CN110238848A - The calculation method of gravitational vectors under a kind of robot coordinate system - Google Patents
The calculation method of gravitational vectors under a kind of robot coordinate system Download PDFInfo
- Publication number
- CN110238848A CN110238848A CN201910461617.6A CN201910461617A CN110238848A CN 110238848 A CN110238848 A CN 110238848A CN 201910461617 A CN201910461617 A CN 201910461617A CN 110238848 A CN110238848 A CN 110238848A
- Authority
- CN
- China
- Prior art keywords
- gravitational vectors
- coordinate system
- straight line
- calculation method
- cusp
- 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.)
- Granted
Links
Classifications
-
- B—PERFORMING OPERATIONS; TRANSPORTING
- B25—HAND TOOLS; PORTABLE POWER-DRIVEN TOOLS; MANIPULATORS
- B25J—MANIPULATORS; CHAMBERS PROVIDED WITH MANIPULATION DEVICES
- B25J9/00—Programme-controlled manipulators
- B25J9/16—Programme controls
- B25J9/1602—Programme controls characterised by the control system, structure, architecture
- B25J9/1607—Calculation of inertia, jacobian matrixes and inverses
Landscapes
- Engineering & Computer Science (AREA)
- Physics & Mathematics (AREA)
- Mathematical Physics (AREA)
- Automation & Control Theory (AREA)
- Robotics (AREA)
- Mechanical Engineering (AREA)
- Manipulator (AREA)
Abstract
The present invention relates to robot dynamics' calculating field, the calculation method of gravitational vectors under specifically a kind of robot coordinate system, the specific steps of which are as follows: S1: locator markers indicate gravity direction；S2: confirmation P1；S3: confirmation P2；S4: unit of account vector；S5: gravitational vectors is calculated；Gravitational vectors direction is become intuitive visible straight line by the cord for hanging with weight using one, then using robot as the coordinate of the point on position sensor measurement straight line, and the coordinate based on these points calculates the unit vector of straight line, gravitational vectors is finally calculated according to the unit vector direction of straight line and local gravitational acceleration value, Setup Type is given dependent on user relative to traditional, can be realized the identification of gravitational vectors under any setting angle；The identification of gravitational vectors can be realized using the coordinate for measuring two or more points, it is easy to operate, select kinematics model more more accurate than kinetic model to recognize gravitational vectors, precision is higher.
Description
Technical field
The present invention relates to robot dynamics' calculating field, the calculating of gravitational vectors under specifically a kind of robot coordinate system
Method.
Background technique
With the development of robot technology, obtained based on dynamic (dynamical) correlation function such as collision detection, dragging teaching etc.
It is widely applied.Description of the setting gravitational vectors under robot coordinate system is required in such applications.Gravitational vectors is arranged
Whether accurately the effect applied to these dynamics is had a huge impact, thus how accurately to measure gravitational vectors to seem non-
It is often important.
Existing following two scheme that generallys use in the related technology determines gravitational vectors:
Scheme one: mounting means selected by user determines: user can be according to robot when using dynamics function
Mounting means selects mounting means, such as formal dress in teaching machine, and upside-down mounting is tilted a certain angle, and then controller is according to selected by
The mounting means selected calculates gravitational vectors, such as user selects formal dress, then controller thinks direction and the machine of gravitational vectors
The z-axis of device people's coordinate system is contrary, and size is gravity acceleration value.User is required to ensure selected peace in this manner
Dress mode is very accurate, but actually since the problems such as processing, assemble, measuring, user are unable to ensure selected robot peace
The accuracy of dress mode, and then it is unable to get accurate description of the gravitational vectors under robot coordinate system.And when robot is pacified
On the platform for having certain tilt angle, and when platform inclination angle is unknown, it will be unable to using the method.
Scheme two: it is determined based on kinetic model and parameter: in this manner, initially setting up the kinetic simulation of robot
Type, then operate robot change its pose constantly, and record the position of each axis under these poses, speed, acceleration with
And the information such as torque, finally gravity arrow is solved based on information such as kinetic model, kinetic parameter and the torques that collects
Measure the description under robot coordinate system.This Scheme algorithm is complex, needs accurate model parameter and establishes dynamics
Model can not be suitable for the robot of no accurate kinetic parameters.
