CN109129427B - Plane parallel mechanism device driven by double five-rod mechanism and control method - Google Patents
Plane parallel mechanism device driven by double five-rod mechanism and control method Download PDFInfo
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- CN109129427B CN109129427B CN201811157610.7A CN201811157610A CN109129427B CN 109129427 B CN109129427 B CN 109129427B CN 201811157610 A CN201811157610 A CN 201811157610A CN 109129427 B CN109129427 B CN 109129427B
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- B—PERFORMING OPERATIONS; TRANSPORTING
- B25—HAND TOOLS; PORTABLE POWER-DRIVEN TOOLS; MANIPULATORS
- B25J—MANIPULATORS; CHAMBERS PROVIDED WITH MANIPULATION DEVICES
- B25J9/00—Programme-controlled manipulators
- B25J9/003—Programme-controlled manipulators having parallel kinematics
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- B—PERFORMING OPERATIONS; TRANSPORTING
- B25—HAND TOOLS; PORTABLE POWER-DRIVEN TOOLS; MANIPULATORS
- B25J—MANIPULATORS; CHAMBERS PROVIDED WITH MANIPULATION DEVICES
- B25J13/00—Controls for manipulators
- B25J13/08—Controls for manipulators by means of sensing devices, e.g. viewing or touching devices
- B25J13/088—Controls for manipulators by means of sensing devices, e.g. viewing or touching devices with position, velocity or acceleration sensors
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- 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
- B25J9/1605—Simulation of manipulator lay-out, design, modelling of manipulator
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- Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
- Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
- Y02P—CLIMATE CHANGE MITIGATION TECHNOLOGIES IN THE PRODUCTION OR PROCESSING OF GOODS
- Y02P90/00—Enabling technologies with a potential contribution to greenhouse gas [GHG] emissions mitigation
- Y02P90/02—Total factory control, e.g. smart factories, flexible manufacturing systems [FMS] or integrated manufacturing systems [IMS]
Abstract
The invention discloses a plane parallel mechanism device driven by a double five-rod mechanism and a control method, comprising a parallel mechanism body part, a detection part and a control part; the parallel mechanism body part comprises two plane five-rod mechanisms, a movable platform and a static platform, and a laser displacement sensor is arranged on the static platform and is used for measuring displacement and gesture information of the movable platform; the magnetic grid ruler sensor is used for measuring the position information of the motor; after being processed by a computer, the control signal is output to control the movement of the linear motor, so as to control the movement of the brake platform. The device takes two five-rod mechanisms as driving branched chains, eliminates the influence of gaps on a system, and utilizes the laser displacement sensor to perform position closed-loop feedback, so that the device has the advantages of high positioning precision, quick closed-loop control response, good control performance and the like.
Description
Technical Field
The invention relates to the field of control of plane parallel mechanisms, in particular to a plane parallel mechanism device driven by a double-five-rod mechanism and a control method.
Background
The parallel robot is characterized in that the end effector with a plurality of degrees of freedom is connected with a fixed foundation through two or more independent movement branched chains, and compared with a serial robot, the parallel robot has the advantages of high rigidity, high precision, high bearing capacity and the like, and is mainly applied to occasions with high rigidity, high precision, high movement speed, good dynamic characteristics, flexible operation and small requirements on working space, such as aerospace, manufacturing equipment, precision measurement and precision positioning fields. In order to improve industrial productivity and save energy, modern machines are continuously developed towards light weight, low energy consumption, high efficiency and the like, and light weight, high speed, high acceleration and high precision parallel robots are beginning to get attention of many researchers and engineers.
The driving modes of the current parallel mechanism mainly comprise direct driving motor direct driving, servo motor driving, hydraulic driving, pneumatic driving, novel driving devices and the like. Along with the progress of technology, the speed and the precision of the mechanism are required to be higher and higher, and the driving mode of the traditional motor acceleration and deceleration device increases the motion inertia of the mechanism due to the fact that the mass of the deceleration device is generally larger, so that the response speed of the mechanism is reduced. The speed reducer often has backlash which is difficult to eliminate, has great influence on the transmission precision of the mechanism, and friction existing in the speed reducer also can bring about energy loss.
