CN116408786A

CN116408786A - Mechanical arm dynamics analysis and modeling method, robot, equipment and medium

Info

Publication number: CN116408786A
Application number: CN202111654782.7A
Authority: CN
Inventors: 杨林; 陈文杰; 侯澈; 何理; 吴文镜; 姬四杰; 金明亮
Original assignee: GD Midea Air Conditioning Equipment Co Ltd; Midea Group Shanghai Co Ltd
Current assignee: GD Midea Air Conditioning Equipment Co Ltd; Midea Group Shanghai Co Ltd
Priority date: 2021-12-30
Filing date: 2021-12-30
Publication date: 2023-07-11

Abstract

The application discloses a mechanical arm dynamics analysis and modeling method, a robot, computer equipment and a storage medium. The mechanical arm dynamics analysis and modeling method provided by the embodiment of the application comprises the following steps: constructing a first dynamic formula of inertia force and moment of mass centers of the first mechanical arm, the second mechanical arm and the third mechanical arm; constructing a second dynamic formula of interaction force and interaction moment between mechanical arms; constructing a third dynamic formula of acting force and moment of the first mechanical arm and the double-link transmission mechanism acting on the second mechanical arm; constructing a first calculation formula of the torque of the first motor; constructing a second calculation formula of the torque of the second motor; the above formula is verified. Therefore, aiming at the series-parallel connection mixing of the rear motors and adopting a double-link transmission robot, a robot dynamics model can be built by utilizing a mechanical arm dynamics analysis and modeling method, and a theoretical basis can be provided for the design of the robot to optimize; a basic model may also be provided for robot control in order to improve the dynamic performance of the robot.

Description

Mechanical arm dynamics analysis and modeling method, robot, equipment and medium

Technical Field

The present disclosure relates to the field of robots, and in particular, to a method for analyzing and modeling dynamics of a mechanical arm, a robot, a computer device, and a storage medium.

Background

The horizontal multi-joint robot (SCARA) mainly comprises 4 joints, wherein the first joint, the second joint and the fourth joint are horizontal rotary joints, and the third joint is an up-and-down moving joint. In the related art, the axial directions of the direct drive motors M1 and M2 are not on the same straight line, and the first mechanical arm and the second mechanical arm are driven to move by the direct drive motors M1 and M2 respectively. Because the mass of the direct-drive motor is heavier, the installation mode of the M2 motor can lead to larger torque demand of the motor M1, so that the mass and the volume of the motor M1 are larger, and finally the weight and the volume of the whole machine are increased. At present, in order to reduce the weight and the volume of the whole machine, the traditional mechanical arm modeling method is not suitable for a SCARA structural model with a rear motor aiming at the proposal of the rear motor M2.

Disclosure of Invention

The embodiment of the application provides a mechanical arm dynamics analysis and modeling method, a robot, computer equipment and a storage medium.

The mechanical arm dynamics analysis and modeling method provided by the embodiment of the application comprises the following steps:

The method comprises the steps of constructing a first dynamic formula of inertia force and moment of mass centers of a first mechanical arm, a second mechanical arm and a third mechanical arm, wherein the first mechanical arm is rotationally connected with the second mechanical arm, the first mechanical arm rotates around a first joint, the second mechanical arm rotates around a second joint, and the third mechanical arm moves in a vertical direction relative to the second mechanical arm;

constructing a second dynamic formula of interaction force and interaction moment between the mechanical arms based on inertial force and moment of mass centers of the first mechanical arm, the second mechanical arm and the third mechanical arm;

constructing a third dynamic formula of acting force and moment of the first mechanical arm and the double-link transmission mechanism acting on the second mechanical arm based on inertial force and moment of mass centers of the first mechanical arm, the second mechanical arm and the third mechanical arm, wherein the double-link transmission mechanism is arranged in the first mechanical arm;

constructing a first calculation formula of torque of a first motor based on inertia force and moment acting on mass centers of a first mechanical arm, a second mechanical arm and a third mechanical arm, wherein the first motor is used for driving the first mechanical arm to rotate;

Constructing a second calculation formula of torque of a second motor based on inertia force and moment acting on mass centers of the first mechanical arm, the second mechanical arm and the third mechanical arm, wherein the second motor is used for driving the second mechanical arm to rotate through the double-link transmission mechanism;

verifying the first dynamic formula, the second dynamic formula, the third dynamic formula, the first calculation formula, and the second calculation formula.

In some embodiments, the constructing a first kinetic equation of inertial force and moment acting on centroids of the first, second, and third robotic arms includes:

constructing formulas of second angular speeds, second angular accelerations and accelerations of the first joint and the second joint and formulas of linear accelerations acting on centroids of the first mechanical arm, the second mechanical arm and the third mechanical arm according to a Newton-Euler iterative dynamics algorithm;

and constructing and obtaining the first dynamics formula based on formulas of the second angular velocity, the second angular acceleration and the linear acceleration of the first joint and the second joint and formulas of linear acceleration of mass centers of the first mechanical arm, the second mechanical arm and the third mechanical arm.

In certain embodiments, the first joint, the second joint second angular velocity, the second angular acceleration, and the linear acceleration are expressed by the following formulas:

wherein R is a rotation transformation matrix between coordinate systems,

is a rotation transformation matrix of the coordinate system { i } to the coordinate system { i+1}, θ,/->

Representing the angle, the first angular velocity and the first angular acceleration of the ith joint, { i+1} of the coordinate system>

The axis is called

ⁱ ω _i 、

Representing the ith joint in the machineThe second angular velocity, the second angular acceleration, and the linear acceleration of the arm coordinate system { i } with respect to the own coordinate system.

In some embodiments, the linear acceleration acting on the centroids of the first, second and third mechanical arms is expressed by the following formula:

wherein,,

for the linear acceleration acting on the centroid of the ith arm, +.>

Is the position vector of the i+1-th mechanical arm centroid relative to the coordinate system { i }, ⁱ P _i+1 is a position vector of the origin of the mechanical arm coordinate system { i+1} under the mechanical arm coordinate system { i }.

In certain embodiments, the first kinetic formula is:

wherein m is _i+1 Is the mass of the (i+1) th mechanical arm, ⁱ⁺¹ F _i+1 an inertial force acting on the mass center of the (i+1) th mechanical arm, ⁱ⁺ ¹ N _i+1 To act on the moment of the centroid of the i +1 th arm,

For the (i+1) th mechanical arm in the centroid coordinate system { C _i+1 Inertial tensor in }.

In certain embodiments, the second kinetic formula is:

wherein,, ⁱ F _i 、 ⁱ N _i for inertial forces and moments at the i-th arm centroid, ⁱ⁺¹ f _i+1 、 ⁱ⁺¹ n _i+1 the force and moment acting on the (i+1) th mechanical arm are the (i) th mechanical arm.

In some embodiments, the third kinetic formula of the force and moment of the second mechanical arm is:

wherein,, ² f ₂ 、 ² n ₂ for the upper inertial forces and moments of the first mechanical arm and the dual link transmission acting at the center of mass of the second mechanical arm, ² F ₂ to act on the inertial force of the centroid of the second mechanical arm, ² N ₂ is a moment acting on the center of mass of the second mechanical arm.

In certain embodiments, the torque of the first electric machine is expressed by the following formula:

τ ₁ ＝ ¹ n ₁ ，

wherein τ ₁ For the torque of the first electric machine, ¹ n ₁ is the torque of the first joint.