User can only be depended on for the determination in gravitational vectors direction in scheme one to input, it can not autonomous identifying gravity motor
Amount, and scheme is second is that mathematical relationship by establishing between gravitational vectors and each axle power square, is then based on this relationship and solves gravity arrow
Amount, this Scheme algorithm is complex, and identification precision depends on the precision of model, but because of the presence of friction etc., dynamics
Generally there are large errors for model, therefore all impracticable.
Summary of the invention
To solve the above-mentioned problems, the present invention proposes a kind of calculation method of gravitational vectors under robot coordinate system.
The calculation method of gravitational vectors under a kind of robot coordinate system, the specific steps of which are as follows:
S1: locator markers indicate gravity direction；
S2: confirmation P1: the position of the cusp of the tool of actuating station is adjusted, cusp is made to be exactly in contact with the one of cord upper end
Then point records position P of the cusp of tool at this time under actuating station coordinate system1；
S3: confirmation P2: adjust the position of the tool cusp of actuating station, make cusp be exactly in contact with cord lower end a bit,
Then position P of the cusp of tool at this time under actuating station coordinate system is recorded2；
S4: unit of account vector: according to point P1And P2Coordinate calculate the unit vector direction V of straight line:
Wherein V=[vx vy vz] be straight line unit direction vector, P=[px py pz] be straight line on a bit, Δ P12
=P1-P2；
S5: it calculates gravitational vectors: after obtaining the unit vector direction of straight line, utilizing straight line unit vector direction and gravity
Direction vector is consistent, calculates gravitational vectors G:
G=gV；
Wherein g is local gravity acceleration value, and value can be obtained according to area inquiry.
As a further improvement of the present invention, the marker is body direction and gravity direction after suspension
Consistent object.
As a further improvement of the present invention, the marker is the cord that one end is connected with weight.
As a further improvement of the present invention, the measurement essence of rectilinear direction is further increased in the step S4
Degree can measure more points and be solved using least-squares algorithm, and selection three points of measurement are illustrated, and be listed below shown in formula
Equation:
The D indicates the distance vector between all measurement points, is shown below:
The least square method finds out unit vector corresponding to straight line, is shown below:
V=(DT·D)-1·DT·ΔP。
Actuating station is used as the coordinate that measuring tool removes each point on measurement straight line, is solved by the forward kinematics solution of actuating station
The position of tool cusp out, is shown below:
P=f (θ)；
Wherein P is the position of the cusp of tool, and θ is the position vector of each axis of actuating station, and f is forward kinematics solution function.
As a further improvement of the present invention, it needs the location error of actuating station accomplishing 1mm or less.
As a further improvement of the present invention, the actuating station is robot.
The beneficial effects of the present invention are: gravitational vectors direction is become intuitive by the cord that the present invention hangs with weight using one
Then visible straight line measures the coordinate of the point on straight line, and the seat based on these points using robot as position sensor
Mark calculates the unit vector of straight line, is finally calculated according to the unit vector direction of straight line and local gravitational acceleration value
Gravitational vectors gives Setup Type dependent on user relative to traditional, and the present invention can be realized gravity under any setting angle
The identification of vector；The identification of gravitational vectors can be realized using the coordinate for measuring two or more points, easy to operate, selection is than dynamic
Mechanical model more accurate kinematics model recognizes gravitational vectors, and precision is higher.
Detailed description of the invention
Present invention will be further explained below with reference to the attached drawings and examples.
Fig. 1 is the structural diagram of the present invention.
Specific embodiment
In order to be easy to understand the technical means, the creative features, the aims and the efficiencies achieved by the present invention, below it is right
The present invention is further described.
