CN113532353A - Precision measuring device - Google Patents

Precision measuring device Download PDF

Info

Publication number
CN113532353A
CN113532353A CN202110865469.1A CN202110865469A CN113532353A CN 113532353 A CN113532353 A CN 113532353A CN 202110865469 A CN202110865469 A CN 202110865469A CN 113532353 A CN113532353 A CN 113532353A
Authority
CN
China
Prior art keywords
joint
link
connecting rod
robot
rotary
Prior art date
Legal status (The legal status 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 status listed.)
Pending
Application number
CN202110865469.1A
Other languages
Chinese (zh)
Inventor
刘慧泉
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
Individual
Original Assignee
Individual
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 Individual filed Critical Individual
Priority to CN202110865469.1A priority Critical patent/CN113532353A/en
Publication of CN113532353A publication Critical patent/CN113532353A/en
Pending legal-status Critical Current

Links

Images

Classifications

    • GPHYSICS
    • G01MEASURING; TESTING
    • G01BMEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
    • G01B21/00Measuring arrangements or details thereof, where the measuring technique is not covered by the other groups of this subclass, unspecified or not relevant
    • G01B21/02Measuring arrangements or details thereof, where the measuring technique is not covered by the other groups of this subclass, unspecified or not relevant for measuring length, width, or thickness
    • G01B21/04Measuring arrangements or details thereof, where the measuring technique is not covered by the other groups of this subclass, unspecified or not relevant for measuring length, width, or thickness by measuring coordinates of points
    • G01B21/045Correction of measurements
    • GPHYSICS
    • G01MEASURING; TESTING
    • G01BMEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
    • G01B21/00Measuring arrangements or details thereof, where the measuring technique is not covered by the other groups of this subclass, unspecified or not relevant
    • G01B21/02Measuring arrangements or details thereof, where the measuring technique is not covered by the other groups of this subclass, unspecified or not relevant for measuring length, width, or thickness
    • G01B21/04Measuring arrangements or details thereof, where the measuring technique is not covered by the other groups of this subclass, unspecified or not relevant for measuring length, width, or thickness by measuring coordinates of points
    • G01B21/047Accessories, e.g. for positioning, for tool-setting, for measuring probes

Landscapes

  • Physics & Mathematics (AREA)
  • General Physics & Mathematics (AREA)
  • Manipulator (AREA)
  • Length Measuring Devices With Unspecified Measuring Means (AREA)

Abstract

The application provides a precision measurement device, including base, first connecting rod, second connecting rod, rotary encoder and ball joint. One end of the first connecting rod is rotatably connected to the base. One end of the second link is rotatably connected to the other end of the first link. The rotary encoder is arranged at the joint of the first connecting rod and the second connecting rod to measure the angle between the first connecting rod and the second connecting rod. The ball joint is arranged at the other end of the second connecting rod and is used for connecting the fixed end of the robot. Therefore, the distance between the two points of the ball joint and one end, fixed on the base, of the first connecting rod is calculated according to the cosine theorem and the lengths of the first connecting rod and the second connecting rod, the robot is calibrated to obtain the real assembly size of the robot, and the compensation coefficient of the robot can be calculated according to the calibration algorithm of the robot and the DH parameters of the robot. The precision measurement device is simple and portable in structure, effectively improves the precision of space measurement, and is beneficial to calibrating the robot in different environments.

