CN115415886B - Method for calculating polishing path of optical surface of inner wall - Google Patents
Method for calculating polishing path of optical surface of inner wall Download PDFInfo
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- CN115415886B CN115415886B CN202211056314.4A CN202211056314A CN115415886B CN 115415886 B CN115415886 B CN 115415886B CN 202211056314 A CN202211056314 A CN 202211056314A CN 115415886 B CN115415886 B CN 115415886B
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- B—PERFORMING OPERATIONS; TRANSPORTING
- B24—GRINDING; POLISHING
- B24B—MACHINES, DEVICES, OR PROCESSES FOR GRINDING OR POLISHING; DRESSING OR CONDITIONING OF ABRADING SURFACES; FEEDING OF GRINDING, POLISHING, OR LAPPING AGENTS
- B24B13/00—Machines or devices designed for grinding or polishing optical surfaces on lenses or surfaces of similar shape on other work; Accessories therefor
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F30/00—Computer-aided design [CAD]
- G06F30/10—Geometric CAD
- G06F30/17—Mechanical parametric or variational design
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F30/00—Computer-aided design [CAD]
- G06F30/20—Design optimisation, verification or simulation
Abstract
The application relates to the field of machining, in particular to a method for calculating an inner wall optical surface polishing path, which comprises the following steps: establishing a mechanical arm coordinate system parallel to the workpiece coordinate system to be polished by utilizing the workpiece coordinate system to be polished; acquiring a polishing path basic vector by using the mechanical arm coordinate system; the polishing path basic vector is utilized to obtain the inner wall optical surface polishing path, the inner wall optical surface distributed on the side wall can be polished, the polishing method can achieve the effect of removing the surface processing texture, the surface quality is improved, and the problems that the inner wall optical surface processing texture is small in space, flexible in position, time-consuming and labor-consuming, and uncontrollable in process, and the texture removal is required to be carried out through manual polishing are solved.
Description
Technical Field
The application relates to the field of machining, in particular to a method for calculating an inner wall optical surface polishing path.
Background
Precision and ultra-precision polishing is an effective post-treatment method for removing machining cutting textures, and is widely applied to optical surfaces and post-treatment for machining with ultra-high surface quality. The traditional method is only suitable for polishing the end surface of an open space, and is not applicable to polishing and removing the processing texture with narrow space limitation and flexible optical surface orientation for the optical surface of the inner wall. The conventional polishing method is mainly used for removing the processing texture on the optical surface of the end-face substrate. Rather than for the machined removal of the inner wall optical surface. Removal of the optical surface texture of the inner wall faces the flexible nature of the surface orientation and therefore a viable method of calculating the inner wall polishing path is needed.
Disclosure of Invention
Aiming at the defects of the prior art, the application provides a method for calculating the polishing path of the optical surface of the inner wall, which calculates the polishing path based on the surface normal vector after a double coordinate system is established and a corresponding relation is established, and has high calculation accuracy and small output path error.
In order to achieve the above object, the present application provides a method for calculating a polishing path of an optical surface of an inner wall, comprising:
s1, establishing a mechanical arm coordinate system parallel to a workpiece coordinate system to be polished by utilizing the workpiece coordinate system to be polished;
s2, acquiring a polishing path basic vector by using the mechanical arm coordinate system;
and S3, obtaining the polishing path of the inner wall optical surface by using the polishing path basic vector.
Preferably, the establishing the mechanical arm coordinate system parallel to the workpiece coordinate system to be polished by using the workpiece coordinate system to be polished includes:
determining an initial mechanical arm coordinate system X, Y axis parallel to a X, Y axis of the workpiece coordinate system to be polished according to a X, Y axis of the workpiece coordinate system to be polished;
determining the Z-axis direction of an initial mechanical arm coordinate system according to the pointing direction of the polishing tool;
and establishing a mechanical arm coordinate system by utilizing the X, Y, Z axis of the initial mechanical arm coordinate system.
Preferably, the acquiring the polishing path base vector by using the mechanical arm coordinate system includes:
acquiring origin vectors of the mechanical arm coordinate system and the workpiece coordinate to be polished by utilizing the origin of the mechanical arm coordinate system and the origin of the workpiece coordinate system to be polished;
and using the origin vector of the mechanical arm coordinate system and the coordinates of the workpiece to be polished as a polishing path basic vector.
