Method and system for determining motor control scheme of parallel mechanism in wind tunnel capture trajectory test

Abstract

The embodiments of this specification provide a method for determining a motor control scheme for a parallel mechanism in a wind tunnel trajectory capture test. The method includes establishing a coordinate system for the parallel mechanism in a wind tunnel trajectory capture test, determining the coordinates of the center points of each moving Hooke's joint in the moving platform coordinate system and the static platform coordinate system based on the mechanical structure dimensions of the moving platform, determining the target position of the external attachment in the static platform coordinate system, determining the displacement of the center point of the static Hooke's joint by calculating the distance between two points in space, and calculating the motor displacement by proportional calculation; solving the operating speed of each motor based on the required displacement speed and Euler angular velocity of the external attachment; calculating the output force of each motor using the Lagrangian algorithm; and deciding on a control scheme for the CTS parallel mechanism based on the obtained displacement, operating speed, and output force of each motor to achieve control of the movement of the external attachment model in the wind tunnel. The present invention not only effectively solves the problem of multiple solutions for the parallel mechanism and improves the certainty of the method, but also significantly improves the calculation speed.

Description

Technical Field

[0001] The present invention relates to the technical field of special wind tunnel tests, and in particular to a method and system for determining a motor control scheme for a parallel mechanism in a wind tunnel capture trajectory test. Background Art

[0002] Captive Trajectory Simulation (CTS) is a special wind tunnel test technology that focuses on studying the motion trajectory of external stores during the initial stage of separation from the carrier aircraft. It simulates the position and attitude (X, Y, Z, pitch, roll, yaw) of the external stores after they detach from the carrier aircraft, providing the necessary test basis for the reasonable layout and safe separation of the external stores on the carrier aircraft.

[0003] The wind tunnel trajectory capture test process is as follows: the aerodynamic parameters of the external attachment's current posture in the wind tunnel can be obtained by the balance measurement system. Based on the aerodynamic parameters of the external attachment and the current wind tunnel state parameters, the target posture of the external attachment at the next moment can be calculated by the flight mechanics formula. The control system plans the motion trajectory and motion speed based on the external attachment's current posture and target posture, controls the movement of the support mechanism, and indirectly controls the external attachment to move to the target posture at the next moment. The balance system then measures the aerodynamic parameters of the current posture. This cycle repeats until the external attachment is safely separated from the carrier or other manually set test termination conditions are met, and finally the wind tunnel test ends.

[0004] Looking at the development of CTS test technology both domestically and internationally, from a control perspective, researchers typically begin with kinematics-based CTS position control. For example, during the early stages of CTS research in China, around the 1970s, the 2.4-meter wind tunnel at the China Aerodynamics Research and Development Center (CARDC) and the FL-2 wind tunnel at the China Academy of Aerodynamics (CARIA) of Aviation Industry Corporation of China (AVIC) were developed. However, as the demand for CTS testing increased, the position control approach's test efficiency and trajectory simulation performance fell short of meeting the demands of aircraft testing. Consequently, dynamics-based CTS speed control was subsequently developed, including the 4-foot transient high-speed wind tunnel at Israel Aircraft Industries (IAI) and the 2-meter supersonic wind tunnel at the China Aerodynamics Research and Development Center (CARDC).

[0005] From the perspective of the mechanical structure of the CTS support mechanism, domestic and international wind tunnels may have fewer than six degrees of freedom (DOF) for simulating external loads. These degrees of freedom may be coupled, with one DOF limiting the test range of another. For example, the five-DOF CTS support system (X, Y, Z, roll, and yaw) developed by the British ARA in the 1970s could not perform tests in which the pitch angle and other DOFs varied simultaneously. The Mordan wind tunnel in France could only perform CTS tests with four DOF (X, pitch, yaw, and roll). Domestic wind tunnels, having started later, generally achieve six DOF operation, such as the FD-12 wind tunnel at the China Academy of Aerospace Aerodynamics (CAAA), the 2m supersonic wind tunnel at the China Aerodynamics Research and Development Center (CARDC), and the FL-2 wind tunnel at the China Aerodynamics Research Institute (CARIA).

[0006] Wind tunnel CTS support mechanisms have diverse structural forms, including series, parallel, and hybrid series-parallel structures. Their configuration is generally determined by the wind tunnel's inherent characteristics and mission requirements. Series and hybrid series-parallel structures are the preferred choice for most wind tunnels due to their simplicity of control and ease of implementation. Few CTS support mechanisms published in domestic and international literature employ a purely parallel structure. Parallel mechanisms offer inherent advantages over series mechanisms, such as high stiffness, high load capacity, compact structure, low inertia, and no cumulative error. These advantages can be applied to wind tunnel testing, reducing wind tunnel blockage, improving test efficiency, and enhancing the accuracy of wind tunnel test data. Despite these advantages, parallel mechanisms are rarely adopted, primarily due to the complexity of their control systems, the lack of systematic and comprehensive calculation methods for the drive motor parameters, and the lack of high certainty. Consequently, the control accuracy and timeliness required for wind tunnel trajectory capture testing remain insufficient. Summary of the Invention

[0007] One or more embodiments of this specification provide a method for determining a motor control scheme for a parallel mechanism for a wind tunnel trajectory capture test. The parallel mechanism includes a static platform connected to an annular dynamic platform via six branch chains. The static platform includes six ball screws driven by six motors, each with a slider disposed on it. One end of each branch chain is connected to the slider via a static Hooke's joint, and the other end is connected to the dynamic platform via a dynamic roll joint and a dynamic Hooke's joint. The six dynamic Hooke's joints are evenly spaced around the circumference of the dynamic platform, and the dynamic platform is fixedly connected to a model of an external attachment. The method comprises the following steps:

[0008] Establish the parallel mechanism coordinate system for wind tunnel capture trajectory test, including the static platform coordinate system and the dynamic platform coordinate system;

[0009] Based on the mechanical structure dimensions of the moving platform, the coordinates of the center points of each moving Hooke's joint in the moving platform coordinate system and the static platform coordinate system are determined. The target position of the external attachment in the static platform coordinate system is determined. The displacement of the center point of the static Hooke's joint is determined by calculating the distance between the two points in space, and then the motor displacement is obtained through proportional calculation.

[0010] According to the displacement speed and Euler angular velocity required by the external attachment, solve the operating speed of each motor;

[0011] Based on the fact that the driving force of the motor acting on the slider through the ball screw is the only generalized force, the output force of each motor is calculated using the Lagrangian algorithm;

[0012] Based on the obtained displacement, operating speed and output force of each motor, a decision is made to control the six-degree-of-freedom pure parallel rod mechanism scheme for the wind tunnel capture trajectory test to realize the control of the movement of the external attachment model in the wind tunnel.

