Vacuum manipulator rigid-flexible coupling modeling analysis method

Abstract

The invention belongs to the field of vacuum manipulator dynamics modeling, and particularly relates to a vacuum manipulator rigid-flexible coupling modeling analysis method. The method comprises the steps that a rigid body model is adopted to describe an arm, a chord model in the continuum field is adopted to describe a steel belt, a rigid body is a finite degree-of-freedom system, a continuum is an infinite degree-of-freedom system, the infinite degree-of-freedom system is discretized into the finite degree-of-freedom systems through a global space discretization method, and then the two finite degree-of-freedom systems are integrated in order; and a vacuum manipulator rigid-flexible coupling kinetic equation is obtained. The system dynamic model is established based on the energy method, the thought is clear, a good solution for dynamic modeling of the rigid-flexible coupling system is provided, and the problem that the vacuum manipulator cannot sense the system state in real time to provide the state feedback quantity for control due to endpoint-free real-time sensing is solved.

Description

Technical Field

[0001] The invention relates to the technical field of vacuum manipulator dynamics modeling, and in particular to a vacuum manipulator rigid-flexible coupling modeling and analysis method. Background Art

[0002] In the production process of integrated circuit chips, the manipulator is responsible for wafer transmission and is an important component of key process equipment such as lithography, etching, measurement, and detection. The atmospheric manipulator has ample space and firm adsorption, and the trajectory tracking accuracy requirements are not high. In addition, a sensor device is installed at the end of the transmission, and the end point repeat positioning accuracy is easy to achieve. Therefore, it does not require high accuracy of the dynamic model, and only the rigid body characteristics of the component need to be considered to meet the control accuracy. As the integrated circuit chip process develops towards the nanometer level, many process flows must be carried out in a vacuum environment, which requires the use of a vacuum manipulator. In a vacuum environment, the limited space and the lack of active clamping result in extremely high tracking accuracy requirements for the manipulator, and the inability to install the end point sensor device means that the repeat positioning accuracy needs to rely on an accurate dynamic model. Therefore, the dynamic model of the vacuum manipulator must consider the flexible modal characteristics of key components. Summary of the invention

[0003] In view of this, the purpose of the present invention is to provide a rigid-flexible coupling dynamic modeling and analysis method taking into account the flexibility of key components of a vacuum manipulator. The present invention establishes a rigid-flexible coupling dynamic model that takes into account the rigidity of the arm and the flexibility of the steel belt by considering the flexible characteristics of the steel belt. The model form is concise and the modeling steps are clear, which can provide a basis for the establishment of an accurate dynamic model of the vacuum manipulator and subsequent control design.

[0004] The technical solution of the present invention is specifically described as follows.

[0005] The present invention provides a rigid-flexible coupling modeling and analysis method for the flexibility of a vacuum manipulator. The method performs dynamic modeling and analysis from the perspective of energy method, adopts a rigid body model to describe the arm, adopts a string model in the field of a continuum to describe the steel belt, the rigid body is a finite degree of freedom system, the continuum is an infinite degree of freedom system, and a global space discretization method is adopted to discretize the infinite degree of freedom system into a finite degree of freedom system, and then the two finite degree of freedom systems are orderly integrated to obtain the rigid-flexible coupling dynamic equation of the vacuum manipulator; the method comprises the following steps:

[0006] 1) Establish a rigid arm dynamics model, consider the upper arm, lower arm and end effector as a rigid body link model, consider the inertia product effect of rigid body rotation, consider the connection joints between the links, consider the joint module as a rigid body model with the center of mass distributed at the connection, calculate the potential energy and kinetic energy of each rigid body, and use the second Lagrangian method to obtain the dynamic equation of the rigid arm;

[0007] 2) Establish a dynamic model of the flexible steel strip, consider the flexibility of the steel strip and the geometric constraints and force constraints on the steel strip, regard the steel strip as a string model in the continuum field, use the generalized Hamiltonian principle to establish a group of partial differential equations with infinite degrees of freedom, use the Galerkin global space discretization method to discretize, and obtain a group of ordinary differential equations with finite degrees of freedom by satisfying the boundaries;

