpiece to be machined center O of the coordinates 1 (x o1, y o1) and a radius R 1, the second track segment BC coordinates of the center O 2 (x o2, y o2 ) and radius R 2 .
  • the transition arc track segment NE can be determined according to the bow height error, and the bow height error is the machining accuracy. Further, the coordinates (x o , y o ) and the radius R of the center O of the transitional arc track segment NE are determined according to the maximum bow height error e, that is, the transition arc track segment NE satisfies the requirement of the maximum bow height error e.
  • the transition arc track segment NE is a part of an arc (dashed line in the figure) that satisfies the maximum bow height error e and is tangent to the first track segment AB and the second track segment BC, and thus according to the maximum bow
  • the high error e, the coordinates (x o1 , y o1 ) of the center O 1 of the first trajectory segment AB and the radius R 1 , the coordinates (x o2 , y o2 ) of the center O 2 of the second trajectory segment BC, and the radius R 2 may be The coordinates (x o , y o ) and the radius R of the center O of the transition arc track segment NE are determined.
  • transition arc track segment NE is the track segment which is the most deviated from the actual track segment (ie, the first track segment AB and the second track segment BC) in the transition track segment MF, when the transition arc track segment NE satisfies the maximum bow height error e
  • the two convoluted curve segments MN, EF connected to the transition arc track segment NE and closer to the actual track segment also satisfy the bow height error.
  • acquiring data of the transition trajectory segment MF connected between the first trajectory segment AB and the second trajectory segment BC refers to acquiring the first gyroscopic curve segment MN, the transition arc trajectory segment NE, and the second gyro curve.
  • the trajectory equation of the trajectory segment EF refers to acquiring the first gyroscopic curve segment MN, the transition arc trajectory segment NE, and the second gyro curve.
  • the point M is the starting point of the first convoluted curve segment MN
  • the point N is the end point of the first recursive curve segment MN.
  • the angle ⁇ 1 is the inclination angle of the straight line O 1 M
  • the angle ⁇ 1 is the inclination angle of the straight line ON.
  • the tangential tilt angle at point M can be obtained for: That is, the tangential inclination angle at the starting point of the first convoluted curve segment MN
  • the tangent inclination angle ⁇ 1 at the point N is: That is, the tangential tilt angle at the end of the first convoluted curve segment MN.
  • the curvature of the first convoluted curve segment MN at the point M is equal to the curvature of the first track segment AB
  • the first convoluted curve segment segment MN at the point N The curvature is equal to the curvature of the transition arc track segment NE.
  • the curvature of the first recursive curve track segment MN at the starting point M is R 1 is the radius of the first track segment AB
  • the curvature of the first tortuous curve track segment MN at the end point N is R is the radius of the transition arc track segment NE.
  • the coordinates of the starting point M of the first recursive curve segment MN are: (x o1 + R 1 cos ⁇ 1 , .y o1 + R 1 sin ⁇ 1 ), and the first recursive curve is obtained.
  • the coordinates of the end point N of the track segment MN are: (x o + Rcos ⁇ 1 , .y o + Rsin ⁇ 1 ). Therefore, the coordinates of the starting point M of the obtained first convoluted curve segment MN, the coordinates of the end point N, the tangent angle and curvature at the starting point M, and the tangent angle and curvature at the end point N are substituted into the above formula (1).
  • the following equation (4) is obtained:
  • ⁇ 1 , ⁇ 1 , s 1 , and c 1 are unknown numbers
  • s 1 is the length of the curve of the first convoluted curve segment MN from the start point M to the end point N
  • c 1 is the proportional coefficient of the track segment of the first reel selection curve.
  • ⁇ 1 , ⁇ 1 , s 1 , and c 1 can be obtained by solving the system of equations (4).
  • the coordinates of the starting point M of the first convoluted curve segment MN can be obtained, and then the coordinates of the starting point M and the length of the curve are substituted into the above formula ( 3), the plane coordinate expression of the first convoluted curve segment MN can be obtained; and the proportional coefficient c 1 is substituted into the above formula (1) to obtain the relationship between the curvature and the curve length; the tangent angle of the starting point M point Substituting the above formula (2), the relationship of the tangential tilt angle can be obtained.
  • the curve equation of the first convoluted curve segment MN can thus be obtained.
  • the curvature of the second convoluted curve segment EF at the point E is equal to the curvature of the transition arc track segment NE
  • the second convoluted curve segment segment EF at the point F The curvature is equal to the curvature of the second track segment BC.
  • the curvature of the second recursive curve segment EF at the starting point E is obtained as follows R is the radius of the transition arc track segment NE, and the curvature of the second convoluted curve segment EF at the end point F is R 2 is the radius of the second track segment BC.
  • the coordinates of the starting point E of the second recursive curve segment EF can be obtained: (x o + Rcos ⁇ 2 , .y o + Rsin ⁇ 2 ), and the second recursive curve trajectory segment EF is obtained.
  • the coordinates of the endpoint F are: (x o2 + R 2 cos ⁇ 2 , .y o2 + R 2 sin ⁇ 2 ). Therefore, the coordinates of the starting point E of the obtained second convoluted curve segment EF, the coordinates of the end point F, the tangent angle and curvature at the starting point E, and the tangent angle and curvature at the end point F are substituted into the above formula (1).
  • the following equation (5) is obtained:
  • ⁇ 2 , ⁇ 2 , s 2 , and c 2 are unknown numbers
  • s 2 is the length of the curve of the second convoluted curve segment EF from the starting point E to the ending point F
  • c 2 is the proportional coefficient of the track segment of the second recursive curve.
  • (x o , y o ) is the coordinate of the center O of the transition arc track segment NE
  • (x o2 , y o2 ) is the coordinate of the center O 2 of the second track segment BC.
  • the coordinates of point N (x o + Rcos ⁇ 1 , y o + Rsin ⁇ 1 ) and the coordinates of point E (x o + Rcos ⁇ 2 , y o + Rsin ⁇ 2 ) can be obtained.
  • This determines the start and end points of the transitional arc track segment NE, which in turn determines the position of the transition arc track segment NE in an arc tangent to the first track segment AB and the second track segment BC.
  • the curve equations of the first convoluted curve segment MN, the transition arc segment segment NE, and the second convoluted curve segment segment NE can be determined, thereby obtaining the data of the transition track segment MF, that is, the processing path data.
  • the first trajectory segment AB may be a straight line, the second trajectory segment BC is an arc, or the first trajectory segment AB is an arc and the second trajectory segment BC is a straight line.
  • the first track segment AB is a straight line, and the second track segment BC is an arc as an example.
  • acquiring the data of the first track segment AB and the data of the second track segment BC includes: obtaining the slope k AB of the first track segment AB and the constant b, and the coordinates of the center O 2 of the second track segment BC (x o2 , y o2 ) and the radius R 2 , the coordinates (x o , y o ) of the center O of the transition arc track segment NE, and the radius R.
  • the curvature of the straight line is 0, and the oblique angle of the tangent is the angle between the straight line and the x-axis, that is, the inverse tangent of the slope.
  • the tangential inclination angle of the first trajectory segment AB is arctank AB , that is, the tangential inclination angle at the point M for: That is, the tangential tilt angle at the start of the first convoluted curve segment MN.
  • the tangent angle ⁇ 1 at point N is: That is, the tangential tilt angle at the end of the first convoluted curve segment MN.
  • the curvature of the first convoluted curve segment MN at the point M is equal to the curvature of the first track segment AB, and the curvature of the first convoluted curve segment MN at the point N is equal to the transition.
  • the curvature of the arc track segment NE is the curvature of the first recursive curve track segment MN at the starting point M, 0, and the curvature of the first convoluted curve segment MN at the end point N is obtained.
  • R is the radius of the transition arc track segment NE.
  • the coordinates of the starting point M of the first recursive curve segment MN are: (x M , k AB x M +b), and the first recursive curve segment MN is obtained.
  • the coordinates of the end point N are: (x o + Rcos ⁇ 1 , .y o + Rsin ⁇ 1 ). Therefore, the coordinates of the starting point M of the obtained first convoluted curve segment MN, the coordinates of the end point N, the tangent angle and curvature at the starting point M, and the tangent angle and curvature at the end point N are substituted into the above formula (1).
  • the following equation (6) is obtained:
  • the solution to the curve equation of the second convoluted curve segment EF can be performed according to the embodiment shown in FIG. 8, and will not be described herein.
  • the starting point N point coordinate and the end point E point coordinate of the transition arc track segment NE can also be determined.
  • the processing precision can be realized, and by making the curvature of all the transitions continuous and the slope continuous, the smooth connection between the continuous processing track segments can be realized, and the transfer can be avoided. Where it is necessary to reduce the speed to zero, the processing efficiency can be improved.
  • the processing device can be a numerical control machining system or a robot for realizing the machining process according to the method of smooth processing of the processing track according to any of the above embodiments. Smooth transition in.
  • the numerical control processing system as an example, the first acquisition module 1001, the second acquisition module 1002, and the control module 1003 are included.
  • the first obtaining module 1001 is configured to acquire data of the first track segment AB and data of the second track segment BC, and the first track segment AB and the second track segment BC intersect to form a corner B.
