CN112847305B - Position inverse solution method of six-axis robot and six-axis robot - Google Patents

Abstract

The invention relates to a six-axis robot and a position inverse solution method thereof. The position inverse solution method of the six-axis robot provided by the invention is a geometric solution method combined with the basic theory of robot kinematics, can visually display the geometric meaning of the six-axis robot, combines the conventional rigid body kinematics and the robot theory, only involves basic mathematical operation and matrix basic operation, has no iterative operation process, and has higher calculation speed after programming.

Description

Position inverse solution method of six-axis robot and six-axis robot

Technical Field

The invention relates to the technical field of industrial robots, in particular to a six-axis robot and a position inverse solution method thereof.

Background

Compared with a series robot, the parallel robot has the characteristics of high rigidity, high precision and large load self-weight, is widely applied to the fields of positioning platforms, simulation equipment, entertainment equipment and the like, and has great potential in automatic processing application scenes.

In the current academic and commercial field, the vast majority of six-axis robots employ either a 6-6 UPS or a 6-6 UPU configuration.

6-6 UPS shows that 6 hooke joint joints are arranged on the static platform, and 6 ball joint joints are arranged on the movable platform. And the middle of each Hooke joint on the static platform and the middle of each Hooke joint on the movable platform are connected through an electric cylinder, and a piston rod of the electric cylinder can stretch out and draw back. The position and the posture of the actuating platform can be changed by the extension and contraction of piston rods of 6 electric cylinders, and the total degree of freedom is 6.

6-6 UPU shows that 6 Hooke joints are arranged on the static platform, and 6 Hooke joints are arranged on the movable platform. And the middle of each hook hinge joint on the static platform and the middle of each hook hinge joint on the movable platform are connected through an electric cylinder, and a piston rod of the electric cylinder can stretch out and draw back. The position and the posture of the actuating platform can be changed by the extension and contraction of piston rods of 6 electric cylinders, and the total degree of freedom is 6.

In order to develop a control system of a novel parallel robot and realize basic motion of the parallel robot, an inverse solution method is a problem to be solved firstly, and the inverse solution method can be used for kinematics simulation before development of a six-axis robot and guides type selection of parts. For example, when a working space is given, it is checked whether the extension value of the piston rod of the electric cylinder is within an allowable range

However, the existing commercial kinematics and dynamics simulation software is closed-source software, and a designer cannot know the operation mechanism of the closed-source software.

Disclosure of Invention

Accordingly, an object of the present invention is to provide a method for solving the inverse position of a six-axis robot and a six-axis robot which can be used for the kinematics simulation before the development of the six-axis robot and which can guide the model selection of parts.

In a first aspect, the present invention provides a position inverse solution method for a six-axis robot, wherein the six-axis robot comprises a static platform 100, a movable platform 200, a hooke joint assembly 300, a joint assembly 400 and an electric cylinder assembly 500;

the joint assembly 400 includes:

a bearing housing 420;

a cross shaft housing 430, wherein the cross shaft housing 430 is rotatably disposed on the bearing housing 420;

the shaft lug 433 is rotatably arranged on the cross shaft housing 430, the rotation axis of the shaft lug 433 on the cross shaft housing 430 intersects with and is perpendicular to the rotation axis of the cross shaft housing 430 on the bearing seat 420, two bearing holes 441 are arranged on the shaft lug 433, the two bearing holes 441 are symmetrically distributed about the rotation axis of the shaft lug 433 on the cross shaft housing 430, the axes of the two bearing holes 441 are parallel to each other and are located on the same horizontal plane, and the axes of the bearing holes 441 are perpendicular to the rotation axis of the cross shaft housing 430 on the bearing seat 420;

the Hooke's hinge component is installed on the static platform 100, the joint component 400 is installed on the movable platform 200, one end of the electric cylinder component 500 is installed on the Hooke's hinge component 300, the other end of the electric cylinder component 500 is rotatably connected to the shaft lug 433 of the joint component 400 through a bearing pin shaft 410, and the bearing pin shaft 410 is rotatably arranged in the bearing hole 441 of the shaft lug 433; the static platform 100 is provided with six hook joint assemblies 300, the six hook joint assemblies 300 are respectively a first hook joint, a second hook joint, a third hook joint, a fourth hook joint, a fifth hook joint and a sixth hook joint, and the movable platform 200 is provided with three joint assemblies 400;

the method comprises the following steps:

s1: establishing a kinematics model based on the six-axis robot, establishing a rectangular coordinate system { O } on the static platform 100 as a base coordinate system, and establishing a rectangular coordinate system { P } on the movable platform 200 as a movable platform coordinate system;

s2: obtaining a given position of the terminal moving platform coordinate system relative to the stationary platform base coordinate system^OOP and given pose^OR_P；

S3: obtaining the virtual circle radius R of the Hooke's joint_bOffset angle beta of Hooke's hinge position_iI is 1 to 6, by R_bMultiplying by a matrix calculation formula of the rotation angle around the Z axis and then multiplying by a Y axis unit vector to obtain a Hooke joint position vector^OOB₁～^OOB₆；

S4: according to the virtual circle radius R of the cross axis_QDistribution angle of axle ear origin

i is 1 to 6, by R_QMultiplying the calculated formula by the matrix of the rotation angle around the Z axis and multiplying the calculated formula by the unit vector of the Y axis to obtain the position vector of the shaft lug^PPQ_i，i＝1～3；

S5: according to the given position^OOP and the given pose^OR_PAccording to the position vector of the shaft lug^PPQ_iI is 1-3 and the Hooke's joint position vector^OOB₁～^OOB₆Then according to the coordinate rotation theorem and the basic operation theorem of the vector in the theory of robotics, the Hooke's hinge-axis ear vector is obtained^oBQ_i,i＝1～6；

S6: according to the given posture^OR_P，^oD_iVector distribution angle delta_i，i＝1～3, according to the theorem of coordinate rotation in the theory of robotics, passing^OR_PMultiplying by a matrix calculation formula of the rotation angle around the Z axis and then multiplying by a Y axis unit vector to obtain a cross axis horizontal axis vector oD_i，i＝1～3；

S7: according to hook hinge-axis ear vector^oBQ₃And^oBQ₂by cross multiplication of vectors^oBQ₃×(-^oBQ₂) Calculating the norm | luminance^oBQ₃×(-^oBQ₂) | l, the component is obtained after the division calculation^Oz_Q1According to component^Oz_QiObtaining the component^Oy_QiSum component^Ox_QiAccording to component^Oz_QiComponent (c)^Oy_QiSum component^Ox_QiTo obtain^OR_Qi，i＝1～3；

S8: the calculation uses X absolute offset value QAX and Y absolute offset value QAY as elements to construct an Axis-rotation center vector with { Q } coordinate system as a reference system^QjQA_i，i＝1～6,j＝1～3；

S9: rotating the matrix according to the axis-ear coordinate system^OR_QiI 1 to 3, axis ear-rotation center vector^QjQA_iI is 1 to 6, j is 1 to 3, and^OR_Qimultiplication by^QQA_iObtaining the axis ear-rotation center vector using the base coordinate system { O } as the reference system^OQA_i，i＝1～6；

S10: according to the axis ear-rotation center vector^QjQA_iI is 1 to 6, j is 1 to 3 and the Hooke's joint-axis ear vector^oBQ_iAnd i is 1-6, and then the basic operation of the vector is used to obtain the position vector of the electric cylinder^OBA_i,i＝1～6。

In a second aspect, the present invention provides a six-axis robot comprising:

at least one memory and at least one processor;

the memory for storing one or more programs;

when executed by the at least one processor, cause the at least one processor to carry out the steps of the method for inverse position solution of a six-axis robot according to the first aspect of the invention.

For a better understanding and practice, the invention is described in detail below with reference to the accompanying drawings.