In certain embodiments, the torque of the second electric machine is expressed by the following formula:

τ ₂ ＝ _link + ² n ₂ ，

wherein τ ₂ For the torque of the second motor, ² n ₂ is the moment on the centroid of the second mechanical arm, τ _link The torque required for the rotation of the double-link transmission mechanism.

The robot provided by the embodiment of the application comprises a first mechanical arm, a second mechanical arm, a third mechanical arm and a double-link transmission mechanism, wherein the first mechanical arm is rotationally connected with the second mechanical arm, the first mechanical arm rotates around a first joint, the second mechanical arm rotates around a second joint, the third mechanical arm moves in the vertical direction relative to the second mechanical arm, the double-link transmission mechanism is arranged in the first mechanical arm, and the mechanical arm dynamics analysis and modeling method in any embodiment can be used for the robot.

An embodiment of the present application provides a computer device, where the computer device includes a memory and a processor, where the memory stores a computer program, and the processor implements the mechanical arm dynamics analysis and modeling method in any of the foregoing embodiments when executing the computer program.

The non-transitory computer-readable storage medium of computer-executable instructions provided by embodiments of the present application, when executed by one or more processors, cause the processors to perform the robotic arm dynamics parsing and modeling method of any one of the above.

In the mechanical arm dynamics analysis and modeling method provided by the embodiment of the application, the mechanical arm dynamics analysis and modeling method can be applied to series-parallel connection mixing with a rear motor, a robot with a double-link transmission mode is adopted, and a mechanical arm dynamics analysis and modeling method is adopted to build a mechanical model of the robot, so that on one hand, theoretical basis can be provided for motor design and structural design of the robot, and the electromechanical system design of the robot is optimized; on the other hand, a basic model can be provided for robot control, and an algorithm designer designs and improves a control algorithm on the basis, so that the dynamic performance of the robot is improved.

Additional aspects and advantages of the application will be set forth in part in the description which follows, and in part will be obvious from the description, or may be learned by practice of the application.

Drawings

The foregoing and/or additional aspects and advantages of the present application will become apparent and readily appreciated from the following description of the embodiments, taken in conjunction with the accompanying drawings, in which:

FIG. 1 is a flow diagram of a method for kinetic resolution and modeling of a robotic arm according to an embodiment of the present application;

fig. 2 is a schematic view of a part of the structure of a robot according to an embodiment of the present application;

FIG. 3 is a schematic structural view of a first mechanical arm and dual link transmission mechanism according to an embodiment of the present application;

fig. 4 is a schematic structural view of a robot according to an embodiment of the present application;

fig. 5 is a schematic structural view of another view of the robot according to the embodiment of the present application;

FIG. 6 is a partially exploded schematic illustration of a dual link transmission of an embodiment of the present application;

FIG. 7 is an exploded schematic view of a first mechanical arm and dual link transmission mechanism of an embodiment of the present application;

FIG. 8 is a block diagram of a computer device according to an embodiment of the present application;

FIG. 9 is a schematic flow chart of a method for dynamic analysis and modeling of a robotic arm according to an embodiment of the present application;

FIG. 10 is a schematic illustration of a method of mechanical arm dynamics analysis and modeling in accordance with an embodiment of the present application;

FIG. 11 is another schematic illustration of a robotic arm dynamics analysis and modeling method according to an embodiment of the present application;

FIG. 12 is a comparative simulation of a method of mechanical arm dynamics analysis and modeling in accordance with an embodiment of the present application;

fig. 13 is another simulated comparison of the mechanical arm dynamics analysis and modeling method of the embodiment of the present application.

Description of main reference numerals:

robot 100, first arm 11, second arm 12, third arm 13, first joint 21, second joint 22, double-link transmission mechanism 30, upper link 31, lower link 32, first flange 331, second flange 332, third flange 333, fourth flange 334, first upper bearing 341, second upper bearing 342, first lower bearing 343, second lower bearing 344, third bearing 35, intermediate shaft 36, baffle ring 37, first motor 41, second motor 42, base 50, computer device 200, memory 201, and processor 202.

Detailed Description

Embodiments of the present application are described in detail below, examples of which are illustrated in the accompanying drawings, wherein the same or similar reference numerals refer to the same or similar elements or elements having the same or similar functions throughout. The embodiments described below by referring to the drawings are exemplary only for the purpose of explaining the present application and are not to be construed as limiting the present application.

In the description of the present application, it is worth mentioning that the terms "center", "longitudinal", "transverse", "length", "width", "thickness", "upper", "lower", "front", "rear", "left", "right", "vertical", "horizontal", "top", "bottom", "inner", "outer", etc. are for ease of understanding of the simplified description of the present application. Features defining "first", "second" may include one or both explicitly and implicitly. In the description of the present application, the meaning of "plurality" is that two or more are possible.

In the description of the present application, it should be noted that the connection may be an electrical connection or may be in communication with each other. The specific meaning of the terms in this application will be understood by those of ordinary skill in the art as the case may be.

In this application, unless specifically limited otherwise, a first feature "above" or "below" a second feature may include the first and second features being in direct contact, or may include the first and second features not being in direct contact but being in contact by another feature therebetween. Moreover, a first feature being "above," "over" and "on" a second feature includes the first feature being directly above and obliquely above the second feature, or simply indicating that the first feature is higher in level than the second feature. The first feature being "under", "below" and "beneath" the second feature includes the first feature being directly under and obliquely below the second feature, or simply means that the first feature is less level than the second feature.

The following disclosure provides many different embodiments or examples for implementing different structures of the present application. In order to simplify the disclosure of the present application, the components and arrangements of specific examples are described below. Of course, they are merely examples and are not intended to limit the present application. The present application may repeat reference numerals and/or letters in the various examples, which are for the purpose of brevity and clarity, and does not in itself indicate a relationship between the various embodiments and/or arrangements discussed. Examples of various specific processes and materials are provided herein, but one of ordinary skill in the art will recognize the application of other processes and/or the use of other materials.

Referring to fig. 1 to fig. 4, the mechanical arm dynamics analysis and modeling method provided in the embodiment of the present application includes:

step S10: a first dynamic formula of inertia force and moment acting on the centroids of the first mechanical arm 11, the second mechanical arm 12 and the third mechanical arm 13 is constructed, the first mechanical arm 11 is rotationally connected with the second mechanical arm 12, the first mechanical arm 11 rotates around a first joint 21, the second mechanical arm 12 rotates around a second joint 22, and the third mechanical arm 13 moves in a vertical direction Z relative to the second mechanical arm 12;

Step S20: constructing a second dynamic formula of interaction force and interaction moment between the mechanical arms based on the inertial force and moment of the mass centers of the first mechanical arm 11, the second mechanical arm 12 and the third mechanical arm 13;

step S30: based on the inertial force and moment of the center of mass of the first arm 11, the second arm 12, the third arm 13, a third dynamic formula of the acting force and moment of the first arm 11 and the double link transmission mechanism 30 acting on the second arm 12 is constructed, and the double link transmission mechanism 30 is provided in the first arm 11.

Step S40: constructing a first calculation formula of the torque of the first motor 41 based on the inertial force and moment acting on the centroids of the first, second and third

mechanical arms

11, 12, 13, the first motor 41 being used to drive the first mechanical arm 11 to rotate;

step S50: constructing a second calculation formula of the torque of the second motor 42 based on the inertial force and moment acting on the centroids of the first mechanical arm 11, the second mechanical arm 12 and the third mechanical arm 13, wherein the second motor 42 is used for driving the second mechanical arm 12 to rotate through the double-link transmission mechanism 30;

step S60: and verifying the first dynamic formula, the second dynamic formula, the third dynamic formula, the first calculation formula and the second calculation formula.