  • the data of the first track segment AB and the data of the second track segment BC are contour data about the workpiece to be processed, That is, the processing path data of the workpiece to be processed.
  • the contour data of the workpiece to be processed may be stored in the storage area in advance, so that when the workpiece needs to be processed, the first acquisition module 1001 first acquires the data of the first track segment AB and the second track segment BC from the storage area, or It may be that data of the first track segment AB and the second track segment BC of the instant input is obtained.
  • the second obtaining module 1002 is configured to acquire data of the transition trajectory segment MF connected between the first trajectory segment AB and the second trajectory segment BC according to the acquired data of the first trajectory segment AB and the second trajectory segment BC, wherein
  • the transition track segment MF is continuous with the curvature of the transition of the first track segment AB and the second track segment BC, respectively, and the slope is continuous.
  • the transition point of the transition track segment MF and the first track segment AB is the point M
  • the transition point of the transition track segment MF and the second track segment BC is the point F, at the point M and the point F.
  • the curvature is continuous and the slope is continuous.
  • the continuous curvature means that the curvatures of the two curves are consistent at the transition
  • the continuous slope means that the two curves have the same tangent at the transition, ie the slopes are consistent. Therefore, in the present embodiment, the transition trajectory segment MF and the first trajectory segment AB have the same slope and curvature at the position of the transit point M, and the position of the transition trajectory segment MF and the second trajectory segment BC at the transit point F Have the same slope and curvature.
  • the control module 1003 is configured to process the data of the transition trajectory segment MF as the machining path data of the corner.
  • the transition trajectory segment MF and the first trajectory segment AB have the same slope and curvature at the position of the transit point M, the position of the transition trajectory segment MF and the second trajectory segment BC at the transit point F Having the same slope and curvature, thereby transitioning from the first trajectory segment AB to the transition trajectory segment MF, and from the transition trajectory segment MF to the second trajectory segment BC, the velocity and acceleration at the transition can be made continuous That is, it is consistent, and it is not necessary to reduce the speed to zero, so that the processing efficiency can be greatly improved.
  • the transition trajectory segment MF adopts a combination of a convoluted curve + an arc + a convoluted curve to achieve continuous curvature and continuous slope at the transition.
  • the transition trajectory segment MF includes a first convoluted curve segment MN, a transition arc segment segment NE, and a second convoluted curve segment segment EF.
  • the first convoluted curve track segment MN is connected between the first track segment AB and the transition arc track segment NE.
  • the transition point of the trajectory trajectory segment MN and the first trajectory segment AB is a point M
  • the transition point of the first gyroscopic trajectory segment MN and the transitional arc trajectory segment NE is a point N.
  • first recursive curve segment MN and the first trajectory segment AB at the point M are continuous in curvature and continuous in slope, and the curvature of the first convoluted curve segment MN and the transition arc segment segment NE at the point N is continuous and the slope is continuous.
  • the second convoluted curve track segment EF is connected between the second track segment BC and the transition arc track segment NE.
  • the transition of the second convoluted curve segment EF and the second track segment BC is point F
  • the transition of the second convoluted curve segment segment EF and the transition arc segment segment NE is point E.
  • the second recursive curve trajectory segment EF and the second trajectory segment BC have continuous curvature and continuous slope
  • the curvature of the second convoluted curve segment EF and the transitional arc segment segment NE are continuous and the slope is continuous.
  • the first track segment AB and the second track segment BC are both arcs.
  • the first obtaining module 1001 is specifically configured to acquire the coordinates (x o1 , y o1 ) of the center O 1 of the first trajectory segment AB and the coordinates (x o2 , y o2 ) of the radius R 1 and the center O 2 of the second trajectory segment BC. And the radius R 2 , the coordinates (x o , y o ) of the center O of the transition arc track segment NE, and the radius R.
  • first track segment AB may be determined according to the contour of the workpiece to be machined center O of the coordinates 1 (x o1, y o1) and a radius R 1, the second track segment BC coordinates of the center O 2 (x o2, y o2 ) and radius R 2 .
  • the transition arc track segment NE can be determined according to the bow height error, and the bow height error is the machining accuracy. Further, the coordinates (x o , y o ) and the radius R of the center O of the transitional arc track segment NE are determined according to the maximum bow height error e, that is, the transition arc track segment NE satisfies the requirement of the maximum bow height error e.
  • the transition arc track segment NE is a part of an arc (dashed line in the figure) that satisfies the maximum bow height error e and is tangent to the first track segment AB and the second track segment BC, and thus according to the maximum bow
  • the high error e, the coordinates (x o1 , y o1 ) of the center O 1 of the first trajectory segment AB and the radius R 1 , the coordinates (x o2 , y o2 ) of the center O 2 of the second trajectory segment BC, and the radius R 2 may be The coordinates (x o , y o ) and the radius R of the center O of the transition arc track segment NE are determined.
  • transition arc track segment NE is the track segment which is the most deviated from the actual track segment (ie, the first track segment AB and the second track segment BC) in the transition track segment MF, when the transition arc track segment NE satisfies the maximum bow height error e
  • the two convoluted curve segments MN, EF connected to the transition arc track segment NE and closer to the actual track segment also satisfy the bow height error.
  • the point M is the starting point of the first convoluted curve segment MN
  • the point N is the end point of the first recursive curve segment MN.
  • the second obtaining module 1002 is configured to calculate the curve length s 1 of the first convoluted curve segment MN and the proportional coefficient c 1 , the inclination angle ⁇ 1 of the straight line O 1 M, and the inclination angle ⁇ of the straight line ON according to the following equation group (7). 1 :
  • ⁇ 1 , ⁇ 1 , s 1 , and c 1 are unknown numbers
  • s 1 is the length of the curve of the first convoluted curve segment MN from the start point M to the end point N
  • c 1 is the proportional coefficient of the track segment of the first reel selection curve.
  • the angle ⁇ 1 is the inclination angle of the straight line O 1 M
  • the angle ⁇ 1 is the inclination angle of the straight line ON.
  • the coordinates of the starting point M of the first convoluted curve segment MN can be obtained, and then the coordinates of the starting point M and the length of the curve are substituted into the above formula ( 3), the plane coordinate expression of the first convoluted curve segment MN can be obtained; and the proportional coefficient c 1 is substituted into the above formula (1) to obtain the relationship between the curvature and the curve length; the tangent angle of the starting point M point Substituting the above formula (2), the relationship of the tangential tilt angle can be obtained.
  • the curve equation of the first convoluted curve segment MN can thus be obtained.
  • the point E is the starting point of the second convoluted curve segment EF
  • the point F is the end point of the second convoluted curve segment EF.
  • the second obtaining module 1002 is configured to calculate the curve length s 2 of the second convoluted curve segment EF and the proportional coefficient c 2 , the inclination angle ⁇ 2 of the straight line OE, and the inclination angle ⁇ 2 of the straight line O 2 F according to the following equation group (8) :
  • ⁇ 2 , ⁇ 2 , s 2 , and c 2 are unknown numbers
  • s 2 is the length of the curve of the second convoluted curve segment EF from the starting point E to the ending point F
  • c 2 is the proportional coefficient of the track segment of the second recursive curve.
  • the angle ⁇ 2 is the inclination angle of the straight line OE
  • the angle ⁇ 2 is the inclination angle of the straight line OF.
  • the first track segment AB may be a straight line and the second track segment BC is an arc.
  • the first obtaining module 1001 is configured to acquire the slope k AB and the constant b of the first track segment AB, the coordinates (x o2 , y o2 ) of the center O 2 of the second track segment BC, and the radius R 2 and the transition arc track.
  • the curvature of the straight line is 0, and the oblique angle of the tangent is the angle between the straight line and the x-axis, that is, the inverse tangent of the slope.
  • the second obtaining module 1002 is configured to calculate a curve length s 1 of the first convoluted curve segment MN and a proportional coefficient c 1 and a tilt angle ⁇ 1 of the straight line according to the following equation group (9):
  • the curve equation of the second convoluted curve segment EF can be obtained according to the equation group (8), and the specific process will not be described here. After determining the first convoluted curve track segment MN and the second convoluted curve track segment EF, the starting point N point coordinate and the end point E point coordinate of the transition arc track segment NE can also be determined. For the specific process, reference may be made to the above description.
  • the processing precision can be realized, and by making the curvature of all the transitions continuous and the slope continuous, the smooth connection between the continuous processing track segments can be realized, and the speed drop required at the transfer point can be avoided. In the case of zero, the processing efficiency can be improved.