Preferably, obtaining the inner wall optical surface polishing path using the polishing path basis vector includes:
acquiring an initial polishing path point set of a workpiece to be polished by utilizing the workpiece to be polished;
calculating a unit normal vector of each polishing path point in the polishing path point set by utilizing a workpiece coordinate system to be polished;
calculating each initial polishing path point in the polishing path point set by using a unit normal vector of each polishing path point in the polishing path point set;
obtaining a test run polishing path point set by utilizing each initial polishing path point in the polishing path point set;
performing space interference check by using the test run polishing path point set to obtain a polishing path point set of a workpiece to be polished;
and utilizing the polishing path point set of the workpiece to be polished to serve as an inner wall optical surface polishing path.
Further, the calculation formula for calculating the unit normal vector of each polishing path point in the polishing path point set by using the workpiece coordinate system to be polished is as follows:
F＝(x,y,z)＝0
wherein f= (x, y, z) is a surface equation analysis expression of each polishing path point in the polishing path point set based on the workpiece coordinate system to be polished, and n= (u, v, w) is a unit normal vector of each polishing path point in the polishing path point set based on the workpiece coordinate system to be polished.
Further, the calculation formula for calculating each initial polishing path point in the polishing path point set by using the unit normal vector of each polishing path point in the polishing path point set is as follows:
wherein (X, Y, Z) is an initial polishing path point, (u, v, w) is a unit normal vector of each polishing path point in a polishing path point set based on a coordinate system of the workpiece to be polished, (X) p ，y p ，z p ) Is the polishing path point, and (a, b, c) is the polishing path base vector.
Further, obtaining a test run polishing path point set using each initial polishing path point in the polishing path point set includes:
when the polishing tool is pointed to the same Z axis as the mechanical arm coordinate system, calculating each test running polishing path point corresponding to the initial polishing path point by utilizing each initial polishing path point in the polishing path point set;
and obtaining a test run polishing path point set by utilizing each test run polishing path point.
Further, the calculation formula for calculating each test run polishing path point corresponding to the initial polishing path point by using each initial polishing path point in the polishing path point set is as follows:
β＝arccos w,γ＝0
(X,Y,Z)＝(x p ,y p ,z p )+(a,0,c)-(c sinθ,0,c cosθ)-(a cosθ,0,a sinθ)
α＝0,
wherein (X, Y, Z, alpha, beta, gamma) is each test run polishing path point corresponding to the initial polishing path point, and (u, v, w) is a unit normal vector of each polishing path point in the polishing path point set based on the coordinate system of the workpiece to be polished.
Further, performing spatial interferometry by using the test run polishing path point set to obtain a polishing path point set of a workpiece to be polished includes:
after visual simulation is carried out by utilizing the test run polishing path point set, judging whether any point in the test run polishing path point set has spatial interference with a workpiece to be polished, if so, carrying out spatial interference priority processing on the test run polishing path point set, otherwise, outputting the test run polishing path point set as the polishing path point set of the workpiece to be polished.
Further, the spatial interference prioritization of the set of trial run polishing path points includes:
the beta value of each test run polishing path point in the test run polishing path point set is adjusted based on a spatial interference angle threshold value to obtain a test run polishing path point processing set;
after the visual simulation is carried out by using the test run polishing path point processing set, judging whether any point in the test run polishing path point processing set has spatial interference with a workpiece to be polished, if so, returning to the step S1, otherwise, outputting the test run polishing path point processing set as a polishing path point set of the workpiece to be polished;
the spatial interference angle is an included angle between the polishing tool and a unit normal vector of each polishing path point in a polishing path point set based on a workpiece coordinate system to be polished, and the threshold value of the spatial interference angle is not more than 20 degrees.
Compared with the closest prior art, the application has the following beneficial effects:
the polishing path is calculated by establishing the dual coordinate system, so that the polishing tool is always over against the surface of the workpiece to be polished, the polishing process is high in efficiency, meanwhile, the calculation output of the path is ensured to be accurate by rechecking based on visual simulation, and the workpiece to be polished is not damaged in the actual operation process.
Drawings
FIG. 1 is a flow chart of a method for calculating an optical surface polishing path of an inner wall according to the present application;
FIG. 2 is a diagram of the type of polishing path of the practical application method for calculating the polishing path of the optical surface of the inner wall;
FIG. 3 is a schematic view showing the state of a polishing tool of a practical application method for calculating the polishing path of the optical surface of the inner wall;
fig. 4 is a diagram of a polishing path of a practical application method for calculating a polishing path of an optical surface of an inner wall according to the present application.