[0013] One or more embodiments of this specification provide a system for determining a motor control scheme for a parallel mechanism used in a wind tunnel trajectory capture test. The parallel mechanism includes a static platform connected to an annular dynamic platform via six branch chains. The static platform includes six ball screws driven by six motors, each with a slider disposed on it. One end of each branch chain is connected to the slider via a static Hooke's joint, and the other end is connected to the dynamic platform via a dynamic roll joint and a dynamic Hooke's joint. The six dynamic Hooke's joints are evenly spaced around the circumference of the dynamic platform. The dynamic platform is fixedly connected to a model of an external attachment, and includes:

[0014] Coordinate establishment module: used to establish the coordinate system of the parallel mechanism for wind tunnel capture trajectory test, including the static platform coordinate system and the dynamic platform coordinate system;

[0015] Motor speed calculation module: This module is used to determine the coordinates of the center points of each moving Hooke's joint in the moving platform coordinate system and the static platform coordinate system based on the mechanical structure dimensions of the moving platform. It also determines the target position of the external attachment in the static platform coordinate system. The displacement of the static Hooke's joint center point is determined by calculating the distance between the two points in space, and the displacement of each motor is then calculated through proportional calculation.

[0016] Motor speed calculation module: used to calculate the speed of each motor according to the displacement speed and Euler angular velocity required by the external attachment;

[0017] Motor speed calculation module: This module is used to calculate the speed of each motor using the Lagrangian algorithm, based on the fact that the driving force of the motor acting on the slider through the ball screw is the only generalized force.

[0018] Decision-making control module: It is used to make decisions and control the six-degree-of-freedom pure parallel rod mechanism scheme of the wind tunnel capture trajectory test based on the obtained displacement, operating speed and output force of each motor, so as to realize the control of the movement of the external attachment model in the wind tunnel.

[0019] By calculating the motor displacement, motor speed, and motor output force, the present invention can control the six motors to reach the specified displacement according to the desired speed and acceleration, indirectly controlling the motion of a six-degree-of-freedom pure parallel rod mechanism, thereby realizing the motion of an external attachment fixed to the parallel mechanism's dynamic platform. The method of the present invention is simple, clear, and has a sufficient theoretical basis. It solves the motor displacement, speed, and output force involved in the kinematic and dynamic analysis of the parallel mechanism all at once, making the method more systematic and comprehensive.

[0020] In addition, embedding all the unchanged mechanical structure parameters in the calculation method of the present invention not only effectively solves the multi-solution problem of the parallel mechanism and improves the certainty of the method, but also significantly improves the calculation speed, providing a strong guarantee for real-time control. It also improves the control accuracy of the motor displacement, speed, and acceleration, and indirectly improves the motion simulation capability of the external attachment posture change, especially the speed and acceleration simulation capability during the movement of the external attachment, thereby improving the wind tunnel capture trajectory test capability with control rate. BRIEF DESCRIPTION OF THE DRAWINGS

[0021] In order to more clearly illustrate one or more embodiments of this specification or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are only some embodiments recorded in this specification. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0022] Figure 1 A flowchart of a method for determining a motor control scheme for a parallel mechanism in a wind tunnel trajectory capture test provided by one or more embodiments of this specification;

[0023] Figure 2 A schematic diagram of the structure of a CTS parallel mechanism in a method for determining a motor control scheme for a wind tunnel trajectory capture test parallel mechanism provided in one or more embodiments of this specification;

[0024] Figure 3 A schematic diagram of the static platform coordinate system and the dynamic platform coordinate system of a CTS parallel mechanism in a method for determining a motor control scheme for a wind tunnel capture trajectory test parallel mechanism provided in one or more embodiments of this specification;

[0025] Figure 4 A coordinate vector diagram of the i-th branch of a CTS parallel mechanism in a method for determining a motor control scheme for a wind tunnel trajectory capture test parallel mechanism provided in one or more embodiments of this specification;

[0026] Figure 5A graph showing the displacement, operating speed, and output force of each motor of the CTS parallel mechanism moving along the X-axis in an experimental case provided in one or more embodiments of this specification;

[0027] Figure 6 A graph showing the displacement, operating speed, and output force of each motor of the CTS parallel mechanism moving along the Y-axis in an experimental case provided in one or more embodiments of this specification;

[0028] Figure 7 A graph showing the displacement, operating speed, and output force of each motor of the CTS parallel mechanism moving along the Z-axis in an experimental case provided in one or more embodiments of this specification;

[0029] Figure 8 A graph showing the displacement, operating speed, and output force of each motor of the CTS parallel mechanism moving along the α and β directions in an experimental case provided in one or more embodiments of this specification;

[0030] Figure 9 A schematic diagram of the module composition of a system for determining a motor control scheme for a parallel mechanism in a wind tunnel trajectory capture test provided by one or more embodiments of this specification;

[0031] Figure 10 A schematic diagram of the structure of a computer provided for one or more embodiments of this specification. DETAILED DESCRIPTION

[0032] In order to help those skilled in the art better understand the technical solutions in one or more embodiments of this specification, the technical solutions in one or more embodiments of this specification will be clearly and completely described below in conjunction with the drawings in one or more embodiments of this specification. Obviously, the described embodiments are only part of the embodiments of this specification, not all of the embodiments. Based on one or more embodiments of this specification, all other embodiments obtained by ordinary technicians in this field without making creative efforts should fall within the scope of protection of this invention.

[0033] The present invention will be described in detail below with reference to specific implementation methods and the accompanying drawings.