Description

Precision measuring device
Technical Field
The application belongs to the technical field of precision measurement, more specifically relates to a precision measurement device for be applied to kinematics calibration of robot.
Background
In the manufacturing and assembling process of the multi-joint robot, the parts have errors. The conventional robot controls the overall deviation of the robot within a certain range through tolerance. Since the robot moves according to the kinematic model of the robot strictly, the motion model of the robot is necessarily deviated from the actual motion model, which is a main reason for the limited precision range of the robot. Along with the use of robot, the wearing and tearing of spare part will aggravate this kind of deviation more, makes the robot can't accomplish the function more accurately.
In order to solve the problem, the existing scheme is to use an expensive laser tracker to perform end tracking on the assembled robot, and obtain the real assembled size of the robot by combining a complex algorithm, so as to compensate errors caused by manufacturing, assembling size and actual size. However, laser trackers are complex to deploy, difficult to use, and expensive. In another method, a stay wire encoder is used for measuring the track change of the robot in the moving process, but the existing stay wire encoder has limited precision and cannot achieve the same effect as a laser tracker.
Disclosure of Invention
The embodiment of the application aims to provide a precision measurement device, which aims to solve the problems that in the prior art, a laser tracker is adopted to calibrate robot deviation, so that the price is high, and the use difficulty is high; and the adoption of a stay wire encoder has the technical problem of limited precision.
In order to achieve the purpose, the technical scheme adopted by the application is as follows: the utility model provides a precision measurement device, includes base, first connecting rod, second connecting rod, rotary encoder and ball joint. One end of the first connecting rod is rotatably connected to the base. One end of the second link is rotatably connected to the other end of the first link. The rotary encoder is arranged at the joint of the first connecting rod and the second connecting rod to measure the angle between the first connecting rod and the second connecting rod. The ball joint is arranged at the other end of the second connecting rod and is used for connecting the fixed end of the robot.
Optionally, the precision measurement device comprises a first rotary joint, and the first link is rotatably connected to the base through the first rotary joint.
Optionally, the first rotational joint is a two-dimensional rotational joint such that the first link is operable to rotate in a horizontal direction and a vertical direction.
Optionally, the first swivel joint comprises a horizontal swivel bearing joint and a vertical swivel bearing joint, the horizontal swivel bearing joint is fixed on the base, and the vertical swivel bearing joint is connected to a side wall of the horizontal swivel bearing joint.
Optionally, the precision measurement device includes a second rotary joint, the first link and the second link are rotatably connected by the second rotary joint, and the second rotary joint is a one-dimensional rotary joint.
Optionally, the second rotary joint is a rotary bearing joint and is coaxially sleeved with the rotary encoder.
Optionally, the ball joint is a magnetic ball joint.
Optionally, the ball joint comprises a magnetic attraction type ball socket and a magnetic conduction stainless steel ball head, and the magnetic conduction stainless steel ball head can be rotationally adsorbed to the magnetic attraction type ball socket in any direction with 3 degrees of freedom.
Optionally, the first and second links are carbon fiber tubes.
Optionally, the base is provided with a communication interface.
The application provides a precision measurement device's beneficial effect lies in: compared with the prior art, the precision measurement device of this application is through rotatably setting up the one end with first connecting rod in the base, the one end of second connecting rod and the other end of first connecting rod are rotatably connected, and measure the angle between first connecting rod and the second connecting rod through rotary encoder, the end of second connecting rod is equipped with the bulb joint, the robot stiff end can be connected to the bulb joint, can calculate the distance between the one end this two points that bulb joint and first connecting rod are fixed in the base according to cosine theorem like this, the length of first connecting rod and second connecting rod, thereby mark the robot, obtain the true assembly size of robot. After the distance from the robot to the same point in different postures in the space is accurately measured, the compensation coefficient of the robot can be calculated according to the calibration algorithm of the robot and the DH parameter of the robot, so that the function of calibrating the robot is achieved. The invention has simple structure, effectively improves the precision of space measurement, is portable, and is beneficial to the calibration work of the robot under different environments.
Drawings
In order to more clearly illustrate the technical solutions in the embodiments of the present application, the drawings needed to be used in the embodiments or the prior art descriptions will be briefly described below, and it is obvious that the drawings in the following description are only some embodiments of the present application, and it is obvious for those skilled in the art to obtain other drawings based on these drawings without inventive exercise.
Fig. 1 is a schematic perspective view of a precision measurement apparatus according to an embodiment of the present disclosure;