Landscapes

  • Engineering & Computer Science (AREA)
  • Human Computer Interaction (AREA)
  • Manufacturing & Machinery (AREA)
  • Physics & Mathematics (AREA)
  • General Physics & Mathematics (AREA)
  • Automation & Control Theory (AREA)
  • Numerical Control (AREA)

Abstract

一种加工轨迹平滑转接的方法，其中，在第一轨迹段AB和第二轨迹段BC之间增加过渡轨迹段MF，其中过渡轨迹段MF分别与第一轨迹段AB和第二轨迹段BC的转接处斜率连续、曲率连续。还公开了一种实现加工轨迹平滑连接的加工装置。使得在加工轨迹的转接处速度和加速度连续，可以避免在转接过程中将速度降为零的情况，提高加工效率。

Description

加工轨迹平滑转接的方法及加工装置 【技术领域】
本发明涉及一种加工轨迹平滑转接的方法及加工装置。
【背景技术】
工件轮廓通常是由直线和圆弧构成。在实际加工中，数控机床或机器人对工件的加工运动包括直线轨迹运动和圆弧轨迹运动。考虑到运动过程中电机实际的加减速能力，会在轨迹运动过程中限制最大加速度和减速度，以及最大加加速度，保证在运动轨迹的任意一点，其加速度和减速度以及加加速度都不超过限定值。而在运动轨迹的交接处，由于轨迹方向发生变化，需要将速度降为零或降到非常低的值才能满足上述要求。
如图1所示，以圆弧运动轨迹到圆弧运动轨迹为例，在两个运动轨迹的交接处由于轨迹方向发生突变，如果在交接前后保持原来的速度大小
Figure PCTCN2015100346-appb-000001
运行，由于速度方向的改变在一个指令周期内完成，设指令周期为T，则会产生一个大小为
Figure PCTCN2015100346-appb-000002
的加速度。如若使
Figure PCTCN2015100346-appb-000003
小于系统最大允许加速度A，则交接处的速度大小应该满足
Figure PCTCN2015100346-appb-000004
即
Figure PCTCN2015100346-appb-000005
如果进一步考虑加加速度的上限问题，则会使这个速度大小调整到更小的值。
若在轨迹精度误差的范围内，将连续的两段运动轨迹的交接处用一段平滑的过渡曲线代替，且该过度曲线与原来的两段运动轨迹相切，则可以使转接处的速度大大提高，从而可以提高加工效率。现有技术中，通常采用圆弧实现两段运动轨迹的平滑转接。然而，虽然圆弧转接可以较好地解决交接处速度方向不一致的问题，但是由于转接圆弧与前后轨 迹的曲率不相等，在转接圆弧上的向心加速度仍然会导致转接时的加速度突变。
如图2所示，假设第一条圆弧运动轨迹O1的半径为R1，第二条圆弧运动轨迹Q2的半径为R2，转接圆弧O的半径为R，在轨迹交接处的速度为
Figure PCTCN2015100346-appb-000006
速度
Figure PCTCN2015100346-appb-000007
在保持匀速的情况下会在圆弧上产生一个向心加速度，在第一条圆弧运动轨迹O1上产生的向心加速度大小为
Figure PCTCN2015100346-appb-000008
在第二条圆弧运动轨迹Q2上的向心加速度大小为
Figure PCTCN2015100346-appb-000009
在转接圆弧O上的向心加速度为
Figure PCTCN2015100346-appb-000010
由于各圆弧轨迹的曲率不连续，因此，即使在转接前后保持速度大小和方向都不变，也会因为向心加速度的突变(在一个插补周期内从
Figure PCTCN2015100346-appb-000011
突变为ar，或从ar突变为
Figure PCTCN2015100346-appb-000012
)，从而造成最终加速度的不连续。因此，用圆弧进行平滑转接的方式仍然无法满足转接点处加速度连续的条件。
【发明内容】
本发明主要解决的技术问题是提供一种加工轨迹平滑转接的方法及加工装置，能够使得在加工轨迹的转接处速度和加速度连续，可以避免在转接过程中将速度降为零的情况，提高加工效率。
为解决上述技术问题，本发明采用的一个技术方案是：提供一种加工轨迹平滑转接的方法，包括：获取第一轨迹段AB的数据和第二轨迹段BC的数据，所述第一轨迹段AB和所述第二轨迹段BC相交形成拐角；根据获取到的所述数据获取连接在第一轨迹段AB和第二轨迹段BC之间的过渡轨迹段MF的数据，其中所述过渡轨迹段MF分别与所述第一轨迹段AB和所述第二轨迹段BC的转接处曲率连续、斜率连续；将所述过渡轨迹段MF的数据作为所述拐角的加工路径数据以进行加工。
其中，所述过渡轨迹段MF分别与所述第一轨迹段AB和所述第二轨迹段BC的转接处曲率连续、斜率连续的实现方法包括：所述过渡轨迹段MF包括第一回旋曲线轨迹段MN、过渡圆弧轨迹段NE以及第二 回旋曲线轨迹段EF，其中所述第一回旋曲线轨迹段MN连接在所述第一轨迹段AB和所述过渡圆弧轨迹段NE之间，且所述第一回旋曲线轨迹段MN分别与所述第一轨迹段AB和所述过渡圆弧轨迹段NE的转接处曲率连续、斜率连续，所述第二回旋曲线轨迹段EF连接在所述第二轨迹段BC和所述过渡圆弧轨迹段NE之间，且所述第二回旋曲线轨迹段EF分别与所述第二轨迹段BC和所述过渡圆弧轨迹段NE的转接处曲率连续、斜率连续。
其中，所述第一轨迹段AB和所述第二轨迹段BC均为圆弧，所述获取第一轨迹段AB的数据和第二轨迹段BC的数据的步骤包括：获取所述第一轨迹段AB的圆心O1的坐标(xo1，yo1)及半径R1、所述第二轨迹段BC的圆心O2的坐标(xo2，yo2)及半径R2、所述过渡圆弧轨迹段NE的圆心O的坐标(xo，yo)及半径R；所述根据获取到的数据获取连接在第一轨迹段AB和第二轨迹段BC之间的过渡轨迹段MF的数据的步骤包括：设点M为所述第一回旋曲线轨迹段MN的起点，点N为所述第一回旋曲线轨迹段MN的终点，则根据如下方程组(1)计算所述第一回旋曲线轨迹段MN的曲线长度s1及比例系数c1、直线O1M的倾斜角θ1以及直线ON的倾斜角β1：
Figure PCTCN2015100346-appb-000013
其中，
Figure PCTCN2015100346-appb-000014
为所述过渡圆弧轨迹段NE的曲率，
Figure PCTCN2015100346-appb-000015
为所述第一轨迹段AB的曲率；
设点E为所述第二回旋曲线轨迹段EF的起点，点F为所述第二回旋曲线轨迹段EF的终点，则根据如下方程组(2)计算所述第二回旋曲线轨迹段EF的曲线长度s2及比例系数c2、直线OE的倾斜角θ2以及直线O2F的倾斜角β2：
Figure PCTCN2015100346-appb-000016
其中，
Figure PCTCN2015100346-appb-000017
为所述过渡圆弧轨迹段NE的曲率，
Figure PCTCN2015100346-appb-000018
为所述第二轨迹段BC的曲率。
其中，获取所述过渡圆弧轨迹段NE的圆心O的坐标(xo，yo)及半径R的步骤包括：获取最大弓高误差e，根据所述最大弓高误差e确定所述过渡圆弧轨迹段NE的圆心O的坐标(xo，yo)及半径R。
其中，所述第一轨迹段AB为直线，所述第二轨迹段BC为圆弧，所述获取第一轨迹段AB的数据和第二轨迹段BC的数据的步骤包括：获取所述第一轨迹段AB的斜率kAB和常量b、所述第二轨迹段BC的圆心O2的坐标(xo2，yo2)及半径R2、所述过渡圆弧轨迹段NE的圆心O的坐标(xo，yo)及半径R；所述根据获取到的数据获取连接在第一轨迹段AB和第二轨迹段BC之间的过渡轨迹段MF的数据的步骤包括：设点M为所述第一回旋曲线轨迹段MN的起点，点N为所述第一回旋曲线轨迹段MN的终点，则根据如下方程组(3)计算所述第一回旋曲线轨迹段MN的曲线长度s1及比例系数c1、直线ON的倾斜角β1：
Figure PCTCN2015100346-appb-000019
其中，(xM，kABxM+b)为点M的坐标，
Figure PCTCN2015100346-appb-000020
为所述过渡圆弧轨迹段NE的曲率；
设点F为所述第二回旋曲线轨迹段EF的终点，点E为所述第二回 旋曲线轨迹段EF的起点，则根据如下方程组(4)计算所述第二回旋曲线轨迹段EF的曲线长度s2及比例系数c2、直线O2F的倾斜角β2以及直线OE的倾斜角θ2：
Figure PCTCN2015100346-appb-000021
其中，
Figure PCTCN2015100346-appb-000022
为所述过渡圆弧轨迹段NE的曲率，
Figure PCTCN2015100346-appb-000023
为所述第二轨迹段BC的曲率。
为解决上述技术问题，本发明采用的另一个技术方案是：提供一种实现加工轨迹平滑连接的加工装置，包括：第一获取模块，用于获取第一轨迹段AB的数据和第二轨迹段BC的数据，所述第一轨迹段AB和所述第二轨迹段BC相交形成拐角；第二获取模块，用于根据获取到的所述数据获取连接在第一轨迹段AB和第二轨迹段BC之间的过渡轨迹段MF的数据，其中所述过渡轨迹段MF分别与所述第一轨迹段AB和所述第二轨迹段BC的转接处曲率连续、斜率连续；控制模块，用于将所述过渡轨迹段MF的数据作为所述拐角的加工路径数据以进行加工。