[0034] Method Example

[0035] According to an embodiment of the present invention, a method for determining a motor control scheme for a parallel mechanism in a wind tunnel trajectory capture test is provided. Figure 1 As shown, according to the method for determining the motor control scheme of the parallel mechanism in the wind tunnel capture trajectory test according to an embodiment of the present invention,

[0036] The parallel mechanism for a wind tunnel trajectory capture test includes a static platform connected to an annular dynamic platform via six branch chains. The static platform includes six ball screws driven by six motors, each with a slider disposed on it. One end of each branch chain is connected to the slider via a static Hooke's joint, and the other end is connected to the dynamic platform via a dynamic roll joint and a dynamic Hooke's joint. The six dynamic Hooke's joints are evenly spaced around the circumference of the dynamic platform, and the dynamic platform is fixedly connected to the external attachment model. Therefore, the method for determining a motor control scheme for a wind tunnel trajectory capture test parallel mechanism in this embodiment includes the following steps:

[0037] Step S1, establishing a parallel mechanism coordinate system for a wind tunnel capture trajectory test, including a static platform coordinate system and a dynamic platform coordinate system;

[0038] Step S2: Determine the coordinates of the center points of each moving Hooke's joint in the moving platform coordinate system and the static platform coordinate system based on the mechanical structure dimensions of the moving platform, determine the target position of the external attachment in the static platform coordinate system, determine the displacement of the center point of the static Hooke's joint by calculating the distance between the two points in space, and then calculate the motor displacement by proportional calculation;

[0039] According to the displacement speed and Euler angular velocity required by the external attachment, solve the operating speed of each motor;

[0040] Based on the fact that the driving force of the motor acting on the slider through the ball screw is the only generalized force, the output force of each motor is calculated using the Lagrangian algorithm;

[0041] Step S3: Based on the obtained displacement, operating speed, and output force of each motor, a decision is made on a six-degree-of-freedom pure parallel rod mechanism scheme for controlling the wind tunnel trajectory capture test, so as to realize the control of the movement of the external attachment model in the wind tunnel.

[0042] In this embodiment, after calculating the motor displacement, motor speed and motor output force, the six motors can be controlled to reach the specified displacement according to the desired speed and acceleration, thereby indirectly controlling the motion of the six-degree-of-freedom pure parallel rod mechanism, thereby realizing the motion of the external attachment fixed to the parallel mechanism dynamic platform. The method of the present invention is simple and clear in concept and has sufficient theoretical basis. The motor displacement, speed and output force involved in the kinematic and dynamic analysis of the parallel mechanism are all solved at one time, making the method more systematic and comprehensive. All unchanging mechanical structure parameters are embedded in the calculation method of the present invention, which not only effectively solves the multi-solution problem of the parallel mechanism and improves the certainty of the method, but also significantly improves the calculation speed, providing a strong guarantee for real-time control, and also improves the control accuracy of the motor displacement, speed and acceleration, indirectly improving the motion simulation capability of the external attachment posture change, especially the speed and acceleration simulation capability during the movement of the external attachment, thereby improving the wind tunnel capture trajectory test capability with control rate.

[0043] In a specific embodiment, please refer to Figure 2, which is a schematic diagram of the parallel mechanism structure for the wind tunnel trajectory capture test provided in this embodiment. The motor part is not shown in this embodiment. The structure specifically includes:

[0044] The static platform includes six motors, six ball screws and six sliders. Figure 2 The motor is not shown. The motor is connected to the ball screw. Figure 2 The horizontal thick solid lines and horizontal thick dashed lines with Arabic numerals 1 to 6 are used for simple illustration, and the six sliders are marked as U i-b ,(i=1,2...6).

[0045] The six branches include six static Hooke's hinges, six supporting rods, six dynamic roll pairs and six dynamic Hooke's hinges. The six static Hooke's hinges are respectively installed on six sliders. The six supporting rods are represented by thin solid lines and thin dotted lines. The six dynamic roll pairs are marked as R. i-d , (i=1,2...6), six moving Hooke's hinges are denoted as U i-d ,(i=1,2...6), Figure 2 For the sake of simplicity, only the dynamic roll joint and dynamic Hooke's joint of the third branch are marked.

[0046] An aircraft external attachment model is installed on the moving platform. The moving platform and the external attachment model are fixedly connected and contain no moving parts inside. Six moving Hooke's hinges are evenly distributed on the circumference of the moving platform A at equal intervals of 60 degrees.

[0047] A coordinate system is established based on the above mechanism, where the static platform coordinate system O b -X b Y b Z b and the moving platform coordinate system O d -X d Y d Z d , you can refer to Figure 2 and Figure 3 Shown: static platform coordinate system O b -X b Y b Z b The origin is set as the center point of the cross section where the endpoints of the six ball screws are located near the motor side, and the slider movement direction is set to the static platform X b Axis, vertical direction is Y b Axis, determine Z according to the right-hand rule b Axis; moving platform coordinate system O d -X d Y d Z d The origin is set to the center of the moving platform, the initial position X d With X b Same direction, Y d With Yb Same direction, Z d With Z b Same direction.

[0048] Based on the coordinate system established above, under the premise of knowing the mechanical structure size of the moving platform, the coordinates U of the six moving Hooke's hinge center points in the moving platform coordinate system can be converted i-d =[x di ,y di ,z di ], (i=1,2...6). Among them,

[0049] The specific parameters of the dynamic platform mechanical structure size are as follows: the distance from the center of mass of the model to the plane of the dynamic platform is 143.87 mm, the vertical distance from the center of mass of the model to the central axis of the dynamic platform is 17.61 mm, the radius from the center of the dynamic platform to the center of the dynamic Hooke's hinge is 103.02 mm, and the interval angle of the dynamic platform Hooke's hinge is 60 degrees.

[0050] Based on the current position of the external attachment in the wind tunnel and the aerodynamic force it is subjected to in the wind tunnel, the position of the external attachment at the next moment can be calculated, that is, the target position q = [x, y, z, α, β, γ] of the external attachment in the static platform coordinate system.

[0051] From the target pose q, we can directly obtain the displacement vector P of the external attachment from the moving platform coordinate system to the static platform coordinate system, where:

[0052] P=[x,y,z] (1)

[0053] The transformation matrix from the moving platform coordinate system to the static platform coordinate system can also be converted b T d ,in:

[0054]

[0055] Where [α, β, γ] is the target posture of the external attachment, sin and cos are abbreviated as s and c respectively;

[0056] Coordinates of the center point of the moving Hooke's joint in the static platform coordinate system b U i-d =[ b x di , b y di , b z di ], (i=1,2...6), can be obtained by formula (3):

[0057] b U i-d ( b x di ,b y di , b z di )= b T d U i-d +P (3)

[0058] According to the constant length of the rod, the displacement of the center point of the static Hooke's joint can be solved by the distance formula between two points in space:

[0059]

[0060] Where, L i (i=1,2...6) are the lengths of the six support rods; y bi , z bi is the Y / Z coordinate of the static Hooke's joint, which is a fixed mechanism parameter. The specific values are shown in Table 1:

[0061] Table 1: Rod length and static Hooke's joint parameters of CTS parallel mechanism

[0062]

[0063] The displacement of the center point of the static Hooke's joint in formula (4) is the displacement of the slider. Since the motor drives the slider indirectly through the ball screw, the reduction ratio is 14:1, and the slider moves 10 mm when the ball screw rotates one circle, the motor displacement can be solved through simple proportional calculation.