Detailed Description
The following describes the embodiments of the present application in further detail with reference to the drawings.
For the purpose of making the objects, technical solutions and advantages of the embodiments of the present application more apparent, the technical solutions of the embodiments of the present application will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present application, and it is apparent that the described embodiments are some embodiments of the present application, but not all embodiments of the present application. All other embodiments, which can be made by those skilled in the art based on the embodiments of the application without making any inventive effort, are intended to be within the scope of the application.
Example 1:
the application provides a method for calculating an inner wall optical surface polishing path, which is shown in figure 1 and comprises the following steps:
s1, establishing a mechanical arm coordinate system parallel to a workpiece coordinate system to be polished by utilizing the workpiece coordinate system to be polished;
s2, acquiring a polishing path basic vector by using the mechanical arm coordinate system;
and S3, obtaining the polishing path of the inner wall optical surface by using the polishing path basic vector.
The step S1 specifically comprises the following steps:
s1-1, determining an initial mechanical arm coordinate system X, Y axis parallel to a X, Y axis of a workpiece coordinate system to be polished according to a X, Y axis of the workpiece coordinate system to be polished;
s1-2, determining the Z-axis direction of an initial mechanical arm coordinate system according to the pointing direction of a polishing tool;
s1-3, establishing a mechanical arm coordinate system by utilizing the X, Y, Z axis of the initial mechanical arm coordinate system.
The step S2 specifically comprises the following steps:
s2-1, acquiring origin vectors of the mechanical arm coordinate system and the workpiece coordinate to be polished by utilizing the origins of the mechanical arm coordinate system and the workpiece coordinate system to be polished;
s2-2, using the origin vector of the mechanical arm coordinate system and the coordinates of the workpiece to be polished as a polishing path basic vector.
The step S3 specifically comprises the following steps:
s3-1, acquiring an initial polishing path point set of a workpiece to be polished by utilizing the workpiece to be polished;
s3-2, calculating a unit normal vector of each polishing path point in the polishing path point set by using a workpiece coordinate system to be polished;
s3-3, calculating each initial polishing path point in the polishing path point set by using a unit normal vector of each polishing path point in the polishing path point set;
s3-4, obtaining a test run polishing path point set by utilizing each initial polishing path point in the polishing path point set;
s3-5, performing space interference inspection by using the test run polishing path point set to obtain a polishing path point set of a workpiece to be polished;
s3-6, utilizing the polishing path point set of the workpiece to be polished to serve as an inner wall optical surface polishing path.
The calculation formula of step S3-2 is as follows:
F＝(x,y,z)＝0
wherein f= (x, y, z) is a surface equation analysis expression of each polishing path point in the polishing path point set based on the workpiece coordinate system to be polished, and n= (u, v, w) is a unit normal vector of each polishing path point in the polishing path point set based on the workpiece coordinate system to be polished.
The calculation formula of step S3-3 is as follows:
wherein (X, Y, Z) is an initial polishing path point and (u, v, w) is a polishing path point set based on a coordinate system of the workpiece to be polishedUnit normal vector of each polishing path point, (x) p ，y p ，z p ) Is the polishing path point, and (a, b, c) is the polishing path base vector.
The step S3-4 specifically comprises the following steps:
s3-4-1, when the polishing tool is pointed to the same Z axis as the mechanical arm coordinate system, calculating each test run polishing path point corresponding to the initial polishing path point by utilizing each initial polishing path point in the polishing path point set;
s3-4-2, obtaining a test run polishing path point set by utilizing each test run polishing path point.
The calculation formula of step S3-4-1 is as follows:
β＝arccos w,γ＝0
(X,Y,Z)＝(x p ,y p ,z p )+(a,0,c)-(c sinθ,0,c cosθ)-(a cosθ,0,a sinθ)
α＝0,
wherein (X, Y, Z, alpha, beta, gamma) is each test run polishing path point corresponding to the initial polishing path point, and (u, v, w) is a unit normal vector of each polishing path point in the polishing path point set based on the coordinate system of the workpiece to be polished.
The step S3-5 specifically comprises the following steps:
s3-5-1, judging whether any point in the test run polishing path point set has spatial interference with a workpiece to be polished after visual simulation is carried out by using the test run polishing path point set, if so, carrying out spatial interference priority processing on the test run polishing path point set, otherwise, outputting the test run polishing path point set as a polishing path point set of the workpiece to be polished.