其中，所述过渡轨迹段MF包括第一回旋曲线轨迹段MN、过渡圆弧轨迹段NE以及第二回旋曲线轨迹段EF，其中所述第一回旋曲线轨迹段MN连接在所述第一轨迹段AB和所述过渡圆弧轨迹段NE之间，且所述第一回旋曲线轨迹段MN分别与所述第一轨迹段AB和所述过渡圆弧轨迹段NE的转接处曲率连续、斜率连续，所述第二回旋曲线轨迹段EF连接在所述第二轨迹段BC和所述过渡圆弧轨迹段NE之间，且所述第二回旋曲线轨迹段EF分别与所述第二轨迹段BC和所述过渡圆弧轨迹段NE的转接处曲率连续、斜率连续。
其中，所述第一轨迹段AB和所述第二轨迹段BC均为圆弧，设点M为所述第一回旋曲线轨迹段MN的起点，点N为所述第一回旋曲线 轨迹段MN的终点，设点E为所述第二回旋曲线轨迹段EF的起点，点F为所述第二回旋曲线轨迹段EF的终点；所述第一获取模块用于获取所述第一轨迹段AB的圆心O1的坐标(xo1，yo1)及半径R1、所述第二轨迹段BC的圆心O2的坐标(xo2，yo2)及半径R2、所述过渡圆弧轨迹段NE的圆心O的坐标(xo，yo)及半径R；所述第二获取模块用于根据如下方程组(1)计算所述第一回旋曲线轨迹段MN的曲线长度s1及比例系数c1、直线O1M的倾斜角θ1以及直线ON的倾斜角β1：
Figure PCTCN2015100346-appb-000024
其中，
Figure PCTCN2015100346-appb-000025
为所述过渡圆弧轨迹段NE的曲率，
Figure PCTCN2015100346-appb-000026
为所述第一轨迹段AB的曲率；
所述第二获取模块用于根据如下方程组(2)计算所述第二回旋曲线轨迹段EF的曲线长度s2及比例系数c2、直线OE的倾斜角θ2以及直线O2F的倾斜角β2：
Figure PCTCN2015100346-appb-000027
其中，
Figure PCTCN2015100346-appb-000028
为所述过渡圆弧轨迹段NE的曲率，
Figure PCTCN2015100346-appb-000029
为所述第二轨迹段BC的曲率。
其中，所述第一获取模块用于获取最大弓高误差e，并根据所述最大弓高误差e确定所述过渡圆弧轨迹段NE的圆心O的坐标(xo，yo)及半径R。
其中，所述第一轨迹段AB为直线，所述第二轨迹段BC为圆弧，设点M为所述第一回旋曲线轨迹段MN的起点，点N为所述第一回旋曲线轨迹段MN的终点，设点F为所述第二回旋曲线轨迹段EF的终点，点E为所述第二回旋曲线轨迹段EF的起点；所述第一获取模块用于获取所述第一轨迹段AB的斜率kAB和常量b、所述第二轨迹段BC的圆心O2的坐标(xo2，yo2)及半径R2、所述过渡圆弧轨迹段NE的圆心O的坐标(xo，yo)及半径R；所述第二获取模块用于根据如下方程组(3)计算所述第一回旋曲线轨迹段MN的曲线长度s1及比例系数c1、直线ON的倾斜角β1：
Figure PCTCN2015100346-appb-000030
其中，(xM，kABxM+b)为点M的坐标，
Figure PCTCN2015100346-appb-000031
为所述过渡圆弧轨迹段NE的曲率；
所述第二获取模块用于根据如下方程组(4)计算所述第二回旋曲线轨迹段EF的曲线长度s2及比例系数c2、直线O2F的倾斜角β2以及直线OE的倾斜角θ2：
Figure PCTCN2015100346-appb-000032
其中，
Figure PCTCN2015100346-appb-000033
为所述过渡圆弧轨迹段NE的曲率，
Figure PCTCN2015100346-appb-000034
为所述第二轨迹段BC的曲率。
本发明的有益效果是：区别于现有技术的情况，本发明通过在第一 轨迹段AB和第二轨迹段BC之间增加过渡轨迹段MF，其中过渡轨迹段MF分别与第一轨迹段AB和第二轨迹段BC的转接处斜率连续、曲率连续，由此在进行平滑转接时可以大大提高转接处的速度，可以使得转接前后速度保持大致相同，同时也可以使得转接前后的加速度保持一致，因此可以避免转接处的速度降为零的情况，有利于提高加工速度。
【附图说明】
图1是现有技术一种圆弧运动轨迹到圆弧运动轨迹的加工路径示意图；
图2是现有技术一种采用过渡圆弧对圆弧运动轨迹和圆弧运动轨迹之间进行平滑转接的示意图；
图3是本发明加工轨迹平滑转接的方法一实施方式的流程图；
图4是本发明加工轨迹平滑转接的方法一实施方式中，第一轨迹段AB和第二轨迹段BC之间采用过渡轨迹段MF转接的示意图；
图5是本发明加工轨迹平滑转接的方法一实施方式中，过渡轨迹段MF的曲线组合示意图；
图6是本发明加工轨迹平滑转接的方法一实施方式中，确定过渡圆弧轨迹段NE的圆心和半径的原理示意图；
图7是本发明加工轨迹平滑转接的方法一实施方式中，确定第一回旋曲线轨迹段MN的曲线方程的原理示意图；
图8是本发明加工轨迹平滑转接的方法一实施方式中，确定第二回旋曲线轨迹段EF的曲线方程的原理示意图；
图9是本发明加工轨迹平滑转接的方法另一实施方式中，确定第一回旋曲线轨迹段MN的曲线方程的原理示意图；
图10是本发明实现加工轨迹平滑转接的加工装置一实施方式的结构示意图。
【具体实施方式】
下面将结合附图和实施方式对本发明进行详细说明。
参阅图3，在本发明加工轨迹平滑转接的方法一实施方式中，所述方法适用于包括但不限于数控加工系统和机器人的连续加工。以数控加工系统为例，实现数控加工系统加工轨迹平滑转接的方法包括如下步骤：
步骤S301：获取第一轨迹段AB和第二轨迹段BC的数据，第一轨迹段AB和第二轨迹段BC相交形成拐角。
结合图4，其中，第一轨迹段AB和第二轨迹段BC为连续的两段加工路径，两段加工路径相交形成拐角B。其中，加工方向为从第一轨迹段AB到第二轨迹段BC，即第二轨迹段BC为下一段加工路径。
第一轨迹段AB的数据和第二轨迹段BC的数据为关于待加工工件的轮廓数据，也即待加工工件的加工路径数据。可预先将待加工工件的轮廓数据存储于存储区中，以从存储区中获取第一轨迹段AB和第二轨迹段BC的数据，或者也可以是获取即时输入的第一轨迹段AB和第二轨迹段BC的数据。
步骤S302：根据获取的第一轨迹段AB和第二轨迹段BC的数据，来获取连接在第一轨迹段AB和第二轨迹段BC之间的过渡轨迹段MF的数据，其中过渡轨迹段MF分别与第一轨迹段AB和第二轨迹段BC的转接处曲率连续、斜率连续。
其中，如图4所示，过渡轨迹段MF与第一轨迹段AB的转接处为点M，过渡轨迹段MF与第二轨迹段BC的转接处为点F，在点M处和点F处曲率连续、斜率连续。
所述曲率连续是指两条曲线在转接处的曲率一致，所述斜率连续是指两条曲线在转接处具有相同的切线，即斜率一致。因此，本实施方式中，过渡轨迹段MF与第一轨迹段AB在转接处点M的位置具有相同的斜率和曲率，过渡轨迹段MF与第二轨迹段BC在转接处点F的位置具有相同的斜率和曲率。
步骤S303：将过渡轨迹段MF的数据作为拐角的加工路径数据以进行加工。
本实施方式中，通过使过渡轨迹段MF与第一轨迹段AB在转接处 点M的位置具有相同的斜率和曲率，过渡轨迹段MF与第二轨迹段BC在转接处点F的位置具有相同的斜率和曲率，由此从第一轨迹段AB过渡到过渡轨迹段MF，以及从过渡轨迹段MF过渡到第二轨迹段BC的过程中，可以使得在转接处的速度和加速度连续，即保持一致，而不需要将速度降为零，从而可以大大提高加工效率。
在本发明加工轨迹平滑转接的方法的实施方式中，过渡轨迹段MF可以采用曲率连续变化的回旋曲线来实现，例如可以是单条回旋曲线，或者多条回旋曲线的组合，以实现转接处的曲率连续、斜率连续；当然过渡轨迹段MF也可以采用不同曲率的圆弧组合来实现，以实现转接处的曲率连续、斜率连续。
下面先对本发明实施方式适用的回旋曲线进行描述。
回旋曲线为螺线的一种，其曲线定义为：曲率和长度呈线性关系，公式表达为：
k(s)＝ka+cs…………(1)
其中，k表示回旋曲线上任意一点(例如H点)的曲率，ka表示回旋曲线起点处的曲率，c为比例系数，s表示回旋曲线起点到该任意点(H点)的曲线长度。
其中，设回旋曲线起点处的切线倾斜角为θa，根据曲率的定义
Figure PCTCN2015100346-appb-000035
可知切线倾斜角为曲率的积分，因此得到回旋曲线上任意一点的切线倾斜角为：
Figure PCTCN2015100346-appb-000036
由此，得到回旋曲线的平面坐标表达式为：
Figure PCTCN2015100346-appb-000037
其中，(xa，ya)为回旋曲线的起点处的坐标，(x，y)表示回旋曲线上的任一点坐标。因此，只需求解出回旋曲线的长度、回旋曲线的起点坐标以及比例系数即可得到回旋曲线的曲线方程，从而确定回旋曲线。
为了更好地实现加工轨迹间的平滑连接，在本发明一实施方式中，过渡轨迹段MF采用回旋曲线+圆弧+回旋曲线的组合方式以实现转接处的曲率连续、斜率连续。
具体地，本实施方式中，参阅图5，过渡轨迹段MF包括第一回旋曲线轨迹段MN、过渡圆弧轨迹段NE以及第二回旋曲线轨迹段EF。其中，第一回旋曲线轨迹段MN连接在第一轨迹段AB和过渡圆弧轨迹段NE之间。第一回旋曲线轨迹段MN与第一轨迹段AB的转接处为点M，第一回旋曲线轨迹段MN与过渡圆弧轨迹段NE的转接处为点N。其中在点M处第一回选曲线轨迹段MN和第一轨迹段AB曲率连续、斜率连续，在点N处第一回旋曲线轨迹段MN和过渡圆弧轨迹段NE的曲率连续、斜率连续。
第二回旋曲线轨迹段EF连接在第二轨迹段BC和过渡圆弧轨迹段NE之间。第二回旋曲线轨迹段EF与第二轨迹段BC的转接处为点F，第二回旋曲线轨迹段EF与过渡圆弧轨迹段NE的转接处为点E。其中在点F处第二回选曲线轨迹段EF和第二轨迹段BC曲率连续、斜率连续，在点E处第二回旋曲线轨迹段EF和过渡圆弧轨迹段NE的曲率连续、斜率连续。