Referring to fig. 2-5, a robot 100 according to an embodiment of the present application may include a dual link transmission mechanism 30, a third mechanical arm 13, a second mechanical arm 12, and a first mechanical arm 11.

The second mechanical arm 12 and the first mechanical arm 11 may be rotatably connected. More specifically, the first robot arm 11 is rotatable about the first joint 21, and the second robot arm 12 is rotatable about the second joint 22.

The third robot arm 13 is movable in the vertical direction Z with respect to the second robot arm 12. The first mechanical arm 11 is provided with a double-link transmission mechanism 30, and the mechanical arm dynamics analysis and modeling method can be used for the robot 100.

The horizontal multi-joint robot (hereinafter referred to as SCARA) mainly comprises 4 joints, wherein the first joint, the second joint and the fourth joint are horizontal rotation joints, and the third joint is an up-and-down movement joint. The first joint, the second joint and the fourth joint are horizontal rotary joints, and the third joint is an up-and-down moving joint. In the related art, a first joint motor M1 is connected with a first joint to drive a first mechanical arm to rotate, a second joint motor M2 is connected with a second joint to drive a second mechanical arm to rotate, and motors of a third joint and a fourth joint adopt a transmission scheme of a synchronous belt and a ball screw. Because the axial directions of the direct drive motors M1 and M2 are not on the same straight line, the first mechanical arm and the second mechanical arm are respectively driven to move by the direct drive motors M1 and M2.

Because the mass of the direct-drive motor is heavier, the installation mode of the M2 motor can lead to larger torque demand of the motor M1, so that the mass and the volume of the motor M1 are larger, and finally the weight and the volume of the whole machine are increased. At present, in order to reduce the weight and the volume of the whole machine, the traditional mechanical arm modeling method is not suitable for a SCARA structural model with a rear motor aiming at the proposal of the rear motor M2.

It can be understood that the mechatronics is based on the modern industry of high development of microelectronic technologies represented by large-scale integrated circuits and microcomputers, high-speed development of precision machinery, and high combination of mechanical and electronic technologies, and comprehensively applies group technologies such as mechanical technologies, microelectronic technologies, automatic control technologies, information technologies, sensing and testing technologies, power electronic technologies, interface technologies, signal conversion technologies, software programming technologies and the like, so that the structure of the product is fundamentally changed, and great economic benefits are brought to human beings. It can be derived that optimizing the electromechanical system design of a robot is a problem to be developed and studied.

Then, the mechanical arm dynamics analysis and modeling method provided in the embodiment of the present application may be applicable to the series-parallel hybrid with the motor at the rear, and the robot 100 adopting the dual-link transmission mode is adopted. By adopting a mechanical arm dynamics analysis and modeling method, a robot 100 dynamics model is built, on one hand, a theoretical basis can be provided for motor design and structural design of the robot 100, and thus, the electromechanical system design of the robot 100 is optimized; on the other hand, a basic model can be provided for the control of the robot 100, and an algorithm designer designs and improves the control algorithm on the basis of the basic model, so that the dynamic performance of the robot 100 is improved.

The first mechanical arm 11 may be driven by the first motor 41 to move, so that the first mechanical arm 11 may rotate around the first joint 21. In the scheme of the rear-mounted second motor 42, the second motor 42 needs to drive the second mechanical arm 12 to rotate, and the dual-link transmission mechanism 30 can play a role in transmission.

The motion of the dual link transmission 30 may be driven by the second motor 42 such that the dual link transmission 30 may rotate the second mechanical arm 12 about the second joint 22. When the first mechanical arm 11 moves, that is, the second motor 42 may drive the second mechanical arm 12 to rotate through the dual-link transmission mechanism 30.

In the embodiment of the present application, the first motor 41 and the second motor 42 of the robot 100 are disposed at the rear positions of the motors, that is, the first motor 41 and the second motor 42 are respectively located at two sides of the first mechanical arm 11 along the vertical direction Z. It should be noted that the axis of the second motor 42 and the axis of the first motor 41 are on the same straight line.

The dual-link transmission mechanism 30 is disposed in the first mechanical arm 11, where the first mechanical arm 11 may be driven by a first motor 41, and when the first mechanical arm 11 moves, the second motor 42 may drive the dual-link transmission mechanism 30 to drive the first mechanical arm 11 and the dual-link transmission mechanism 30 to jointly drive the second mechanical arm 12 to move.

In some embodiments, the first motor 41 may be disposed at an upper end of the first robot arm 11 and the second motor 42 may be disposed at a lower end of the second robot arm 12 along the vertical direction Z. The second mechanical arm 12 is disposed at an end of the first mechanical arm 11 remote from the first motor 41 and the second motor 42. The third arm 12 is disposed at an end of the second arm 12 remote from the first machine 11.

The shape of the first mechanical arm 11 may be a cuboid, the shape of the first mechanical arm 11 may also be a round rod, and the first mechanical arm 11 may also be a shape with two ends being cylindrical and a middle being a cuboid, which is not limited herein. Similarly, the shape of the second mechanical arm 12 may be a cuboid, the second mechanical arm 12 may also be a round rod, and the second mechanical arm 12 may also be a cuboid with two ends being cylindrical and the middle being non-limiting here.

The shape of the third mechanical arm 13 may be a rectangular parallelepiped, and the third mechanical arm 13 may also be a rectangular parallelepiped with two ends being cylindrical and the middle being non-limiting here. In one embodiment, the third mechanical arm 13 may be shaped like a round rod, so that the third mechanical arm 13 is convenient to move along the vertical direction Z, and wear during the movement of the third mechanical arm 13 may be reduced.

The shapes of the third mechanical arm 13, the second mechanical arm 12 and the first mechanical arm 11 may be the same or different, and the shapes of the third mechanical arm 13, the second mechanical arm 12 and the first mechanical arm 11 may be selected according to actual requirements without limitation.

It should be noted that the robot 100 may refer to an electromechanical system composed of a mechanical structure and electronic components. In some embodiments, electromechanical systems such as automated robotic arms and steerable wheeled platforms commonly used in the industry may also be referred to as "industrial robots".

The robot 100 referred to in this application may be a SCARA (Selective Compliance Assembly Robot Arm, selectively compliant assembly robot arm) robot, which is a robot with a selectively flexible approximately cylindrical working space. The SCARA robot has high horizontal plane flexibility and good plumb plane rigidity, and can be widely applied to sorting, assembling, stacking and other works. That is, the SCARA robot has a light structure and a quick response, and is therefore suitable for planar positioning and assembling in a vertical direction. In one example, a SCARA robot may be used to insert a round-headed needle into a round hole. The robot provided by the application can be widely applied to the fields of electronic product industry, automobile industry, plastic industry, medicine industry and food industry and is used for completing operations such as carrying, assembling, spraying, welding and the like.

The SCARA robot is required to have high-speed and high-precision characteristics in industrial application, namely, the SCARA robot is required to have an accurate motion control algorithm. The motion control algorithm is not separated from the mechanical arm dynamics analysis of the robot, and in order to obtain a more accurate dynamics equation, the dynamics parameters of the robot need to be identified.