[0008] 3) Establish a rigid-flexible coupling dynamics model of the vacuum manipulator, and obtain the rigid-flexible coupling dynamics equations by orderly integrating them by increasing the degree of freedom;

[0009] Furthermore, the above step 1) is specifically as follows:

[0010] 11) Establish the coordinate systems of each axis: World coordinate system O0: The origin is the front vertex of the boom, Z0 is perpendicular to the plane of the boom and upward, X0 is horizontally to the right, and Y0 is established according to the right-hand spiral rule; 1-axis coordinate system O1: Z1 coincides with Z0, X1 is along the direction of the boom, and Y1 is established according to the right-hand spiral rule; 2-axis coordinate system O2: The origin is the front vertex of the forearm, Z2 is perpendicular to the plane of the forearm and upward, X2 is along the direction of the forearm, and Y2 is established according to the right-hand spiral rule; 3-axis coordinate system O3: The origin is the front vertex of the end effector, Z3 is perpendicular to the plane of the end effector and upward, X3 is along the direction of the end effector, and Y3 is established according to the right-hand spiral rule; 4-axis coordinate system: The origin is the rear vertex of the end effector, Z4 is perpendicular to the plane of the end effector and upward, X4 is along the direction of the end effector, and Y4 is established according to the right-hand spiral rule;

[0011] 12) Based on the coordinate system established in step 11), an MDH (Modified Denavit-Hartenberg) parameter table is established according to the MDH parameter definition rule, and the homogeneous transformation matrix between each coordinate system is determined by the MDH parameter, and then the homogeneous transformation matrix of each coordinate system relative to the world coordinate system is established;

[0012] 13) The steps to calculate potential energy and kinetic energy are as follows:

[0013] Note the homogeneous coordinates of the center of mass of rod i in coordinate system i, and take the transformation matrix of coordinate system i relative to the world coordinate system on the left to obtain the homogeneous coordinates of the center of mass of rod i relative to the world coordinate system Calculate the potential energy of rod i m i is the mass of the i-th rod, g is the gravitational constant, and the potential energy of the entire rigid arm is obtained by accumulation n is the number of rods.

[0014] Note the homogeneous coordinates of any one-element particle in rod i in coordinate system i, and the transformation matrix of coordinate system i relative to the world coordinate system on the left to obtain the homogeneous coordinates of rod i relative to the world coordinate system calculate The total differential of gives the velocity of the elementary particle Calculating the kinetic energy of a particle The kinetic energy T of rod i is obtained by integration i =∫ 杆i dT i , the kinetic energy of the entire rigid arm is obtained by accumulation n is the number of rods.

[0015] 14) Subtract the potential energy T and kinetic energy V obtained in step 13) to obtain the Lagrangian quantity L, and bring L into the second kind of Lagrangian equation for calculation. The second kind of Lagrangian equation is as follows:

[0016]

[0017] Where q is the generalized coordinate, Q is the generalized force, is the total differential symbol, is the variation symbol;

[0018] By solving the second kind of Lagrange equation, we can get the dynamic equation of the rigid arm:

[0019]

[0020] Where M1 is the mass matrix, C1 is the damping matrix, G1 is the stiffness matrix, and τ1 is the torque matrix;

[0021] Furthermore, the above step 2) is specifically as follows:

[0022] 21) Establish the steel belt coordinate system and derive the position transformation matrix of the steel belt coordinate system relative to the world coordinate system. The steel belt is attached to the connecting rod where it is located, and the coordinates of the connecting rod are the coordinate system of the steel belt;

[0023] 22) The steps for calculating the kinetic energy, potential energy and virtual work done by non-conservative forces of the steel strip are as follows:

[0024] Select a single particle at random in the string of length L, and the formula for calculating the kinetic energy T of the steel is as follows:

[0025]

[0026] Where ρ(x) is the mass distribution function along the length of the string, y(x,t) is the lateral displacement function of the string at time t, and dx is the length of the elementary particle.

