Design method of parallel mechanism with high normal rigidity and high lateral rigidity

Abstract

The invention relates to a design method of a parallel mechanism with high normal rigidity and high lateral rigidity. The design method comprises the following steps: S1, determining the motion freedom degree requirement of a movable platform of the parallel mechanism, establishing a mechanism motion spinor system and a constraint spinor system, and determining a branch chain constraint spinor system and a motion spinor system of the parallel mechanism; s2, establishing a force transmission model of the parallel mechanism, and determining a normal stiffness maximum design criterion; s3, a force balance equation of the parallel mechanism is established, an additional force system is provided by introducing auxiliary configuration so as to adjust the overall stress state of the mechanism, and a design criterion of maximizing transverse rigidity is determined; and S4, the design criterion of the maximum normal stiffness and the design criterion of the maximum transverse stiffness are combined with the dynamic and static force model, and the parallel mechanism with the high normal stiffness and the high lateral stiffness is obtained. According to the method, the design criterion of the maximum normal stiffness of the parallel mechanism is established, the normal stiffness of the mechanism is improved to the maximum extent, and the method has important application prospects in the parallel mechanism under the heavy load working condition.

Description

Technical Field

[0001] The present invention relates to the field of parallel mechanism configuration design, and more specifically, to a design method for a parallel mechanism with both high normal stiffness and high lateral stiffness. Background Art

[0002] Parallel mechanisms are widely used in handling, packaging, forming and other fields because of their advantages such as strong load-bearing capacity, high rigidity and high precision. The primary task of parallel mechanism research and development is to design a configuration that meets the requirements of motion freedom / motion trajectory. At present, a variety of comprehensive methods have been proposed by scholars, mainly including those based on screw theory, displacement group theory, virtual loop method and POC set method. However, the stiffness performance of the parallel mechanism synthesized by the above methods is difficult to be effectively guaranteed. The low-rigidity mechanism leads to reduced mechanism forming accuracy, especially under heavy-load conditions in the forming manufacturing field. With the increasing demand for lightweight, large-scale, extreme structures, high-temperature resistant and high-load-bearing components, greater forming force and higher rigidity are required for parallel mechanism forming equipment. The main and lateral rigidity of the existing parallel mechanism is low, resulting in poor stability of the equipment structure and low accuracy of movement. Summary of the invention

[0003] The technical problem to be solved by the present invention is to provide a design method for a parallel mechanism with both high normal stiffness and high lateral stiffness, and to establish a design criterion for the maximum normal stiffness of the parallel mechanism to maximize the normal stiffness of the mechanism, which has important application prospects in parallel mechanisms under heavy load conditions.

[0004] The technical solution adopted by the present invention to solve the technical problem is: constructing a design method of a parallel mechanism with high normal stiffness and high lateral stiffness, comprising the following steps:

[0005] S1. Determine the motion freedom requirements of the parallel mechanism dynamic platform, establish the mechanism motion screw system and constraint screw system, on this basis, establish the branch constraint screw system and motion screw system of the parallel mechanism, and select the motion branch and mechanism configuration that meet the design constraints and motion requirements of the parallel mechanism;

[0006] S2. Establish a force transmission model of the parallel mechanism and determine the maximum design criterion for normal stiffness;

[0007] S3. Establish the force balance equation of the parallel mechanism, introduce auxiliary configuration to provide additional force system to adjust the overall force state of the mechanism, and determine the design criteria for maximizing lateral stiffness;

[0008] S4. Combining the design criteria of maximum normal stiffness and maximum lateral stiffness with the static and dynamic force model, a parallel mechanism with both high normal stiffness and high lateral stiffness is obtained.