In some embodiments, the robot 100 may be subjected to dynamic analysis and modeling of the mechanical arm by a disassembly experimental measurement method, a CAD method, a theoretical identification method, or the like. The disassembly experiment measurement method needs to disassemble the robot and perform inertial parameter measurement experiments after the robot is arranged on a specific measurement platform, and the disassembly experiment measurement method needs a specific experimental device and has larger workload; and the kinetic parameters identified by the CAD model method cannot accurately correspond to the actual kinetic model of the robot.

Therefore, in the embodiment of the application, the theoretical identification method is adopted to identify the parameters of the mechanical energy dynamics of the robot, and the kinetic parameters obtained by identification can enable the mechanical arm dynamics model of the robot to operate more accurately.

Referring to fig. 2-4 in combination, in some embodiments, the robot 100 may further include a first motor 41 connected to the first mechanical arm 11, and a second motor 42 connected to the dual link transmission mechanism 30, wherein an axial direction of the second motor 42 is in the same axial direction as an axial direction of the first motor 41.

In this way, since the second motor 42 is not mounted on the first mechanical arm 11, the moment of inertia is significantly reduced with respect to the rotation axis of the first joint 21, so that the torque requirement on the first motor 41 is reduced, and the mass and volume of the first motor 41 can be reduced, and the overall mass and volume of the robot 100 can be further reduced.

Referring to fig. 2, 4, 6 and 7, the dual-link transmission mechanism 30 may include an upper link 31 and a lower link 32, wherein a left end of the upper link 31 is connected to the first flange 331 and is connected to the first mechanical arm 11 through a first upper bearing 341, and a right end of the upper link 31 is connected to the second flange 332 and is connected to the first mechanical arm 11 through a second upper bearing 342.

The left end of the lower link 32 of the double link transmission mechanism 30 is connected with the third flange 333 and the first mechanical arm 11 through the first lower bearing 343, and the left end of the lower link 32 is connected with the fourth flange 334 and the first mechanical arm 11 through the second lower bearing 344. The upper link 31 and the lower link 32 may be connected to an intermediate shaft 36 through a third bearing 35. The double link transmission mechanism 30 may further include a plurality of stopper rings 37, and the stopper rings 37 may be installed at both upper and lower end surfaces of the third bearing 35.

When the double link transmission mechanism 30 is mounted on the robot 100, the double link transmission mechanism 30 may be provided in the first arm 11. More specifically, the second motor 42 may be connected to the left end of the upper link 31 through the first flange 331, and the second robot arm 12 is connected to the right end of the upper link 31 through the second flange 332.

Thus, when the second motor 42 rotates, the first flange 331 connected to the left end of the upper link 31 is driven to rotate, and the second flange 332 connected to the right end of the upper link 31 is driven to rotate by the transmission of the upper link 31 and the lower link 32, so as to finally drive the second mechanical arm 12 to rotate, and the second motor 42 can drive the second mechanical arm 12 to rotate by the double-link transmission mechanism 30.

Wherein the first flange 331, the second flange 332, the third flange 333, and the fourth flange 334 may be made of carbon steel, low alloy steel, stainless steel, or the like. The first flange 331, the second flange 332, the third flange 333, and the fourth flange 334 may each be annular disk-shaped bodies.

The first flange 331 is connected to the left ends of the first robot arm 11 and the upper link 31, and the second flange 332 is connected to the right ends of the first robot arm 11 and the upper link 32. The third flange 333 is connected to the left ends of the first arm 11 and the lower link 31, and the fourth flange 334 is connected to the right ends of the first arm 11 and the lower link 31. The upper and

lower links

31 and 32 may be disposed in the first robot arm 11 through a first upper bearing 341, a second upper bearing 342, a first lower bearing 343, a second lower bearing 344, a third bearing 35, an intermediate shaft 36, and a check ring 37.

Wherein, the first upper bearing 341, the second upper bearing 342, the first lower bearing 343, the second lower bearing 344 and the third bearing 35 can play a role in supporting the mechanical rotating body, reducing the friction coefficient (friction coefficient) during the movement of the rotating body, and ensuring the rotation precision (accuracies) of the rotating body. The common bearings can be rolling bearings, deep groove ball bearings, aligning ball bearings, needle bearings and the like.

In one example, the third bearing 35 may be a deep groove ball bearing. The deep groove ball bearing is a rolling bearing with wider application. The deep groove ball bearing features small friction resistance and high rotation speed, and can be used for bearing radial load or combined load of radial and axial actions, or axial load, and can be used for bearing small-power motor, gearbox of automobile and tractor, gearbox of machine tool, etc. The deep groove ball bearing consists of an outer ring, an inner ring, a group of steel balls and a group of retainers.

In the present embodiment, the rotation angle of the first robot arm 11 is determined by the first motor 41, and the rotation angle of the second robot arm 12 is determined by both the first motor 41 and the second motor 42. The robot 100 has a serial-parallel hybrid mechanism of a first arm 11 and a second arm 12 connected in parallel.

The mechanical arm dynamics analysis and modeling of the robot 100 are performed by analyzing the mechanical arm by a dynamics modeling method of the serial robot 100, and then the parallel structure dynamics model is considered, so that the dynamics model of the serial-parallel hybrid mechanism robot 100 is established.

In some embodiments, the robot 100 may also include a base 50. When the robot 100 is placed on an arbitrary plane, the base 50 contacts the plane, and the base 50 can provide a smooth supporting function for the body of the robot 100. The base 50 may also be used to carry the first motor 41.

In some embodiments, the third mechanical arm 13 is detachably provided with a load, so that the carrying or assembling of the load and the like can be completed through the common movement of the third mechanical arm 13, the second mechanical arm 12 and the first mechanical arm 13.

The third mechanical arm 13, the base 50, the second mechanical arm 12 and the first mechanical arm 11 may be made of an alloy to ensure the strength of the robot. In one embodiment, the third arm 13, the base 50, the second arm 12 and the first arm 11 are all made of aluminum alloy materials, so that the robot 100 is light and strong.

In some embodiments, the third mechanical arm 13, the base 50, the second mechanical arm 12 and the first mechanical arm 11 may also be made of composite plastics, which is not limited herein.

In summary, in the robot 100 provided in the embodiment of the present application, when the first motor 41 rotates, the first mechanical arm 11 can be driven to rotate. When the second motor 42 rotates, the first flange 331 connected to the left end of the upper link 31 is driven to rotate, and the second flange 332 connected to the right end of the upper link 31 is driven to rotate by the transmission of the upper link 31 and the lower link 32, so as to finally drive the second mechanical arm 12 to rotate, and the second motor 42 can drive the second mechanical arm 12 to rotate by the double-link transmission mechanism 30. In this case, since the double link transmission mechanism 30 is located in the first arm 11 of the robot 100, the double link transmission mechanism 30 rotates while the double link transmission mechanism 30 rotates with itself, and the double link transmission mechanism 30 revolves along with the first arm 11.

In some embodiments, the robot 100 may further include a third motor connected to the third mechanical arm 13, wherein the third motor may employ a timing belt and ball screw transmission scheme. More specifically, the third motor may drive the third mechanical arm 13 to move up and down along the vertical direction Z through a pulley.

In this way, the first motor 41, the second motor 42 and the dual-link transmission mechanism 30 can jointly drive the first mechanical arm 11 to rotate around the first joint 21 and the second mechanical arm 12 to rotate around the second joint 22. In the vertical direction Z, the third mechanical arm 13 is driven to move by the third motor. When the third arm 13 is mounted with a load, the robot 100 may be caused to perform operations of carrying the load, assembling the load, or the like.