[0027] Select a single particle at random in the string of length L, and the formula for calculating the kinetic energy V of the steel is as follows:

[0028]

[0029] Where T(x) is the distribution function of the tension in the string along the length direction;

[0030] Choose a particle at random in the string of length L and calculate the virtual work W done by the non-conservative force. nc The formula is as follows,

[0031]

[0032] Where f(x,t) is the tension on the string at time t;

[0033] 23) Substitute the potential energy V, kinetic energy T and virtual work W done by non-conservative forces obtained in step 22) nc Substitute it into the generalized Hamiltonian equation for calculation. The generalized Hamiltonian equation is as follows:

[0034]

[0035] Where t1 and t2 are time, dt is the integration of time, and the dynamic equation y(x,t) of the flexible steel strip is obtained by solving the generalized Hamiltonian equation;

[0036] Taking an embodiment as an example, the partial differential equations for y(x, t) are obtained as follows:

[0037]

[0038] Where T is the tension in the string, f is the external force, and ρ is the mass of the string per unit length.

[0039] 24) The Galerkin global space discretization method is used to discretize y(x,t). The Galerkin discretization formula is as follows:

[0040]

[0041] Where N is the order of truncation, ψ i (x) is the basis function, β i (t) is the displacement function based on the basis function. The infinite degree of freedom system is discretized into a finite degree of freedom system through discretization. The dynamic equation of the finite degree of freedom system is as follows:

[0042]

[0043] Where β is the generalized coordinate, M2 is the equivalent mass matrix, C2 is the equivalent damping matrix, G2 is the equivalent stiffness matrix, and τ2 is the equivalent torque matrix;

[0044] 25) Convert boundary conditions into basis functions ψ i The initial conditions of (x) are as follows:

[0045] y(0,t)→ψ i (0)

[0046] y(L,t)→ψ i (L)

[0047] Furthermore, the above step 3) is specifically as follows:

[0048] 31) The dynamic equation of the rigid arm and the dynamic equation of the discretized flexible steel belt are orderly integrated into the dynamic equation of the rigid-flexible coupling system by increasing the degree of freedom. The integration method is shown in the following formula:

[0049]

[0050] Where M is the equivalent mass matrix, C is the equivalent damping matrix, G is the equivalent stiffness matrix, and τ is the equivalent torque matrix;

[0051] 32) Order The formula in step 31) is transformed into the following formula:

[0052]

[0053] This formula is the rigid-flexible coupling dynamic equation of the vacuum manipulator.

[0054] Compared with the prior art, the present invention has the following advantages and positive effects:

[0055] The present invention aims at the flexible characteristics of the steel strip, based on the distributed parameter method and the principle of elastic mechanics, and equates the steel strip to a string model in the field of continuum. Starting from refined modeling, the flexible characteristics of the steel strip and the rigid-flexible coupling characteristics are fully considered to establish a rigid-flexible coupling dynamic model of the vacuum manipulator, improve the accuracy of the dynamic modeling of the vacuum manipulator, predict the system state based on the refined model, and solve the problem that the vacuum manipulator has no end point real-time sensing and cannot perceive the system state in real time to provide state feedback for control. The present invention provides theoretical guidance for the engineering application scenario of the vacuum manipulator, performs dynamic modeling analysis from the perspective of the energy method, has clear ideas, is easy to implement, and has universality and applicability. BRIEF DESCRIPTION OF THE DRAWINGS

[0056] Figure 1 Schematic diagram of the vacuum manipulator structure and transmission.

[0057] Figure 2 Flowchart for modeling rigid-flexible coupling of vacuum manipulator.

[0058] Figure 3 Schematic diagram of the rigid arm dynamics model.