The step S3-5-1 specifically comprises the following steps:
s3-5-1-1, adjusting beta values of each test run polishing path point in the test run polishing path point set based on a spatial interference angle threshold value to obtain a test run polishing path point processing set;
s3-5-1-2, judging whether any point in the test run polishing path point processing set has spatial interference with the workpiece to be polished after performing visual simulation by using the test run polishing path point processing set, returning to the step S1 if yes, otherwise, outputting the test run polishing path point processing set as a polishing path point set of the workpiece to be polished;
the spatial interference angle is an included angle between the polishing tool and a unit normal vector of each polishing path point in a polishing path point set based on a workpiece coordinate system to be polished, and the threshold value of the spatial interference angle is not more than 20 degrees.
Example 2:
the application provides a practical application method for calculating an inner wall optical surface polishing path of an inner wall optical surface, which comprises the following steps:
s1: defining a mechanical arm motion coordinate system, wherein the mechanical arm motion coordinate system comprises, but is not limited to, using each axis of the mechanical arm as a motion coordinate system or using the motion of the tail end of the mechanical arm as a coordinate system, the coordinate system is selected from a mechanical arm tail end motion construction coordinate system, denoted as (XM, YM, ZM), a workpiece coordinate system is denoted as (XW, YW, ZW), the motion axes of the mechanical arm are regulated, the mechanical arm tail end coordinate system is parallel to each axis of a workpiece coordinate system, the direction pointed by a polishing tool coincides with the ZM (or ZW) direction, the mechanical arm tail end coordinate system origin OM under the state and the workpiece coordinate system origin OW are set, and the vector of the vector OMOW can be expressed as in the mechanical arm tail end coordinate system
O M O W ＝(a,b,c)
Wherein a is the distance from the center of the end flange of the polishing tool and the end flange of the mechanical arm to the polishing head in the XM (or XW) direction, b is the distance from the center of the end flange of the polishing tool and the end flange of the mechanical arm to the polishing head in the YM (or YW) direction, and c is the distance from the center of the end flange of the polishing tool and the end flange of the mechanical arm to the polishing head in the ZM (or ZW) direction; the positive and negative directions of the coordinate axes of (XM, YM, ZM) or (XW, YW, ZW) are determined.
S2: setting a path point on the surface of a workpiece to be processed to form a polishing head end on the workpiece to be processedProcessing track of workpiece surface (x m ,y m ,z m ) The processing trajectory includes, but is not limited to, grid lines, spirals, arches, and other random trajectories.
In this embodiment, an actual application method for calculating an inner-wall optical surface polishing path of an inner-wall optical surface, and a sampling point track, as shown in fig. 2, is an arcuate track.
S3: to ensure that the polishing tool is working on the surface of the workpiece, the workpiece is processed in a workpiece coordinate system with a coordinate (x p ,y p ,z p ) For the points of (2), calculating a surface normal vector N corresponding to the processing track point, wherein the calculation mode can adopt but is not limited to an analytic geometry mode of using a surface equation to calculate a bias derivative or a three-dimensional software modeling to derive the unit normal vector n= (u, v, w);
s4: and generating coordinate instructions (X, Y, Z, alpha, beta, gamma) of the movement required by the tail end of the mechanical arm according to the processing track points. Since the polishing tool in this embodiment is long, only the surface normal vector X is considered at this time in order to ensure that the polishing tool does not spatially interfere with the workpiece to be processed during exposure W Z W Projection of the plane ensures that the polishing tool is normal to the surface to be machined, as shown in fig. 3. For a coordinate in the object coordinate system (x p ,y p ,z p ) For the points of (a), the coordinate instruction is calculated by
(X,Y,Z)＝(x p ,y p ,z p )+(a,0,c)-(c sinθ,0,c cosθ)-(a cosθ,0,a sinθ)
β＝θ,α＝γ＝0
Where θ=arctan (u/w) is defined by the surface of the workpiece to be machined at (x) p ,y p ,z p ) Normal vector determination at.
S5: inputting coordinate points (X, Y, Z, alpha, beta, gamma) containing the track into a mechanical arm controller through a program instruction, controlling the mechanical arm to move by the controller, judging whether the polishing tool and a workpiece to be processed have spatial interference or not, if no spatial interference exists, performing the next step, and if the spatial interference exists, performing the following processing steps:
(1) The polishing tool contacts with the workpiece to be processed in the moving process, at this time, the step S4 can be firstly carried out, the beta value is modified to achieve the effect of no interference, but the included angle between the polishing head direction and the normal vector N of the surface of the workpiece to be processed at this time is required to be ensured to be smaller than a certain threshold, and the threshold can be 20 degrees in the embodiment.