In some embodiments, the first motor 41 and the second motor 42 may be servo motors, the servo motors may control the speed, the position accuracy is very accurate, and the voltage signals may be converted into the torque and the rotation speed to drive the control object. The rotation speed of the rotor of the servo motor is controlled by an input signal, can react quickly, is used as an executive component in an automatic control system, has the characteristics of small electromechanical time constant, high linearity and the like, and can convert the received electric signal into angular displacement or angular speed output on the motor shaft. The motor is divided into two major types of direct current and alternating current servo motors, and is mainly characterized in that when the signal voltage is zero, no autorotation phenomenon exists, and the rotating speed is reduced at a constant speed along with the increase of the torque.

In some embodiments, the first motor 41 and the second motor 42 may also be stepper motors to reduce cost. A stepper motor is a motor that converts an electrical pulse signal into a corresponding angular or linear displacement. Each time a pulse signal is input, the rotor rotates by an angle or further, the output angular displacement or linear displacement is proportional to the input pulse number, and the rotating speed is proportional to the pulse frequency. Therefore, the stepping motor is also called a pulse motor, and is based on the basic electromagnet principle, namely an electromagnet capable of freely rotating, and the action principle is to generate electromagnetic torque by means of the change of air gap flux guide.

Referring to fig. 8, an embodiment of the present application provides a computer device 200, where the computer device 200 includes a memory 201 and a processor 202, the memory 201 stores a computer program, and the processor 202 implements the mechanical arm dynamics analysis and modeling method in the above embodiment when executing the computer program.

Specifically, the computer device 200 in the embodiment of the present application may be a device such as a calculator, a programmable controller, a desktop computer, a laptop computer, a tablet computer, a server, etc., and the computer device 200 may include a processor 202, a memory 201, a communication interface, a display screen, and an input device connected through a system bus.

The processor 202 of the computer device 200 is configured to provide computing and control capabilities, and the memory 201 includes a non-volatile storage medium, an internal memory 201, where the non-volatile storage medium stores an operating system and a computer program, and the internal memory 201 provides an environment for the operating system and the computer program in the non-volatile storage medium to run.

In certain embodiments, the processor 202 is configured to execute a computer program to implement the method for dynamic analysis and modeling of a robotic arm described in step S10, step S20, step S30, step S40, step S50, and step S60.

The communication interface of the computer device 200 is used for performing wired or wireless communication with an external terminal, the wireless communication can be implemented through WIFI, an operator network, NFC (near field communication) or other technologies, and the computer program when executed by the processor 202 is used to implement a mechanical arm dynamics analysis and modeling method of the high-freedom robot 100, which is oriented to more complex application scenarios.

The display screen of the computer device 200 may be a liquid crystal display screen or an electronic ink display screen, and the input device of the computer device 200 may be a touch layer covered on the display screen, or may be a key, a track ball or a touch pad arranged on the casing of the computer device 200, or may be an external keyboard, a touch pad or a mouse.

In one embodiment, the memory 201 and the processor 202 may be implemented using a general purpose personal computer, or a robot 100 computer installed on the robot 100. The robot 100 has installed necessary components such as sensors and actuators according to the prior art, and can acquire necessary data for the processor 202 to process, and the actuators can execute the processing results of the processor 202.

Referring to fig. 9, in some embodiments, constructing a first kinetic equation of inertial force and moment acting on centroids of the first arm 11, the second arm 12, and the third arm 13 includes:

Step S11: constructing formulas of second angular speeds, second angular accelerations and linear accelerations of the first joint 21 and the second joint 22 and formulas of linear accelerations acting on centroids of the first mechanical arm 11, the second mechanical arm 12 and the third mechanical arm 13 according to a Newton-Euler iterative dynamics algorithm;

step S12: the first dynamic formula is constructed based on the formulas of the angular velocities, the angular accelerations, and the accelerations of the first joint 21, the second joint 22, and the formulas of the linear accelerations acting on the centroids of the first arm 11, the second arm 12, and the third arm 13.

In certain embodiments, the processor 202 is configured to execute a computer program to implement the mechanical arm dynamics parsing and modeling method as in step S11, step S12.

In particular, many methods of mechanical arm dynamics analysis and modeling are studied, such as Newton-Euler (Newton-Euler) method, generalized darbert (G-D' Alermbert) method, lagrangian (Lagrange) method, hamilton (Hamilton) method, kane equation, gauss (Gauss) method, abell (Apel) equation, and the like. One of the methods, newton-Euler, is a commonly used iterative dynamics algorithm for the robot 100, which is based on Newton's second law and Euler's equation.

More specifically, the mechanical arm is a typical multi-body system, and the most common method for establishing the multi-body system is to use a Newton-Euler method, and the translation and rotation of a single rigid body under force and moment can be well described due to a Newton-Euler mechanical equation.

The single rigid body dynamics mainly solves the modeling problem of translation and rotation, and the Newton equation mainly aims to solve the translation problem, namely the relation between external acting force and acceleration, in the Newton-Euler equation. The euler equation mainly deals with the rotation problem of the rigid body, and relates to the angular velocity and the angular acceleration of the rigid body.

The Newton-Euler dynamics equation can obtain a set of forward and reverse recurrence equations, and the Newton-Euler dynamics has the remarkable advantage that the calculation time of the driving moment can be shortened to the extent that the driving moment can be controlled in real time.

The newton-euler kinetic equation is a static equilibrium problem that applies the darbert principle to transform the kinetic problem into a newton-euler form. That is, when a non-free particle system is moving, the primary force system, the restraining reaction system and the inertial force system of the particle system form a balanced force system (algebraic sum in any direction is zero).

Referring to fig. 2 and 10, fig. 10 is a schematic diagram showing the derivation of the velocity and the acceleration when the i+1th joint is a rotary joint. In certain embodiments, the second angular velocity, second angular acceleration, and linear acceleration of the first joint 21, second joint 22 are expressed by the following formulas:

wherein R is a rotation transformation matrix between coordinate systems,

The axis is called

ⁱ ω _i 、

Representing the second angular velocity, the second angular acceleration and the linear acceleration of the ith joint in the mechanical arm coordinate system { i } relative to the self coordinate system.

Specifically, coordinate transformation is a description of the position of a spatial entity, a process of transforming from one coordinate system to another. By establishing a one-to-one correspondence between the two coordinate systems. The rotation transformation matrix R between the two coordinate systems can be derived from the relation between the coordinate system { i } and the coordinate system { i+1 }. That is, a rotation transformation matrix may be used to represent the relationship between two coordinate systems. The rotation matrix is mainly used to calculate the conversion between representations of the same point in different coordinate systems.

It should be noted that in the formulas (1) and (2),

angular velocity vectors and angular acceleration vectors provided by the i+1th motor for the i+1th joint.

In the present embodiment, the first joint 21 and the second joint 22 are both revolute joints.

Wherein, the first joint 21 is located in the coordinate system { i }, the second joint 22 is located in the coordinate system { i+1}, and when calculating the second angular velocity, the second angular acceleration and the linear acceleration of the first joint 21 and the second joint 22 in the mechanical arm coordinate system { i } relative to the self coordinate system. It should be noted that the angles, the first angular velocities, and the first angular accelerations of the first joint 21 and the second joint 22 refer to the angles, the angular velocities, and the angular accelerations of the first joint 21 and the second joint 22 in their own coordinate systems.