[0059] Figure 4 This is the dynamic model diagram of flexible steel strip.

[0060] Figure 5 Schematic diagram of the coordinate system of each axis.

[0061] Figure 6 Schematic diagram of the string model.

[0062] Markings in the figure: 1—Z-axis motor, 2—θ-axis motor, 3—R-axis motor, 4—upper arm housing, 5—first pulley in the upper arm, 6—second pulley in the upper arm, 7—forearm housing, 8—first pulley in the forearm, 9—second pulley in the forearm, 10—end effector housing, 11—first steel belt, 12—second steel belt. DETAILED DESCRIPTION

[0063] The present invention is described below in conjunction with specific embodiments.

[0064] The present invention provides a method for establishing a rigid-flexible coupling dynamic model of arm rigidity and steel belt flexibility; the method of the present invention comprises: using a rigid body model to describe the arm, using a string model in the continuum field to describe the steel belt, the rigid body is a finite degree of freedom system, the continuum is an infinite degree of freedom system, using a global space discretization method to discretize the infinite degree of freedom system into a finite degree of freedom system, and then orderly integrating the two finite degree of freedom systems to obtain a vacuum manipulator rigid-flexible coupling dynamic equation. The present invention establishes a system dynamic model based on the energy method, has a clear idea, and provides a good solution for dynamic modeling of a rigid-flexible coupling system.

[0065] Figure 1 FIG. 1 is a schematic diagram of a vacuum manipulator structure and transmission provided in an embodiment. Figure 1 As shown, in this embodiment, the vacuum manipulator is composed of a Z-axis motor 1, a θ-axis motor 2, an R-axis motor 3, a large arm housing 4, a first pulley 5 in the large arm, a second pulley 6 in the large arm, a small arm housing 7, a first pulley 8 in the small arm, a second pulley 9 in the small arm, an end effector, a first steel belt 11 and a second steel belt 12, wherein the first steel belt 11 and the second steel belt 12 are as shown in FIG. Figure 4 As shown. The Z-axis motor 1 is responsible for Z-direction translation, and the Z-direction movement and the planar movement of the arm are uncoupled. The output shaft of the θ-axis motor 2 is fixedly connected to the upper arm housing 4. When the θ-axis motor 2 rotates, it drives the entire arm to rotate; the output shaft of the R-axis motor 3 is fixedly connected to the first pulley 5 in the upper arm, one end of the first steel belt 11 is fixedly connected to the first pulley 5 in the upper arm, and the other end is fixedly connected to the second pulley 6 in the upper arm. At the same time, the second pulley 6 in the upper arm is fixedly connected to the first pulley 8 in the forearm, and one end of the second steel belt 12 is fixedly connected to the first pulley 8 in the forearm, and the other end is fixedly connected to the second pulley 9 in the forearm. At the same time, the second pulley 9 in the forearm is fixedly connected to the end effector housing 10. In this way, when the R-axis motor 3 rotates, the forearm and the end effector 10 are driven to rotate through the first steel belt 11 and the second steel belt 12.

[0066] Figure 2 FIG. 1 is a flow chart of rigid-flexible coupling modeling of a vacuum manipulator in one embodiment. Figure 2As shown, in this embodiment, a vacuum manipulator rigid-flexible coupling modeling and analysis method is proposed, which can specifically include the following steps:

[0067] S1) Establish a rigid arm dynamics model, such as Figure 3 As shown, the upper arm housing 4, the lower arm housing 7 and the end effector housing 10 are regarded as rigid body connecting rod models, the inertia product effect of the rigid body rotation is considered, the connecting joints between the connecting rods are considered, the first pulley 5 in the upper arm is regarded as the shoulder joint, the second pulley 6 in the upper arm and the first pulley 8 in the lower arm are regarded as the elbow joint, the second pulley 9 in the lower arm is regarded as the wrist joint, the shoulder joint, elbow joint and wrist joint are regarded as rigid body models with the center of mass distributed at the connection, the potential energy and kinetic energy of each rigid body are calculated, and the dynamic equation of the rigid arm is obtained by using the second Lagrangian method; θ1 is the upper arm The angle between the arm housing 4 and the x-axis of the world coordinate system, θ2 is the angle between the upper arm housing 4 and the lower arm housing 7, θ3 is the angle between the lower arm housing 7 and the end effector housing 10, L1 is the length of the upper arm housing 4, L2 is the length of the lower arm housing 7, L3 is the length of the end effector housing 10, O1 is the front end vertex of the upper arm housing 4, O2 is the front end vertex of the lower arm housing 7, O3 is the front end vertex of the end effector 10, A, B, C, D, E, F, G, H, A2, and A3 are the endpoints of the line segments used in calculating potential energy and kinetic energy.

[0068] S2) Establish a dynamic model of flexible steel strip, such as Figure 4 As shown, one end of the first steel belt 11 is fixedly connected to the first pulley 5 in the boom, and the other end is fixedly connected to the second pulley 6 in the boom. One end of the second steel belt 12 is fixedly connected to the first pulley 8 in the forearm, and the other end is fixedly connected to the second pulley 9 in the forearm. Figure 1 The fixed connection relationship of each component described in the figure is as follows. When the R-axis motor 3 rotates, it drives the first pulley 5 in the upper arm, the first steel belt 11, the second pulley 6 in the upper arm, the first pulley 8 in the forearm, the second steel belt 12, the second pulley 9 in the forearm and the end effector housing 10 to rotate in sequence. Considering the flexibility of the steel belt and the geometric constraints and force constraints on the steel belt, the steel belt is regarded as a string model in the continuum field. The generalized Hamiltonian principle is used to establish a group of partial differential equations with infinite degrees of freedom. The Galerkin global space discretization method is used for discretization processing, and the boundary is satisfied to obtain a group of ordinary differential equations with finite degrees of freedom.

[0069] S3) establishing a rigid-flexible coupling dynamics model of the vacuum manipulator, and obtaining a rigid-flexible coupling dynamics equation set by orderly integrating the model by increasing the degree of freedom;

[0070] Furthermore, the above step S1) is specifically as follows:

[0071] S1001) Establish the coordinate system of each axis, such as Figure 5As shown, first establish the world coordinate system O0: the origin is the front end vertex of the boom, Z0 is perpendicular to the boom plane and upward, X0 is horizontally to the right, and Y0 is established according to the right-hand spiral rule; 1-axis coordinate system O1: Z1 coincides with Z0, X1 is along the direction of the boom, and Y1 is established according to the right-hand spiral rule; 2-axis coordinate system O2: the origin is the front end vertex of the forearm, Z2 is perpendicular to the forearm plane and upward, X2 is along the forearm direction, and Y2 is established according to the right-hand spiral rule; 3-axis coordinate system O3: the origin is the front end vertex of the end effector, Z3 is perpendicular to the end effector plane and upward, X3 is along the end effector direction, and Y3 is established according to the right-hand spiral rule; 4-axis coordinate system: the origin is the rear end vertex of the end effector shell, Z4 is perpendicular to the end effector plane and upward, X4 is along the end effector direction, and Y4 is established according to the right-hand spiral rule;

[0072] S1002) Based on the coordinate system established in step S1001), an MDH parameter table is established according to the MDH parameter definition rule, and the homogeneous transformation matrix between each coordinate system is determined according to the MDH parameter, thereby establishing the homogeneous transformation matrix of each coordinate system relative to the world coordinate system;

[0073] S1003) Record the homogeneous coordinates of the center of mass of rod i in coordinate system i, and calculate the transformation matrix of coordinate system i relative to the world coordinate system on the left to obtain the homogeneous coordinates of the center of mass of rod i relative to the world coordinate system Calculate the potential energy of rod i m i is the mass of the i-th rod, g is the gravitational constant, and the potential energy of the entire rigid arm is obtained by accumulation n is the number of rods.