(2) And (3) returning to S1 to modify the geometric dimension of the polishing tool and recalculate under the condition that S4 is not satisfied all the time so as to satisfy the space non-interference requirement.
In this embodiment, a practical application method for calculating an inner wall optical surface and an inner wall optical surface polishing path is shown in fig. 4.
It will be appreciated by those skilled in the art that embodiments of the present application may be provided as a method, system, or computer program product. Accordingly, the present application may take the form of an entirely hardware embodiment, an entirely software embodiment or an embodiment combining software and hardware aspects. Furthermore, the present application may take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, and the like) having computer-usable program code embodied therein.
The present application is described with reference to flowchart illustrations and/or block diagrams of methods, apparatus (systems) and computer program products according to embodiments of the application. It will be understood that each flow and/or block of the flowchart illustrations and/or block diagrams, and combinations of flows and/or blocks in the flowchart illustrations and/or block diagrams, can be implemented by computer program instructions. These computer program instructions may be provided to a processor of a general purpose computer, special purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create means for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be stored in a computer-readable memory that can direct a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer-readable memory produce an article of manufacture including instruction means which implement the function specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
Finally, it should be noted that: the above embodiments are only for illustrating the technical aspects of the present application and not for limiting the same, and although the present application has been described in detail with reference to the above embodiments, it should be understood by those of ordinary skill in the art that: modifications and equivalents may be made to the specific embodiments of the application without departing from the spirit and scope of the application, which is intended to be covered by the claims.
Claims (8)
1. A method for calculating an optical surface polishing path of an inner wall, comprising:
s1, establishing a mechanical arm coordinate system parallel to a workpiece coordinate system to be polished by utilizing the workpiece coordinate system to be polished;
s2, acquiring a polishing path basic vector by using the mechanical arm coordinate system;
s3, obtaining an inner wall optical surface polishing path by using the polishing path basic vector;
s3-1, acquiring an initial polishing path point set of a workpiece to be polished by utilizing the workpiece to be polished;
s3-2, calculating a unit normal vector of each polishing path point in the polishing path point set by using a workpiece coordinate system to be polished;
s3-3, calculating each initial polishing path point in the polishing path point set by using a unit normal vector of each polishing path point in the polishing path point set;
the calculation formula of S3-3 is as follows:
wherein (X, Y, Z) is an initial polishing path point, (u, v, w) is a unit normal vector of each polishing path point in a polishing path point set based on a coordinate system of the workpiece to be polished, (X) p ，y p ，z p ) As polishing path points, (a, b, c) is a polishing path basis vector;
s3-4, obtaining a test run polishing path point set by utilizing each initial polishing path point in the polishing path point set;
s3-5, performing space interference inspection by using the test run polishing path point set to obtain a polishing path point set of a workpiece to be polished;
s3-6, utilizing the polishing path point set of the workpiece to be polished to serve as an inner wall optical surface polishing path.
2. The method of claim 1, wherein the establishing a robot coordinate system parallel to the workpiece coordinate system to be polished using the workpiece coordinate system to be polished comprises:
determining an initial mechanical arm coordinate system X, Y axis parallel to a X, Y axis of the workpiece coordinate system to be polished according to a X, Y axis of the workpiece coordinate system to be polished;
determining the Z-axis direction of an initial mechanical arm coordinate system according to the pointing direction of the polishing tool;
and establishing a mechanical arm coordinate system by utilizing the X, Y, Z axis of the initial mechanical arm coordinate system.
3. The method of claim 1, wherein obtaining a polishing path base vector using the robot coordinate system comprises:
acquiring origin vectors of the mechanical arm coordinate system and the workpiece coordinate to be polished by utilizing the origin of the mechanical arm coordinate system and the origin of the workpiece coordinate system to be polished;
and using the origin vector of the mechanical arm coordinate system and the coordinates of the workpiece to be polished as a polishing path basic vector.
4. The method of claim 1, wherein the unit normal vector of each polishing path point in the polishing path point set is calculated by using a coordinate system of the workpiece to be polished as follows:
F＝(x,y,z)＝0
wherein f= (x, y, z) is a surface equation analysis expression of each polishing path point in the polishing path point set based on the workpiece coordinate system to be polished, and n= (u, v, w) is a unit normal vector of each polishing path point in the polishing path point set based on the workpiece coordinate system to be polished.