Specifically, the calculation of the outward iteration of the first arm 11 to the third arm 13 may be performed by the newton-euler iterative dynamics algorithm, and when i=0, the second angular velocity of the first joint 21 is calculated according to formula (1) ¹ ω ₁ After that, will ¹ ω ₁ Bringing into equation (2) to obtain the second angular acceleration of the first joint 21

And then->

Substituting into equation (3) the linear acceleration of the first joint 21 can finally be derived +.>

Similarly, when i=1, the second angular velocity of the second joint 22 can be calculated according to formula (1) ² ω ₂ After that, will ² ω ₂ Bringing into equation (2) to obtain a second angular acceleration of the second joint 22

And then->

Substituting into equation (3) finally the linear acceleration of the second joint 22 can be derived +.>

Similarly, when i=2, the second angular velocity of the third joint can be calculated according to formula (1) ³ ω ₃ After that, will ³ ω ₃ And then the second angular acceleration of the third joint is obtained by taking the second angular acceleration into the formula (2)

And then->

Substituting into formula (3), the linear acceleration of the third joint can be finally obtained>

The center of mass is simply referred to as the centroid and refers to an imaginary point on the mass system where the mass is considered to be concentrated. Unlike the center of gravity, the center of mass does not have to be in a system with a gravitational field. Notably, unless the gravitational field is uniform, the centroid and center of gravity of the same material system are typically not at the same imaginary point. The mass center of the object refers to that the object only translates when the action line of the external force passes through a certain point on the object; when the external force acting line does not pass through the fixed point, the whole object is superposition of two motions of translation along with the fixed point and rotation around the fixed point.

Referring to fig. 2 and 10, in some embodiments, the linear acceleration acting on the centroids of the first arm 11, the second arm 12, and the third arm 13 is expressed by the following formula:

Wherein,,

for the linear acceleration acting on the centroid of the ith arm, +.>

Is the centroid of the (i+1) th mechanical arm relative to a coordinate system { i }The position vector is used to determine the position of the object, ⁱ P _i+1 is a position vector of the origin of the mechanical arm coordinate system { i+1} under the mechanical arm coordinate system { i }. The meaning of the remaining parameters is the same as the foregoing, and will not be described in detail here.

Specifically, the position vector is a directional line segment that starts at the origin of coordinates and ends at the position of the moving particle at a certain point in time.

More specifically, the calculation of the outward iteration may be performed by the first to third mechanical arms of the newton-euler iterative dynamics algorithm.

When i=0, the formula (1) can be given as ¹ ω ₁ In formula (2)

And +.>

Substituting the linear acceleration into the formula (4) to calculate the linear acceleration which acts on the mass center of the first mechanical arm 11>

When i=1, the formula (1) can be given as ² ω ₂ In formula (2)

And +.>

Substituting the linear acceleration into the formula (4) to calculate the linear acceleration acting on the mass center of the second mechanical arm 12>

When i=2, the formula (1) can be given as ³ ω ₃ In formula (2)

And +.>

Substituting the linear acceleration into the formula (4) to calculate the linear acceleration which acts on the mass center of the third mechanical arm 13>

Referring to fig. 2 and 11, in some embodiments, the first dynamic formula is:

for the (i+1) th mechanical arm in the centroid coordinate system { C _i+1 Inertial tensor in }. The meaning of the remaining parameters is the same as the foregoing, and will not be described in detail here.

The inertial tensor refers to a rectangular coordinate system Kxyz with an arbitrary reference point K in the three-dimensional space and the reference point as the origin.

Specifically, the second law of motion of newtons is commonly expressed as that the magnitude of acceleration of an object is proportional to the applied force, inversely proportional to the mass of the object, and proportional to the inverse of the mass of the object; the direction of the acceleration is the same as the direction of the force.

Knowing the mass m of the first arm 11 ₁ Mass m of second mechanical wall ₂ Linear acceleration acting on the centre of mass of the first arm 11

And linear acceleration acting on the centre of mass of the second arm 12 +.>

Can be calculated according to Newton's second law of motion to obtain the inertial force acting on the centroid of the first mechanical arm 11 ¹ F ₁ Inertial force acting on the centre of mass of the second arm 12 ² F ₂ 。

When i=0, the linear acceleration acting on the centroid of the first mechanical arm 11 calculated in the formula (4) is calculated

Substituting into equation (5), the inertial force acting on the centroid of the first arm 11 can be derived ¹ F ₁ . And then will be ¹ F ₁ Is substituted into the formula (6), and finally the moment acting on the mass center of the first mechanical arm 11 is calculated ¹ N ₁ 。

When i=1, the linear acceleration acting on the centroid of the second mechanical arm 12 calculated in the formula (4) is calculated

Substituting into equation (5) to obtain inertial force acting on the centroid of the second mechanical arm 12 ² F ₂ . And then will be ² F ₂ Is substituted into equation (6) and the moment acting on the center of mass of the second arm 12 is finally calculated ² N ₂ 。

When i=2, the linear acceleration acting on the center of mass of the third mechanical arm 13 calculated in the formula (4) is calculated

Substituting into equation (5), the inertial force acting on the center of mass of the third arm 13 can be obtained ³ F ₃ . And then will be ³ F ₃ Is substituted into the formula (6), and finally the moment acting on the center of mass of the third mechanical arm 13 is calculated ³ N ₃ 。

Referring to fig. 2 and 11, in some embodiments, the second kinetic equation is:

wherein,, ⁱ F _i 、 ⁱ N _i for inertial forces and moments at the i-th arm centroid, ⁱ⁺¹ f _i+1 、 ⁱ⁺¹ n _i+1 the force and moment acting on the (i+1) th mechanical arm are the (i) th mechanical arm. The meaning of the remaining parameters is the same as the foregoing, and will not be described in detail here.

Specifically, when the inertial force acting on the centroid of the first mechanical arm 11 is derived ¹ F ₁ And moment of force ¹ N ₁ Inertial force acting on the centre of mass of the second mechanical arm 12 ² F ₂ And moment of force ² N ₂ Inertial force acting on the center of mass of the third mechanical arm 13 ³ F ₃ And moment of force ³ N ₃ Then, the iterative manner from the third mechanical arm 13 to the first mechanical arm 11 can be performed by the Newton-Euler iterative dynamics algorithm, and the interaction force and the interaction moment between the mechanical arms can be calculated.

Wherein, calculate ³ f ₃ And ³ n ₃ at the time, it will be used to ⁴ f ₄ And ⁴ n ₄ . As shown in fig. 2, since the tip 131 of the third mechanical arm 13 in the vertical direction Z is not applied with an applied force and moment, the third mechanical arm is ⁴ f ₄ ＝0, ⁴ n ₄ ＝0。

When i=3, the calculated inertial force acting on the centroid of the third arm 13 in the case of i=2 can be used ³ F ₃ Is brought into the formula (7), thereby deriving the force of the second arm 12 acting on the third arm 13 ³ f ₃ 。

When i=3, the calculated inertial force acting on the centroid of the third arm 13 in the case of i=2 can be used ³ F ₃ And moment of force ³ N ₃ Is brought into the formula (7), thereby deriving the moment of the second mechanical arm 12 acting on the third mechanical arm 13 ³ n ₃ 。

When i=2, the calculated inertial force acting on the centroid of the third arm 12 in the case of i=1 can be calculated ² F ₂ And the calculated force of the second arm 12 acting on the third arm 13 in the case of i=3 ³ f ₃ Is brought into formula (7) to derive the force of the first arm 11 on the second arm 12 ² f ₂ 。

When i=2, the calculated inertial force acting on the centroid of the third arm 13 in the case of i=1 can be calculated ² F ₂ And moment of force ² N ₂ And the calculated moment of the second arm 12 acting on the third arm 13 in the case of i=3 ³ N ₃ Is brought into the formula (8), so that the moment of the first mechanical arm 11 acting on the second mechanical arm 12 can be obtained ² n ₂ . It can be appreciated that the calculation method of the remaining parameters is explained in the foregoing, and will not be repeated.