在一种实施方式中，第一轨迹段AB和第二轨迹段BC均为圆弧，如图5所示。获取第一轨迹段AB的数据和第二轨迹段BC的数据的步骤包括：获取第一轨迹段AB的圆心O1的坐标(xo1，yo1)及半径R1、第二轨迹段BC的圆心O2的坐标(xo2，yo2)及半径R2、过渡圆弧轨迹段NE的圆心O的坐标(xo，yo)及半径R。
其中，根据待加工工件的轮廓可确定第一轨迹段AB的圆心O1的坐标(xo1，yo1)及半径R1、第二轨迹段BC的圆心O2的坐标(xo2，yo2)及半径R2。
过渡圆弧轨迹段NE可以根据弓高误差进行确定，弓高误差即加工精度。进一步地，根据最大弓高误差e确定过渡圆弧轨迹段NE的圆心O的坐标(xo，yo)及半径R，即使得过渡圆弧轨迹段NE满足最大弓高误差e的要求。其中，参阅图6，过渡圆弧轨迹段NE为满足最大弓高 误差e、且与第一轨迹段AB和第二轨迹段BC相切的圆弧(图中虚线)的一部分，因此根据最大弓高误差e、第一轨迹段AB的圆心O1的坐标(xo1，yo1)及半径R1、第二轨迹段BC的圆心O2的坐标(xo2，yo2)及半径R2可以确定过渡圆弧轨迹段NE的圆心O的坐标(xo，yo)及半径R。
由于过渡圆弧轨迹段NE为过渡轨迹段MF中最偏离实际轨迹段(即第一轨迹段AB和第二轨迹段BC)的轨迹段，因此当过渡圆弧轨迹段NE满足最大弓高误差e的要求时，与过渡圆弧轨迹段NE连接且比较靠近实际轨迹段的两条回旋曲线轨迹段MN、EF也满足弓高误差。
下面将具体描述如何确定本实施方式的第一回旋曲线轨迹段MN、过渡圆弧轨迹段NE以及第二回旋曲线轨迹段EF。
本实施方式中，获取连接在第一轨迹段AB和第二轨迹段BC之间的过渡轨迹段MF的数据是指获取第一回旋曲线轨迹段MN、过渡圆弧轨迹段NE以及第二回旋曲线轨迹段EF的轨迹方程。
参阅图7，设点M为第一回旋曲线轨迹段MN的起点，点N为第一回选曲线轨迹段MN的终点。如图所示，以圆心O所在水平线为x轴，则θ1角为直线O1M的倾斜角，β1角为直线ON的倾斜角。由此可得到点M处的切线倾斜角
Figure PCTCN2015100346-appb-000038
为：
Figure PCTCN2015100346-appb-000039
也即第一回旋曲线轨迹段MN的起点处的切线倾斜角；以及点N处的切线倾斜角α1为：
Figure PCTCN2015100346-appb-000040
也即第一回旋曲线轨迹段MN的终点处的切线倾斜角。
由于点M和点N处都为曲率连续、斜率连续，因此在点M处第一回旋曲线轨迹段MN的曲率等于第一轨迹段AB的曲率，在点N处第一回旋曲线轨迹段MN的曲率等于过渡圆弧轨迹段NE的曲率。由此得到第一回选曲线轨迹段MN在起点M处的曲率为
Figure PCTCN2015100346-appb-000041
R1为第一轨迹段AB的半径，以及得到第一回旋曲线轨迹段MN在终点N处的曲率为
Figure PCTCN2015100346-appb-000042
R为过渡圆弧轨迹段NE的半径。
此外，根据圆弧坐标公式可得到第一回选曲线轨迹段MN的起点M的坐标为：(xo1+R1cosθ1，.yo1+R1sinθ1)，以及得到第一回选曲线轨迹段 MN的终点N的坐标为：(xo+Rcosβ1，.yo+Rsinβ1)。因此，将所得到的第一回旋曲线轨迹段MN的起点M的坐标、终点N的坐标、起点M处的切线倾斜角和曲率以及终点N处的切线倾斜角和曲率对应代入上述公式(1)(2)(3)中，得到如下方程组(4)：
Figure PCTCN2015100346-appb-000043
其中，θ1、β1、s1、c1为未知数，s1为第一回旋曲线轨迹段MN从起点M到终点N的曲线长度，c1为第一回选曲线轨迹段的比例系数。
Figure PCTCN2015100346-appb-000044
为第一轨迹段AB的曲率，
Figure PCTCN2015100346-appb-000045
为过渡圆弧轨迹段NE的曲率，(xo，yo)为过渡圆弧轨迹段NE的圆心O的坐标，(xo1，yo1)为第一轨迹段AB的圆心O1的坐标。由此，通过对方程组(4)求解可得到θ1、β1、s1、c1。
在求解得到θ1、β1、s1、c1的值后，第一回旋曲线轨迹段MN的起点M点的坐标即可得出，然后将起点M点的坐标和曲线长度代入上述公式(3)，即可得第一回旋曲线轨迹段MN的平面坐标表达式；并将比例系数c1代入上述公式(1)即可得到曲率和曲线长度的关系式；将起点M点的切线倾斜角
Figure PCTCN2015100346-appb-000046
代入上述公式(2)即可得到切线倾斜角的关系式。由此可得到第一回旋曲线轨迹段MN的曲线方程。
基于相似原理获取第二回旋曲线轨迹段EF的曲线方程。
参阅图8，设点E为第二回旋曲线轨迹段EF的起点，点F为第二回旋曲线轨迹段EF的终点，则θ2角为直线OE的倾斜角，β2角为直线OF的倾斜角。由此可得到点E处的切线倾斜角
Figure PCTCN2015100346-appb-000047
为：
Figure PCTCN2015100346-appb-000048
也即第二回旋曲线轨迹段EF的起点处的切线倾斜角；以及点F处的切线倾 斜角α2为：
Figure PCTCN2015100346-appb-000049
也即第二回旋曲线轨迹段EF的终点处的切线倾斜角。
由于点E和点F处都为曲率连续、斜率连续，因此在点E处第二回旋曲线轨迹段EF的曲率等于过渡圆弧轨迹段NE的曲率，在点F处第二回旋曲线轨迹段EF的曲率等于第二轨迹段BC的曲率。由此得到第二回选曲线轨迹段EF在起点E处的曲率为
Figure PCTCN2015100346-appb-000050
R为过渡圆弧轨迹段NE的半径，以及得到第二回旋曲线轨迹段EF在终点F处的曲率为
Figure PCTCN2015100346-appb-000051
R2为第二轨迹段BC的半径。
此外，根据圆弧坐标公式可得到第二回选曲线轨迹段EF的起点E的坐标为：(xo+Rcosθ2，.yo+Rsinθ2)，以及得到第二回选曲线轨迹段EF的终点F的坐标为：(xo2+R2cosβ2，.yo2+R2sinβ2)。因此，将所得到的第二回旋曲线轨迹段EF的起点E的坐标、终点F的坐标、起点E处的切线倾斜角和曲率以及终点F处的切线倾斜角和曲率对应代入上述公式(1)(2)(3)中，得到如下方程组(5)：
Figure PCTCN2015100346-appb-000052
其中，θ2、β2、s2、c2为未知数，s2为第二回旋曲线轨迹段EF从起点E到终点F的曲线长度，c2为第二回选曲线轨迹段的比例系数。
Figure PCTCN2015100346-appb-000053
为第二轨迹段BC的曲率，
Figure PCTCN2015100346-appb-000054
为过渡圆弧轨迹段NE的曲率，(xo，yo)为过渡圆弧轨迹段NE的圆心O的坐标，(xo2，yo2)为第二轨迹段BC的圆心O2的坐标。由此，通过对方程组(5)求解可得到θ2、β2、s2、c2，由此可得到第二回旋曲线轨迹段EF的曲线方程。
在求解出β1、θ2后，可得到点N的坐标(xo+Rcosβ1，yo+Rsinβ1)， 以及点E的坐标(xo+Rcosθ2，yo+Rsinθ2)，由此确定过渡圆弧轨迹段NE的起点和终点，进而可以确定过渡圆弧轨迹段NE在与第一轨迹段AB和第二轨迹段BC相切的圆弧中的位置。
通过上述方式，可以确定第一回旋曲线轨迹段MN、过渡圆弧轨迹段NE以及第二回旋曲线轨迹段NE的曲线方程，进而得到过渡轨迹段MF的数据，即加工路径数据。
在本发明的另一实施方式中，第一轨迹段AB可以是直线、第二轨迹段BC为圆弧，或者第一轨迹段AB为圆弧、第二轨迹段BC为直线。以第一轨迹段AB为直线、第二轨迹段BC为圆弧为例进行说明。
参阅图9，获取第一轨迹段AB的数据和第二轨迹段BC的数据包括：获取第一轨迹段AB的斜率kAB和常量b、第二轨迹段BC的圆心O2的坐标(xo2，yo2)及半径R2、过渡圆弧轨迹段NE的圆心O的坐标(xo，yo)及半径R。
根据直线的特性可知，直线的曲率为0，切线倾斜角为直线与x轴的夹角，即斜率的反正切值。
如图9所示，第一轨迹段AB的切线倾斜角为arctankAB，即点M处的切线倾斜角
Figure PCTCN2015100346-appb-000055
为：
Figure PCTCN2015100346-appb-000056
也即第一回旋曲线轨迹段MN的起点处的切线倾斜角。点N处的切线倾斜角α1为：
Figure PCTCN2015100346-appb-000057
也即第一回旋曲线轨迹段MN的终点处的切线倾斜角。
由于点M和点N曲率连续、斜率连续，因此在点M处第一回旋曲线轨迹段MN的曲率等于第一轨迹段AB的曲率，在点N处第一回旋曲线轨迹段MN的曲率等于过渡圆弧轨迹段NE的曲率。由此得到第一回选曲线轨迹段MN在起点M处的曲率为0，以及得到第一回旋曲线轨迹段MN在终点N处的曲率为
Figure PCTCN2015100346-appb-000058
R为过渡圆弧轨迹段NE的半径。
此外，根据直线坐标公式和圆弧坐标公式可得到第一回选曲线轨迹段MN的起点M的坐标为：(xM，kABxM+b)，以及得到第一回选曲线轨迹段MN的终点N的坐标为：(xo+Rcosβ1，.yo+Rsinβ1)。因此，将所得到的第一回旋曲线轨迹段MN的起点M的坐标、终点N的坐标、起点 M处的切线倾斜角和曲率以及终点N处的切线倾斜角和曲率对应代入上述公式(1)(2)(3)中，得到如下方程组(6)：
Figure PCTCN2015100346-appb-000059
其中，xM、β1、s1、c1为未知数，通过方程组(6)求解可得到xM、β1、s1、c1，由此可得到第一回旋曲线轨迹段MN的曲线方程。