fig. 2 is a schematic perspective view of a precision measurement apparatus provided in an embodiment of the present application, viewed from another perspective;
fig. 3 is an exploded schematic view of a precision measurement apparatus according to an embodiment of the present disclosure.
Wherein, in the figures, the respective reference numerals:
10-a base; 11-a communication interface; 20-a first link; 21-a socket; 30-a second link; 31-a socket; 311-a rotating shaft; 40-a rotary encoder; 50-ball joint; 51-magnetic stainless steel ball head; 60-a first rotary joint; 61-horizontal swivel bearing joint; 62-vertical swivel bearing joint; 70-second rotational joint.
Detailed Description
In order to make the technical problems, technical solutions and advantageous effects to be solved by the present application clearer, the present application is further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the present application and are not intended to limit the present application.
It will be understood that when an element is referred to as being "secured to" or "disposed on" another element, it can be directly on the other element or be indirectly on the other element. When an element is referred to as being "connected to" another element, it can be directly connected to the other element or be indirectly connected to the other element.
It will be understood that the terms "length," "width," "upper," "lower," "front," "rear," "left," "right," "vertical," "horizontal," "top," "bottom," "inner," "outer," and the like, as used herein, refer to an orientation or positional relationship indicated in the drawings that is solely for the purpose of facilitating the description and simplifying the description, and do not indicate or imply that the device or element being referred to must have a particular orientation, be constructed and operated in a particular orientation, and thus should not be considered as limiting the present application.
Furthermore, the terms "first", "second" and "first" are used for descriptive purposes only and are not to be construed as indicating or implying relative importance or implicitly indicating the number of technical features indicated. Thus, a feature defined as "first" or "second" may explicitly or implicitly include one or more of that feature. In the description of the present application, "a plurality" means two or more unless specifically limited otherwise.
Referring to fig. 1 to fig. 3 together, a precision measurement apparatus according to an embodiment of the present application will be described. The precision measuring device comprises a base 10, a first connecting rod 20, a second connecting rod 30, a rotary encoder 40 and a ball joint 50.
The base 10 is the mounting and support structure for the entire precision measurement apparatus. One end of the first link 20 is rotatably connected to the base 10 such that the first link 20 can rotate with respect to the base 10. One end of the second link 30 is rotatably connected to the other end of the first link 20 such that the second link 30 can rotate with respect to the first link 20. The rotary encoder 40 is provided at the junction of the first link 20 and the second link 30 to measure the angle between the first link 20 and the second link 30. The ball joint 50 is provided at the other end of the second link 30 and is used to connect a robot fixing end.
In use, the base 10 is located at a predetermined distance from the robot, and the ball joint 50 is connected to the fixed end of the robot. As the robot moves in different postures in the space, the first connecting rod 20 and the base 10 rotate, the second connecting rod 30 and the first connecting rod 20 also rotate relatively, at this time, the rotary encoder 40 measures the included angle between the first connecting rod 20 and the second connecting rod 30 in real time, and the included angle between the first connecting rod 20 and the second connecting rod 30 is recorded as θ. Since the lengths of the first link 20 and the second link 30 are fixed values, for example, the length of the first link 20 is denoted as L1, the length of the second link 30 is denoted as L2, and the distance between two points, i.e., the point from the ball joint 50 to the end of the first link 20 fixed to the base 10 is denoted as S, it can be known from the cosine law that:
Figure BDA0003187130220000041
accordingly, the following can be deduced: the distance S between the ball joint 50 and the end of the first link 20 fixed to the base 10 is:
Figure BDA0003187130220000042
since the ball joint 50 is connected to the robot fixing end, the position of the base 10 is predetermined, and thus, the position of the robot fixing end can be calibrated and calibrated in this way. By sequentially calibrating the positions of the joints of the robot in such a way, the real assembly size of the robot can be obtained. And then, according to a robot calibration algorithm and by combining robot DH parameters, the compensation coefficient of the robot can be calculated, so that the function of calibrating the robot is achieved.
Compared with the prior art, the precision measurement device has the advantages that the structure is simple, the precision of space measurement is effectively improved, the device is portable, and the robot can be calibrated conveniently without environment.
In another embodiment of the present application, the precision measuring apparatus includes a first rotary joint 60, and the first link 20 is rotatably connected to the base 10 by the first rotary joint 60, so that the first link 20 smoothly rotates with respect to the base 10.
Further, the first rotary joint 60 is a two-dimensional rotary joint, i.e., the two-dimensional rotary joint can be rotated in both horizontal and vertical directions, so that the first link 20 can be operatively rotated in both horizontal and vertical directions with respect to the base 10. In the illustrated embodiment, the base 10 has a cylindrical shape, wherein the horizontal direction refers to a direction parallel to the top surface of the base 10, and the vertical direction refers to a direction perpendicular to the top surface of the base 10 (i.e., a direction parallel to the central axis of the base 10).