5. The method of claim 1, wherein obtaining a test run polishing path point set using each initial polishing path point in the polishing path point set comprises:
when the polishing tool is pointed to the same Z axis as the mechanical arm coordinate system, calculating each test running polishing path point corresponding to the initial polishing path point by utilizing each initial polishing path point in the polishing path point set;
and obtaining a test run polishing path point set by utilizing each test run polishing path point.
6. The method of calculating an inner wall optical surface polishing path according to claim 5, wherein each of the test run polishing path points corresponding to the initial polishing path point is calculated using each of the initial polishing path points in the set of polishing path points as follows:
β＝arccosw,γ＝0
(X,Y,Z)＝(x p ,y p ,z p )+(a,0,c)-(csinθ,0,ccosθ)-(acosθ,0,asinθ)
α＝0,γ＝0
wherein (X, Y, Z, alpha, beta, gamma) is each test run polishing path point corresponding to the initial polishing path point, and (u, v, w) is a unit normal vector of each polishing path point in the polishing path point set based on the coordinate system of the workpiece to be polished.
7. The method of claim 1, wherein performing a spatial interferometry with the set of run-on polishing path points to obtain a set of polishing path points for a workpiece to be polished comprises:
after visual simulation is carried out by utilizing the test run polishing path point set, judging whether any point in the test run polishing path point set has spatial interference with a workpiece to be polished, if so, carrying out spatial interference priority processing on the test run polishing path point set, otherwise, outputting the test run polishing path point set as the polishing path point set of the workpiece to be polished.
8. The method of claim 7, wherein spatially interferometrically prioritizing the set of test run polishing path points comprises:
the beta value of each test run polishing path point in the test run polishing path point set is adjusted based on a spatial interference angle threshold value to obtain a test run polishing path point processing set;
after the visual simulation is carried out by using the test run polishing path point processing set, judging whether any point in the test run polishing path point processing set has spatial interference with a workpiece to be polished, if so, returning to the step S1, otherwise, outputting the test run polishing path point processing set as a polishing path point set of the workpiece to be polished;
the spatial interference angle is an included angle between the polishing tool and a unit normal vector of each polishing path point in a polishing path point set based on a workpiece coordinate system to be polished, and the threshold value of the spatial interference angle is not more than 20 degrees.
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| JP2002264013A (en) * | 2001-03-09 | 2002-09-18 | Ricoh Co Ltd | Curved surface corrective polishing system, nc polishing device, nc program creating method for polishing optical component, nc program creating method for polishing, creating method for two-dimensional coordinate point group file for nc program, nc program creating method, automatic creating program for nc program, recording medium recorded with nc program for polishing, optical component or mold therefor |
| JP2004174665A (en) * | 2002-11-27 | 2004-06-24 | Ricoh Co Ltd | Curved surface machining method and curved surface machining device |
| CN102699817A (en) * | 2012-06-01 | 2012-10-03 | 厦门大学 | Polishing precessional motion control method for large-aperture aspherical air bag |
| JP2016002627A (en) * | 2014-06-18 | 2016-01-12 | 株式会社Ihi | Working trajectory generation apparatus and method |
| CN105269565A (en) * | 2015-10-30 | 2016-01-27 | 福建长江工业有限公司 | Offline programming and modifying method of six-axis grinding and polishing industrial robot |
| CN105643399A (en) * | 2015-12-29 | 2016-06-08 | 沈阳理工大学 | Automatic lapping and polishing system for complex surface of compliant control-based robot and machining method |
| CN106182018A (en) * | 2016-07-30 | 2016-12-07 | 福州大学 | A kind of grinding and polishing industrial robot off-line programing method based on workpiece three-dimensional graph |
| CN107369127A (en) * | 2017-06-09 | 2017-11-21 | 华南理工大学 | A kind of three-dimensional class cycloid polishing locus generation method that path feeding is cut along row |
| CN107422693A (en) * | 2017-08-02 | 2017-12-01 | 辽宁科技大学 | Center line is reconstructed to space bent pipe inner surface polishing locus generation method |
| CN113752263A (en) * | 2021-09-29 | 2021-12-07 | 杭州申昊科技股份有限公司 | Tool calibration method and device based on laser sensor and electronic equipment |
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