Drawings

FIG. 1 is a schematic structural diagram of a six-axis robot according to an embodiment;

FIG. 2 is an exploded view of a six-axis robot according to an embodiment;

FIG. 3 is a schematic diagram illustrating the connection between a hook joint assembly and a stationary platform according to an embodiment;

FIG. 4 is a schematic connection diagram of the joint assembly, the electric cylinder assembly and the movable platform according to the embodiment;

FIG. 5 is a schematic view of a hooke joint assembly of an embodiment distributed on a stationary platform;

FIG. 6 is an exploded view of an embodiment of a hook and loop assembly;

FIG. 7 is a schematic connection diagram of a fixed shaft system of a hook hinge assembly according to an embodiment;

FIG. 8 is a schematic view of a connection of a swing shaft system of the hook-and-loop assembly according to the embodiment;

FIG. 9 is a schematic diagram of the distribution of the joint assembly on the movable platform according to the embodiment;

FIG. 10 is an exploded view of the joint assembly according to the example;

FIG. 11 is an assembled view of the joint assembly according to an embodiment;

FIG. 12 is an internal schematic view of a cross-shaft housing according to an embodiment;

FIG. 13 is a schematic structural view of a shank according to an embodiment;

FIG. 14 is a schematic connection diagram of a bearing pin axis of the joint assembly according to the embodiment;

FIG. 15 is a schematic structural diagram of an electric cylinder assembly according to an embodiment;

FIG. 16 is a schematic view of the definition of the origin of a Hooke's hinge;

FIG. 17 is a schematic diagram of constructing a base coordinate system;

FIG. 18 is a schematic view of a hook joint position vector;

FIG. 19 is a schematic illustration of constructing a cross-axis origin;

FIG. 20 is a schematic diagram of the construction of a moving platform coordinate system;

FIG. 21 is a schematic diagram of a cross-axis horizontal vector;

FIG. 22 is a schematic view of the origin of the trunnion;

FIG. 23 is a schematic view of a hook hinge-journal vector;

FIG. 24 is a schematic view of an axis ear coordinate system;

FIG. 25 is a schematic view of distribution angles of pivot points;

FIG. 26 is a schematic view of a position vector of the origin of the moving platform coordinate system relative to the origin of the stationary platform coordinate system;

FIG. 27 is a schematic view of the hinge center of the pin;

FIG. 28 is a schematic illustration of angular velocity vectors of the joint assembly 400;

FIG. 29 is a schematic diagram of an application of the inverse position solution method of the six-axis robot of the present invention;

reference numerals: 100. a static platform; 200. a movable platform; 300. a hook hinge assembly; 310. a hook hinge lower base; 311. a first tapered roller bearing; 312. a cross shaft; 313. a first end cap; 314. a first flat gasket; 315. a first spring washer; 316. A first bolt; 320. a Hooke hinge upper seat; 321. a second tapered roller bearing; 322. a second end cap; 323. a second flat gasket; 324. a second spring washer; 325. a second bolt; 400. a joint assembly; 410. a force bearing pin shaft; 411. a circlip for a hole; 412. a needle bearing; 413. a circlip for the shaft; 420. a bearing seat; 421. a third tapered roller bearing; 422. a central shaft; 423. a third end cap; 430. a cross-axis housing; 431. a fourth tapered roller bearing; 432. a fifth tapered roller bearing; 433. a shaft lug; 434. locking the nut; 435. a flat washer; 436. a stop washer; 437. a first through hole; 438. a second through hole; 439. a boss; 440. a cylindrical portion; 441. a bearing bore; 500. an electric cylinder assembly; 510. a cylinder body; 520. a piston rod; 530. a speed reducer; 540. an electric motor.

Detailed Description

In view of the technical problems in the background art, the present invention provides a six-axis robot and an inverse solution method and apparatus thereof, and referring to fig. 1 and 2, the six-axis robot includes a static platform 100, a moving platform 200, six hooke joint assemblies 300, three joint assemblies 400, and six electric cylinder assemblies 500. Wherein, the hooke joint subassembly is installed on static platform 100, and joint subassembly 400 is installed on moving platform 200, and the one end of electricity jar subassembly 500 is installed on hooke joint subassembly 300, and the other end of electricity jar subassembly 500 passes through bearing pin 410 and rotates and connect on joint subassembly 400.

The configuration of the robot can be considered as being defined by the arrangement of the joints, including the type of joints, the number of joints, and the fitting size parameters. The six-axis robot in the embodiment can form a 6-3UPU configuration (representing that the leg configuration is Hooke joint-translation joint-cross shaft joint) by using the components according to a specific assembly mode. The types and the number of joints which can be formed by the parts are as follows:

(1) each hooke joint assembly 300 fixedly connected with the static platform 100 is provided with 2 rotary joints so as to realize that the cylinder body 510 of the electric cylinder assembly 500 has 2 rotary degrees of freedom relative to the static platform 100, and the rotary shafts are shown as J1-J12 in fig. 3;

(2) each electric cylinder assembly 500 has 1 translation joint, so that the piston rod 520 of the electric cylinder assembly 500 has one translation degree of freedom and 6 translation degrees of freedom relative to the cylinder body 510 of the electric cylinder assembly 500, and the moving axes are shown as J13-J18 in FIG. 4;

(3) the bottom of the shaft lug 433 of the joint component 400 is provided with 2 single-shaft rotary joints so as to realize that each shaft lug 433 has 1 degree of freedom of rotation and 6 degrees of freedom of rotation relative to the connected 2 piston rods 520, and the rotary shafts are J19-J24 in FIG. 4;

(4) each joint assembly 400 has 2 rotary joints, one rotary joint is capable of realizing single-axis rotation of the shaft lug 433 of the joint assembly 400 relative to the cross-shaft shell 430 of the joint assembly 400, and the rotary shafts are shown as J25-J27 in FIG. 4; the other rotary joint is a joint assembly 400 in which the cross shaft housing 430 is capable of single-axis rotation with respect to the movable platform 200 for a total of 3 degrees of freedom, and the axes of rotation are shown as J28 to J30 in fig. 4.

Referring to fig. 5, each hooke's hinge assembly 300 is fixedly mounted to the stationary platform 100 by bolts. During assembly, six hooke's joint assemblies 300 need to be mounted on the stationary platform 100 in the arrangement of fig. 5. In order to clearly explain the distribution of the six hooke joint assemblies 300 on the stationary platform 100, the six hooke joint assemblies 300 are respectively defined as a first hooke joint, a second hooke joint, a third hooke joint, a fourth hooke joint, a fifth hooke joint, and a sixth hooke joint. Specifically, an intersection point of two rotation axes of the cross shaft 312 of the hooke joint assembly 300 is defined as a hooke joint rotation center, in this embodiment, a hooke joint rotation center of the first hooke joint is B1, a hooke joint rotation center of the second hooke joint is B2, a hooke joint rotation center of the third hooke joint is B3, a hooke joint rotation center of the fourth hooke joint is B4, a hooke joint rotation center of the fifth hooke joint is B5, and a hooke joint rotation center of the sixth hooke joint is B6. The Hooke joint rotation centers B1-B6 are arranged on a virtual circle with the circle center of O and the radius of Rb. Three rays extend from the center O of the virtual circle, which are ray Y1, ray Y2, and ray Y3. The included angle between the ray Y1 and the ray Y2, the included angle between the ray Y1 and the ray Y3 and the included angle between the ray Y2 and the ray Y3 are all equal to 120 degrees. The Hooke's hinge center of rotation B1 is symmetric about ray Y1 with the Hooke's hinge center of rotation B2. The Hooke's hinge center of rotation B3 is symmetric about ray Y2 with the Hooke's hinge center of rotation B4. The Hooke's hinge center of rotation B5 is symmetric about ray Y3 with the Hooke's hinge center of rotation B6. The axis of the fixed shaft portion of the first hooke's cross 312 is at a 30 degree angle to ray Y1. The axis of the fixed shaft portion of the second hook joint cross 312 is at a 30 degree angle to ray Y1. The axis of the fixed shaft portion of the spider 312 of the third hook joint is at an angle of 30 degrees to the ray Y1. The axis of the fixed shaft portion of cross-shaft 312 of the fourth hook joint is at a 90 degree angle to ray Y1. The axis of the fixed shaft portion of cross-shaft 312 of the fifth hook joint is at a 90 degree angle to ray Y1. The axis of the fixed shaft portion of the sixth hook joint cross 312 makes a 30 degree angle with the ray Y1.