Specifically, the first rotary joint 60 includes a horizontal rotary bearing joint 61 and a vertical rotary bearing joint 62, wherein the horizontal rotary bearing joint 61 is fixed on the top surface of the base 10, and the horizontal rotary bearing joint 61 and the base 10 are arranged in an up-and-down overlapping manner. The vertical swivel bearing joint 62 is connected to a sidewall of the horizontal swivel bearing joint 61. Thus, the first link 20 can be rotated 360 in the horizontal direction by the horizontal rotary bearing joint 61, and the first link 20 can be rotated 360 in the vertical direction by the vertical rotary bearing joint. That is, the first link 20 has two degrees of freedom in the horizontal direction and the vertical direction, and the intersection point of the horizontal and vertical rotation axes is the starting point of the measurement point. The hinge structure with horizontal and vertical design can ensure that the precision measuring device does not generate sagging or movement in other directions due to the redundancy of degrees of freedom during horizontal measurement.
In another embodiment of the present application, the precision measuring apparatus includes a second rotating joint 70, the first link 20 and the second link 30 are rotatably connected by the second rotating joint 70, and the second rotating joint 70 is a one-dimensional rotating joint, such that the first link 20 and the second link 30 can only relatively rotate on a plane formed by the two.
In another embodiment of the present application, the second rotary joint 70 is a rotary bearing joint and is coaxially sleeved with the rotary encoder 40. Specifically, as shown in fig. 3, a sleeve 31 is sleeved on an end portion of the second connecting rod 30, a rotating shaft 311 perpendicular to the length direction of the second connecting rod 30 extends from the sleeve 31, a sleeve 21 is sleeved on an end portion of the first connecting rod 20, and the sleeve 21 has a through hole and is sleeved on the periphery of the rotating shaft 311. The second rotary joint 70 and the rotary encoder 40 are also sleeved on the periphery of the rotating shaft 311, so that the two are coaxially sleeved. The second rotary joint 70 and the rotary encoder 40 are coaxially sleeved together, which can facilitate the rotary encoder 40 to measure the angle θ between the first connecting rod 20 and the second connecting rod 30 through the second rotary joint 70.
In another embodiment of this application, ball joint 50 is magnetism-type ball joint, and the mode of connecting through magnetism is inhaled between ball joint 50 and the robot stiff end of can being convenient for like this, and it is convenient fast to install and connect.
Specifically, the ball joint 50 includes a magnetic attraction type ball socket and a magnetic conductive stainless steel ball head 51, and the magnetic conductive stainless steel ball head 51 can be rotationally adsorbed to the magnetic attraction type ball socket in any direction with 3 degrees of freedom. The center of the ball joint 50 is the end point of the measuring point. Thus, ball joint 50 has three degrees of freedom. The large-angle magnetic-type ball joint 50 is adopted, so that the installation and the use can be rapidly and conveniently carried out, and the reliable connection and the smooth rotation of the robot or equipment are ensured during the movement.
In another embodiment of the present application, the first link 20 and the second link 30 are both carbon fiber tubes. The carbon fiber can reduce the structural deformation caused by temperature change to the maximum extent, and meanwhile, the light characteristic of the carbon fiber enables the precision measuring device to be more portable and the response to be quick and accurate.
In another embodiment of the present application, the side wall of the base 10 is provided with a communication interface 11, and the communication interface 11 is used for the precision measuring apparatus and an external device to perform communication connection for data transmission and processing.
The precision measurement device has the following advantages: first, the precision measuring device is a one-dimensional measuring device, the ball joint 50 has 3 degrees of freedom, the first rotary joint 60 has 2 degrees of freedom, and the second rotary joint 70 has 1 degree of freedom, and the whole precision measuring device has 6 degrees of freedom in space, and can realize space one-dimensional high-precision distance measurement with itself as an origin. Secondly, the distance between the two points can be determined by adopting the first connecting rod 20, the second connecting rod 30 and the high-precision rotary encoder 40 which are light, and then by simple cosine law, the purpose of accurate measurement is achieved, and the precision is not inferior to that of a laser tracker and a stay wire measuring device. Thirdly, the precision measurement device has the main characteristics of simple structure stability measurement principle, very good effectiveness and precision, stable mechanism and high precision and response speed of equipment. The precision measuring device has the advantages of low cost, high measuring precision, convenient use and strong anti-interference capability, has great significance for the robot industry, can be widely applied to space one-dimensional high-precision demand scenes, and brings revolutionary change to the calibration and measurement of the robot.
The above description is only exemplary of the present application and should not be taken as limiting the present application, as any modification, equivalent replacement, or improvement made within the spirit and principle of the present application should be included in the protection scope of the present application.