As shown in Figure 1, a in figure is gravity direction, the calculation method of gravitational vectors, tool under a kind of robot coordinate system
Steps are as follows for body:
S1: locator markers 4 indicate gravity direction；
S2: confirmation P1: the position of the cusp of the tool 3 of adjustment actuating station 1 makes cusp be exactly in contact with 4 upper end of marker
A bit, then record position P of the cusp of tool 3 at this time under actuating station coordinate system1；
S3: confirmation P2: the position of 3 cusp of tool of adjustment actuating station 1 makes cusp be exactly in contact with 4 lower end of marker
A bit, position P of the cusp of tool 3 at this time under actuating station coordinate system is then recorded2；
S4: unit of account vector: according to point P1And P2Coordinate calculate the unit vector direction V of straight line:
Wherein V=[vx vy vz] be straight line unit direction vector, P=[px py pz] be straight line on a bit, Δ P12
=P1-P2；
S5: it calculates gravitational vectors: after obtaining the unit vector direction of straight line, utilizing straight line unit vector direction and gravity
Direction vector is consistent, calculates gravitational vectors G:
G=gV；
Wherein g is local gravity acceleration value, and value can be obtained according to area inquiry.
The tool 3 is the object of any bar shaped or the fixed shape of Else Rule with cusp.
The marker 4 is body direction and the consistent object of gravity direction after suspension.
The marker 4 is the cord that one end is connected with weight 5.
For marker 4, because of its light weight, flexibility is high, can be straightened under the action of weight 5, be known according to physics
Know it is found that the direction that rear rope length is straightened of marker 4 is consistent with the direction of gravitational vectors, thus can pass through direct measurement markers object
4 length direction determines the direction of gravitational vectors.
Gravitational vectors direction is become intuitive visible straight line by the marker 4 for hanging with weight using one, then utilizes machine
Coordinate of the device people 1 as the point on position sensor measurement straight line, and the coordinate based on these points calculates the Unit Vector of straight line
Amount, is finally calculated gravitational vectors according to the unit vector direction of straight line and local gravitational acceleration value, relative to tradition
Give Setup Type dependent on user, the present invention can be realized the identification of gravitational vectors under any setting angle.
The measurement accuracy that rectilinear direction is further increased in the step S4 can measure more points and using most
Small two multiplication algorithm solves, and selection three points of measurement are illustrated, and is listed below equation shown in formula:
The D indicates the distance vector between all measurement points, is shown below:
The least square method finds out unit vector corresponding to straight line, is shown below:
V=(DT·D)-1·DT·ΔP。
Actuating station 1 is used as the coordinate that measuring tool removes each point on measurement straight line, is asked by the forward kinematics solution of actuating station 1
Solution comes out the position of tool tip point, is shown below:
P=f (θ)；
Wherein P is the position of the cusp of tool 3, and θ is the position vector of each axis of actuating station, and f is forward kinematics solution function.
The location error by actuating station 1 is needed to accomplish 1mm or less.
The actuating station 1 is robot.
The label 2 of Fig. 1 is the mounting platform of robot 1.
The unit direction vector of arbitrary line can be determined by two points on measurement straight line in space, in the present invention
Two o'clock be respectively P1、P2。
The identification of gravitational vectors can be realized using the coordinate for measuring two or more points, easy to operate, power is compared in selection
The more accurate kinematics model of model is learned to recognize gravitational vectors, precision is higher.
The basic principles, main features and advantages of the present invention have been shown and described above.The technology of the industry
Personnel are it should be appreciated that the present invention is not limited to the above embodiments, and what is described in the above embodiment and the description is only the present invention
Principle, without departing from the spirit and scope of the present invention, various changes and improvements may be made to the invention, these variation and
Improvement all fall within the protetion scope of the claimed invention.The claimed scope of the invention is imitated by appended claims and its class
Object defines.
Claims (9)
1. the calculation method of gravitational vectors under a kind of robot coordinate system, it is characterised in that: the specific steps of which are as follows:
S1: locator markers (4) indicate gravity direction；
S2: confirmation P1: the position of the cusp of the tool (3) of adjustment actuating station (1) makes cusp be exactly in contact with marker (4) upper end
A bit, then record position P of the cusp of tool (3) at this time under actuating station coordinate system1；
S3: confirmation P2: the position of tool (3) cusp of adjustment actuating station (1) makes cusp be exactly in contact with marker (4) lower end
A bit, position P of the cusp of tool (3) at this time under actuating station coordinate system is then recorded2；
S4: unit of account vector: according to point P1And P2Coordinate calculate the unit vector direction V of straight line:
Wherein V=[vx vy vz] be straight line unit direction vector, P=[px py pz] be straight line on a bit, Δ P12=P1-
P2；
S5: it calculates gravitational vectors: after obtaining the unit vector direction of straight line, utilizing straight line unit vector direction and gravitational vectors
Direction is consistent, calculates gravitational vectorsG:
G=gV；
Wherein g is local gravity acceleration value, and value can be obtained according to area inquiry.