The structures of the six hooke joint assemblies 300 are completely the same, and the specific structure of one hooke joint assembly 300 is described in detail below, referring to fig. 6 to 8, the hooke joint assembly 300 is composed of a fixed shaft system and a swinging shaft system. The fixed axis system is to realize the relative rotation of the cross shaft 312 of the hooke joint assembly 300 with respect to the hooke joint lower base 310 of the hooke joint assembly 300, and the axis of the fixed axis portion of the cross shaft 312 is used as a rotation axis. The swing axis system is used for realizing the relative rotation of the hooke joint upper seat 320 of the hooke joint assembly 300 relative to the swing shaft part of the cross shaft 312 of the hooke joint assembly 300, and takes the axis of the swing shaft part of the cross shaft 312 as a rotating shaft.

Referring to fig. 6 and 7, the fixed shafting includes a hooke's lower base 310, a first tapered roller bearing 311, a cross shaft 312, a first end cover 313, a first flat gasket 314, a first spring gasket 315, and a first bolt 316. Wherein, the hooke's lower base 310 is fixedly installed on the stationary platform 100 through bolts. Two first tapered roller bearings 311 are mounted on the hooke's joint lower base 310, and the two first tapered roller bearings 311 are coaxially arranged. The outer ring of the first tapered roller bearing 311 is tightly fitted with the hooke joint lower base 310, and the outer ring of the first tapered roller bearing 311 and the hooke joint lower base 310 cannot rotate relatively. Both ends of the fixed shaft portion of the cross 312 are respectively installed in the two first tapered roller bearings 311, and the fixed shaft portion of the cross 312 is tightly fitted with the inner ring of the first tapered roller bearing 311, and the fixed shaft portion of the cross 312 and the inner ring of the first tapered roller bearing 311 cannot rotate relatively. A first end cover 313, a first flat gasket 314, a first spring gasket 315 and a first bolt 316 are sequentially arranged on one side of the first tapered roller bearing 311 away from the hooke joint lower base 310, the first bolt 316 sequentially penetrates through the first spring gasket 315, the first gasket and the first end cover 313 and then is in threaded connection with the fixed shaft part of the cross shaft 312, the head part of the first bolt 316 abuts against the first spring gasket 315, and the first end cover 313 abuts against the end face of the inner ring of the first tapered roller bearing 311.

Referring to fig. 6 and 8, the swing shaft system includes a hooke upper seat 320, a second tapered roller bearing 321, a second end cap 322, a second flat gasket 323, a second spring gasket 324, and a second bolt 325. Hooke's hinge upper mount 320 is used to mount electric cylinder assembly 500. Two second tapered roller bearings 321 are mounted on the hooke joint upper seat 320, and the two second tapered roller bearings 321 are coaxially arranged. The outer ring of the second tapered roller bearing 321 is tightly fitted with the hooke joint upper seat 320, and the outer ring of the second tapered roller bearing 321 and the hooke joint upper seat 320 cannot rotate relatively. The inner ring of the second tapered roller bearing 321 is in close fit with the swing shaft of the cross 312, and the swing shaft of the cross 312 and the inner ring of the second tapered roller bearing 321 cannot rotate relative to each other. A second end cover 322, a second flat gasket 323, a second spring gasket 324 and a second bolt 325 are sequentially arranged on one side of the second tapered roller bearing 321 away from the hooke joint upper seat 320, the second bolt 325 sequentially penetrates through the second spring gasket 324, the second gasket and the second end cover 322 and then is in threaded connection with the swing shaft part of the cross shaft 312, the head of the second bolt presses the second spring gasket 324, and the second end cover 322 presses against the end face of the inner ring of the second tapered roller bearing 321.

Referring to fig. 9, each joint assembly 400 is fixedly mounted on the movable platform 200 by bolts. During assembly, the three joint assemblies 400 need to be mounted on the motion platform 200 according to the distribution of fig. 9. In order to clearly explain the distribution of the three joint assemblies 400 on the movable platform 200, the three joint assemblies 400 are defined as a first joint, a second joint, and a third joint, respectively. The intersection of the axis of the central shaft 422 of the joint assembly 400 and the axis of the cylindrical portion 440 of the axle ear 433 of the joint assembly 400 is defined as the joint center, and in this embodiment, the joint center of the first joint is Q1, the joint center of the second joint is Q2, and the joint center of the third joint is Q3. The joint centers Q1-Q3 are arranged on a virtual circle with a circle center P and a radius Rq, wherein the Rq is smaller than Rb. The three joint assemblies 400 are equally spaced on a virtual circle with a center P, that is, the connecting line PQ1 forms an angle of 120 degrees with the connecting line PQ2, the connecting line PQ1 forms an angle of 120 degrees with the connecting line PQ3, and the connecting line PQ2 forms an angle of 120 degrees with the connecting line PQ 3. The axis of the central axis 422 of the first joint is perpendicular to the connecting line PQ1, the axis of the central axis 422 of the second joint is perpendicular to the connecting line PQ2, and the axis of the central axis 422 of the third joint is perpendicular to the connecting line PQ 3.

The three joint assemblies 400 have the same structure, and the specific structure of one joint assembly 400 is described in detail below, referring to fig. 10 to 14, the joint assembly 400 is composed of a horizontal shaft system, a vertical shaft system, and a force-bearing pin shaft 410 shaft system. The horizontal axis is to enable rotation of the cross-shaft housing 430 of the joint assembly 400 relative to the bearing housing 420 of the joint assembly 400, and the vertical axis is to enable rotation of the trunnions 433 of the joint assembly 400 relative to the cross-shaft housing 430 of the joint assembly 400. Bearing pin shaft 410 shafting realizes the rotation of the shaft lug 433 of the joint assembly 400 relative to the piston rod 520 of the electric cylinder assembly 500.

Referring to fig. 10 and 11, the horizontal shafting includes a bearing seat 420, a third tapered roller bearing 421, a central shaft 422, and a third end cap 423. Wherein, the bearing seat 420 is fixedly installed on the movable platform 200 by bolts. Two third tapered roller bearings 421 are mounted on the bearing housing 420, and the two third tapered roller bearings 421 are coaxially disposed. The outer ring of the third tapered roller bearing 421 is tightly fitted with the bearing seat 420, and the outer ring of the third tapered roller bearing 421 and the bearing seat 420 cannot rotate relatively. Two ends of the central shaft 422 are respectively installed in the two third tapered roller bearings 421, the central shaft 422 is tightly fitted with the inner rings of the third tapered roller bearings 421, and the central shaft 422 and the inner rings of the third tapered roller bearings 421 cannot rotate relatively. At both ends of the central shaft 422, a third end cap 423 is respectively provided, the third end cap 423 is bolted to the bearing housing 420, and the third end cap 423 defines the third conical roller bearing 421 in the bearing housing 420.