对于第二回旋曲线轨迹段EF的曲线方程的求解可根据图8所示的实施例进行，在此不进行一一赘述。当确定第一回旋曲线轨迹段MN和第二回旋曲线轨迹段EF后，过渡圆弧轨迹段NE的起点N点坐标和终点E点坐标也可以得到确定，具体的过程可参考上述描述。
本领域技术人员可以理解的是，当第二轨迹段BC为直线、第一轨迹段AB为圆弧时，以及当两个轨迹段AB、BC均为直线时，同样可以根据上述实施方式所述的方法得到过渡轨迹段MF的三个方程，具体可参考上述描述进行，此处不进行一一赘述。
通过本发明实施方式的加工轨迹平滑转接的方法，可以实现加工精度的要求，并且通过使所有转接处曲率连续、斜率连续，可以实现连续加工轨迹段之间的平滑连接，避免在转接处需要将速度降为零的情况，可以提高加工效率。
参阅图10，本发明实现加工轨迹平滑连接的加工装置一实施方式中，加工装置可以是数控加工系统或机器人，用于根据上述任一实施方式所述的加工轨迹平滑转接的方法实现加工过程中的平滑转接。以数控加工系统为例，包括第一获取模块1001、第二获取模块1002以及控制模块1003。
第一获取模块1001用于获取第一轨迹段AB的数据和第二轨迹段BC的数据，第一轨迹段AB和第二轨迹段BC相交形成拐角B。第一轨迹段AB的数据和第二轨迹段BC的数据为关于待加工工件的轮廓数据， 也即待加工工件的加工路径数据。可预先将待加工工件的轮廓数据存储于存储区中，从而当需要进行加工工件时，第一获取模块1001先从存储区中获取第一轨迹段AB和第二轨迹段BC的数据，或者也可以是获取即时输入的第一轨迹段AB和第二轨迹段BC的数据。
第二获取模块1002用于根据获取的第一轨迹段AB和第二轨迹段BC的数据，来获取连接在第一轨迹段AB和第二轨迹段BC之间的过渡轨迹段MF的数据，其中过渡轨迹段MF分别与第一轨迹段AB和第二轨迹段BC的转接处曲率连续、斜率连续。
其中，结合图4，过渡轨迹段MF与第一轨迹段AB的转接处为点M，过渡轨迹段MF与第二轨迹段BC的转接处为点F，在点M处和点F处曲率连续、斜率连续。
所述曲率连续是指两条曲线在转接处的曲率一致，所述斜率连续是指两条曲线在转接处具有相同的切线，即斜率一致。因此，本实施方式中，过渡轨迹段MF与第一轨迹段AB在转接处点M的位置具有相同的斜率和曲率，过渡轨迹段MF与第二轨迹段BC在转接处点F的位置具有相同的斜率和曲率。
控制模块1003用于将过渡轨迹段MF的数据作为拐角的加工路径数据以进行加工。
本实施方式中，通过使过渡轨迹段MF与第一轨迹段AB在转接处点M的位置具有相同的斜率和曲率，过渡轨迹段MF与第二轨迹段BC在转接处点F的位置具有相同的斜率和曲率，由此从第一轨迹段AB过渡到过渡轨迹段MF，以及从过渡轨迹段MF过渡到第二轨迹段BC的过程中，可以使得在转接处的速度和加速度连续，即保持一致，而不需要将速度降为零，从而可以大大提高加工效率。
在本发明一实施方式中，过渡轨迹段MF采用回旋曲线+圆弧+回旋曲线的组合方式以实现转接处的曲率连续、斜率连续。
具体地，结合图5，过渡轨迹段MF包括第一回旋曲线轨迹段MN、过渡圆弧轨迹段NE以及第二回旋曲线轨迹段EF。其中，第一回旋曲线轨迹段MN连接在第一轨迹段AB和过渡圆弧轨迹段NE之间。第一回 旋曲线轨迹段MN与第一轨迹段AB的转接处为点M，第一回旋曲线轨迹段MN与过渡圆弧轨迹段NE的转接处为点N。其中在点M处第一回选曲线轨迹段MN和第一轨迹段AB曲率连续、斜率连续，在点N处第一回旋曲线轨迹段MN和过渡圆弧轨迹段NE的曲率连续、斜率连续。
第二回旋曲线轨迹段EF连接在第二轨迹段BC和过渡圆弧轨迹段NE之间。第二回旋曲线轨迹段EF与第二轨迹段BC的转接处为点F，第二回旋曲线轨迹段EF与过渡圆弧轨迹段NE的转接处为点E。其中在点F处第二回选曲线轨迹段EF和第二轨迹段BC曲率连续、斜率连续，在点E处第二回旋曲线轨迹段EF和过渡圆弧轨迹段NE的曲率连续、斜率连续。
其中，第一轨迹段AB和第二轨迹段BC均为圆弧。第一获取模块1001具体用于获取第一轨迹段AB的圆心O1的坐标(xo1，yo1)及半径R1、第二轨迹段BC的圆心O2的坐标(xo2，yo2)及半径R2、过渡圆弧轨迹段NE的圆心O的坐标(xo，yo)及半径R。
其中，根据待加工工件的轮廓可确定第一轨迹段AB的圆心O1的坐标(xo1，yo1)及半径R1、第二轨迹段BC的圆心O2的坐标(xo2，yo2)及半径R2。
过渡圆弧轨迹段NE可以根据弓高误差进行确定，弓高误差即加工精度。进一步地，根据最大弓高误差e确定过渡圆弧轨迹段NE的圆心O的坐标(xo，yo)及半径R，即使得过渡圆弧轨迹段NE满足最大弓高误差e的要求。其中，参阅图6，过渡圆弧轨迹段NE为满足最大弓高误差e、且与第一轨迹段AB和第二轨迹段BC相切的圆弧(图中虚线)的一部分，因此根据最大弓高误差e、第一轨迹段AB的圆心O1的坐标(xo1，yo1)及半径R1、第二轨迹段BC的圆心O2的坐标(xo2，yo2)及半径R2可以确定过渡圆弧轨迹段NE的圆心O的坐标(xo，yo)及半径R。
由于过渡圆弧轨迹段NE为过渡轨迹段MF中最偏离实际轨迹段(即第一轨迹段AB和第二轨迹段BC)的轨迹段，因此当过渡圆弧轨迹段NE满足最大弓高误差e的要求时，与过渡圆弧轨迹段NE连接且比较靠近实际轨迹段的两条回旋曲线轨迹段MN、EF也满足弓高误差。
结合图7，设点M为第一回旋曲线轨迹段MN的起点，点N为第一回选曲线轨迹段MN的终点。第二获取模块1002用于根据如下方程组(7)计算得到第一回旋曲线轨迹段MN的曲线长度s1及比例系数c1、直线O1M的倾斜角θ1以及直线ON的倾斜角β1：
Figure PCTCN2015100346-appb-000060
其中，θ1、β1、s1、c1为未知数，s1为第一回旋曲线轨迹段MN从起点M到终点N的曲线长度，c1为第一回选曲线轨迹段的比例系数。θ1角为直线O1M的倾斜角，β1角为直线ON的倾斜角。
Figure PCTCN2015100346-appb-000061
为第一轨迹段AB的曲率，
Figure PCTCN2015100346-appb-000062
为过渡圆弧轨迹段NE的曲率，(xo，yo)为过渡圆弧轨迹段NE的圆心O的坐标，(xo1，yo1)为第一轨迹段AB的圆心O1的坐标。
在求解得到θ1、β1、s1、c1的值后，第一回旋曲线轨迹段MN的起点M点的坐标即可得出，然后将起点M点的坐标和曲线长度代入上述公式(3)，即可得第一回旋曲线轨迹段MN的平面坐标表达式；并将比例系数c1代入上述公式(1)即可得到曲率和曲线长度的关系式；将起点M点的切线倾斜角
Figure PCTCN2015100346-appb-000063
代入上述公式(2)即可得到切线倾斜角的关系式。由此可得到第一回旋曲线轨迹段MN的曲线方程。
根据相似原理获取第二回旋曲线轨迹段EF的曲线方程。
其中，结合图8，设点E为第二回旋曲线轨迹段EF的起点，点F为第二回旋曲线轨迹段EF的终点。第二获取模块1002用于根据如下方程组(8)计算第二回旋曲线轨迹段EF的曲线长度s2及比例系数c2、直线OE的倾斜角θ2以及直线O2F的倾斜角β2：
Figure PCTCN2015100346-appb-000064
其中，θ2、β2、s2、c2为未知数，s2为第二回旋曲线轨迹段EF从起点E到终点F的曲线长度，c2为第二回选曲线轨迹段的比例系数。θ2角为直线OE的倾斜角，β2角为直线OF的倾斜角。
Figure PCTCN2015100346-appb-000065
为第二轨迹段BC的曲率，
Figure PCTCN2015100346-appb-000066
为过渡圆弧轨迹段NE的曲率，(xo，yo)为过渡圆弧轨迹段NE的圆心O的坐标，(xo2，yo2)为第二轨迹段BC的圆心O2的坐标。由此，通过对方程组(8)求解可得到θ2、β2、s2、c2，由此可得到第二回旋曲线轨迹段EF的曲线方程。
在本发明加工装置另一实施方式中，第一轨迹段AB可以是直线、第二轨迹段BC为圆弧。
其中，第一获取模块1001用于获取第一轨迹段AB的斜率kAB和常量b、第二轨迹段BC的圆心O2的坐标(xo2，yo2)及半径R2、过渡圆弧轨迹段NE的圆心O的坐标(xo，yo)及半径R。
根据直线的特性可知，直线的曲率为0，切线倾斜角为直线与x轴的夹角，即斜率的反正切值。
第二获取模块1002用于根据如下方程组(9)计算第一回旋曲线轨迹段MN的曲线长度s1及比例系数c1、直线ON的倾斜角β1：
Figure PCTCN2015100346-appb-000067
其中，xM、β1、s1、c1为未知数，(xM，kABxM+b)为点M的坐标， 通过方程组(9)求解可得到xM、β1、s1、c1，由此可得到第一回旋曲线轨迹段MN的曲线方程。
第二回旋曲线轨迹段EF的曲线方程可根据方程组(8)得出，具体过程在此不进行一一赘述。当确定第一回旋曲线轨迹段MN和第二回旋曲线轨迹段EF后，过渡圆弧轨迹段NE的起点N点坐标和终点E点坐标也可以得到确定，具体的过程可参考上述描述。
本领域技术人员可以理解的是，当第二轨迹段BC为直线、第一轨迹段AB为圆弧时，以及当两个轨迹段AB、BC均为直线时，同样可以根据上述实施方式所述的方法得到过渡轨迹段MF的三个方程，具体可参考上述描述进行，此处不进行一一赘述。
通过本发明实施方式的加工装置，可以实现加工精度的要求，并且通过使所有转接处曲率连续、斜率连续，可以实现连续加工轨迹段之间的平滑连接，避免在转接处需要将速度降为零的情况，可以提高加工效率。
以上所述仅为本发明的实施方式，并非因此限制本发明的专利范围，凡是利用本发明说明书及附图内容所作的等效结构或等效流程变换，或直接或间接运用在其他相关的技术领域，均同理包括在本发明的专利保护范围内。