[0064] Since fixed mechanical parameters are embedded in the calculation method, the determinism of the method of this embodiment is improved, the multi-solution problem of the parallel mechanism is solved, the complex solutions and the symmetric solutions of the mechanical structure are eliminated, and a unique solution for the motor displacement can be obtained, while the calculation speed of the method is improved.

[0065] refer to Figure 4 As shown, the velocity v of the center point of the moving Hooke joint i is di It can be expressed as:

[0066] v di =v od +ω od ×r di (5)

[0067] Among them, v od is the velocity of the center point of the moving platform; ω od is the angular velocity of the moving platform; r di v is the vector from the center of the moving platform to the center of the moving Hooke's hinge i; di is the velocity of the center point of the moving Hooke joint i; v bi is the velocity of the center point of the static Hooke joint i; n bi For rod L i Unit direction vector.

[0068] According to the velocity v of the center of the moving Hooke hinge di Hejing Hooke hinge center velocity v bi On the rod L i The projections in the directions are equal, establishing the equation:

[0069]

[0070] From the characteristics of the CTS parallel mechanism, we can know that v bi =[v bix ,0,0] T , n bi =[n biix ,n biy ,n biz ], (6) is organized as follows:

[0071]

[0072] From formula (7), we can know that the Jacobian matrix of the CTS parallel mechanism is:

[0073]

[0074] The ZYX Euler angle (α, β, γ) is used to describe the posture of the CTS parallel mechanism moving platform. The relationship between the Euler angular velocity and the angular velocity of the moving platform is:

[0075]

[0076] According to formulas (7)-(9), the relationship between the moving speed of the static Hooke's joint center and the posture transformation speed of the moving platform is:

[0077]

[0078] In this embodiment, the moving platform moving speed ( b v odx ; b v ody ; b v ody ) and Euler angular velocity In wind tunnel tests, the speed is determined by the actual project requirements and the wind tunnel flow field stability. Formula (10) can be used to solve the moving speed of the center point of the static Hooke's hinge, and the motor running speed can be solved by a simple proportional operation.

[0079] In this embodiment, the premise for calculating the output force of each motor is to set all the sliders, static Hooke's joints, support rods, dynamic Hooke's joints, dynamic roll pairs, dynamic Hooke's joints, and dynamic platforms as a whole. The output force of the motor acting on the slider through the ball screw is considered to be the only generalized force. Then the Lagrange equation can be written as:

[0080]

[0081] Where q is the generalized coordinate of the system mechanism; is the generalized velocity; U is the system potential energy related to the mechanism configuration; K is the system kinetic energy; τ is the system generalized force, that is, the motor output force.

[0082] Arranging (11) we can get:

[0083]

[0084] Set the static platform coordinate system O b -X b Y b Z b The established XZ surface is the zero potential energy surface. The potential energy of the mechanism can be calculated according to the mechanism configuration.

[0085] The system kinetic energy K can be expressed as:

[0086]

[0087] Where M(q) is the mass matrix;

[0088] The system consists of six branches, so the system kinetic energy K can be considered as the kinetic energy K of the six branches. i The sum is:

[0089]

[0090]

[0091] Where, v ci represents the velocity at the center of mass of the i-th branch, I ci represents the moment of inertia of the center of mass c of the i-th branch, m i represents the mass of the i-th branch chain, which is a known structural parameter. The specific values are shown in Table 2:

[0092] Table 2: CTS parallel mechanism branch chain quality parameters

[0093] i 1 2 3 4 5 6 <![CDATA[m i (kg)]]> 2.4611 2.7046 2.2107 2.4653 2.2189 2.7088

[0094] Among them, I ci The moment of inertia can be calculated using formula (16):

[0095]

[0096] Where ρ represents the material density of the mechanism, and p = [x, y, z] represents the rigid body coordinates of the mechanism.

[0097] If different rigid body components are defined in different coordinate systems and ultimately need to be transformed into the same reference coordinate system, the parallel axis theory shown in formula (17) can be used to simplify the calculation:

[0098] I o =I c +m[(p c T p c )I3-p c p c T ] (17)

[0099] Where p c is the vector from the c-coordinate point to the o-coordinate point;

[0100] The final calculated moment of inertia parameters of the center of mass c of the six branches are shown in Table 3:

[0101] Table 3: CTS parallel mechanism branch chain moment of inertia

[0102]

[0103] (15) In the formula, v ci and ω i It can be expressed as a Jacobian matrix:

[0104]

[0105] Where, the Jacobian matrix J can be obtained by formula (8);

[0106] By combining (13)-(15) and (18) to establish equations, the mass matrix M(q) can be obtained:

[0107]

[0108] According to the above formula (19), substituting formula (13) into formula (12), the motor output force can be solved:

[0109]

[0110] In this embodiment, based on the aforementioned wind tunnel trajectory capture test parallel mechanism settings, after calculating the parallel mechanism's motor displacement, motor speed, and motor output force, the six motors can be controlled to reach the specified displacement at the desired speed and acceleration, indirectly controlling the motion of the six-degree-of-freedom pure parallel rod mechanism, thereby achieving the motion of the external attachment fixed to the parallel mechanism's dynamic platform. The method of the present invention is simple, clear, and theoretically well-founded. It solves the motor displacement, speed, and output force involved in the parallel mechanism's kinematic and dynamic analysis all at once, making the method more systematic and comprehensive. All unchanging mechanical structure parameters are embedded in the calculation method of the present invention, effectively resolving the parallel mechanism's multiple solution problem and improving the method's determinism. It also significantly increases the calculation speed, providing a strong guarantee for real-time control. It also improves the control accuracy of the motor displacement, speed, and acceleration, indirectly enhancing the motion simulation capability of the external attachment's posture changes, particularly the velocity and acceleration simulation capability during the attachment's motion, thereby improving the wind tunnel trajectory capture test capability with controllability.

[0111] The feasibility and effectiveness of this method are illustrated below through specific experimental cases. Specifically, given the specific target position q = [x, y, z, α, β, γ] of the external attachment, the motor control parameter calculation method of the parallel mechanism for wind tunnel capture trajectory test described in the present invention is demonstrated in four specific motion forms.