Referring to fig. 10 to 13, the vertical shafting includes a cross shaft housing 430, a fourth tapered roller bearing 431, a fifth tapered roller bearing 432, a shaft lug 433, a lock nut 434, a flat washer 435, and a stop washer 436. The cross shaft housing 430 has a first through hole 437 and a second through hole 438, and the axis of the first through hole 437 and the axis of the second through hole 438 intersect and are perpendicular to each other. The first through hole 437 is tightly fitted to the center shaft 422, and the cross shaft housing 430 moves in synchronization with the center shaft 422. A boss 439 is disposed within the second through-hole 438, the boss 439 extending from an inner wall of the second through-hole 438 to an inner cavity of the second through-hole 438. A fourth tapered roller bearing 431 and a fifth tapered roller bearing 432 are mounted in the second through hole 438, the fourth tapered roller bearing 431 and the fifth tapered roller bearing 432 are respectively located on both sides of the boss 439, and the fourth tapered roller bearing 431 and the fifth tapered roller bearing 432 are coaxially arranged. The outer ring of the fourth tapered roller bearing 431 is tightly fitted to the inner wall of the second through hole 438, the outer ring of the fourth tapered roller bearing 431 and the cross shaft housing 430 cannot rotate relative to each other, and the end surface of the outer ring of the fourth tapered roller bearing 431 abuts against the end surface of the boss 439. The outer ring of the fifth tapered roller bearing 432 is tightly fitted to the inner wall of the second through hole 438, the outer ring of the fifth tapered roller bearing 432 and the cross shaft housing 430 cannot rotate relative to each other, and the end surface of the outer ring of the fifth tapered roller bearing 432 abuts against the other end surface of the boss 439. A cylindrical portion 440 is provided in the lug 433, and the cylindrical portion 440 passes through the fifth tapered roller bearing 432 and the fourth tapered roller bearing 431 in this order. A lock nut 434 is screwed to an end of the cylindrical portion 440, and the lock nut 434 presses an end surface of the inner ring of the fourth tapered roller bearing 431. A flat washer 435 is provided between the journal 433 and the fifth tapered roller bearing 432, and the flat washer 435 abuts against the inner ring of the fifth tapered roller bearing 432 to reduce the contact area between the journal 433 and the fifth tapered roller bearing 432. A lock washer 436 is provided between the lock nut 434 and the fourth tapered roller bearing 431 to prevent the lock nut 434 from loosening. In addition, two bearing holes 441 are further disposed on the shaft lug 433, the two bearing holes 441 are symmetrically distributed about an axis of the cylindrical portion 440, axes of the two bearing holes 441 are parallel to each other and are located on the same horizontal plane, and the axes of the bearing holes 441 are perpendicular to an axis of the central shaft 422.

Referring to fig. 10, 11 and 14, the bearing pin 410 shaft system includes a bearing pin 410, a hole circlip 411, a needle bearing 412 and a shaft circlip 413. The circlip 411 for hole is fitted in the bearing hole 441 of the boss 433. The needle roller bearing 412 is installed in a bearing hole 441 of the shaft lug 433, an outer ring of the needle roller bearing 412 is tightly matched with the bearing hole 441, and the outer ring of the needle roller bearing 412 and the shaft lug 433 cannot rotate relatively. The outer race of the needle bearing 412 abuts against the circlip for hole 411, and the position of the needle bearing 412 is defined by the circlip for hole 411. The bearing pin shaft 410 is arranged in the needle bearing 412, the bearing pin shaft 410 is tightly matched with the inner ring of the needle bearing 412, and the bearing pin shaft 410 and the inner ring of the needle bearing 412 cannot rotate relatively. Bearing pin 410 is also inserted through piston rod 520 of electric cylinder assembly 500. Two ends of the bearing pin shaft 410 are respectively provided with a retainer ring groove, each retainer ring groove is internally provided with one elastic collar 413 for a shaft, the two elastic collars 413 for the shafts are respectively positioned at two sides of a piston rod 520 of the electric cylinder assembly 500, and the elastic collars 413 for the shafts are abutted against the piston rod 520 so as to prevent the bearing pin shaft 410 from axially shifting on a shaft lug 433 or the piston rod 520 of the electric pole assembly.

Referring to fig. 15, the electric cylinder assembly 500 includes a cylinder block 510, a piston rod 520, a speed reducer 530, and a motor 540. Since the prior art is adopted for the electric cylinder assembly 500, the specific structure of the electric cylinder assembly 500, and the connection and position relationship among the cylinder 510, the piston rod 520, the speed reducer 530, and the motor 540 are not discussed herein. However, it should be noted that, during assembly, the axis of the spindle hole of the yoke at the end of the piston rod 520 needs to be parallel to the axis of the swing shaft portion of the cross shaft 312 of the hooke's joint assembly 300.

Compared with the prior art, the six-axis robot provided by the embodiment of the invention has the following beneficial effects:

1. the motor 540 of the electric cylinder assembly 500 is driven to rotate by the servo driver, and the screw rod mechanism in the electric cylinder can convert the rotation motion of the motor 540 into the parallel movement of the piston rod 520. The whole machine only has the 6 actively-movable translational joints, and applying motion to the 6 joints can drive the platform 200 to generate motion with 6 degrees of freedom, including translation along the X axis, the Y axis and the Z axis and rotation around the X axis, the Y axis and the Z axis;

2. the joint assembly 400 can increase the working space range, such as the position range and the posture overturning range, of the movable platform 200;

3. the joint assembly 400 of the present embodiment is assembled by conventional transmission parts and machining parts, so as to reduce the manufacturing cost;

4. the joint assembly 400 described in this embodiment is a modular structure, which reduces the assembly complexity of the six-axis robot;

5. by adopting the joint assembly 400 of the embodiment, the six-axis robot can be hung for use.

Aiming at the six-axis robot in the embodiment, the invention also provides a position inverse solution method of the six-axis robot, which mainly comprises the steps of geometric element and kinematic element construction, position inverse solution and speed inverse solution.

The above steps are described below:

the method comprises the following steps of firstly, constructing geometric elements and kinematic elements, wherein the steps are used for defining the geometric elements required in the position inverse solution method of the six-axis robot and constructing the kinematic elements:

establishing Hooke joint origin B_iAnd i is 1 to 6. As shown in FIG. 16, the origin B of the hook joint is set_iAnd the points i are 1-6 and are respectively arranged at the centers of the cross shafts of the six hook joint assemblies 300.

Establishing a base coordinate system { O }: a rectangular coordinate system { O } is established on the static platform 100, and the origin O of the rectangular coordinate system is set at the origin B of the hook joint₁～B₆On a certain plane and located at B₁～B₆The center position of the circle is determined, and the y-axis direction is arranged at OB₁,OB₂The angular bisector position of the line segment, at this time, the six hook hinge assemblies 300 are symmetrical relative to the y axis, the z axis is arranged upwards, the x axis can be automatically determined according to the right-hand rule, and the final rectangular coordinate system { O } is shown in FIG. 17.

R_b: is represented by B₁～B₆The determined radius of the circle, as shown in fig. 17, is referred to as the "hook-hinge virtual circle radius".

^OOB₁～^OOB₆：^OOB_i: the Hooke's joint position vector, as shown in FIG. 18, specifically represents the ith Hooke's joint origin B using the origin O of the base coordinate system as the starting point_iI is a vector with 1 to 6 as an end point, and the reference coordinate system is a base coordinate system { O }.

β_iAnd i is 1-6: hooke's joint offset angle, as shown in FIG. 18, represents a Hooke's joint position vector^OOB_iAngle to the y-axis of the base coordinate system { O }.

U_i: the origin of the intersecting axes, as shown in FIG. 19, is the point where the axes of the two cylindrical surfaces of the joint assembly 400 intersect, and this point is designated as U_i，i＝1～3。

{U_iAnd^OR_Uiand i is 1-3: respectively represent a cross axis coordinate system and a cross axis coordinate system (U)_iRotation matrix relative to the base coordinate system { O }. The method of establishment is as shown in "step 2.1" of the inverse velocity solution method below.

R_Q: referred to as the "cross-axis virtual circle radius", as shown in fig. 20, represents the radius value of the circle defined by the three cross-axis origins.

{ P }: and a moving platform coordinate system. As shown in FIG. 20, a rectangular coordinate system { P }, with the origin P of { P } located at U, is established on the mobile platform 200_iI is 1-3 determined plane and is located on three U_iThe position of the center of the circle is determined, and the y-axis of the rectangular coordinate system { P } is shown in the figure, wherein U₂In the negative direction of the y-axis, U₁,U₃Symmetrical with respect to the y-axis, the z-axis up, and the x-axis can be determined with the right-hand rule.

^oD_iAnd i is 1-3: referred to as cross-axis horizontal axis vector, as shown in fig. 21, the base coordinate system { O } is used as a reference system.

δ_i，i＝1～3：^oD_iThe vector distribution angle is represented by a cross-axis horizontal-axis vector as shown in FIG. 21^oD_iThe angle with the y-axis of the moving platform coordinate system { P },

Q_iand i is 1-3: the pivot ear origin. As shown in fig. 21 and 22, the upper part of the shaft lug 433 is connected with the U_iAnd i is 1-3 corresponding to the overlapped points.

^oBQ_iAnd i is 1-6: the Hooke's hinge-axis ear vector, as shown in FIG. 23, uses the base coordinate system { O } as the reference system.