2. the calculation method of gravitational vectors under a kind of robot coordinate system according to claim 1, it is characterised in that: described
Marker (4) be body direction and the consistent object of gravity direction after suspension.
3. the calculation method of gravitational vectors under a kind of robot coordinate system according to claim 1, it is characterised in that: described
Marker (4) is the cord that one end is connected with weight (5).
4. the calculation method of gravitational vectors under a kind of robot coordinate system according to claim 1, it is characterised in that: described
Step S4 in order to further increase the measurement accuracy of rectilinear direction, more points can be measured and asked using least-squares algorithm
Solution, selection three points of measurement are illustrated, and are listed below equation shown in formula:
5. the calculation method of gravitational vectors under a kind of robot coordinate system according to claim 4, it is characterised in that: described
D indicate the distance vector between all measurement points, be shown below:
6. the calculation method of gravitational vectors under a kind of robot coordinate system according to claim 5, it is characterised in that: described
Least square method find out unit vector corresponding to straight line, be shown below:
V=(DT·D)-1·DT·ΔP。
7. the calculation method of gravitational vectors under a kind of robot coordinate system according to claim 6, it is characterised in that: will hold
Row end (1) is used as the coordinate that measuring tool removes each point on measurement straight line, is solved by the forward kinematics solution of actuating station (1) come work
Have the position of cusp, be shown below:
P=f (θ)；
Wherein P is the position of the cusp of tool (3), and θ is the position vector of each axis of actuating station, and f is forward kinematics solution function.
8. the calculation method of gravitational vectors under a kind of robot coordinate system according to claim 7, it is characterised in that: need
The location error of actuating station (1) is accomplished into 1mm or less.
9. the calculation method of gravitational vectors under a kind of robot coordinate system according to claim 1 to 8, special
Sign is: the actuating station (1) is robot.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201910461617.6A CN110238848B (en) | 2019-05-30 | 2019-05-30 | Method for calculating gravity vector under robot coordinate system |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201910461617.6A CN110238848B (en) | 2019-05-30 | 2019-05-30 | Method for calculating gravity vector under robot coordinate system |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| CN110238848A true CN110238848A (en) | 2019-09-17 |
| CN110238848B CN110238848B (en) | 2022-07-05 |
Family
ID=67885314
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN201910461617.6A Active CN110238848B (en) | 2019-05-30 | 2019-05-30 | Method for calculating gravity vector under robot coordinate system |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN110238848B (en) |
Cited By (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN112476435A (en) * | 2020-11-25 | 2021-03-12 | 北京配天技术有限公司 | Calibration method and calibration device for gravity acceleration direction and storage medium |
| CN113492398A (en) * | 2020-04-02 | 2021-10-12 | 北京配天技术有限公司 | Calibration rod, calibration system for gravity acceleration direction and calibration method thereof |
Citations (18)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| JPH05237782A (en) * | 1992-02-26 | 1993-09-17 | Daikin Ind Ltd | Work holding position setting method and device thereof |
| US6442439B1 (en) * | 1999-06-24 | 2002-08-27 | Sandia Corporation | Pendulation control system and method for rotary boom cranes |
| JP2008002867A (en) * | 2006-06-21 | 2008-01-10 | Toyota Motor Corp | Attitude angle determining apparatus and determining method for the same |