The linear motor has the advantages of simple structure, no need of a motion conversion mechanism, small motion inertia, high dynamic response performance and high positioning precision; the linear motor has no mechanical contact during movement, no friction and noise, and can realize very high-speed and very low-speed movement; compared with other screw rods, synchronous belts and gear rack drives, the linear motor drive can obtain high acceleration.
Disclosure of Invention
In order to overcome the defects and shortcomings in the prior art, the invention provides a plane parallel mechanism device driven by a double-five-rod mechanism and a control method, so that the plane three-degree-of-freedom parallel mechanism moves more flexibly and rapidly, and the precise positioning of the plane three-degree-of-freedom parallel mechanism is realized.
The invention adopts the following technical scheme:
a plane parallel mechanism device driven by a double five-rod mechanism comprises a parallel mechanism body part, a detection part and a control part;
the parallel mechanism body part comprises two planar five-rod mechanisms, a movable platform and a static platform, wherein the movable platform is arranged on the static platform and comprises an equilateral triangle platform and a parallelogram platform, the parallelogram platform is arranged on the static platform, the equilateral triangle platform is arranged above the parallelogram platform, the two planar five-rod mechanisms have the same structure and comprise two rigid driven rod body units, the two rigid driven rod body units have the same structure and comprise rigid driven rods, a linear motor and a linear moving unit, one end of each rigid driven rod is arranged on the linear moving unit, the other end of each rigid driven rod is connected with one corner of the parallelogram platform through a rotating shaft to form a composite hinge, and the linear motor drives the linear moving unit to move;
the detection part comprises three laser detection heads and a magnetic grating ruler displacement sensor, wherein the three laser detection heads are fixed on the static platform, and laser of the laser detection heads is beaten on the equilateral triangle platform;
the magnetic grating ruler displacement sensor is arranged on the rigid driven rod body unit and used for measuring the position information of the linear motor;
the control part comprises a linear motor servo unit, a motion control card, a laser displacement sensor controller, a data acquisition card and a computer;
the linear motor and the magnetic grating ruler displacement sensor are connected with the linear motor servo unit in a speed control or position control mode, the linear motor servo unit is connected with the motion control card, the motion control card is connected with the computer, the laser displacement sensor detects displacement information and posture information of the movable platform, the displacement information and the posture information are output to the data acquisition card through the laser displacement sensor controller and then input to the computer, the computer obtains control quantity, and the control quantity further drives the linear motor to move through the motion control card and the linear motor servo unit to control the movable platform to move to a designated position according to an expected track.
Two laser detection heads in the three laser detection heads are positioned on the right side of the movable platform, the third laser detection head is arranged above the movable platform, and the two laser detection heads on the right side are arranged in parallel.
The linear moving unit comprises a linear guide rail, a sliding block and a connecting plate, wherein the linear guide rail and a stator of the linear motor are arranged on a motor base, the connecting plate is fixed on the sliding block, and the sliding block moves on the linear guide rail.
One of the two rigid driven rod body units is arranged above the parallelogram platform, and the other rigid driven rod body unit is arranged below the parallelogram platform.
The magnetic grating ruler displacement sensor comprises a magnetic pick-up head and a magnetic ruler, wherein the magnetic pick-up head is fixed on the connecting plate, and the magnetic ruler is arranged on the motor base.
The device has three degrees of freedom, specifically two degrees of freedom in the horizontal direction and one degree of freedom in the rotational direction.
A control method of a plane parallel mechanism device driven by a double five-rod mechanism comprises the following steps:
firstly, a computer performs kinematic inverse solution according to a given track, a target position and a moving platform posture to obtain the output quantity of each linear motor, and outputs the output quantity to a linear motor servo unit through a motion control card to control a linear motor rotor to move so as to drive a platform to move;
step two, in the moving process of the movable platform, the laser probe heads arranged around the movable platform measure the position information and the attitude information of the movable platform in real time, and the position information and the attitude information are output to a data acquisition card through a laser displacement sensor controller, are subjected to A/D conversion and then are transmitted to a computer;
the magnetic grid ruler position sensor measures the position information of the linear motor rotor in real time, transmits the information to the linear motor servo unit, and then transmits the information to the computer through the motion control card;
and thirdly, calculating a control signal by the computer according to the feedback information obtained in the second step, outputting the control signal to the linear motor servo unit through the motion control card, driving the linear motor rotor to move, and further controlling the movable platform to move according to a desired track and move to a designated position in a desired gesture.