Referring to fig. 2 and 11, in some embodiments, the third dynamic formula is:

wherein,, ² f ₂ 、 ² n ₂ for the upper inertial forces and moments of the first mechanical arm 11 and the dual link transmission 30 acting at the center of mass of the second mechanical arm 12, ² F ₂ to act on the inertial force of the centroid of the second robotic arm 12, ² N ₂ is the moment acting on the centre of mass of the second arm 12.

More specifically, the calculated effect of i=1 may be applied to the third mechanical arm12 mass center inertial force ² F ₂ And the calculated force of the second arm 12 acting on the third arm 13 in the case of i=3 ³ f ₃ Is brought into formula (9) to derive the force of the first arm 11 on the second arm 12 ² f ₂ 。

The calculated inertial force acting on the centroid of the third arm 13 in the case of i=1 can be calculated ² F ₂ And moment of force ² N ₂ And the calculated moment of the second arm 12 acting on the third arm 13 in the case of i=3 ³ N ₃ Is brought into the formula (10) so as to obtain the moment of the first mechanical arm 11 acting on the second mechanical arm 12 ² N ₂ . It should be noted that the calculation method of the remaining parameters is explained in the foregoing, and will not be repeated.

In some embodiments, the torque of the first motor 41 is expressed by the following formula:

τ ₁ ＝ ¹ n ₁ ， (11)

wherein τ ₁ As the torque of the first motor 41, ¹ n ₁ is the torque of the first joint 21.

The torque of the second joint 22 is provided by the second motor 42, the second motor 42 adopts a rear mounting mode, the reaction force generated by the motor torque of the second motor 42 can directly act on the first flange 331 through the double-link transmission mechanism 30, and unlike a series structure dynamics modeling method, the reaction torque of the rotation of the second motor 42 cannot act on the first joint 21.

Meanwhile, the double-link transmission mechanism 30 rotates and the double-link transmission mechanism 30 is located in the first mechanical arm 11 of the robot 100, so that the double-link transmission mechanism 30 can revolve along with the first mechanical arm 11 and also can influence the torque of the first joint 21. In summary, the calculation formula for the torque of the first joint 21 can be obtained as:

Wherein,, ¹ N ₁ for the inertial force at the centre of mass of the first arm 11 +.>

Is a position vector of the centroid of the first mechanical arm 11 with respect to the coordinate system {1}, ¹ F ₁ for the moment at the centre of mass of the first arm 11, ¹ P ₂ is a position vector of an origin of the mechanical arm coordinate system {2} under the mechanical arm coordinate system {1}, and is +.>

Is a rotation transformation matrix from a coordinate system {1} to a coordinate system {2}, ² f ₂ a force acting on the second arm 12 for the first arm 11.

Substituting equation (12) into equation (11) yields

The torque τ of the first motor 41 can thus be calculated by equation (13) ₁ 。

In some embodiments, the torque of the second motor 42 is expressed using the following equation:

τ ₂ ＝τ _link + ² n ₂ ， (14)

wherein τ ₂ As the torque of the second motor 42, ² n ₂ is the moment on the centroid of the second arm 12, τ _link The torque required for rotation of the dual link transmission 30.

Specifically, for the second motor 42, the second motor 42 is responsible for the torque generated by the rotation of the second mechanical arm 12, and also needs to provide the torque required by the rotation of the double link transmission mechanism 30. Let the radius of rotation of the double link transmission 30 be r and the rotational speed of the second motor 42 be

The mass of the double link transmission mechanism 30 is m _L Movement of the double link transmission 30Can be T, so that the calculation formula of the kinetic energy T of the double link transmission 30 can be further deduced as follows:

According to the Lagrangian kinetic equation, the dual link transmission 30 only has kinetic energy, and the torque required by the dual link transmission 30 can be deduced to be:

where l=t-V, v=0, so that equations (15) and (16) can be substituted into equation (14) to derive the second motor 42 torque τ ₂ ＝τ _link + ² n ₂ Wherein, the method comprises the steps of, wherein, ² n ₂ can be calculated from equation (10), and is not limited herein.

In summary, the linear acceleration, the second angular velocity, and the second angular acceleration of the second joint 22 and the first joint 21 are obtained by the above-described construction, and the inertial force and the moment acting on the centers of mass of the third mechanical arm 13, the second mechanical arm 12, and the first mechanical arm 11 are constructed, so that the interaction force and the interaction moment between the second mechanical arm 12 and the third mechanical arm 13, and the first mechanical arm 11 and the double-link transmission mechanism 30 and the second mechanical arm 12 are constructed, and the first calculation formula of the torque of the first motor 41 and the second calculation formula of the torque of the second motor 42 are constructed, thereby completing the power analysis and the modeling of the mechanical arm of the robot 100.

After the dynamic analysis and modeling of the mechanical arm of the robot 100 are completed, the dynamic analysis and modeling method provided by the embodiment of the application can be subjected to simulation verification with the existing dynamic modeling software ADAMS (Automatic Dynamic Analysis of Mechanical Systems) to judge whether the dynamic analysis and modeling method of the mechanical arm of the embodiment of the application is effective.

ADAMS software uses an interactive graphic environment, a part library, a constraint library and a force library to create a completely parameterized mechanical system geometric model, and a solver of the ADAMS software adopts a Lagrange equation method in a multi-rigid-body system dynamics theory to build a system dynamics equation, performs statics, kinematics and dynamics analysis on a virtual mechanical system, and outputs displacement, speed, acceleration and reaction force curves. Simulation of ADAMS software can be used to predict performance, range of motion, collision detection, peak load, calculate finite element input load, etc. of a mechanical system. The calculation process is a 'black box' for users, and is used for verifying the dynamics of a mechanical system.

ADAMS is application software of virtual prototype analysis, and a user can use the software to perform statics, kinematics and dynamics analysis on a virtual mechanical system very conveniently. On the other hand, the virtual prototype analysis development tool is an open program structure and various interfaces of the virtual prototype analysis development tool, and can be a secondary development tool platform for special type virtual prototype analysis of users in special industries. ADAMS software has two versions of operating systems: UNIX version and Windows NT/2000 version. ADAMS l2.0 of Windows 2000 version is described herein as the blue book.

Substituting the CAD model of the SCARA robot 100 based on the double-link transmission mechanism 30 into the dynamics analysis and modeling method proposed in the embodiment of the present application, inputting the beat test track, and calculating the torques of the rear first motor 41 and the second motor 42. Meanwhile, modeling is performed in the dynamics simulation software ADAMS of the robot 100 by using the same CAD model, and the beat track is tested, so that a torque comparison graph is obtained, as shown in fig. 12 and 13.

Fig. 12 is a torque comparison chart of the CAD model of the first motor 41 and the dynamics simulation software ADAMS according to the embodiment of the present application. Fig. 13 is a graph comparing torque in the CAD model of the first motor 42 and the dynamics simulation software ADAMS according to the embodiment of the present application.

As can be seen from fig. 12 and 13, the mechanical arm dynamics analysis and modeling method according to the embodiment of the present application is consistent with the calculation result of the ADAMS dynamics simulation software, so as to prove the effectiveness of the mechanical arm dynamics analysis and modeling method according to the embodiment of the present application.