Claims (10)

  1. 一种加工轨迹平滑转接的方法，其特征在于，包括：
    获取第一轨迹段AB的数据和第二轨迹段BC的数据，所述第一轨迹段AB和所述第二轨迹段BC相交形成拐角；
    根据获取到的所述数据获取连接在第一轨迹段AB和第二轨迹段BC之间的过渡轨迹段MF的数据，其中所述过渡轨迹段MF分别与所述第一轨迹段AB和所述第二轨迹段BC的转接处曲率连续、斜率连续；
    将所述过渡轨迹段MF的数据作为所述拐角的加工路径数据以进行加工。
  2. 根据权利要求1所述的方法，其特征在于，所述过渡轨迹段MF分别与所述第一轨迹段AB和所述第二轨迹段BC的转接处曲率连续、斜率连续的实现方法包括：
    所述过渡轨迹段MF包括第一回旋曲线轨迹段MN、过渡圆弧轨迹段NE以及第二回旋曲线轨迹段EF，其中所述第一回旋曲线轨迹段MN连接在所述第一轨迹段AB和所述过渡圆弧轨迹段NE之间，且所述第一回旋曲线轨迹段MN分别与所述第一轨迹段AB和所述过渡圆弧轨迹段NE的转接处曲率连续、斜率连续，所述第二回旋曲线轨迹段EF连接在所述第二轨迹段BC和所述过渡圆弧轨迹段NE之间，且所述第二回旋曲线轨迹段EF分别与所述第二轨迹段BC和所述过渡圆弧轨迹段NE的转接处曲率连续、斜率连续。
  3. 根据权利要求2所述的方法，其特征在于，所述第一轨迹段AB和所述第二轨迹段BC均为圆弧，所述获取第一轨迹段AB的数据和第二轨迹段BC的数据的步骤包括：
    获取所述第一轨迹段AB的圆心O1的坐标(xo1，yo1)及半径R1、所述第二轨迹段BC的圆心O2的坐标(xo2，yo2)及半径R2、所述过渡圆弧轨迹段NE的圆心O的坐标(xo，yo)及半径R；
    所述根据获取到的数据获取连接在第一轨迹段AB和第二轨迹段BC之间的过渡轨迹段MF的数据的步骤包括：
    设点M为所述第一回旋曲线轨迹段MN的起点，点N为所述第一回旋曲线轨迹段MN的终点，则根据如下方程组(1)计算所述第一回旋曲线轨迹段MN的曲线长度s1及比例系数c1、直线O1M的倾斜角θ1以及直线ON的倾斜角β1：
    Figure PCTCN2015100346-appb-100001
    其中，
    Figure PCTCN2015100346-appb-100002
    为所述过渡圆弧轨迹段NE的曲率，
    Figure PCTCN2015100346-appb-100003
    为所述第一轨迹段AB的曲率；
    设点E为所述第二回旋曲线轨迹段EF的起点，点F为所述第二回旋曲线轨迹段EF的终点，则根据如下方程组(2)计算所述第二回旋曲线轨迹段EF的曲线长度s2及比例系数c2、直线OE的倾斜角θ2以及直线O2F的倾斜角β2：
    Figure PCTCN2015100346-appb-100004
    其中，
    Figure PCTCN2015100346-appb-100005
    为所述过渡圆弧轨迹段NE的曲率，
    Figure PCTCN2015100346-appb-100006
    为所述第二轨迹段BC的曲率。
  4. 根据权利要求3所述的方法，其特征在于，获取所述过渡圆弧轨迹段NE的圆心O的坐标(xo，yo)及半径R的步骤包括：
    获取最大弓高误差e，根据所述最大弓高误差e确定所述过渡圆弧轨迹段NE的圆心O的坐标(xo，yo)及半径R。
  5. 根据权利要求2所述的方法，其特征在于，所述第一轨迹段AB为直线，所述第二轨迹段BC为圆弧，所述获取第一轨迹段AB的数据和第二轨迹段BC的数据的步骤包括：
    获取所述第一轨迹段AB的斜率kAB和常量b、所述第二轨迹段BC的圆心O2的坐标(xo2，yo2)及半径R2、所述过渡圆弧轨迹段NE的圆心O的坐标(xo，yo)及半径R；
    所述根据获取到的数据获取连接在第一轨迹段AB和第二轨迹段BC之间的 过渡轨迹段MF的数据的步骤包括：
    设点M为所述第一回旋曲线轨迹段MN的起点，点N为所述第一回旋曲线轨迹段MN的终点，则根据如下方程组(3)计算所述第一回旋曲线轨迹段MN的曲线长度s1及比例系数c1、直线ON的倾斜角β1：
    Figure PCTCN2015100346-appb-100007
    其中，(xM，kABxM+b)为点M的坐标，
    Figure PCTCN2015100346-appb-100008
    为所述过渡圆弧轨迹段NE的曲率；
    设点F为所述第二回旋曲线轨迹段EF的终点，点E为所述第二回旋曲线轨迹段EF的起点，则根据如下方程组(4)计算所述第二回旋曲线轨迹段EF的曲线长度s2及比例系数c2、直线O2F的倾斜角β2以及直线OE的倾斜角θ2：
    Figure PCTCN2015100346-appb-100009
    其中，
    Figure PCTCN2015100346-appb-100010
    为所述过渡圆弧轨迹段NE的曲率，
    Figure PCTCN2015100346-appb-100011
    为所述第二轨迹段BC的曲率。
  6. 一种实现加工轨迹平滑连接的加工装置，其特征在于，包括：
    第一获取模块，用于获取第一轨迹段AB的数据和第二轨迹段BC的数据，所述第一轨迹段AB和所述第二轨迹段BC相交形成拐角；
    第二获取模块，用于根据获取到的所述数据获取连接在第一轨迹段AB和第二轨迹段BC之间的过渡轨迹段MF的数据，其中所述过渡轨迹段MF分别与所述第一轨迹段AB和所述第二轨迹段BC的转接处曲率连续、斜率连续；
    控制模块，用于将所述过渡轨迹段MF的数据作为所述拐角的加工路径数据以进行加工。
  7. 根据权利要求6所述的装置，其特征在于，所述过渡轨迹段MF包括第一回旋曲线轨迹段MN、过渡圆弧轨迹段NE以及第二回旋曲线轨迹段EF，其中所述第一回旋曲线轨迹段MN连接在所述第一轨迹段AB和所述过渡圆弧轨迹段NE之间，且所述第一回旋曲线轨迹段MN分别与所述第一轨迹段AB和所述过渡圆弧轨迹段NE的转接处曲率连续、斜率连续，所述第二回旋曲线轨迹段EF连接在所述第二轨迹段BC和所述过渡圆弧轨迹段NE之间，且所述第二回旋曲线轨迹段EF分别与所述第二轨迹段BC和所述过渡圆弧轨迹段NE的转接处曲率连续、斜率连续。
  8. 根据权利要求7所述的装置，其特征在于，所述第一轨迹段AB和所述第二轨迹段BC均为圆弧，设点M为所述第一回旋曲线轨迹段MN的起点，点N为所述第一回旋曲线轨迹段MN的终点，设点E为所述第二回旋曲线轨迹段EF的起点，点F为所述第二回旋曲线轨迹段EF的终点；
    所述第一获取模块用于获取所述第一轨迹段AB的圆心O1的坐标(xo1，yo1)及半径R1、所述第二轨迹段BC的圆心O2的坐标(xo2，yo2)及半径R2、所述过渡圆弧轨迹段NE的圆心O的坐标(xo，yo)及半径R；
    所述第二获取模块用于根据如下方程组(1)计算所述第一回旋曲线轨迹段MN的曲线长度s1及比例系数c1、直线O1M的倾斜角θ1以及直线ON的倾斜角β1：
    Figure PCTCN2015100346-appb-100012
    其中，
    Figure PCTCN2015100346-appb-100013
    为所述过渡圆弧轨迹段NE的曲率，
    Figure PCTCN2015100346-appb-100014
    为所述第一轨迹段AB的曲率；
    所述第二获取模块用于根据如下方程组(2)计算所述第二回旋曲线轨迹段EF的曲线长度s2及比例系数c2、直线OE的倾斜角θ2以及直线O2F的倾斜角β2：
    Figure PCTCN2015100346-appb-100015
    其中，
    Figure PCTCN2015100346-appb-100016
    为所述过渡圆弧轨迹段NE的曲率，
    Figure PCTCN2015100346-appb-100017
    为所述第二轨迹段BC的曲率。
  9. 根据权利要求8所述的装置，其特征在于，所述第一获取模块用于获取最大弓高误差e，并根据所述最大弓高误差e确定所述过渡圆弧轨迹段NE的圆心O的坐标(xo，yo)及半径R。
  10. 根据权利要求7所述的装置，其特征在于，所述第一轨迹段AB为直线，所述第二轨迹段BC为圆弧，设点M为所述第一回旋曲线轨迹段MN的起点，点N为所述第一回旋曲线轨迹段MN的终点，设点F为所述第二回旋曲线轨迹段EF的终点，点E为所述第二回旋曲线轨迹段EF的起点；
    所述第一获取模块用于获取所述第一轨迹段AB的斜率kAB和常量b、所述第二轨迹段BC的圆心O2的坐标(xo2，yo2)及半径R2、所述过渡圆弧轨迹段NE的圆心O的坐标(xo，yo)及半径R；
    所述第二获取模块用于根据如下方程组(3)计算所述第一回旋曲线轨迹段MN的曲线长度s1及比例系数c1、直线ON的倾斜角β1：
    Figure PCTCN2015100346-appb-100018
    其中，(xM，kABxM+b)为点M的坐标，
    Figure PCTCN2015100346-appb-100019
    为所述过渡圆弧轨迹段NE的曲率；
    所述第二获取模块用于根据如下方程组(4)计算所述第二回旋曲线轨迹段EF的曲线长度s2及比例系数c2、直线O2F的倾斜角β2以及直线OE的倾斜角θ2：
    Figure PCTCN2015100346-appb-100020
    其中，
    Figure PCTCN2015100346-appb-100021
    为所述过渡圆弧轨迹段NE的曲率，
    Figure PCTCN2015100346-appb-100022
    为所述第二轨迹段BC的曲率。
PCT/CN2015/100346 2015-12-31 2015-12-31 加工轨迹平滑转接的方法及加工装置 WO2017113416A1 (zh)