Step two, position information and attitude information of the movable platform are obtained, and the method specifically comprises the following steps:
let the coordinate of the first laser probe be P 1 (x 1 ,y 1 ) The coordinate of the second laser detecting head is P 2 (x 2 ,y 2 ) The coordinate of the first laser detecting head is P 3 (x 3 ,y 3 ) The side length of the triangle on the upper part of the movable platform 12 is a,
the rotation angle of the movable platform is:
the position of the center of the movable platform along the x direction is as follows:
the position of the center of the movable platform along the y direction is as follows:
wherein the method comprises the steps of
The invention has the beneficial effects that:
(1) The invention adopts the linear motor to drive, does not contain a speed reducer, eliminates the influence of a transmission mechanism, has small friction, stable and quick movement in the driving process, and adopts the high-precision magnetic grid ruler as a position feedback unit, so that the driving and control effects are better;
(2) The invention adopts three laser displacement sensors to measure the position information and the attitude information of the movable platform, is a non-contact measurement mode, does not change the structure of the device, does not increase additional mass, has high measurement precision and quick response, and the whole system forms a full-closed loop feedback circuit, and the feedback information is used for designing a control algorithm so as to realize the precise positioning control of the platform;
(3) The invention adopts two five-rod mechanisms as driving branched chains, which can also be called a plane two-degree-of-freedom parallel mechanism, and the kinematic forward and reverse solutions are relatively easy, so that the kinematic forward and reverse solutions of the whole plane parallel mechanism are simpler, the operation performance of the mechanism is improved, but the degree of freedom of a terminal platform is not lost;
(4) The invention has three degrees of freedom, namely two degrees of freedom in the horizontal direction and one degree of freedom in the rotating direction, and four driving motors, so that driving redundancy is formed, the redundancy of the mechanism is increased, and the control is more flexible;
(5) The device adopts two composite hinges, so that the installation difficulty can be increased, and the precision can be reduced due to errors;
(6) The invention adopts four sets of servo motor systems, and the tail end platform has only three degrees of freedom, so that drive redundancy is formed, the control is more flexible, and the cost of the whole mechanism is increased.
Drawings
FIG. 1 is a schematic diagram of the structure of the present invention;
FIG. 2 is a top view of FIG. 1;
FIG. 3 is a right side view of FIG. 1;
FIG. 4 is a schematic diagram of a driving arm of a five-bar mechanism in the present embodiment
FIG. 5 is a diagram of a dynamic platform position solution according to the present embodiment;
FIG. 6 is a schematic diagram of the structure of the laser displacement sensor in the present embodiment;
fig. 7 is a schematic diagram of a solution for the position and posture information of the moving platform in this embodiment.
Detailed Description
The present invention will be described in further detail with reference to examples and drawings, but embodiments of the present invention are not limited thereto.
Examples
As shown in fig. 1-6, a planar parallel mechanism device driven by a double five-rod mechanism and a control method thereof, wherein hardware equipment comprises a parallel mechanism body part, a detection part and a control part;
the parallel mechanism body part comprises two plane five-rod mechanisms, a movable platform 12 and a static platform 1, wherein the static platform 1 is a square section bar seat and is used as an experiment table for supporting the whole device. The movable platform 12 is divided into two parts, the lower part is a parallelogram platform, two bearing holes are formed at the upper and lower diagonal positions, the movable platform is connected with each driving branched chain through a rotating shaft, and the upper part is an equilateral triangle platform.
The two plane five-rod mechanisms are identical in structure and comprise two rigid driven rod body units, the two rigid driven rod body units are identical in structure and comprise rigid driven rods, a linear motor, a linear guide rail 4, a sliding block 6 and a connecting plate, the linear motor is fixed on a motor base 2, a stator 3 of the linear motor and the linear guide rail 4 are fixed on the motor base 2 through bolts, the upper surface of the sliding block on the linear guide rail is in the same plane with a rotor 5 of the linear motor and is fixed with the connecting plate 7 through screws respectively, and therefore the rotor 5, the sliding block 6 and the connecting plate 7 of the linear motor can be guaranteed to be integrated and move together; at the center of each connecting plate 7, a bearing seat 8 is fixedly arranged through a bolt, the rotating shaft end of a shaft sleeve 9 is inserted into the bearing seat 8, one ends of two rigid driven rods are fixed together with the sleeve end through bolts, the other ends of the two rigid driven rods and one bottom corner of a parallelogram platform of a movable platform 12 form a composite hinge through the rotating shaft, two rigid driven rods 10 and 11 are respectively positioned above and below the parallelogram platform, and two rigid driven rod body units are respectively positioned on two opposite angles of the parallelogram platform. Each plane five-rod mechanism is driven by two linear motors, and a rotor 5 of each linear motor drives a sliding block 6 and a connecting plate 7 to integrally move, so that a movable rigid driven rod is driven to move, and finally a movable platform 12 is driven to move to a designated position.