Kinetic parameter identification is the basis of robot kinetic control, and kinetic parameter accuracy directly influences the accuracy of a kinetic model. The higher the accuracy of the mechanical arm dynamics analysis and modeling is, the more accurate the estimation of the joint moment of the moving robot is when the mechanical arm dynamics analysis and modeling method is applied to the robot, so that the better the control effect on the force of the robot is, and the working efficiency of the robot can be improved.

The non-transitory computer-readable storage medium of computer-executable instructions provided by embodiments of the present application, when executed by one or more processors, cause the processors to perform the method of mechanical arm dynamics analysis and modeling of any one of the above.

The algorithms or displays presented herein are not inherently related to any particular computer, virtual system, or other apparatus. Various general-purpose systems may also be used with the teachings herein. The required structure for a construction of such a system is apparent from the description above. In addition, embodiments of the present invention are not directed to any particular programming language. It will be appreciated that the teachings of the present invention described herein may be implemented in a variety of programming languages, and the above description of specific languages is provided for disclosure of enablement and best mode of the present invention.

In the description of the present specification, reference to the terms "one embodiment," "some embodiments," "illustrative embodiments," "examples," "specific examples," or "some examples," etc., means that a particular feature, structure, material, or characteristic described in connection with the embodiment or example is included in at least one embodiment or example of the present application. In this specification, schematic representations of the above terms do not necessarily refer to the same embodiments or examples. Furthermore, the particular features, structures, materials, or characteristics described may be combined in any suitable manner in any one or more embodiments or examples.

Any process or method descriptions in flow charts or otherwise described herein may be understood as representing modules, segments, or portions of code which include one or more executable instructions for implementing specific logical functions or steps of the process, and further implementations are included within the scope of the preferred embodiment of the present application in which functions may be executed out of order from that shown or discussed, including substantially concurrently or in reverse order, depending on the functionality involved, as would be understood by those reasonably skilled in the art of the embodiments of the present application.

Logic and/or steps represented in the flow diagrams or otherwise described herein, may be considered a ordered listing of executable instructions for implementing logical functions, and can be embodied in any computer-readable medium for use by or in connection with an instruction execution system, apparatus, or device, such as a computer-based system, system that includes a processing module, or other system that can fetch the instructions from the instruction execution system, apparatus, or device and execute the instructions. For the purposes of this description, a "computer-readable medium" can be any means that can contain, store, communicate, propagate, or transport the program for use by or in connection with the instruction execution system, apparatus, or device.

More specific examples (a non-exhaustive list) of the computer-readable medium would include the following: an electrical connection (electronic device) having one or more wires, a portable computer diskette (magnetic device), a Random Access Memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM or flash memory), an optical fiber device, and a portable compact disc read-only memory (CDROM). In addition, the computer readable medium may even be paper or other suitable medium on which the program is printed, as the program may be electronically captured, via optical scanning of the paper or other medium, then compiled, interpreted or otherwise processed in a suitable manner if necessary, and then stored in a computer memory.

The processor may be a central processing unit (CentralProcessingUnit, CPU), but may also be other general purpose processors, digital signal processors (DigitalSignalProcessor, DSP), application specific integrated circuits (ApplicationSpecificIntegratedCircuit, ASIC), off-the-shelf programmable gate arrays (Field-ProgrammableGateArray, FPGA) or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, or the like. A general purpose processor may be a microprocessor or the processor may be any conventional processor or the like. It is to be understood that portions of embodiments of the present application may be implemented in hardware, software, firmware, or a combination thereof.

In the above-described embodiments, the various steps or methods may be implemented in software or firmware stored in a memory and executed by a suitable instruction execution system. In one embodiment, if implemented in hardware, as in another embodiment, may be implemented using any one or a combination of the following techniques, as is well known in the art: discrete logic circuits having logic gates for implementing logic functions on data signals, application specific integrated circuits having suitable combinational logic gates, programmable Gate Arrays (PGAs), field Programmable Gate Arrays (FPGAs), and the like.

Those of ordinary skill in the art will appreciate that all or a portion of the steps carried out in the method of the above-described embodiments may be implemented by a program to instruct related hardware, where the program may be stored in a computer readable storage medium, and where the program, when executed, includes one or a combination of the steps of the method embodiments.

Furthermore, each functional unit in the embodiments of the present application may be integrated in one processing module, or each unit may exist alone physically, or two or more units may be integrated in one module. The integrated modules may be implemented in hardware or in software functional modules. The integrated modules may also be stored in a computer readable storage medium if implemented in the form of software functional modules and sold or used as a stand-alone product. The above-mentioned storage medium may be a read-only memory, a magnetic disk or an optical disk, or the like.

Although the embodiments of the present application have been shown and described above, it will be understood that the above embodiments are illustrative and not to be construed as limiting the application, and that variations, modifications, alternatives and variations may be made to the embodiments described above by those of ordinary skill in the art within the scope of the application.

Claims

1. The mechanical arm dynamics analysis and modeling method is characterized by comprising the following steps of:

2. The method of claim 1, wherein constructing a first kinetic equation of inertial force and moment acting on centroids of the first, second, and third mechanical arms comprises:

3. The method of claim 2, wherein the second angular velocity, the second angular acceleration, and the linear acceleration of the first joint and the second joint are expressed by the following formulas:

wherein, the rotation transformation matrix is a rotation transformation matrix between coordinate systems,

The axis is called +.>

ⁱ ω _i 、

Representing the second angular velocity, the second angular acceleration and the linear acceleration of the ith joint in the mechanical arm coordinate system { i } relative to the own coordinate system, i=0, 1,2, …, N.

4. The method of claim 3, wherein the linear acceleration acting on the centroids of the first, second and third mechanical arms is expressed by the following formula:

Wherein,,

for linear acceleration acting on the i+1th arm centroid, +.>

5. The method of claim 4, wherein the first dynamic formula is:

wherein m is _i+1 Is the mass of the (i+1) th mechanical arm, ⁱ⁺¹ F _i+1 an inertial force acting on the mass center of the (i+1) th mechanical arm, ⁱ⁺¹ N _i+1 To act on the moment of the centroid of the i +1 th arm,

6. The method of claim 5, wherein the second kinetic equation is:

7. The method of claim 6, wherein the third dynamic formula is:

8. The method of claim 7, wherein the torque of the first motor is expressed by the following formula:

τ ₁ ＝ ¹ n ₁ ，

9. The method of claim 8, wherein the torque of the second motor is expressed by the following formula:

τ ₂ ＝τ _link + ² n ₂ ，

10. A robot, characterized in that the robot comprises a first mechanical arm, a second mechanical arm, a third mechanical arm and a double-link transmission mechanism, wherein the first mechanical arm is rotationally connected with the second mechanical arm, the first mechanical arm rotates around a first joint, the second mechanical arm rotates around a second joint, the third mechanical arm moves in a vertical direction relative to the second mechanical arm, the double-link transmission mechanism is arranged in the first mechanical arm, and the mechanical arm dynamics analysis and modeling method of any one of claims 1-9 can be used for the robot.

11. A computer device, characterized in that it comprises a memory storing a computer program and a processor implementing the method of kinetic resolution and modeling of a mechanical arm according to any of claims 1-9 when executing the computer program.

12. A non-transitory computer-readable storage medium of computer-executable instructions, which when executed by one or more processors, cause the processors to perform the robotic arm dynamics parsing and modeling method of any one of claims 1-9.