| US20100138030A1 (en) * | 2006-10-19 | 2010-06-03 | Abb Ag | System and method for calibrating a handling device |
| CN102175185A (en) * | 2011-01-20 | 2011-09-07 | 中南大学 | Fiber bragg grating tilt sensor and calibrating method thereof |
| CN102990642A (en) * | 2011-09-09 | 2013-03-27 | 发那科株式会社 | Robot having workpiece mass measurement function |
| CN103019096A (en) * | 2012-11-23 | 2013-04-03 | 北京理工大学 | Humanoid robot inverse dynamics controller based on acceleration optimization |
| CN103018784A (en) * | 2012-11-28 | 2013-04-03 | 华中科技大学 | Simple-pendulum absolute gravimeter based on two-point fixed differential measurement |
| CN103482089A (en) * | 2013-10-09 | 2014-01-01 | 北京航空航天大学 | Design method of unrestricted suspension type initiative gravity compensation system |
| CN103814279A (en) * | 2011-09-20 | 2014-05-21 | 株式会社石田 | Mass measurement device |
| CN103808461A (en) * | 2012-11-14 | 2014-05-21 | 陈均钧 | Device for measuring rotational inertia of rigid body through magnetic suspension rotating platform |
| CN104057290A (en) * | 2014-06-24 | 2014-09-24 | 中国科学院自动化研究所 | Method and system for assembling robot based on visual sense and force feedback control |
| CN104443448A (en) * | 2014-10-27 | 2015-03-25 | 清华大学 | Cable drive robot device for simulating zero-gravity and low-gravity environment |
| CN105447856A (en) * | 2015-11-17 | 2016-03-30 | 天津工业大学 | Marking point coupling method based on robot motion parameters and characteristic vectors |
| CN105606127A (en) * | 2016-01-11 | 2016-05-25 | 北京邮电大学 | Calibration method for relative attitude of binocular stereo camera and inertial measurement unit |
| CN108463314A (en) * | 2016-01-11 | 2018-08-28 | 库卡德国有限公司 | Determination of the robot relative to the orientation of gravity direction |
| CN109211174A (en) * | 2017-07-06 | 2019-01-15 | 中国航空制造技术研究院 | A kind of space vector guy-rope measuring method and device |
| CN109520486A (en) * | 2019-01-02 | 2019-03-26 | 中国船舶重工集团公司第七0七研究所 | A kind of deviation of plumb line real-time computing technique based on horizontal tensor gravity gradient |
-
2019
- 2019-05-30 CN CN201910461617.6A patent/CN110238848B/en active Active
Patent Citations (18)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| JPH05237782A (en) * | 1992-02-26 | 1993-09-17 | Daikin Ind Ltd | Work holding position setting method and device thereof |
| US6442439B1 (en) * | 1999-06-24 | 2002-08-27 | Sandia Corporation | Pendulation control system and method for rotary boom cranes |
| JP2008002867A (en) * | 2006-06-21 | 2008-01-10 | Toyota Motor Corp | Attitude angle determining apparatus and determining method for the same |
| US20100138030A1 (en) * | 2006-10-19 | 2010-06-03 | Abb Ag | System and method for calibrating a handling device |
| CN102175185A (en) * | 2011-01-20 | 2011-09-07 | 中南大学 | Fiber bragg grating tilt sensor and calibrating method thereof |
| CN102990642A (en) * | 2011-09-09 | 2013-03-27 | 发那科株式会社 | Robot having workpiece mass measurement function |
| CN103814279A (en) * | 2011-09-20 | 2014-05-21 | 株式会社石田 | Mass measurement device |
| CN103808461A (en) * | 2012-11-14 | 2014-05-21 | 陈均钧 | Device for measuring rotational inertia of rigid body through magnetic suspension rotating platform |
| CN103019096A (en) * | 2012-11-23 | 2013-04-03 | 北京理工大学 | Humanoid robot inverse dynamics controller based on acceleration optimization |
| CN103018784A (en) * | 2012-11-28 | 2013-04-03 | 华中科技大学 | Simple-pendulum absolute gravimeter based on two-point fixed differential measurement |
| CN103482089A (en) * | 2013-10-09 | 2014-01-01 | 北京航空航天大学 | Design method of unrestricted suspension type initiative gravity compensation system |
| CN104057290A (en) * | 2014-06-24 | 2014-09-24 | 中国科学院自动化研究所 | Method and system for assembling robot based on visual sense and force feedback control |
| CN104443448A (en) * | 2014-10-27 | 2015-03-25 | 清华大学 | Cable drive robot device for simulating zero-gravity and low-gravity environment |
| CN105447856A (en) * | 2015-11-17 | 2016-03-30 | 天津工业大学 | Marking point coupling method based on robot motion parameters and characteristic vectors |