[0074] Note the homogeneous coordinates of any one-element particle in rod i in coordinate system i, and the transformation matrix of coordinate system i relative to the world coordinate system on the left to obtain the homogeneous coordinates of rod i relative to the world coordinate system calculate The total differential of gives the velocity of the elementary particle Calculating the kinetic energy of a particle The kinetic energy T of rod i is obtained by integration i =∫ 杆i dT i , the kinetic energy of the entire rigid arm is obtained by accumulation

[0075] S1004) Subtract the potential energy T and kinetic energy V obtained in step S1003) to obtain the Lagrangian quantity L, and bring L into the second kind of Lagrangian equation for calculation. The second kind of Lagrangian equation is as follows:

[0076]

[0077] Where q is the generalized coordinate and Q is the generalized force.

[0078] By solving the second kind of Lagrange equation, we can get the dynamic equation of the rigid arm:

[0079]

[0080] Among them, M1 is the mass matrix, C1 is the damping matrix, G1 is the stiffness matrix, and τ1 is the torque matrix; M1, C1, G1, and τ1 are specifically expanded as follows:

[0081]

[0082] Furthermore, the above step S2) is specifically as follows:

[0083] S2001) Establishing a steel strip coordinate system, deriving a position transformation matrix of the steel strip coordinate system relative to the world coordinate system, the steel strip is attached to the connecting rod where it is located, and the coordinates of the connecting rod are the coordinate system of the steel strip;

[0084] S2002) String model diagram Figure 6 As shown, the steps for calculating the kinetic energy, potential energy and virtual work done by non-conservative forces of the steel strip are as follows:

[0085] Select a single particle at random in the string of length L, and the formula for calculating the kinetic energy T of the steel is as follows:

[0086]

[0087] Where ρ(x) is the mass distribution function of the string along its length, and y(x,t) is the lateral displacement function of the string at time t;

[0088] Select a single particle at random in the string of length L, and the formula for calculating the kinetic energy V of the steel is as follows:

[0089]

[0090] Where T(x) is the distribution function of the tension in the string along the length direction;

[0091] Choose a particle at random in the string of length L and calculate the virtual work W done by the non-conservative force. nc The formula is as follows,

[0092]

[0093] Where f(x,t) is the tension on the string at time t;

[0094] S2003) The potential energy V, kinetic energy T and virtual work W of non-conservative forces obtained in step S2002) are nc Substitute it into the generalized Hamiltonian equation for calculation. The generalized Hamiltonian equation is as follows:

[0095]

[0096] Solve the generalized Hamiltonian equation to obtain the dynamic equation y(x,t) of the flexible steel strip;

[0097] S2004) The Galerkin global space discretization method is used to discretize y(x,t). The Galerkin discretization formula is as follows:

[0098]

[0099] Where N is the order of truncation, ψ i (x) is the basis function, β i (t) is the displacement function based on the basis function. The infinite degree of freedom system is discretized into a finite degree of freedom system through discretization. The dynamic equation of the finite degree of freedom system is as follows:

[0100]

[0101] Where β is the generalized coordinate, M2 is the equivalent mass matrix, C2 is the equivalent damping matrix, G2 is the equivalent stiffness matrix, and τ2 is the equivalent torque matrix; M2, C2, G2, and τ2 are specifically expanded as follows:

[0102]

[0103] Taking the truncation order N = 2 as an example, we can get

[0104]

[0105] S2005) Convert boundary conditions into basis functions ψ i The initial conditions of (x) are as follows:

[0106] y(0,t)→ψ i (0)

[0107] y(L,t)→ψ i (L)

[0108] Furthermore, the above step S3) is specifically as follows:

[0109] S3001) The rigid arm dynamics equation and the discretized flexible steel belt dynamics equation are orderly integrated into the rigid-flexible coupling system dynamics equation by increasing the degree of freedom. The integration method is shown in the following formula:

[0110]

[0111] Where M is the equivalent mass matrix, C is the equivalent damping matrix, G is the equivalent stiffness matrix, and τ is the equivalent torque matrix;

[0112] S3002) Order The formula in step 31) is transformed into the following formula:

[0113]

[0114] This formula is the rigid-flexible coupling dynamic equation of the vacuum manipulator.