{Q_i1-3 and^OR_Qiand i is 1-3: respectively, an "axis-ear coordinate system" and a "rotation matrix of the axis-ear coordinate system with respect to the base coordinate system { O }. The origin of the coordinate system is fixedly connected with the origin Q of the shaft lug_i，{Q_iThe three xyz axes of the method are shown in FIG. 24, and the specific solving method is according to the "inverse position algorithmStep 5 of (4).

1-3: representing the "distribution angle of the axis ears", as shown in FIG. 25, the origin Q of the axis ears_iI is a distribution angle of 1 to 3

^PPQ_i: as shown in fig. 25, the "position vector distributed on the movable platform 200 with the movable platform coordinate system { P } as the reference frame and the axis ear origin" is shown.

^OOP: a position is given. As shown in fig. 26, a position vector representing the origin P of the moving platform coordinate system { P } relative to the origin O of the stationary platform coordinate system is known.

^OR_P: a pose is given. As shown in FIG. 26, the rotation matrix of the moving platform coordinate system { P } relative to the stationary platform coordinate system { O } is shown as a known term.

A₁～A₆: the hinge center of the pin shaft. As shown in fig. 26 and fig. 27, among the three lugs 433, the hinge center points a of the two bearing pin shafts 410₂(Point A)₄Point A of₆) And point A₃(Point A)₅Point A₁) Point relative to { Q₁}({Q₂}，{Q₃) } about the y-axis, point A₂(Point A)₄Point A₆) And point A₃(Point A)₅Point A of₁) Is placed in { Q₁}({Q₂}，{Q₃}) in the xy plane, a is represented by QAX₁And A₂In { Q₁The absolute offset value in the X-axis direction of the device, called "X absolute offset value", A is represented by QAY₁And A₂In { Q₁The absolute offset value in the Y-axis direction of the wave is referred to as "Y absolute offset value".

^ΟΒΑ_i: as shown in FIG. 26, is represented by^OR_PAnd^OOP, an electric cylinder position vector obtained by a position inverse solution method,the base coordinate system { O } is used as a reference system.

^QjQA_iI is 1 to 6, j is 1 to 3: axis ear-rotation center vector, as shown in FIG. 26 and FIG. 27, in an axis ear coordinate system { Q }_jIs a reference frame, wherein^Q1QA₂，^Q1QA₃In { Q₁In the step (c) of the step (c),^Q2QA₄，^Q2QA₅in { Q₂In the step (c) of the step (c),^Q3QA₁，^Q3QA₆in { Q₃In.

^OQA_iAnd i is 1-6: the axis ear-rotation center vector, as shown in FIG. 27, has a base coordinate system { O } as a reference frame.

^PV_P,O: as shown in fig. 23, the linear velocity vector of the movable stage 200 with respect to the stationary stage 100 is defined by the movable stage coordinate system { P }.^PW_P,O: and (3) an angular velocity vector of the movable platform relative to the static platform by taking the movable platform coordinate system { P } as a reference system.^PV_QiAnd i is 1-3: as shown in FIG. 24, the origin Q of the axis-ear coordinate system using the movable platform coordinate system { P } as the reference system_iLinear velocity vector of (2).^QiV_QiAnd i is 1-3: in its own coordinate system { Q_iAn axis ear coordinate system origin Q with a reference system_iLinear velocity vector of (2).

^QiW_QiAnd i is 1-3: as shown in FIG. 24, the coordinate system of the camera is { Q }_iThe angular velocity vector of the trunnion 433 of the reference frame.

^UiW_UiI is 1 to 3 and^QiW_Uiand i is 1-3: as shown in FIG. 28, the coordinate systems are set to their own coordinate systems { U }_iThe angular velocity vector of the joint assembly 400 in reference frame and in the axis ear coordinate system Q_iThe angular velocity vector of the joint assembly 400 is the reference frame.

^OR_UiAnd i is 1-3: cross axis coordinate system { U_iRotation matrix relative to the base coordinate system { O }.

^UiR_PAnd i is 1-3: the coordinate system of the movable platform { P } is relative to the coordinate system of the cross axis { U }_iThe rotation matrix of.

^UiW_P,OAnd i is 1-3: as shown in FIG. 23, in a cross-axis coordinate system { U }_iThe angular velocity vector of the movable platform 200 relative to the stationary platform 100 is referred to as a reference coordinate system.

^QiR_UiAnd i is 1-3: cross axis coordinate system { U_iRelative to the axis ear coordinate system { Q }_iThe rotation matrix of.

^QiWZ_QiAnd i is 1-3: angular velocity of the trunnion 433 in its own coordinate system { Q_iThe Z component of.

^QjV_AiI is 1 to 6, j is 1 to 3: in the axis ear coordinate system { Q_jAnd the linear velocity vector of the hinge center of the bearing pin shaft 410 of the reference system.

^QjBA_iI is 1 to 6, j is 1 to 3: in the axis ear coordinate system { Q_jThe electric cylinder position vector of electric cylinder assembly 500 is the frame of reference.

θ_AQiAnd i is 1-6: hinge-electric cylinder deflection angle, display^QjV_AiI is 1 to 6, j is 1 to 3 and vector^QjBA_iI is 1 to 6, and j is an angle of 1 to 3.

V_BAiAnd i is 1-6: the expansion and contraction speed of the electric cylinder represents the linear speed of the hinge center of the bearing pin shaft 410 relative to the origin of the Hooke's hinge.

Second, the procedure of the position inverse solution algorithm

Step 1: computing vectors^OOB₁～^OOB₆. According to the ' Hooke ' joint virtual circle radius ' R_bOffset angle beta of Hooke's joint position_iAnd i is 1-6, and then passes through R according to the coordinate rotation theorem in robotics theory_bMultiplying the ' rotation angle matrix around the Z axis ' by the ' Y axis unit vector ' to obtain the Hooke's joint position vector^OOB₁～^OOB₆。

And 2, step: computing vectors^PPQ_iAnd i is 1 to 3. According to "virtual circle radius of intersecting axis" R_QDistribution angle of axle ear origin

1-6, and then according to the coordinate rotation theorem in the theory of robotics, passing through R_QMultiplying the 'rotation angle matrix around the Z axis' by the 'Y axis unit vector' to obtain the position vector of the shaft lug^PPQ_i，i＝1～3。

And step 3: calculating Hooke's hinge-axis ear vector^oBQ_iAnd i is 1-6. According to a known quantity "given position"^OOP, known quantity "given attitude"^OR_PAnd 2, obtaining the position vector of the shaft lug^PPQ_iI is 1-3, and the obtained Hooke's joint position vector^OOB₁～^OOB₆Then according to the coordinate rotation theorem and the basic operation theorem of the vector in the theory of robotics, the Hooke's hinge-axis ear vector is obtained by the following formula^oBQ_i,i＝1～6。

^oBQ₁＝^OOP+^OR_P*^PPQ₃-^OOB₁

^oBQ₂＝^OOP+^OR_P*^PPQ₁-^OOB₂

^oBQ₃＝^OOP+^OR_P*^PPQ₁-^OOB₃

^oBQ₄＝^OOP+^OR_P*^PPQ₂-^OOB₄

^oBQ₅＝^OOP+^OR_P*^PPQ₂-^OOB₅

^oBQ₆＝^OOP+^OR_P*^PPQ₃-^OOB₆

And 4, step 4: calculating cross axis horizontal axis vector^oD_iAnd i is 1-3, and is obtained by the following method: according to a known quantity "give attitude"^OR_P，^oD_iVector distribution angle delta_iAnd i is 1-3, and then passes through the coordinate rotation theorem in the robotics theory "^OR_PMultiplying the vector by a calculation formula of a matrix of the rotation angle around the Z axis and multiplying the vector by a unit vector of the Y axis to obtain a vector of the cross axis^oD_i，i＝1～3。