| CN105606127A (en) * | 2016-01-11 | 2016-05-25 | 北京邮电大学 | Calibration method for relative attitude of binocular stereo camera and inertial measurement unit |
| CN108463314A (en) * | 2016-01-11 | 2018-08-28 | 库卡德国有限公司 | Determination of the robot relative to the orientation of gravity direction |
| CN109211174A (en) * | 2017-07-06 | 2019-01-15 | 中国航空制造技术研究院 | A kind of space vector guy-rope measuring method and device |
| CN109520486A (en) * | 2019-01-02 | 2019-03-26 | 中国船舶重工集团公司第七0七研究所 | A kind of deviation of plumb line real-time computing technique based on horizontal tensor gravity gradient |
Non-Patent Citations (2)
| Title |
|---|
| WEIFU WANG;DMITRY BERENSON;DEVIN BALKCOM: "An online method for tight-tolerance insertion tasks for string and rope", 《ROBOTICS AND AUTOMATION》, 2 July 2015 (2015-07-02) * |
| 宋韬: "轮式移动机械臂倾覆与滑移问题研究", 《中国博士学位论文全文数据库 (信息科技辑)》, no. 02, 15 February 2017 (2017-02-15) * |
Cited By (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN113492398A (en) * | 2020-04-02 | 2021-10-12 | 北京配天技术有限公司 | Calibration rod, calibration system for gravity acceleration direction and calibration method thereof |
| CN112476435A (en) * | 2020-11-25 | 2021-03-12 | 北京配天技术有限公司 | Calibration method and calibration device for gravity acceleration direction and storage medium |
Also Published As
| Publication number | Publication date |
|---|---|
| CN110238848B (en) | 2022-07-05 |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| CN106370189B (en) | Indoor navigation device and method based on multi-sensor fusion | |
| CN102990642B (en) | Robot having workpiece mass measurement function | |
| KR100843096B1 (en) | Apparatus and method for distinguishing the movement state of moving robot | |
| CN108638053A (en) | A kind of detection method and its antidote of robot skidding | |
| CN104458124B (en) | A kind of centroid measurement method | |
| CN106125548A (en) | Industrial robot kinetic parameters discrimination method | |
| US20220314445A1 (en) | Kinematics model-free trajectory tracking method for robotic arms and robotic arm system | |
| CN111624941A (en) | Unknown environment-oriented six-degree-of-freedom robot power control method | |
| CN109099913B (en) | Wearable navigation device and method based on MEMS inertial device | |
| CN111360820B (en) | Distance space and image feature space fused hybrid visual servo method | |
| KR102285631B1 (en) | System and method for collision recognition using robot skin | |
| CN106153069A (en) | Attitude rectification apparatus and method in autonomous navigation system | |
| CN110238848A (en) | The calculation method of gravitational vectors under a kind of robot coordinate system | |
| CN114054302B (en) | Accurate positioning control method and system of dispenser | |
| CN102768006A (en) | Method for automatically measuring and adjusting large-curvature curve part in normal direction | |
| CN110561424A (en) | online robot kinematic calibration method based on multi-sensor hybrid filter | |
| CN104215229A (en) | RTK device adjusting method, RTK device adjusting system and RTK measuring method | |
| CN109583067B (en) | Design method of high-speed aircraft transition position measurement sensor based on temperature balance | |
| CN110967522B (en) | Wind field gradient measuring method | |
| CN105740482B (en) | A kind of pump load torque model method for building up and analogue system | |
| CN103391871B (en) | For the method and apparatus determining the obliquity of vehicle | |
| CN113799130B (en) | Robot pose calibration method in man-machine cooperation assembly | |
| CN101720422A (en) | Method for compensating for temperature measurement error in a sond. | |
| CN105588512B (en) | The measuring device and method of class rectangle tunnel tunnel segment component size | |
| TWI402489B (en) | Method for measuring inclination angle of plane via electronic device |
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 | ||
| GR01 | Patent grant | ||
| GR01 | Patent grant |