[0115] Taking the results in step S1004) and step S2004) as an example, we can get

[0116]

Claims

1. A vacuum manipulator rigid-flexible coupling modeling and analysis method, characterized in that: The dynamic modeling analysis is carried out from the perspective of energy method. The rigid body model is used to describe the arm, and the string model in the continuum field is used to describe the steel belt. The rigid body is a finite degree of freedom system, and the continuum is an infinite degree of freedom system. The infinite degree of freedom system is discretized into a finite degree of freedom system using the global space discretization method. Then the two finite degree of freedom systems are orderly integrated to obtain the rigid-flexible coupling dynamic equation of the vacuum manipulator; the following steps are included: 1) Establish a rigid arm dynamics model, consider the upper arm, lower arm and end effector as a rigid body link model, consider the inertia product effect of rigid body rotation, consider the connection joints between the links, consider the joint module as a rigid body model with the center of mass distributed at the connection, calculate the potential energy and kinetic energy of each rigid body, and use the second Lagrangian method to obtain the dynamic equation of the rigid arm; 2) Establish a dynamic model of the flexible steel strip, consider the flexibility of the steel strip and the geometric constraints and force constraints on the steel strip, regard the steel strip as a string model in the continuum field, use the generalized Hamiltonian principle to establish a group of partial differential equations with infinite degrees of freedom, use the Galerkin global space discretization method to discretize, and obtain a group of ordinary differential equations with finite degrees of freedom by satisfying the boundaries; 3) Establish a rigid-flexible coupling dynamic model of the vacuum manipulator, and obtain the rigid-flexible coupling dynamic equations in an orderly manner by increasing the degrees of freedom.

2. The method for modeling and analyzing the rigid-flexible coupling of a vacuum manipulator according to claim 1 is characterized in that: Step 1) is specifically as follows: 11) Establish the coordinate systems of each axis: World coordinate system O0: The origin is the front vertex of the boom, Z0 is perpendicular to the plane of the boom and upward, X0 is horizontally to the right, and Y0 is established according to the right-hand spiral rule; 1-axis coordinate system O1: Z1 coincides with Z0, X1 is along the direction of the boom, and Y1 is established according to the right-hand spiral rule; 2-axis coordinate system O2: The origin is the front vertex of the forearm, Z2 is perpendicular to the plane of the forearm and upward, X2 is along the direction of the forearm, and Y2 is established according to the right-hand spiral rule; 3-axis coordinate system O3: The origin is the front vertex of the end effector, Z3 is perpendicular to the plane of the end effector and upward, X3 is along the direction of the end effector, and Y3 is established according to the right-hand spiral rule; 4-axis coordinate system: The origin is the rear vertex of the end effector, Z4 is perpendicular to the plane of the end effector and upward, X4 is along the direction of the end effector, and Y4 is established according to the right-hand spiral rule; 12) Based on the coordinate system established in step 11), an MDH parameter table is established according to the MDH parameter definition rule, the homogeneous transformation matrix between each coordinate system is determined by the MDH parameter, and then the homogeneous transformation matrix of each coordinate system relative to the world coordinate system is established; 13) Calculate potential energy and kinetic energy; Note the homogeneous coordinates of the center of mass of rod i in coordinate system i, and take the transformation matrix of coordinate system i relative to the world coordinate system on the left to obtain the homogeneous coordinates of the center of mass of rod i relative to the world coordinate system Calculate the potential energy of rod i m i is the mass of the i-th rod, g is the gravitational constant, and the potential energy of the entire rigid arm is obtained by accumulation n is the number of rods. Note the homogeneous coordinates of any one-element particle in rod i in coordinate system i, and the transformation matrix of coordinate system i relative to the world coordinate system on the left to obtain the homogeneous coordinates of rod i relative to the world coordinate system calculate The total differential of gives the velocity of the elementary particle Calculating the kinetic energy of a particle The kinetic energy T of rod i is obtained by integration i =∫ 杆i dT i , the kinetic energy of the entire rigid arm is obtained by accumulation 14) Subtract the potential energy T and kinetic energy V obtained in step 13) to obtain the Lagrangian quantity L, and bring L into the second kind of Lagrangian equation for calculation. The second kind of Lagrangian equation is as follows: Where q is the generalized coordinate, Q is the generalized force, is the total differential symbol, is the variation symbol; By solving the second kind of Lagrange equation, the dynamic equation of the rigid arm is obtained: Where M1 is the mass matrix, C1 is the damping matrix, G1 is the stiffness matrix, and τ1 is the torque matrix.