[0112] The first motion mode: The CTS parallel mechanism performs sine or cosine motion along the X-axis, and the other five degrees of freedom are fixed at different values. The formulas are shown in (21) to (23):

[0113]

[0114]

[0115]

[0116] The Matlab simulation step size is 0.1s. The motor displacement, speed and output force on the six branches are as follows: Figure 5 As shown in the figure, when the moving platform is displaced only in the X direction, the displacement increments and speeds of the six motors are the same, which is consistent with the structural characteristics of the mechanism. Figure 5 In state A, the other five degrees of freedom of the platform are all zero. The output forces of the six motors are different from each other, but the output forces of each motor remain unchanged. Since the platform has no displacement in the Y and Z directions, the motor output forces show obvious symmetry in the XY plane. The output forces of motors 1 and 4 are the same, the output forces of motors 2 and 5 are the same, and the output forces of motors 3 and 6 are the same. The directions of the output forces of motors 1 and 4 are opposite to those of motors 3 and 6. Figure 5In the middle state B stage, the Y and Z displacements of the dynamic platform are 200mm, and the other degrees of freedom are 0. From the displacement and output force curves, it can be seen that the dynamic platform posture loses symmetry at this time, and the initial displacements and output forces of the six motors vary greatly. Figure 5 In the middle state C stage, the α and β of the moving platform are both 25°, and the Y, Z, and γ are all 0. The displacement and output force are also not symmetrical. Combining the three states, it can be concluded that the X displacement does not affect the symmetry of the displacement and output force of the mechanism, and does not affect the output force of the motor.

[0117] The second motion mode: The CTS parallel support mechanism moving platform performs sinusoidal motion along the Y direction, the other five degrees of freedom are 0, and the initial Y position of the moving platform is three different values. The specific motion trajectory is formula (24):

[0118]

[0119] The Matlab simulation step size is 0.1s. The motor displacement, speed and output force on the six branches are as follows: Figure 6 As shown in formula (24), the moving platform is Figure 6 The motion trajectories of the three stages A, B, and C shown in the figure are the same, with only the initial Y displacement being different. Figure 6 It can be seen that motors 1 and 6 form a group, motors 2 and 5 form a group, and motors 3 and 4 form a group. The displacement, velocity, and output force of the motors within the same group show clear consistency, indicating that the moving platform is symmetrical in the XY plane. In state B, when the moving platform performs sinusoidal motion in the Y direction, the displacement of motors 1 and 6 remains almost unchanged, and their velocity is close to zero, but their output force is very large. This indicates that the internal force of the moving platform in this state is relatively large, and motors 1 and 6 are highly sensitive, making control more difficult and the corresponding moving platform accuracy difficult to ensure. Similarly, in state C, the displacement of motors 2 and 5 remains almost unchanged, and their output force is also relatively large, indicating high sensitivity and reduced accuracy. In state A, as the moving platform performs sinusoidal motion in the Y direction, the displacement increments of the six motors are similar. The output forces of motors 1 and 6 are symmetrical with those of motors 2 and 5, and are smaller than those in states B and C. The output forces of motors 3 and 4 are close to zero, indicating that the mechanism is not sensitive in this state, making it easier to control and ensure control accuracy. This also indicates that the Y state zero point is appropriately selected.

[0120] The third motion mode: The CTS parallel support mechanism moving platform performs sinusoidal motion along the Z direction, the other five degrees of freedom are 0, and the initial Z position of the moving platform is three different values. The specific motion trajectory is formula (25):

[0121]

[0122] The Matlab simulation step size is 0.1s. The motor displacement, speed and output force on the six branches are as follows: Figure 7 As shown in formula (25), the moving platform is Figure 7 The motion trajectories of the three stages of state A, B, and C are the same, and the initial Z displacements of state A and C are symmetrical along the XY plane. Figure 7 It can be seen that the motor displacement, speed, and output force in state A and C are symmetrical along the XY plane. That is, motors 1, 2, and 3 are mirror-symmetrical with motors 4, 5, and 6 along the XY plane, which is consistent with the structural characteristics of the mechanism.

[0123] The fourth motion mode: The CTS parallel support mechanism platform performs sinusoidal motion along the α direction, sinusoidal motion along the β direction, and sinusoidal motion along the α and β directions simultaneously. The other five degrees of freedom are 0. The specific motion trajectory is shown in (26) to (28):

[0124]

[0125]

[0126]

[0127] The Matlab simulation step size is 0.1s. The motor displacement, speed and output force on the six branches are as follows: Figure 7 As shown, in state A, when the platform performs sinusoidal motion in the α direction, the displacement increments of motors 1, 2, 5, and 6 are identical. The output forces of motors 1 and 6 are of equal magnitude and opposite direction to those of motors 2 and 5, which is consistent with the structural characteristics of the mechanism. In state B, when the platform performs sinusoidal motion in the β direction, the output forces of motors 3 and 4 are of equal magnitude and opposite direction. The output forces of motors 2 and 5 also change in opposite directions, while the output forces of motors 1 and 6 also change in opposite directions, indicating that the internal forces of the mechanism cancel each other out. In state C, the platform moves simultaneously in the α and β directions, and the mechanism is coupled. The displacement, velocity, and output force curves vary dramatically, but a symmetrical trend can still be observed. Similarly, it can be inferred that when the platform moves simultaneously along all six degrees of freedom, the degree of coupling will be higher, and the displacement, velocity, and output force changes will be even more dramatic.

[0128] System Example

[0129] According to an embodiment of the present invention, a system for determining a motor control scheme for a parallel mechanism in a wind tunnel trajectory capture test is provided. Figure 9 As shown, according to the wind tunnel capture trajectory test parallel mechanism motor control scheme determination system of an embodiment of the present invention, wherein,

[0130] The parallel mechanism for the wind tunnel trajectory capture test consists of a static platform connected to a circular dynamic platform via six branch chains. The static platform includes six ball screws driven by six motors, each with a slider mounted on it. One end of each branch chain is connected to the slider via a static Hooke's joint, and the other end is connected to the dynamic platform via a dynamic roll joint and a dynamic Hooke's joint. The six dynamic Hooke's joints are evenly spaced around the circumference of the dynamic platform, which is fixedly connected to the external attachment model.

[0131] Specifically, refer to Figure 2-4 The static platform includes six motors, six ball screws and six sliders. The motors are connected to the ball screws. Figure 2 The horizontal thick solid lines and horizontal thick dashed lines with Arabic numerals 1 to 6 are used for simple illustration, and the six sliders are marked as U i-b ,(i=1,2...6).