Priority Applications (2)

Application Number Priority Date Filing Date Title
PCT/CN2015/100346 WO2017113416A1 (zh) 2015-12-31 2015-12-31 加工轨迹平滑转接的方法及加工装置
CN201580079812.2A CN107615194B (zh) 2015-12-31 2015-12-31 加工轨迹平滑转接的方法及加工装置

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
PCT/CN2015/100346 WO2017113416A1 (zh) 2015-12-31 2015-12-31 加工轨迹平滑转接的方法及加工装置

Publications (1)

Publication Number Publication Date
WO2017113416A1 true WO2017113416A1 (zh) 2017-07-06

Family

ID=59224347

Family Applications (1)

Application Number Title Priority Date Filing Date
PCT/CN2015/100346 WO2017113416A1 (zh) 2015-12-31 2015-12-31 加工轨迹平滑转接的方法及加工装置

Country Status (2)

Country Link
CN (1) CN107615194B (zh)
WO (1) WO2017113416A1 (zh)

Cited By (11)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN109407658A (zh) * 2017-08-18 2019-03-01 厦门雅迅网络股份有限公司 无人车的行车轨迹规划方法及计算机可读存储介质
CN110348128A (zh) * 2019-07-12 2019-10-18 长安大学 一种基于k型曲线的公路平曲线设计方法
CN111857037A (zh) * 2020-06-19 2020-10-30 深圳市亿维自动化技术有限公司 一种过渡轨迹的生成方法、机器人及计算机可读存储介质
CN111913441A (zh) * 2020-08-06 2020-11-10 南京工程学院 一种基于轨迹模式的拐角平滑过渡方法
CN112180835A (zh) * 2020-10-14 2021-01-05 合肥宏晶微电子科技股份有限公司 轨迹信息确定方法及装置
CN113791576A (zh) * 2021-08-19 2021-12-14 五邑大学 一种轨迹间的局部光顺过渡方法、装置、设备及存储介质
CN114115112A (zh) * 2020-09-01 2022-03-01 大族激光科技产业集团股份有限公司 数控加工方法及装置
CN114296399A (zh) * 2021-12-28 2022-04-08 睿珀智能科技(兰溪)有限公司 一种经过圆弧局部光顺优化的c机能刀具半径补偿算法
CN114310921A (zh) * 2022-03-16 2022-04-12 珞石（北京）科技有限公司 一种最小曲率的直线过渡路径生成方法
CN114326584A (zh) * 2022-01-18 2022-04-12 深圳数马电子技术有限公司 拐角的过渡轨迹规划方法、装置、计算机设备和存储介质
CN114415598A (zh) * 2021-12-29 2022-04-29 深圳数马电子技术有限公司 加工路径的过渡方法、装置、存储介质及计算机设备

Families Citing this family (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
WO2020124606A1 (zh) * 2018-12-21 2020-06-25 深圳配天智能技术研究院有限公司 数控加工方法及系统、具有存储功能的装置
CN112276957B (zh) * 2020-11-05 2022-03-11 哈工大机器人（合肥）国际创新研究院 一种直线段和圆弧的平滑过渡方法及系统
CN114406453B (zh) * 2021-12-28 2023-11-24 大族激光科技产业集团股份有限公司 加工轨迹调整方法、装置、终端设备及存储介质

Citations (6)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
JP2005352662A (ja) * 2004-06-09 2005-12-22 Citizen Watch Co Ltd 工作機械の可動部の移動を制御する制御装置、制御装置を有する工作機械及び可動部の移動方法
CN101206472A (zh) * 2007-12-06 2008-06-25 上海交通大学 用于高速数控加工轨迹拐角的速度平滑方法
CN103268081A (zh) * 2013-03-25 2013-08-28 昆山天大精益数控科技发展有限公司 一种用于数控机床的基于精度误差控制的轨迹段转接处理算法
CN103365244A (zh) * 2013-07-12 2013-10-23 北京配天大富精密机械有限公司 机器人连续加工方法、装置及平滑转接方法、装置
CN103616849A (zh) * 2013-12-06 2014-03-05 北京配天大富精密机械有限公司 一种刀具轨迹规划方法、装置，工件加工方法、装置
CN104678894A (zh) * 2015-02-11 2015-06-03 北京配天技术有限公司 数控加工路径的规划方法、数控加工系统和方法

Family Cites Families (5)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
JP2013217306A (ja) * 2012-04-10 2013-10-24 Isuzu Motors Ltd 直噴式エンジンの燃焼室構造
JP6161942B2 (ja) * 2013-04-19 2017-07-12 株式会社デンソーアイティーラボラトリ カーブ形状モデル化装置、車両情報処理システム、カーブ形状モデル化方法、及びカーブ形状モデル化プログラム
CN103353737B (zh) * 2013-07-12 2016-08-10 北京配天技术有限公司 机器人连续加工方法、装置及平滑转接方法、装置
CN103646150B (zh) * 2013-12-23 2017-01-25 北京航空航天大学 一种基于5次Bezier曲线的G3连续过渡曲线构造方法
CN103949705B (zh) * 2014-05-14 2016-02-17 南京航空航天大学 槽特征腹板摆线螺旋复合铣加工方法

Patent Citations (6)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
JP2005352662A (ja) * 2004-06-09 2005-12-22 Citizen Watch Co Ltd 工作機械の可動部の移動を制御する制御装置、制御装置を有する工作機械及び可動部の移動方法
CN101206472A (zh) * 2007-12-06 2008-06-25 上海交通大学 用于高速数控加工轨迹拐角的速度平滑方法
CN103268081A (zh) * 2013-03-25 2013-08-28 昆山天大精益数控科技发展有限公司 一种用于数控机床的基于精度误差控制的轨迹段转接处理算法
CN103365244A (zh) * 2013-07-12 2013-10-23 北京配天大富精密机械有限公司 机器人连续加工方法、装置及平滑转接方法、装置
CN103616849A (zh) * 2013-12-06 2014-03-05 北京配天大富精密机械有限公司 一种刀具轨迹规划方法、装置，工件加工方法、装置
CN104678894A (zh) * 2015-02-11 2015-06-03 北京配天技术有限公司 数控加工路径的规划方法、数控加工系统和方法

Cited By (19)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN109407658A (zh) * 2017-08-18 2019-03-01 厦门雅迅网络股份有限公司 无人车的行车轨迹规划方法及计算机可读存储介质
CN110348128A (zh) * 2019-07-12 2019-10-18 长安大学 一种基于k型曲线的公路平曲线设计方法
CN110348128B (zh) * 2019-07-12 2022-10-14 长安大学 一种基于k型曲线的公路平曲线设计方法
CN111857037B (zh) * 2020-06-19 2022-07-26 深圳市亿维自动化技术有限公司 一种过渡轨迹的生成方法、机器人及计算机可读存储介质
CN111857037A (zh) * 2020-06-19 2020-10-30 深圳市亿维自动化技术有限公司 一种过渡轨迹的生成方法、机器人及计算机可读存储介质
CN111913441A (zh) * 2020-08-06 2020-11-10 南京工程学院 一种基于轨迹模式的拐角平滑过渡方法
CN111913441B (zh) * 2020-08-06 2021-11-09 南京工程学院 一种基于轨迹模式的拐角平滑过渡方法
CN114115112A (zh) * 2020-09-01 2022-03-01 大族激光科技产业集团股份有限公司 数控加工方法及装置
CN114115112B (zh) * 2020-09-01 2024-02-09 大族激光科技产业集团股份有限公司 数控加工方法及装置
CN112180835A (zh) * 2020-10-14 2021-01-05 合肥宏晶微电子科技股份有限公司 轨迹信息确定方法及装置
CN113791576A (zh) * 2021-08-19 2021-12-14 五邑大学 一种轨迹间的局部光顺过渡方法、装置、设备及存储介质
CN113791576B (zh) * 2021-08-19 2023-10-17 五邑大学 一种轨迹间的局部光顺过渡方法、装置、设备及存储介质
CN114296399A (zh) * 2021-12-28 2022-04-08 睿珀智能科技(兰溪)有限公司 一种经过圆弧局部光顺优化的c机能刀具半径补偿算法
CN114415598A (zh) * 2021-12-29 2022-04-29 深圳数马电子技术有限公司 加工路径的过渡方法、装置、存储介质及计算机设备
CN114415598B (zh) * 2021-12-29 2023-09-12 深圳数马电子技术有限公司 加工路径的过渡方法、装置、存储介质及计算机设备
CN114326584B (zh) * 2022-01-18 2023-09-12 深圳数马电子技术有限公司 拐角的过渡轨迹规划方法、装置、计算机设备和存储介质
CN114326584A (zh) * 2022-01-18 2022-04-12 深圳数马电子技术有限公司 拐角的过渡轨迹规划方法、装置、计算机设备和存储介质
CN114310921B (zh) * 2022-03-16 2022-06-10 珞石（北京）科技有限公司 一种最小曲率的直线过渡路径生成方法
CN114310921A (zh) * 2022-03-16 2022-04-12 珞石（北京）科技有限公司 一种最小曲率的直线过渡路径生成方法

Also Published As

Publication number Publication date
CN107615194A (zh) 2018-01-19
CN107615194B (zh) 2020-06-02

Similar Documents

Publication Publication Date Title
WO2017113416A1 (zh) 加工轨迹平滑转接的方法及加工装置
CN108594815B (zh) 一种分阶段的轮式机器人移动路径规划方法
WO2017113195A1 (zh) 一种加工路径规划方法、加工路径规划装置及数控机床
WO2018205276A1 (zh) 运动轨迹平滑转接的方法和装置及其相关设备
JP3286334B2 (ja) 移動体の制御装置
CN107390691B (zh) 一种agv路径跟踪方法
CN110865610B (zh) 一种基于机床振动抑制的刀具轨迹插值和速度规划方法
US10222801B2 (en) Movement route generating apparatus and movement route generating method
CN110900612B (zh) 一种位姿同步的六轴工业机器人轨迹平顺方法
CN110006419B (zh) 一种基于预瞄的车辆轨迹跟踪点确定方法
JP5417391B2 (ja) 数値制御装置
CN109623166B (zh) 一种激光切割的拐角处理方法及系统
CN109794943B (zh) 一种拐角过渡路径及确定方法
CN112965443B (zh) 一种裁床拐角轨迹跟踪高精度插值控制方法
CN106094737A (zh) 一种指定加工误差条件下的数控加工速度优化控制方法
CN111630461B (zh) 数控加工方法及系统、具有存储功能的装置
CN109031950B (zh) 基于俯仰角反转和角度平滑的跟踪转台程序导引过顶方法
JP4577247B2 (ja) 移動体及びその制御方法
CN116627033A (zh) 基于自适应横程走廊的再入滑翔飞行器预测校正方法
CN110625617B (zh) 一种智能机器人轨迹规划方法
TWI688844B (zh) 用於控制機械設備的控制裝置與方法
CN112129291B (zh) 一种基于Bezier曲线的固定翼无人机航迹优化方法
US20210260761A1 (en) Method And Control System For Controlling An Industrial Actuator
US7110853B2 (en) Processes and devices for computer-aided adaptation of an application program for a machine tool
CN113885514B (zh) 基于模糊控制和几何追踪的agv路径跟踪方法及系统

Legal Events

Date Code Title Description
121 Ep: the epo has been informed by wipo that ep was designated in this application

Ref document number: 15912040

Country of ref document: EP

Kind code of ref document: A1

NENP Non-entry into the national phase

Ref country code: DE

122 Ep: pct application non-entry in european phase

Ref document number: 15912040

Country of ref document: EP

Kind code of ref document: A1