[0009] 2. The design method of a parallel mechanism with high normal stiffness and high lateral stiffness according to claim 1, characterized in that, in step S1, the arbitrary motion in space is characterized by a six-dimensional motion spinor:

[0010]

[0011] In the formula, The system of kinematic spinors representing spatial motion, S mpi Represents the orthogonal spinor of spatial motion; based on the spinor theory, the relationship between the spinor system of the parallel mechanism motion platform and the spinor of the branch joint motion is expressed as:

[0012]

[0013] In the formula, represents the constrained screw system that is reciprocal with the moving platform motion screw system, represents the constrained screw system of the parallel mechanism branch chain, The motion screw system of the parallel mechanism branch chain; various types of branches are generated by using the linear combination of the branch chain motion screws, and the parallel mechanism that meets the motion requirements is obtained through system assembly and drive design.

[0014] According to the above scheme, in step S2, the total static balance of the parallel mechanism is expressed as:

[0015]

[0016] in, represents the constraint force of the drive joint on the platform, represents the drive provided by the driving joint, Σ represents the angle of the base guide, and F n represents the normal force; the overall static equilibrium of the parallel mechanism can be expressed as:

[0017]

[0018] in, represents the components of the connecting rod along the x, y, and z directions, J g Represents the Jacobian matrix of the connecting rod force transmission of the parallel mechanism; the design criterion for maximizing the normal stiffness of the parallel mechanism is:

[0019]

[0020] According to the above scheme, in step S3, by specifying the point of action of the external force as the force analysis origin, when the parallel mechanism is acted upon by the lateral force, the force system of the parallel mechanism is expressed as:

[0021]

[0022] Among them, ξr The coefficient representing the radial force, ξ t The coefficient representing the tangential force, the driving force provided by each branch chain is expressed as follows:

[0023]

[0024] in, represents the connecting rod force rotation, Represents the three components of the connecting rod lever arm; the force balance condition is:

[0025]

[0026] because, The force balance in the z-axis is expressed as:

[0027]

[0028] In order to minimize the connecting rod force, the optimization goal is:

[0029]

[0030] Another parallel mechanism is introduced to avoid the motion singularity and withstand the lateral force. The force balance condition of the other parallel mechanism is:

[0031]

[0032] in, The sub-table represents the vector components of the hydraulic connecting rod, Represents the forces of the three hydraulic connecting rods and is solved by the following equation:

[0033]

[0034] Among them, J h is the force transmission Jacobian matrix of the two parallel mechanisms; in order to maximize the lateral stiffness, the design criteria of the other parallel mechanism are as follows:

[0035]

[0036] According to the above scheme, in step S4, the force rotation of the six connecting rods and the force rotation of the hydraulic connecting rod are calculated as follows:

[0037]

[0038] in, and is the force twist and The unit spinor, r l i and Represents the direction vector of the connecting rod and the hydraulic connecting rod, d l0 Indicates the length of the connecting rod, d h0 and They represent the initial length and extension length of the hydraulic connecting rod respectively; the static equilibrium equation is expressed as follows:

[0039]

[0040] Among them, J g is the connecting rod force Jacobian matrix, J h is the Jacobian matrix of the hydraulic connecting rod force.

[0041] The driving force vector is expressed as:

[0042]

[0043] The parameters of the two parallel mechanisms are integrated into the following optimization problem:

[0044]

[0046] The design method of the parallel mechanism with high normal stiffness and high lateral stiffness of the present invention has the following beneficial effects:

[0047] The present invention establishes a design criterion for the maximum normal stiffness of a parallel mechanism to maximize the normal stiffness of the mechanism, and obtains a nearly singular 6-PSS parallel mechanism with maximum normal stiffness; further introduces a new auxiliary 3-SPS configuration to provide an additional force system to maximize the lateral stiffness of the mechanism, and proposes a design criterion for maximizing lateral stiffness, that is, all SS connecting rod forces should remain positive. The present invention provides a new method for the synthesis of heavy-duty parallel mechanisms with high normal and high lateral stiffness, and has important application prospects in parallel mechanisms under heavy-duty conditions. BRIEF DESCRIPTION OF THE DRAWINGS

[0048] The present invention will be further described below with reference to the accompanying drawings and embodiments, in which:

[0049] Figure 1 It is a basic structural diagram of 6-PSS / 3-SPS parallel mechanism;