[0132] The six branches include six static Hooke's hinges, six supporting rods, six dynamic roll pairs and six dynamic Hooke's hinges. The six static Hooke's hinges are respectively installed on six sliders. The six supporting rods are represented by thin solid lines and thin dotted lines. The six dynamic roll pairs are marked as R. i-d , (i=1,2...6), six moving Hooke's hinges are denoted as U i-d ,(i=1,2...6).

[0133] Coordinate establishment module: used to establish the coordinate system of the parallel mechanism for wind tunnel trajectory capture test, including the static platform coordinate system and the dynamic platform coordinate system. The coordinate establishment module includes:

[0134] Static platform coordinate system O b -X b Y b Z b The origin is set as the center point of the cross section where the endpoints of the six ball screws are located near the motor side, and the slider moves in the direction of the static platform X b Axis, vertical direction is Y b Axis, determine Z according to the right-hand rule b axis;

[0135] Moving platform coordinate system O d -X d Y d Z d The origin is set to the center of the moving platform, the initial position X d With X b Same direction, Y d With Y b Same direction, Z d With Z b Same direction.

[0136] Motor displacement calculation module: This module is used to determine the coordinates of the center points of each moving Hooke's joint in the moving platform coordinate system and the static platform coordinate system based on the mechanical structure dimensions of the moving platform, determine the target position of the external attachment in the static platform coordinate system, calculate the displacement of the center point of the static Hooke's joint by calculating the distance between two points in space, and then calculate the motor displacement through proportional calculation;

[0137] Motor speed calculation module: used to calculate the speed of each motor according to the displacement speed and Euler angular velocity required by the external attachment;

[0138] Motor output force calculation module: used to calculate the output force of each motor using the Lagrangian algorithm based on the driving force of the motor acting on the slider through the ball screw as the only generalized force;

[0139] Decision-making control module: It is used to make decisions and control the six-degree-of-freedom pure parallel rod mechanism scheme of the wind tunnel capture trajectory test based on the obtained displacement, operating speed and output force of each motor, so as to realize the control of the movement of the external attachment model in the wind tunnel.

[0140] In this embodiment, based on the coordinate system established by the above-mentioned coordinate establishment module, the coordinates U of the six moving Hooke's joint center points in the moving platform coordinate system can be converted under the premise of knowing the mechanical structure dimensions of the moving platform. i-d =[x di ,y di ,z di ], (i=1,2...6). Among them,

[0141] The specific parameters of the dynamic platform mechanical structure size are as follows: the distance from the center of mass of the model to the plane of the dynamic platform is 143.87 mm, the vertical distance from the center of mass of the model to the central axis of the dynamic platform is 17.61 mm, the radius from the center of the dynamic platform to the center of the dynamic Hooke's hinge is 103.02 mm, and the interval angle of the dynamic platform Hooke's hinge is 60 degrees.

[0142] In this embodiment, the calculation process of solving the displacement of each motor by the motor operation displacement calculation module, solving the speed of each motor by the motor operation speed calculation module, and solving the output force of each motor by the motor output force calculation module can refer to formulas (1)-(20) in the above method embodiment. The embodiment of the present invention is a system method embodiment corresponding to the above method embodiment. The specific operations of the processing steps of each module can be understood by referring to the description of the method embodiment, and will not be repeated here.

[0143] like Figure 10As shown, the present invention further provides a computer-readable storage medium having a computer program stored thereon. When the computer program is executed by a processor, the method for determining a motor control scheme for a parallel mechanism in a wind tunnel trajectory capture test in the above embodiment is implemented. Alternatively, when the computer program is executed by a processor, the method for determining a motor control scheme for a parallel mechanism in a wind tunnel trajectory capture test in the above embodiment is implemented. When the computer program is executed by the processor, the following method steps are implemented:

[0144] Step S1, establishing a parallel mechanism coordinate system for a wind tunnel capture trajectory test, including a static platform coordinate system and a dynamic platform coordinate system;

[0145] Step S2: Determine the coordinates of the center points of each moving Hooke's joint in the moving platform coordinate system and the static platform coordinate system based on the mechanical structure dimensions of the moving platform, determine the target position of the external attachment in the static platform coordinate system, determine the displacement of the center point of the static Hooke's joint by calculating the distance between the two points in space, and then calculate the motor displacement by proportional calculation;

[0146] According to the displacement speed and Euler angular velocity required by the external attachment, solve the operating speed of each motor;

[0147] Based on the fact that the driving force of the motor acting on the slider through the ball screw is the only generalized force, the output force of each motor is calculated using the Lagrangian algorithm;

[0148] Step S3: Based on the obtained displacement, operating speed, and output force of each motor, a decision is made on a six-degree-of-freedom pure parallel rod mechanism scheme for controlling the wind tunnel trajectory capture test, so as to realize the control of the movement of the external attachment model in the wind tunnel.

[0149] Those skilled in the art will appreciate that all or part of the processes in the above-mentioned embodiments can be implemented by instructing the relevant hardware through a computer program. The computer program can be stored in a non-volatile computer-readable storage medium. When the computer program is executed, it can include the processes of the embodiments of the above-mentioned methods. Among them, any reference to memory, storage, database or other media used in the embodiments provided in this application can include non-volatile and / or volatile memory. Non-volatile memory can include read-only memory (ROM), programmable ROM (PROM), electrically programmable ROM (EPROM), electrically erasable programmable ROM (EEPROM) or flash memory. Volatile memory can include random access memory (RAM) or external cache memory. By way of illustration and not limitation, RAM is available in various forms, such as static RAM (SRAM), dynamic RAM (DRAM), synchronous DRAM (SDRAM), double data rate SDRAM (DDRSDRAM), enhanced SDRAM (ESDRAM), synchronous link (Synchlink) DRAM (SLDRAM), memory bus (Rambus) direct RAM (RDRAM), direct memory bus dynamic RAM (DRDRAM), and memory bus dynamic RAM (RDRAM).

[0150] Each embodiment in this specification is described in a progressive manner. The same or similar parts between the embodiments can be referred to each other. Each embodiment focuses on the differences from other embodiments. In particular, for the device or system embodiments, since they are basically similar to the method embodiments, the description is relatively simple. For the relevant parts, refer to the partial description of the method embodiments. The device and system embodiments described above are merely schematic, wherein the units described as separate components may or may not be physically separated, and the components displayed as units may or may not be physical units, that is, they may be located in one place, or they may be distributed on multiple network units. Some or all of the modules can be selected according to actual needs to achieve the purpose of the scheme of this embodiment. A person of ordinary skill in the art can understand and implement it without making any creative efforts.