And 5: computing^OR_QiAnd i is 1 to 3. According to the kinematic theory basis of robotics, can be expressed as^OR_Qi＝[^Ox_Qi ^Oy_Qi ^Oz_Qi]，^Ox_Qi，^Oy_Qi，^Oz_QiIs a split axis of the rectangular coordinate system and accords with the right-hand rule, so that the following are respectively obtained: [^Ox_Q1 ^Oy_Q1 ^Oz_Q1]，[^Ox_Q2 ^Oy_Q2 ^Oz_Q2]，[^Ox_Q3 ^Oy_Q3 ^Oz_Q3]A total of 9 factors. According to hook hinge-axis ear vector^oBQ₃And^oBQ₂by cross multiplication of vectors^oBQ₃×(-^oBQ₂) Calculating the norm | luminance^oBQ₃×(-^oBQ₂) If the division is calculated, the component can be obtained^Oz_Q1. Obtained according to the previous step^Oz_Q1And the cross axis and horizontal axis vector obtained above^oD₁By cross multiplication of vectors^oz_Q1×^OD₁Calculating the norm | luminance^oz_Q1×^OD₁If the division is calculated, the component can be obtained^Oy_Q1. From the Z component and the Y component obtained above, a component can be obtained according to the right-hand rule^Ox_Q1。^Ox_Q2 ^Ox_Q3 ^Oy_Q2 ^Oy_Q3 ^Oz_Q2 ^Oz_Q3The same is as follows:

step 6: computing^QjQA_iI is 1 to 6, j is 1 to 3, and an axis ear-rotation center vector using a { Q } coordinate system as a reference system is constructed by using an X absolute offset value QAX and a Y absolute offset value QAY as elements "^QjQA_i，i＝1～6,j＝1～3：

^Q3QA₁＝^Q1QA₃＝^Q2QA₅＝[-QAX -QAY 0]^T

^Q1QA₂＝^Q2QA₄＝^Q3QA₆＝[QAX QAY 0]^T

And 7: computing^OQA_iAnd i is 1-6. Using the above-obtained rotation matrix of the axis ear coordinate system^OR_QiI is 1 to 3, and the above-mentioned obtained axis ear-rotation center vector^QjQA_iI is 1 to 6, j is 1 to 3, and the method is carried out according to the coordinate transformation theorem in the kinematics theory of robotics^OR_QiMultiplication by^QQA_iThe 'Axis ear-rotation center vector taking the base coordinate system { O } as a reference system' can be calculated "^OQA_i，i＝1～6。

^OQA₁＝^OR_Q3*^Q3QA₁

^OQA₂＝^OR_Q1*^Q1QA₂

^OQA₃＝^OR_Q1*^Q1QA₃

^OQA₄＝^OR_Q2*^Q2QA₄

^OQA₅＝^OR_Q2*^Q2QA₅

^OQA₆＝^OR_Q3*^Q3QA₆

And 8: solving for^OBA_iAnd i is 1 to 6, and the above-obtained axial lug-rotation center vector using the base coordinate system { O } as a reference system is used^QQA_iI is 1-6 and the Hooke's hinge-axis ear vector obtained by the method^oBQ_iAnd i is 1-6, then the basic operation of the vector is used, and the electric cylinder position vector can be obtained by the following formula, namely the position inverse solution:

^OBA_i＝^OBQ_i+^OQA_i

wherein i is 1-6.

Third, the flow of speed inverse solution algorithm

Step 1: computing the Axis ear coordinate System { Q_iThe linear velocity of the origin of the (z),^QiV_Qitaking itself as a reference coordinate system. The calculation can be performed in several sub-steps as follows.

Substep 1.1: according to a known quantity "give attitude"^OR_PAnd a known quantity "linear velocity vector of the moving versus stationary platen"^OV_P,OAnd a known quantity of angular velocity vector calculation of the movable platform relative to the stationary platform takes the movable platform { P } as a parameterLinear velocity vector of movable platform relative to static platform of test system "^PV_P,OAnd "angular velocity vector of moving platform relative to stationary platform with moving platform { P } as reference frame"^PW_P,O. Then according to the coordinate transformation theorem of the kinematics theory of robotics, firstly carrying out the pair^OR_PTo find the transposition, i.e. to^OR_P ^TAnd multiplying the two to obtain the product.

^PV_P,O＝^OR_P ^T*^OV_P,O

^PW_P,O＝^OR_P ^T*^OW_P,O

Substep 1.2: the linear velocity vector of the movable platform relative to the static platform with the movable platform { P } as a reference frame obtained in the above way is used "^PV_P,OAnd the angular velocity vector of the movable platform relative to the static platform by taking the movable platform { P } as a reference frame obtained above "^PW_P,OAccording to the theorem of calculating speed by the base point method of rigid body kinematics, an axis ear coordinate system { Q) using a' moving platform coordinate system { P } as a reference system can be calculated_iQ of the origin of_iAnd i is a linear velocity of 1 to 3 "^PV_Qi，i＝1～3：

^PV_Qi＝^PV_P,O+^PW_P,O×^PPQ_i

Wherein i is 1 to 3.

Substep 1.3: using a known quantity "give attitude"^OR_PThe above-obtained "rotation matrix of axis-ear coordinate system"^OR_QiAnd the above-obtained movable platform coordinate system { P } is used as an axis ear coordinate system { Q of a reference system_iQ of the origin_iAnd i is a linear velocity of 1 to 3 "^PV_QiI is 1 to 3, and "the coordinate system of the robot { Q } is calculated by the following equation according to the theorem of coordinate transformation in the kinematics theory of robotics_iThe axis ear coordinate system origin Q_iAnd i is a linear velocity of 1 to 3 "^QiV_Qi：

^QiV_Qi＝(^OR_P ^T*^OR_Qi)^T*^PV_Qi

Wherein i is 1-3.

Step 2: to find^UiW_UiI is 1 to 3, and can be calculated in the following substeps.

Substep 2.1: calculating out^OR_UiAnd i is 1 to 3. "Cross-axis transverse axis vector" obtained as described above "^oD_iI is 1 to 3 and the "rotation matrix of the axis ear coordinate system" obtained above "^OR_QiComponent (b) of^Oy_QiAccording to the rotation matrix construction method of the kinematics theory of robotics, a cross axis coordinate system (U) can be constructed by the following formula_iRotation matrix relative to a base coordinate system { O }) "^OR_Ui，i＝1～3：

^OR_Ui＝[^oD_i ^Oy_Qi ^oD_i×^Oy_Qi]^T

Wherein i is 1-3.

Substep 2.2: computing^UiR_PAnd i is 1 to 3. According to the obtained' cross axis coordinate system { U_iRotation matrix relative to a base coordinate system { O } -) "^OR_UiI 1-3, and a known quantity "given attitude"^OR_PAccording to the coordinate transformation theorem of kinematics theory of robotics, a' moving platform coordinate system { P } can be obtained relative to a cross axis coordinate system { U_iRotation matrix of } "^UiR_P，i＝1～3。

^UiR_P＝^OR_Ui ^T*^OR_P

Wherein i is 1 to 3.

Step 2.3: computing^UiW_P,OAnd i is 1 to 3. Obtaining' moving platform coordinate system { P } relative to cross axis coordinate system { U } according to the above_iRotation matrix of } "^UiR_PI is 1-3 and the known quantity' the angular speed of the movable platform relative to the static platform by taking the movable platform { P } as a reference systemDegree vector "^PW_P,OAccording to the coordinate transformation theorem of kinematics theory of robotics, a cross-axis coordinate system { U } can be obtained_iAngular velocity vector of moving platform relative to static platform using reference coordinate system "^UiW_P,O，i＝1～3。

^UiW_P,O＝^UiR_P*^PW_P,O

Wherein i is 1-3.

Step 2.4: computing^UiW_UiAnd i is 1 to 3. Using the "Cross-Axis coordinate System { U ] obtained above_iAngular velocity vector of moving platform relative to static platform using reference coordinate system "^UiW_P,OAnd i is 1 to 3, and then according to the model characteristics of the parallel six-axis joint assembly, the angular velocity vector of the joint assembly 400 with the self coordinate system { Ui } as a reference system can be constructed "^UiW_Ui，i＝1～3。

^UiW_Ui＝[0 ^UiW_P,O(2) ^UiW_P,O(3)]^T

Wherein: i is 1 to 3,^UiW_P,O(2) to represent^UiW_P,OTerm 2 of the vector.