[0050] Figure 2 It is a schematic diagram of the static model of the 6-PSS / 3-SPS parallel mechanism;

[0051] Figure 3 It is a schematic diagram of the comprehensive error of the dynamic platform of the 6-PSS / 3-SPS parallel mechanism under the maximum normal force;

[0052] Figure 4It is a schematic diagram of the comprehensive error of the dynamic platform of the 6-PSS / 3-SPS parallel mechanism under different normal forces;

[0053] Figure 5 It is a schematic diagram of the normal stiffness of the 6-PSS / 3-SPS parallel mechanism;

[0054] Figure 6 It is the schematic diagram of the moving platform error of 6-PSS parallel mechanism under different lateral forces;

[0055] Figure 7 It is a schematic diagram of the moving platform error of the 6-PSS / 3-SPS parallel mechanism under different lateral forces;

[0056] Figure 8 It is a schematic diagram of the lateral stiffness of the 6-PSS and 6-PSS / 3-SPS parallel mechanisms. DETAILED DESCRIPTION

[0057] In order to have a clearer understanding of the technical features, purposes and effects of the present invention, specific embodiments of the present invention are now described in detail with reference to the accompanying drawings.

[0058] The design method of the parallel mechanism with both high normal stiffness and high lateral stiffness of the present invention comprises the following steps:

[0059] S1. According to the required spatial motion, determine the motion freedom requirements of the parallel mechanism dynamic platform, establish the mechanism motion screw system and constraint screw system, and on this basis establish the branch constraint screw system and motion screw system of the parallel mechanism. Arbitrary spatial motion can be characterized by six-dimensional motion screws:

[0060]

[0061] In the formula, The system of kinematic spinors representing spatial motion, S mpi Represents the orthogonal spinor of spatial motion. Obviously, the rank of the spinor system of spatial motion is the degree of freedom of the required parallel mechanism. Based on the spinor theory, the relationship between the spinor system of the parallel mechanism motion platform and the spinor of the branch joint motion can be expressed as:

[0062]

[0063] In the formula, represents the constrained screw system that is reciprocal with the moving platform motion screw system, represents the constrained screw system of the parallel mechanism branch chain, The kinematic rotation system of the parallel mechanism branch. Based on the above process, various types of branches can be generated using the linear combination of the branch kinematic rotation. Subsequently, through system assembly and drive design, many parallel mechanisms that meet the kinematic requirements can be obtained, as shown in Table 1. In the table, P represents a translation joint, R represents a rotation joint, U represents a universal joint, S represents a ball joint, and C represents a cylindrical joint.

[0064] Table 1 Typical joint layout between the driving joint and the moving platform.

[0065]

[0066]

[0067] For heavy-load working conditions, it is best to minimize the number of joints. Therefore, the joint configuration of the branch with the least joints can be SU, US or CS, with only two joints in each branch. In addition, for the convenience of manufacturing, the change of joint type should be minimized, and the structure of the U-joint generally contains two rotating shafts connected by a cross axis, which is complex in structure and low in stiffness, while the S-joint can be designed as the contact of spherical parts, which is simplified in structure and high in stiffness. Therefore, the U-joint of the US branch and the SU branch can be configured as SS. In this arrangement, there is freedom of two branches. From a kinematic point of view, the rotation of the connecting rod along the axis does not affect the structure, making the joint layout of SS feasible. From the perspective of statics and dynamics, the deformation of the connecting rod is caused by the forces at the joints at both ends. For the SS node and the US node, the total force acting on both ends of the node is the same, so there is no significant difference in deformation. Therefore, under heavy-load conditions, the 6-PSS or 6-RSS parallel mechanism has unique advantages.