The detection part comprises three laser detection heads 16 and a magnetic grating ruler displacement sensor, wherein the three laser detection heads are fixed on an adjusting bracket 17, the adjusting bracket 17 can adjust the height of the laser detection heads 16, and the laser can strike the upper triangle part of the movable platform 12; the adjusting brackets are fixed on the static platform, wherein two laser detecting heads 16 are positioned on the right side of the movable platform 12, the third laser detecting head is positioned in front of the movable platform 12, two adjusting brackets 17 on the right side are parallel and horizontally arranged, and the front adjusting brackets are vertically arranged 17; the laser displacement sensor can accurately measure the displacement information and the posture information of the movable platform 12.
The center of the static platform is the origin of coordinates, an XY axis coordinate system is established, the right side is the positive X axis direction, and the front side is the positive Y axis direction.
The displacement sensor of the magnetic grating ruler comprises a magnetic pick-up head and a magnetic scale, wherein the magnetic pick-up head 14 is fixed with the connecting plate 7 through a connecting block 15, the magnetic scale 13 is arranged on the motor base 2, and the magnetic grating ruler can accurately measure the position information of the linear motor rotor in the process that the magnetic pick-up head 14 moves along with the linear motor rotor 5.
The control part comprises a linear motor servo unit 18, a motion control card 19, a laser displacement sensor controller 20, a data acquisition card 21 and a computer 22;
the linear motor and the magnetic grating ruler are connected to the linear motor servo unit 18 in a speed control or position control mode, the linear motor servo unit 18 is connected with the motion control card 19, and the magnetic grating ruler feeds back position information to the linear motor servo unit 18 and then transmits the position information to the computer 22 through the motion control card 19; the displacement information and the gesture information of the movable platform 12 detected by the laser detector head are output to a data acquisition card 21 through a laser displacement sensor controller 20, are subjected to A/D conversion and then are transmitted to a computer 22; the computer 22 runs the corresponding algorithm according to the feedback information before and then sends out the corresponding control quantity, and the control quantity is transmitted to the linear motor servo unit 18 through the motion control card 19 to drive the linear motor rotor to move, so that the movable platform is controlled to move to a designated position according to the expected track.
Compared with a plane 3-RRR parallel mechanism, the three parallel branched chains are replaced by two five-rod mechanisms, but the degree of freedom of the mechanism is not changed; the device still has three degrees of freedom, namely two degrees of freedom in the horizontal direction and one degree of freedom in the rotating direction, and four driving motors are arranged, so that driving redundancy is formed, the redundancy of the mechanism is increased, and the control is more flexible.
The linear motor is used as a driver, and the problems of friction force, clearance, nonlinearity and the like are reduced without passing through intermediate transmission mechanisms such as a speed reducer and the like, so that the motion control precision and response speed of the mechanism are greatly improved.
The working process of the invention comprises the following steps:
firstly, a computer performs kinematic inverse solution according to a given track, a target position and a moving platform posture to obtain the output quantity of each linear motor, and outputs the output quantity to a linear motor servo unit through a motion control card to control a linear motor rotor to move so as to drive a platform to move;
step two, in the moving process of the movable platform, the laser probe heads arranged around the movable platform measure the position information and the attitude information of the movable platform in real time, and the position information and the attitude information are output to a data acquisition card through a laser displacement sensor controller, are subjected to A/D conversion and then are transmitted to a computer;
the magnetic grid ruler position sensor measures the position information of the linear motor rotor in real time, transmits the information to the linear motor servo unit, and then transmits the information to the computer through the motion control card;
and thirdly, calculating a control signal by the computer according to the feedback information obtained in the second step, outputting the control signal to the linear motor servo unit through the motion control card, driving the linear motor rotor to move, and further controlling the movable platform to move according to a desired track and move to a designated position in a desired gesture.