Claims (10)

1. A precision measurement apparatus, comprising:
a base;
one end of the first connecting rod is rotatably connected to the base;
a second link having one end rotatably connected to the other end of the first link;
a rotary encoder provided at a junction of the first link and the second link to measure an angle between the first link and the second link;
and the ball joint is arranged at the other end of the second connecting rod and is used for connecting the fixed end of the robot.
2. The precision measuring device of claim 1, wherein the precision measuring device comprises a first rotary joint, the first link being rotatably connected to the base by the first rotary joint.
3. The precision measuring device of claim 2, wherein the first rotational joint is a two-dimensional rotational joint such that the first link is operable to rotate in a horizontal direction and a vertical direction.
4. The precision measuring device of claim 3, wherein the first rotary joint comprises a horizontal rotary bearing joint and a vertical rotary bearing joint, the horizontal rotary bearing joint being secured to the base, the vertical rotary bearing joint being attached to a sidewall of the horizontal rotary bearing joint.
5. The precision measuring device according to claim 1, wherein the precision measuring device comprises a second rotary joint, the first link and the second link are rotatably connected by the second rotary joint, and the second rotary joint is a one-dimensional rotary joint.
6. The precision measuring device of claim 5, wherein the second rotary joint is a rotary bearing joint and is coaxially sleeved with the rotary encoder.
7. The precision measuring device of claim 1, wherein the ball joint is a magnetic ball joint.
8. The precision measuring device of claim 7, wherein the ball joint comprises a magnetic ball socket and a magnetic stainless steel ball head, and the magnetic stainless steel ball head can be rotationally attached to the magnetic ball socket in any direction with 3 degrees of freedom.
9. The precision measuring device of any one of claims 1-8, wherein the first link and the second link are carbon fiber tubes.
10. A precision measuring device according to any of claims 1 to 8 wherein the base is provided with a communication interface.
CN202110865469.1A 2021-07-29 2021-07-29 Precision measuring device Pending CN113532353A (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
CN202110865469.1A CN113532353A (en) 2021-07-29 2021-07-29 Precision measuring device

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
CN202110865469.1A CN113532353A (en) 2021-07-29 2021-07-29 Precision measuring device

Publications (1)

Publication Number Publication Date
CN113532353A true CN113532353A (en) 2021-10-22

Family

ID=78089685

Family Applications (1)

Application Number Title Priority Date Filing Date
CN202110865469.1A Pending CN113532353A (en) 2021-07-29 2021-07-29 Precision measuring device

Country Status (1)

Country Link
CN (1) CN113532353A (en)