And step 3: computing^QiW_QiI is 1-3, and the component of the angular velocity in the Z direction. The calculation is performed in the following substeps.

Step 3.1: computing^QiR_UiAnd i is 1 to 3. According to the obtained 'rotation matrix of the axis ear coordinate system'^OR_QiAnd the obtained cross-axis coordinate system { U_iRotation matrix relative to a base coordinate system { O } -) "^OR_UiAccording to the coordinate transformation theorem of the robot motion theory, a cross axis coordinate system (U) can be obtained_iRotation matrix relative to a base coordinate system { O } -) "^QiR_Ui，i＝1～3。

^QiR_Ui＝^OR_Qi ^T*^OR_Ui

Wherein i is 1 to 3.

Step 3.2: computing^QiW_UiAnd i is 1 to 3. According to the obtained' cross axis coordinate system { U_iRotation matrix relative to a base coordinate system { O } -) "^QiR_UiAnd the above-obtained "angular velocity vector of the joint component with its own coordinate system { Ui } as a reference frame"^UiW_UiAccording to the coordinate transformation theorem of the robot motion theory, the angular velocity vector of the joint component taking the axis ear coordinate system (Qi) as a reference system can be obtained "^QiW_Ui。

^QiW_Ui＝^QiR_Ui*^UiW_Ui

Wherein i is 1-3.

Step 3.3: computing^QiWZ_QiAnd i is 1 to 3. The angular velocity vector of the joint component using the above-obtained "Axis ear coordinate System { Qi } as a reference frame"^QiW_UiAccording to the configuration characteristics of the six-axis robot, the angular velocity of the axis ear 433 in the coordinate system thereof { Q [ ] can be constructed as follows_iComponent on the Z-axis of } "^QiWZ_Qi。

^QiWZ_Qi＝[0 0 ^QiW_Ui(3)]^T

Wherein i is 1-3.

And 4, step 4: calculating V_BAiI is 1 to 6, and can be calculated in the following substeps.

Step 4.1: computing^QjV_AiI is 1 to 6, and j is 1 to 3. Using the angular velocity of the "journal bar 433" obtained above, the coordinate system { Q of the journal bar is determined_iComponent on the Z-axis of } "^QiWZ_Qi"Axis ear-rotation center vector using { Q } coordinate system as reference system"^QjQA_iAnd "in its own coordinate System { Q_iThe axis ear coordinate system origin Q_iAnd i is a linear velocity of 1 to 3 "^QiV_QiThen, the velocity principle is calculated according to the base point method of rigid body kinematics to obtain the' axle ear coordinate system { Q_jLinear velocity of hinge center of pin shaft with reference system "^QjV_Ai。

^Q3V_A1＝^Q3V_Q3+^Q3WZ_Q3×^Q3QA₁

^Q1V_A2＝^Q1V_Q1+^Q1WZ_Q1×^Q1QA₂

^Q1V_A3＝^Q1V_Q1+^Q1WZ_Q1×^Q1QA₃

^Q2V_A4＝^Q2V_Q2+^Q2WZ_Q2×^Q2QA₄

^Q2V_A5＝^Q2V_Q2+^Q2WZ_Q2×^Q2QA₅

^Q3V_A6＝^Q3V_Q3+^Q3WZ_Q3×^Q3QA₆

Step 4.2: computing^QjBA_iI is 1 to 6, and j is 1 to 3. Using the above-obtained position inverse solution^OBA_iI is 1 to 6, and the axis ear coordinate system rotation matrix obtained above^OR_QiAnd i is 1-3, and then according to the coordinate conversion theorem of the kinematics theory of the robot, a vector of an electric cylinder position vector i taking a response axis ear coordinate system (Qj) as a reference system can be obtained "^QjBA_i。

^Q3BA₁＝^OR_Q3 ^T*^OBA₁

^Q1BA₂＝^OR_Q1 ^T*^OBA₂

^Q1BA₃＝^OR_Q1 ^T*^OBA₃

^Q2BA₄＝^OR_Q2 ^T*^OBA₄

^Q2BA₅＝^OR_Q2 ^T*^OBA₅

^Q3BA₆＝^OR_Q3 ^T*^OBA₆

Step 4.3: calculating theta_AQiI is 1 to 6, as follows. Using the vector of "electric cylinder position vector i with reference to the axis-ear coordinate system of response { Qj }" obtained above "^QjBA_iAnd the above-obtained "axial coordinate system { Q_jLinear velocity at center of hinge pin with reference system "^QjV_AiAccording to the vector point multiplication operation, the 'hinge-electric cylinder deflection angle' theta can be obtained_AQi,i＝1～6。

Step 4.4: calculating V_BAiAnd i is 1-6. The linear velocity of the center of the pin shaft hinge relative to the origin of the Hooke's hinge obtained by the method^QjV_Ai"and" hinge-electric cylinder deflection angle "θ obtained as described above_AQiAccording to the general theorem of rigid body kinematics, the component in the direction of the electric cylinder is solved, namely the linear velocity V of the center of the pin shaft hinge relative to the origin of the Hooke hinge_BAi。

V_BAi＝|^QjV_Ai|·cos(θ_AQi)i＝1～6

Compared with the prior art, the position inverse solution method of the six-axis robot can be used for the kinematics simulation before the six-axis robot is developed and guiding the model selection of parts. For example, when a working space is given, it is checked whether the extension value and the telescopic speed of the piston rod of the electric cylinder are within the allowable range.

The invention also provides an application case of the position inverse solution method according to the six-axis robot, as shown in fig. 28, a simulation cabin is installed on a movable platform of the six-axis robot, an operator operates a control system in the simulation cabin, and a software part of the control system comprises the position inverse solution algorithm and the speed inverse solution algorithm in the scheme.

The application comprises the following steps:

receiving an action instruction, the action instruction comprising at least one of: translation and rotation;

outputting a track sequence according to the action instruction;

calling the position inverse solution method or the position inverse solution method plus the speed inverse solution method to obtain the position vector of the electric cylinder or the expansion speed of the electric cylinder;

and outputting the position vector or the telescopic speed of the electric cylinder to a motor servo system, so that the motor servo system controls the movement of the electric cylinder component to achieve the target movement track.

When an operator operates the control system to give an action command (translation, rotation, translation and rotation), the action command is calculated and interpolated by the control system to output a track sequence. The track sequence calls a position inverse solution algorithm or a position inverse solution algorithm and a speed inverse solution method according to the instruction requirement of a user, and the position or speed sequence, namely the OBA, can be calculated_i(t), i is 1 to 6 or V_BAi(t), i is 1 to 6. And then the motion is input into a motor servo system, and the motor servo controls the electric cylinder assembly to move so as to achieve a target motion track.

The present invention also provides a six-axis robot, comprising:

at least one memory and at least one processor;

the memory for storing one or more programs;

when executed by the at least one processor, cause the at least one processor to implement the steps of the six-axis robot position inverse solution method as described above in the present invention.

The above-mentioned embodiments only express several embodiments of the present invention, and the description thereof is more specific and detailed, but not construed as limiting the scope of the invention. It should be noted that, for a person skilled in the art, several variations and modifications can be made without departing from the inventive concept, which falls within the scope of the present invention.