And step four, repeated test is carried out, and control parameters are modified, so that the control precision reaches the expected requirement.
In the second step, the position information and the posture information of the moving platform are obtained, as shown in fig. 7, specifically:
let the coordinate of the first laser probe be P 1 (x 1 ,y 1 ) The coordinate of the second laser detecting head is P 2 (x 2 ,y 2 ) The coordinate of the first laser detecting head is P 3 (x 3 ,y 3 ) The side length of the triangle on the upper part of the movable platform 12 is a,
the rotation angle of the movable platform is:
the position of the center of the movable platform along the x direction is as follows:
the position of the center of the movable platform along the y direction is as follows:
wherein the method comprises the steps of
The attitude information, namely, the center point coordinates (x G ,y G ) And a rotation angle alpha.
The dashed connection in fig. 1 represents a connection diagram of the electrical signal to the detection drive control, the directional arrow indicating the direction of transmission of the detection and control signal flow.
In this embodiment:
the static platform is formed by assembling three aluminum profiles with the lengths of 1200mm, 1200mm and 1000mm respectively, the table top is a 1320mm multiplied by 10mm stainless steel plate, the static platform is connected with the profiles through screws, and angle irons are fixed at each connecting position of the profiles.
The magnetic grating ruler is selected from Italy GIVI magnetic grating ruler, the magnetic head type is MTSH2C0528VL, the scale magnetic grating type is MP200, the precision of the magnetic grating ruler is 40 μm, the power supply voltage is 5-28V, and the output is LINE-DRIVER.
The linear motor can be a WMU series U-shaped vertical linear motor produced by Zhengzhou micro-nano technology limited company, the rated output force is 90N, and the maximum running speed is 2.5m/s.
The motion control card used was PMAC2 of the PMAC card series from DELTA TAU company, usa. First, the drive mode, electronic gear ratio, and also PMAC2 card I variables are configured. The motion mode used is a position control mode. The driver load is set to a corresponding value of 1, the stiffness is neutral, and the value is 3. The electronic gear ratio is set to 0.04 ° for each pulse corresponding to the motor rotation.
The laser detector and the laser displacement sensor controller are a series of laser displacement sensors manufactured by Japanese Kienshi company, the laser detector is LK-G500, the diffuse reflection type installation of the triangulation method is realized, the wavelength of the visible red semiconductor laser is 655mm, the reference distance is 500mm, the measuring range is 100mm to 4 μm, the linearity is FS (FS=100 mm) with 0.05 percent of the measuring reproducibility, and the sampling period can be selected in each grade. The model of the laser displacement sensing controller is LK-G300lV, the output range of analog voltage is-10V to 10V, and the laser displacement sensing controller has the functions of synchronous measurement function, operation function, averaging function, filtering function, calibration function, auto-zero function, sampling rate setting and the like of two laser detection heads
The model of the data acquisition card is PCI-8193 produced by Beijing Altai technology Co., ltd, and the analog input range is-10V to +10V.
The CPU model of the selected computer is intel-Core i74790, the frequency is 3.6Hz, and the memory is 4G.
The embodiments described above are preferred embodiments of the present invention, but the embodiments of the present invention are not limited to the embodiments described above, and any other changes, modifications, substitutions, combinations, and simplifications that do not depart from the spirit and principles of the present invention should be made in the equivalent manner, and are included in the scope of the present invention.