[0151] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the above embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the above embodiments, or replace some or all of the technical features therein with equivalents. However, these modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for determining a motor control scheme for a parallel mechanism in a wind tunnel capture trajectory test, characterized in that: The wind tunnel trajectory capture test parallel mechanism includes a static platform connected to an annular dynamic platform via six branch chains. The static platform includes six ball screws driven by six motors, each with a slider provided on it. One end of each branch chain is connected to the slider via a static Hooke's joint, and the other end is connected to the dynamic platform via a dynamic roll joint and a dynamic Hooke's joint. The six dynamic Hooke's joints are evenly spaced around the circumference of the dynamic platform, and the dynamic platform is fixedly connected to the external attachment model. The method comprises the following steps: Establish the parallel mechanism coordinate system for wind tunnel capture trajectory test, including the static platform coordinate system and the dynamic platform coordinate system; Based on the mechanical structure dimensions of the moving platform, the coordinates of the center points of each moving Hooke's joint in the moving platform coordinate system and the static platform coordinate system are determined. The target position of the external attachment in the static platform coordinate system is determined. The displacement of the center point of the static Hooke's joint is determined by calculating the distance between the two points in space, and then the motor displacement is obtained through proportional calculation. According to the displacement speed and Euler angular velocity required by the external attachment, solve the operating speed of each motor; Based on the fact that the driving force of the motor acting on the slider through the ball screw is the only generalized force, the output force of each motor is calculated using the Lagrangian algorithm; Based on the obtained displacement, operating speed and output force of each motor, a decision is made to control the six-degree-of-freedom pure parallel rod mechanism scheme for the wind tunnel capture trajectory test to realize the control of the movement of the external attachment model in the wind tunnel.

2. The method for determining a motor control scheme for a parallel mechanism in a wind tunnel trajectory capture test according to claim 1, wherein: The static platform coordinate system - The origin is set as the center point of the cross section where the endpoints of the six ball screws are located near the motor side, and the slider moves in the direction of the static platform. Axis, vertical direction is Axis, determined by the right-hand rule axis; Moving platform coordinate system - The origin is set to the center of the moving platform, the initial position and Same direction, and Same direction, and Same direction.

3. The method for determining a motor control scheme for a parallel mechanism in a wind tunnel trajectory capture test according to claim 2, wherein: According to the mechanical structure size of the moving platform, the coordinates of the center points of each moving Hooke's joint in the moving platform coordinate system and the static platform coordinate system are determined, the target position of the external attachment in the static platform coordinate system is determined, the displacement of the center point of the static Hooke's joint is determined by calculating the distance between two points in space, and then the motor displacement is obtained by proportional calculation, including the following calculation steps: According to the mechanical structure size of the moving platform, determine the coordinates of the center points of each moving Hooke's joint in the moving platform coordinate system ; Coordinates of the center point of the moving Hooke's joint in the static platform coordinate system , calculated from formula (1): (1) Where, is the displacement vector of the external attachment from the moving platform coordinate system to the static platform coordinate system: (2) is the transformation matrix from the moving platform coordinate system to the static platform coordinate system: (3) Where, is the target posture of the external attachment, sin and cos are denoted as s and c respectively; Based on the constant rod length characteristic, the displacement of the center point of the static Hookean joint is calculated by the distance between two points in space, and the motor displacement is obtained through proportional calculation: (4) Where, The length of six poles; , is the Y / Z coordinate of the static Hooke's joint, which is a fixed mechanism parameter.

4. The method for determining a motor control scheme for a parallel mechanism in a wind tunnel trajectory capture test according to claim 2, wherein: The calculation steps of solving the operating speed of each motor according to the displacement speed and Euler angular velocity required by the external attachment include: Determine the dynamic Hooke hinge i Center point speed v di for: (5) Where, is the velocity of the center point of the moving platform; is the angular velocity of the moving platform; From the center of the moving platform to the Hooke joint The vector of the center; Based on the center velocity of the moving Hooke hinge Hejing Hooke hinge center velocity In the branch chain The projections in the directions are equal, establishing the equation: (6) Where, For the rod Unit direction vector; From the characteristics of the CTS parallel mechanism, we can see that , , (6) is organized as follows: (7) According to formula (7), the Jacobian matrix of the CTS parallel mechanism is: (8) Since the dynamic platform is fixedly connected to the external attachment, use the ZYX Euler angle Describing the posture of the CTS parallel mechanism moving platform, the relationship between the Euler angular velocity and the moving platform angular velocity is: (9) According to formulas (7)-(9), the relationship between the moving speed of the static Hooke's joint center and the posture transformation speed of the moving platform is: (10) When the moving platform speed ( ; ; ) and Euler angular velocity ( ; ; ), the moving speed of the center point of the static Hookean joint in formula (10) is obtained, and the motor speed is solved by proportional operation, where sin and cos are recorded as s and c respectively.

5. The method for determining a motor control scheme for a parallel mechanism in a wind tunnel trajectory capture test according to claim 2, wherein: The driving force of the motor acting on the slider through the ball screw is the only generalized force, and the output force of each motor is calculated by the Lagrangian algorithm, including the following calculation steps: All the sliders, static Hooke's joints, support rods, dynamic roll pairs, dynamic Hooke's joints, and dynamic platforms are set as a whole. The driving force of the motor acting on the slider through the ball screw is the only generalized force. The Lagrange equation can be written as: (11) Where, is the generalized coordinate of the system mechanism; is the generalized speed; U is the system potential energy related to the configuration of the mechanism; K is the system kinetic energy; is the generalized force of the system, i.e. the motor output force; Arranging (11) we can get: (12) Set the static platform coordinate system - The established XZ surface is the zero potential energy surface, and the potential energy of the mechanism is calculated according to the mechanism configuration. ; System kinetic energy K Expressed as: (13) Where, is the mass matrix; System kinetic energy K The six branch chain kinetic energy The sum is: (14) (15) Where, Indicates the The quality of the branches; Indicates the The velocity of the branch chain at the center of mass c; Indicates the Angular velocity of the branch chain; Indicates the The moment of inertia of the center of mass c of the branch chain; and Expressed in the form of Jacobian matrix: (16) Where, the Jacobian matrix Obtained by formula (8); Combine (13) - (16) to establish equations and find the mass matrix : (17) Where, The moment of inertia is calculated by formula (18): (18) in, Indicates the density of the material of the structure, Represents the rigid body coordinates of the mechanism; If different rigid body components are defined in different coordinate systems, they can be transformed into the same reference coordinate system and the parallel axis theory shown in formula (19) can be used to simplify the calculation: (19) Where, is the vector from the c-coordinate point to the o-coordinate point; Substitute (13) into (12) to solve the motor output force: (20)； Where M is the mass matrix, is the first-order derivative of M with respect to time t.