Claims (10)

1. The position inverse solution method of the six-axis robot is characterized in that the six-axis robot comprises a static platform (100), a movable platform (200), a Hooke joint assembly (300), a joint assembly (400) and an electric cylinder assembly (500);

the joint assembly (400) comprises:

a bearing seat (420);

the cross shaft housing (430), the cross shaft housing (430) is rotatably arranged on the bearing seat (420);

the lug (433), the lug (433) is rotatably arranged on the cross shaft housing (430), the rotation axis of the lug (433) on the cross shaft housing (430) intersects with and is perpendicular to the rotation axis of the cross shaft housing (430) on the bearing seat (420), two bearing holes (441) are arranged on the lug (433), the two bearing holes (441) are symmetrically distributed about the rotation axis of the lug (433) on the cross shaft housing (430), the axes of the two bearing holes (441) are parallel to each other and are located on the same horizontal plane, and the axes of the bearing holes (441) are perpendicular to the rotation axis of the cross shaft housing (430) on the bearing seat (420);

the Hooke joint component is installed on the static platform (100), the joint component (400) is installed on the movable platform (200), one end of the electric cylinder component (500) is installed on the Hooke joint component (300), the other end of the electric cylinder component (500) is rotatably connected to the shaft lug (433) of the joint component (400) through a bearing pin shaft (410), and the bearing pin shaft (410) is rotatably arranged in the bearing hole (441) of the shaft lug (433); six Hooke joint components (300) are mounted on the static platform (100), the six Hooke joint components (300) are respectively a first Hooke joint, a second Hooke joint, a third Hooke joint, a fourth Hooke joint, a fifth Hooke joint and a sixth Hooke joint, and three joint components (400) are arranged on the movable platform (200);

the method comprises the following steps:

s1: establishing a kinematics model based on the six-axis robot, establishing a rectangular coordinate system (O) on a static platform (100) as a base coordinate system, and establishing a rectangular coordinate system (P) on a movable platform (200) as a movable platform coordinate system;

s2: obtaining a given position of the terminal moving platform coordinate system relative to the stationary platform base coordinate system^OOP and given pose^OR_P；

S3: obtaining the virtual circle radius R of the Hooke's joint_bOffset angle beta of Hooke's joint position_iI is 1 to 6, by R_bMultiplying by a matrix calculation formula of the rotation angle around the Z axis and then multiplying by a Y axis unit vector to obtain a Hooke joint position vector^OOB₁～^OOB₆Wherein R is_bIs represented by B₁～B₆Radius of the circle determined, B₁～B₆The origin of the Hooke joint is respectively arranged at the centers of the cross shafts of the six Hooke joint components (300); hooke joint position offset angle represents Hooke joint position vector^OOB_iAn angle to the y-axis of the base coordinate system { O };

s4: according to the virtual circle radius R of the cross axis_QDistribution angle of axle ear origin

i is 1 to 6, by R_QMultiplying the calculated formula by the matrix of the rotation angle around the Z axis and multiplying the calculated formula by the unit vector of the Y axis to obtain the position vector of the shaft lug^PPQ_iI is 1 to 3, wherein R_QRepresenting the radius values of the circles defined by the three cross-axis origins,

i represents an axis lug distribution angle of 1-6;

s5: according to the given position^OOP and the given pose^OR_PAccording to the position vector of the shaft lug^PPQ_iI is 1-3 and the Hooke's joint position vector^OOB₁～^OOB₆Then according to the coordinate rotation theorem and the basic operation theorem of the vector in the theory of robotics, the Hooke's hinge-axis ear vector is obtained^oBQ_i,i＝1～6；

S6: according to the given posture^OR_P，^oD_iVector distribution angle delta_iI is 1-3, and then passes through the coordinate rotation theorem in the robotics theory^OR_PMultiplying by a Z-axis rotation angle matrix calculation formula and then multiplying by a Y-axis unit vector to obtain a cross-axis vector^oD_iI is 1 to 3, wherein,^oD_ii is a cross axis vector of 1 to 3, and a base coordinate system { O } is a reference system;^oD_ivector distribution angle delta_iAnd i represents a cross-axis horizontal-axis vector of 1 to 3^oD_iThe angle with the y-axis of the movable platform coordinate system { P };

s7: according to the Hooke's hinge-axis ear vector, the component is obtained after the cross multiplication, the modulus calculation and the division calculation of the vector^Oz_QiAccording to component^Oz_QiObtaining the components^Oy_QiSum component^Ox_QiAccording to component^Oz_QiComponent (c)^Oy_QiSum component^Ox_QiTo obtain^OR_QiI is 1 to 3, wherein,^OR_Qiis a rotation matrix of the axis ear coordinate system relative to the base coordinate system { O };

s8: the calculation uses X absolute offset value QAX and Y absolute offset value QAY as elements to construct an Axis-rotation center vector with { Q } coordinate system as a reference system^QjQA_iWherein i is 1 to 6 and j is 1 to 3, wherein QAX represents A₁And A₂In { Q₁Absolute offset value in x-axis direction of (A) }, QAY denotes A₁And A₂In { Q₁Absolute offset value of y-axis direction, A₁And A₂Is the hinge central point of two bearing pin shafts (410);

s9: rotating the matrix according to the axis-ear coordinate system^OR_QiI 1 to 3, axis ear-rotation center vector^QjQA_iI is 1 to 6, j is 1 to 3, and^OR_Qimultiplication by^QiQA_iObtaining the axis ear-rotation center vector using the base coordinate system { O } as the reference system^OQA_i，i＝1～6；

S10: according to the axis ear-rotation center vector^QjQA_iI is 1 to 6, j is 1 to 3 and the Hooke's joint-axis ear vector^oBQ_iAnd i is 1-6, and then the basic operation of the vector is used to obtain the position vector of the electric cylinder^OBA_i,i＝1～6。

2. The method of inverse position solution of a six-axis robot according to claim 1, wherein the pass-through R is_bMultiplying by a matrix calculation formula of the rotation angle around the Z axis and then multiplying by a Y axis unit vector to obtain a Hooke joint position vector^OOB₁～^OOB₆The calculation formula is as follows:

3. the method of inverse position solution of a six-axis robot according to claim 1, wherein the pass-through R is_QMultiplying the calculated formula by the matrix of the rotation angle around the Z axis and multiplying the calculated formula by the unit vector of the Y axis to obtain the position vector of the shaft lug^PPQ_iAnd i is 1-3, and the calculation formula is as follows:

4. the six-axis robot position inverse solution method according to claim 1, wherein the position inverse solution is based on the axis ear position vector^PPQ_iI is 1-3 and the Hooke's joint position vector^OOB₁～^OOB₆Then according to the coordinate rotation theorem and the basic operation theorem of the vector in the theory of robotics, the Hooke's hinge-axis ear vector is obtained^oBQ_iAnd i is 1-6, and the calculation formula is as follows:

5. the six-axis robot position inverse solution method according to claim 1, wherein the passing^OR_PMultiplying by a Z-axis rotation angle matrix calculation formula and then multiplying by a Y-axis unit vector to obtain a cross-axis vector^oD_iAnd i is 1-3, and the calculation formula is as follows:

6. the six-axis robot position inverse solution method according to claim 1, wherein the component^Oz_Q1The obtaining method comprises the following steps:

according to hook hinge-axis ear vector^oBQ₃And^oBQ₂by cross multiplication of vectors^oBQ₃×(-^oBQ₂) Calculating the norm | luminance^oBQ₃×(-^oBQ₂) | l, the component is obtained after the division calculation^Oz_Q1。

7. The method of claim 1, wherein the calculation uses X absolute offset value QAX and Y absolute offset value QAY as elements to construct an axis ear-rotation center vector with a { Q } coordinate system as a reference system^QjQA_iThe calculation formula of i is 1-6, and j is 1-3 is as follows:

^Q3QA₁＝^Q1QA₃＝^Q2QA₅＝[-QAX -QAY 0]^T

^Q1QA₂＝^Q2QA₄＝^Q3QA₆＝[QAX QAY 0]^T。

8. the six-axis robot position inverse solution method according to claim 1, wherein the rotation matrix according to the axis-ear coordinate system^OR_QiI 1 to 3, axis ear-rotation center vector^QjQA_iI is 1 to 6, j is 1 to 3, and^OR_Qimultiplication by^QjQA_iObtaining the axis ear-rotation center vector using the base coordinate system { O } as the reference system^OQA_iAnd i is 1-6, and the calculation formula is as follows:

9. the method of solving the inverse position of the six-axis robot according to claim 1, further comprising the steps of:

receiving an action instruction of the six-axis robot, wherein the action instruction comprises at least one of the following items: translation and rotation;

outputting a track sequence according to the action instruction;

acquiring a position vector of the electric cylinder;

and outputting the position vector of the electric cylinder to a motor servo system, so that the motor servo system controls the electric cylinder assembly (500) to move to complete the target motion track.

10. A six-axis robot, comprising:

at least one memory and at least one processor;

the memory for storing one or more programs;

when executed by the at least one processor, cause the at least one processor to carry out the steps of the six-axis robot position inverse solution method of any one of claims 1 to 9.

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