Claims (6)
1. The plane parallel mechanism device driven by the double five-rod mechanism is characterized by comprising a parallel mechanism body part, a detection part and a control part;
the parallel mechanism body part comprises two planar five-rod mechanisms, a movable platform and a static platform, wherein the movable platform is arranged on the static platform and comprises an equilateral triangle platform and a parallelogram platform, the parallelogram platform is arranged on the static platform, the equilateral triangle platform is arranged above the parallelogram platform, the two planar five-rod mechanisms have the same structure and comprise two rigid driven rod body units, the two rigid driven rod body units have the same structure and comprise rigid driven rods, a linear motor and a linear moving unit, one end of each rigid driven rod is arranged on the linear moving unit, the other end of each rigid driven rod is connected with one corner of the parallelogram platform through a rotating shaft to form a composite hinge, and the linear motor drives the linear moving unit to move;
the detection part comprises three laser detection heads and a magnetic grating ruler displacement sensor, wherein the three laser detection heads are fixed on the static platform, and laser of the laser detection heads is beaten on the equilateral triangle platform;
the magnetic grating ruler displacement sensor is arranged on the rigid driven rod body unit and used for measuring the position information of the linear motor;
the control part comprises a linear motor servo unit, a motion control card, a laser displacement sensor controller, a data acquisition card and a computer;
the linear motor and the magnetic grating ruler displacement sensor are connected with the linear motor servo unit in a speed control or position control mode, the linear motor servo unit is connected with the motion control card, the motion control card is connected with the computer, the laser displacement sensor detects displacement information and posture information of the movable platform, the displacement information and the posture information are output to the data acquisition card through the laser displacement sensor controller and then input to the computer, the computer obtains control quantity, and the control quantity further drives the linear motor to move through the motion control card and the linear motor servo unit to control the movable platform to move to a designated position according to an expected track;
one of the two rigid driven rod body units is arranged above the parallelogram platform, and the other rigid driven rod body unit is arranged below the parallelogram platform;
the plane parallel mechanism device comprises three degrees of freedom, specifically two degrees of freedom in the horizontal direction and one degree of freedom in the rotation direction.
2. The planar shunt mechanism apparatus according to claim 1, wherein two of the three laser detection heads are located on the right side of the movable platform, the third laser detection head is disposed above the movable platform, and the two laser detection heads on the right side are placed in parallel.
3. The planar shunt mechanism device according to claim 1, wherein the linear moving unit comprises a linear guide rail, a slider, and a connection plate, the linear guide rail and a stator of the linear motor are provided on a motor base, the connection plate is fixed on the slider, and the slider moves on the linear guide rail.
4. The planar shunt mechanism device according to claim 1, wherein the magnetic grating ruler displacement sensor comprises a magnetic pick-up head and a magnetic ruler, the magnetic pick-up head is fixed on the connecting plate, and the magnetic ruler is mounted on the motor base.
5. A control method of a double five-bar mechanism driven planar parallel mechanism device according to any one of claims 1 to 4, comprising the steps of:
firstly, a computer performs kinematic inverse solution according to a given track, a target position and a moving platform posture to obtain the output quantity of each linear motor, and outputs the output quantity to a linear motor servo unit through a motion control card to control a linear motor rotor to move so as to drive a platform to move;
step two, in the moving process of the movable platform, the laser probe heads arranged around the movable platform measure the position information and the attitude information of the movable platform in real time, and the position information and the attitude information are output to a data acquisition card through a laser displacement sensor controller, are subjected to A/D conversion and then are transmitted to a computer;
the magnetic grid ruler position sensor measures the position information of the linear motor rotor in real time, transmits the information to the linear motor servo unit, and then transmits the information to the computer through the motion control card;
and thirdly, calculating a control signal by the computer according to the feedback information obtained in the second step, outputting the control signal to the linear motor servo unit through the motion control card, driving the linear motor rotor to move, and further controlling the movable platform to move according to a desired track and move to a designated position in a desired gesture.
6. The control method according to claim 5, wherein the obtaining the position information and the posture information of the mobile platform in the second step is specifically:
let the coordinate of the first laser probe be P 1 (x 1 ,y 1 ) The coordinate of the second laser detecting head is P 2 (x 2 ,y 2 ) The coordinate of the third laser detecting head is P 3 (x 3 ,y 3 ) The side length of the equilateral triangle part of the movable platform is a, and then the corner of the movable platform is:
the position of the center of the movable platform along the x direction is as follows:
the position of the center of the movable platform along the y direction is as follows:
wherein the method comprises the steps of
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| EP1414626A4 (en) * | 2001-07-05 | 2008-08-13 | Microdexterity Systems Inc | Parallel manipulator |
| CN203003875U (en) * | 2012-12-27 | 2013-06-19 | 广西大学 | Parallel mechanism with prr open loop sub-chain and prrrp closed loop sub-chain |
| CN203003873U (en) * | 2012-12-27 | 2013-06-19 | 广西大学 | Parallel mechanism provided with prrrp kinematic pair closed-loop subchain and rprpr kinematic pair closed-loop subchain |
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