6. Wind tunnel capture trajectory test parallel mechanism motor control scheme determination system, characterized by: The wind tunnel trajectory capture test parallel mechanism includes a static platform connected to an annular dynamic platform via six branch chains. The static platform includes six ball screws driven by six motors, each with a slider provided on it. One end of each branch chain is connected to the slider via a static Hooke's joint, and the other end is connected to the dynamic platform via a dynamic roll joint and a dynamic Hooke's joint. The six dynamic Hooke's joints are evenly spaced around the circumference of the dynamic platform. The dynamic platform is fixedly connected to the external attachment model. The system includes: Coordinate establishment module: used to establish the coordinate system of the parallel mechanism for wind tunnel capture trajectory test, including the static platform coordinate system and the dynamic platform coordinate system; Motor displacement calculation module: This module is used to determine the coordinates of the center points of each moving Hooke's joint in the moving platform coordinate system and the static platform coordinate system based on the mechanical structure dimensions of the moving platform, determine the target position of the external attachment in the static platform coordinate system, calculate the displacement of the center point of the static Hooke's joint by calculating the distance between two points in space, and then calculate the displacement of each motor through proportional calculation; Motor speed calculation module: used to calculate the speed of each motor according to the displacement speed and Euler angular velocity required by the external attachment; Motor output force calculation module: This module is used to calculate the output force of each motor using the Lagrangian algorithm, based on the driving force of the motor acting on the slider through the ball screw as the only generalized force; Decision-making control module: It is used to make decisions and control the six-degree-of-freedom pure parallel rod mechanism scheme of the wind tunnel capture trajectory test based on the obtained displacement, operating speed and output force of each motor, so as to realize the control of the movement of the external attachment model in the wind tunnel.

7. The system for determining a motor control scheme for a parallel mechanism in a wind tunnel trajectory capture test according to claim 6, wherein: The coordinate establishment module establishes coordinates including: Static platform coordinate system - The origin is set as the center point of the cross section where the endpoints of the six ball screws are located near the motor side, and the slider moves in the direction of the static platform. Axis, vertical direction is Axis, determined by the right-hand rule axis; Moving platform coordinate system - The origin is set to the center of the moving platform, the initial position and Same direction, and Same direction, and Same direction.

8. The system for determining a motor control scheme for a parallel mechanism in a wind tunnel trajectory capture test according to claim 7, wherein: The motor operation displacement calculation module includes the following calculation steps: According to the mechanical structure size of the moving platform, determine the coordinates of the center points of each moving Hooke's joint in the moving platform coordinate system ; Coordinates of the center point of the moving Hooke's joint in the static platform coordinate system , calculated from formula (1): (1) Where, is the displacement vector of the external attachment from the moving platform coordinate system to the static platform coordinate system: (2) is the transformation matrix from the moving platform coordinate system to the static platform coordinate system: (3) Where, is the target posture of the external attachment, sin and cos are denoted as s and c respectively; Based on the constant rod length characteristic, the displacement of the center point of the static Hookean joint is calculated by the distance between two points in space, and the motor displacement is obtained through proportional calculation: (4) Where, The length of six poles; , is the Y / Z coordinate of the static Hooke's joint, which is a fixed mechanism parameter.

9. The system for determining a motor control scheme for a parallel mechanism in a wind tunnel trajectory capture test according to claim 7, wherein: The motor speed calculation module includes the following calculation steps: Determine the dynamic Hooke hinge i Center point speed v di for: (5) Where, is the velocity of the center point of the moving platform; is the angular velocity of the moving platform; From the center of the moving platform to the Hooke joint The vector of the center; Based on the center velocity of the moving Hooke hinge Hejing Hooke hinge center velocity In the branch chain The projections in the directions are equal, establishing the equation: (6) Where, For the rod Unit direction vector; From the characteristics of the CTS parallel mechanism, we can see that , , (6) is organized as follows: (7) According to formula (7), the Jacobian matrix of the CTS parallel mechanism is: (8) Since the dynamic platform is fixedly connected to the external attachment, use the ZYX Euler angle Describing the posture of the CTS parallel mechanism moving platform, the relationship between the Euler angular velocity and the moving platform angular velocity is: (9) According to formulas (7)-(9), the relationship between the moving speed of the static Hooke's joint center and the posture transformation speed of the moving platform is: (10) When the moving platform speed ( ; ; ) and Euler angular velocity ( ; ; ), the moving speed of the center point of the static Hookean joint in formula (10) is obtained, and the motor speed is solved by proportional operation, where sin and cos are recorded as s and c respectively.

10. The system for determining a motor control scheme for a parallel mechanism in a wind tunnel trajectory capture test according to claim 7, wherein: The motor output force calculation module includes the following calculation steps: Considering the slider, static Hooke's joint, support rod, dynamic roll pair, dynamic Hooke's joint, and dynamic platform as a whole, the driving force of the motor acting on the slider through the ball screw is the only generalized force, and the Lagrange equation can be written as: (11) Where, is the generalized coordinate of the system mechanism; is the generalized speed; U is the system potential energy related to the configuration of the mechanism; K is the system kinetic energy; is the generalized force of the system, i.e. the motor output force; Arranging (11) we can get: (12) Set the static platform coordinate system - The established XZ surface is the zero potential energy surface, and the potential energy of the mechanism is calculated according to the mechanism configuration. ; System kinetic energy K Expressed as: (13) Where, is the mass matrix; System kinetic energy K The six branch chain kinetic energy The sum is: (14) (15) Where, Indicates the The quality of the branches; Indicates the The velocity of the branch chain at the center of mass c; Indicates the Angular velocity of the branch chain; Indicates the The moment of inertia of the center of mass c of the branch chain; and Expressed in the form of Jacobian matrix: (16) Where, the Jacobian matrix It can be obtained by formula (8); Combine (13) - (16) to establish equations and find the mass matrix : (17) Where, The moment of inertia is calculated by formula (18): (18) in, Indicates the density of the material of the structure, Represents the rigid body coordinates of the mechanism; If different rigid body components are defined in different coordinate systems, they can be transformed into the same reference coordinate system and the parallel axis theory shown in formula (19) can be used to simplify the calculation: (19) Where, is the vector from the c-coordinate point to the o-coordinate point; Substitute (13) into (12) to solve the motor output force: (20); Where M is the mass matrix, is the first-order derivative of M with respect to time t.

Images