3. The rigid-flexible coupling modeling and analysis method for a vacuum manipulator according to claim 1 is characterized in that: Step 2) is specifically as follows: 21) Establish the steel belt coordinate system and derive the position transformation matrix of the steel belt coordinate system relative to the world coordinate system. The steel belt is attached to the connecting rod where it is located, and the coordinates of the connecting rod are the coordinate system of the steel belt; 22) Calculate the kinetic energy, potential energy and virtual work done by non-conservative forces of the steel strip; Select a single particle at random in the string of length L, and the formula for calculating the kinetic energy T of the steel is as follows: Where ρ(x) is the mass distribution function of the string along its length, y(x,t) is the lateral displacement function of the string at time t, and dx is the length of the elementary particle; Select a single particle at random in the string of length L, and the formula for calculating the kinetic energy V of the steel is as follows: Where T(x) is the distribution function of the tension in the string along the length direction; Choose a particle at random in the string of length L and calculate the virtual work W done by the non-conservative force. nc The formula is as follows, W nc =∫0 L f(x,t)y(x,t)dx Where f(x,t) is the tension on the string at time t; 23) Substitute the potential energy V, kinetic energy T and virtual work W done by non-conservative forces obtained in step 22) nc Bring it into the generalized Hamiltonian equation to participate in the calculation; The generalized Hamiltonian equation is as follows, Where t1 and t2 are time, dt is the integration of time, and the dynamic equation y(x,t) of the flexible steel strip is obtained by solving the generalized Hamiltonian equation; 24) Use the Galerkin global space discretization method to discretize y(x,t); The Galerkin discretization formula is as follows: Where N is the order of truncation, ψ i (x) is the basis function, β i (t) is the displacement function based on the basis function; The infinite degree of freedom system is discretized into a finite degree of freedom system through discretization. The dynamic equation of the finite degree of freedom system is as follows: Where β is the generalized coordinate, M2 is the equivalent mass matrix, C2 is the equivalent damping matrix, G2 is the equivalent stiffness matrix, and τ2 is the equivalent torque matrix; 25) Convert boundary conditions into basis functions ψ i The initial conditions of (x) are as follows: y(0,t)→ψ i (0) y(L,t)→ψ i (L).

4. The method for modeling and analyzing the rigid-flexible coupling of a vacuum manipulator according to claim 1 is characterized in that: Step 3) is specifically: 31) The dynamic equation of the rigid arm and the dynamic equation of the discretized flexible steel belt are orderly integrated into the dynamic equation of the rigid-flexible coupling system by increasing the freedom. The integration method is shown in the following formula: Where M is the equivalent mass matrix, C is the equivalent damping matrix, G is the equivalent stiffness matrix, and τ is the equivalent torque matrix; 32) Order The formula in step 31) is transformed into the following formula: This formula is the rigid-flexible coupling dynamic equation of the vacuum manipulator.

Images