Citations (8)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
JP2010082189A (en) * 2008-09-30 2010-04-15 Olympus Corp Calibration method of manipulator in surgical manipulator system
CN104165586A (en) * 2013-05-17 2014-11-26 上海三菱电梯有限公司 Non-contact high-precision calibration method and application of workpiece coordinate system of robot
CN104991518A (en) * 2011-09-28 2015-10-21 Ur机器人有限公司 Calibration and programming of robots
CN105021144A (en) * 2015-07-08 2015-11-04 合肥泰禾光电科技股份有限公司 Industrial robot kinematics parameter calibration device and calibration method
CN106441183A (en) * 2016-11-18 2017-02-22 九江如洋精密科技有限公司 Portable probe measuring machine
CN110181558A (en) * 2019-06-20 2019-08-30 佛山市天目工业测量科技有限公司 A kind of devices and methods therefor becoming shoulder joint formula coordinate measuring machine calibration robot
CN111216138A (en) * 2020-04-09 2020-06-02 季华实验室 Robot calibration method, robot calibration system and readable storage medium
CN111771099A (en) * 2018-02-26 2020-10-13 瑞尼斯豪公司 Coordinate positioning machine

Patent Citations (8)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
JP2010082189A (en) * 2008-09-30 2010-04-15 Olympus Corp Calibration method of manipulator in surgical manipulator system
CN104991518A (en) * 2011-09-28 2015-10-21 Ur机器人有限公司 Calibration and programming of robots
CN104165586A (en) * 2013-05-17 2014-11-26 上海三菱电梯有限公司 Non-contact high-precision calibration method and application of workpiece coordinate system of robot
CN105021144A (en) * 2015-07-08 2015-11-04 合肥泰禾光电科技股份有限公司 Industrial robot kinematics parameter calibration device and calibration method
CN106441183A (en) * 2016-11-18 2017-02-22 九江如洋精密科技有限公司 Portable probe measuring machine
CN111771099A (en) * 2018-02-26 2020-10-13 瑞尼斯豪公司 Coordinate positioning machine
CN110181558A (en) * 2019-06-20 2019-08-30 佛山市天目工业测量科技有限公司 A kind of devices and methods therefor becoming shoulder joint formula coordinate measuring machine calibration robot
CN111216138A (en) * 2020-04-09 2020-06-02 季华实验室 Robot calibration method, robot calibration system and readable storage medium

Similar Documents

Publication Publication Date Title
JP5511387B2 (en) Improved joint shaft for coordinate measuring machine
JP4005921B2 (en) Industrial robot calibration apparatus, method and computer program product for calibration
CN105666490B (en) The calibration system and method for a kind of robot
KR102309861B1 (en) Method of adjusting posture of 6-axis robot
JP2000074691A (en) Planar coupler for coordinate measuring apparatus
JP2010520075A (en) Locating
TWI639494B (en) Method and apparatus for robot calibration
JPH0126833B2 (en)
CN112288823B (en) Calibration method of standard cylinder curved surface point measuring equipment
CN109211152A (en) The method for detecting accurate spherical hinge bulb eccentricity and club spatial attitude simultaneously
US5743020A (en) Three-axis continuous probe
CN113532353A (en) Precision measuring device
JP2000337807A (en) Movement error correcting method of parallel mechanism, and its apparatus
CN205497483U (en) Calibration system of robot
CN115062482B (en) Kinematic modeling method of serial robots considering positioning errors of rotary joints
CN114001622B (en) Robot movement distance measuring device and method based on double pull wire sensors
CN111220074B (en) Laser three-dimensional measurement positioning system and target determination method
JPS60155394A (en) Wrist mechanism of robot
CN112212822B (en) Method for detecting ball center space offset error of ball joint by using three-ball bar instrument
CN116448030A (en) Measurement system, control method and control device thereof, and readable storage medium
CN113664614A (en) Robot capable of realizing online high-precision measurement based on six degrees of freedom
CN214560922U (en) Non-contact type calibration device for mechanical arm workpiece
KR100264397B1 (en) Apparatus for precision measuring of six-degrees of freedom with wire
CN212779012U (en) Device for measuring ball joint ball head space displacement error by ball rod instrument
CN114459353B (en) Pipeline pose measuring device and method

Legal Events

Date Code Title Description
PB01 Publication
PB01 Publication
SE01 Entry into force of request for substantive examination
SE01 Entry into force of request for substantive examination
RJ01 Rejection of invention patent application after publication

Application publication date: 20211022

RJ01 Rejection of invention patent application after publication