[0068] S2. Establish the force transmission model of the parallel mechanism and propose the maximum design criterion of normal stiffness. The total static balance of the 6-PSS parallel mechanism can be expressed as:

[0069]

[0070] in, represents the constraint force of the drive joint on the platform, represents the drive provided by the driving joint, Σ represents the angle of the base guide, and F n Indicates the normal force. Considering that the normal force on the mechanism is large under heavy load conditions, when Σ approaches 0, The smaller it is, the greater the system stiffness is, which means that the driving force along the horizontal direction is optimal. Further, the overall static balance of 6-PSS can be expressed as:

[0071]

[0072] in, represents the components of the connecting rod along the x, y, and z directions, J g The Jacobian matrix of the connecting rod force transmission of the 6-PSS parallel mechanism is represented by n acts mainly in the vertical direction, so the connecting rod force should also be in the vertical direction to minimize the connecting rod force. This means that the horizontal component of the connecting rod force and, It should be minimized as much as possible. Therefore, the design criterion for maximizing the normal stiffness of the 6-PSS parallel mechanism is:

[0073]

[0074] S3, the force balance equation of the parallel mechanism is derived, and an auxiliary configuration is introduced to provide an additional force system to adjust the overall force state of the mechanism, and the design criteria for maximizing lateral stiffness are proposed accordingly; through the design criteria of S2, the 6-PSS parallel mechanism is very suitable for bearing normal forces, but balancing lateral forces is challenging. Further, by specifying the point of action of the external force as the force analysis origin, when the parallel mechanism is subjected to lateral forces, the force system of the 6-PSS mechanism can be expressed as:

[0075]

[0076] Among them, ξ r The coefficient representing the radial force, ξ t The coefficient representing the tangential force, the driving force provided by each branch chain is expressed as follows:

[0077]

[0078] in, represents the connecting rod force rotation, represents the three components of the connecting rod lever arm; the force balance condition can be further written as:

[0079]

[0080] because, Therefore, the force balance in the z-axis can be expressed as:

[0081]

[0082] In order to minimize the connecting rod force, the optimization goal is:

[0083]

[0084] It can be seen from equation (12) that in order to minimize the value of the equation, all terms should be greater than zero; that is, all link forces are greater than 0. This provides a design criterion for improving lateral stiffness. Therefore, all terms in equation (12) are greater than zero, and the contribution of each term is positive, that is, the work of each link is positive. This illustrates the mechanism of enhancing stiffness by making the link perform positive work, which has never been disclosed before. However, for this nearly singular 6-PSS parallel mechanism configuration, it is difficult to achieve force balance. Therefore, a 3-SPS parallel mechanism is introduced to circumvent the motion singularity and withstand the lateral force. In order to reduce the complexity of control, a flexible hydraulic link is used to balance the lateral force and coordinate with the 6-PSS parallel mechanism to adjust the position error.

[0085] The force balance condition of the new parallel mechanism will be:

[0086]

[0087] in, The sub-table represents the vector components of the hydraulic connecting rod, The force of the three hydraulic connecting rods can be solved by the following formula:

[0088]

[0089] Among them, J h is the force transmission Jacobian matrix of the 6-PSS / 3-SPS parallel mechanism. In order to maximize the lateral stiffness, the design criteria of the 3-SPS parallel mechanism are as follows:

[0090]

[0091] The purpose of adding a 3-SPS parallel mechanism is to achieve lateral force balance by actively adjusting the hydraulic force while maintaining the positive link force of the 6-PSS parallel mechanism. The hydraulic force should be neither too large nor too small, because either extreme force will destroy the balance. Nevertheless, the configuration may not be unique, so the design goal is to minimize the hydraulic link force.

[0092] S4. Combining the above design criteria with the static model, a near-singular 6-PSS / 3-SPS parallel mechanism with high main and lateral stiffness is obtained. The force rotation of the six connecting rods and the force rotation of the hydraulic connecting rod can be calculated as follows:

[0093]

[0094] in, and is the force twist and The unit spinor, r l iand Represents the direction vector of the connecting rod and the hydraulic connecting rod, d l0 Indicates the length of the connecting rod, d h0 and d h i They represent the initial length and extension length of the hydraulic connecting rod respectively. The static equilibrium equation can be expressed as follows:

[0095]

[0096] Among them, J g is the connecting rod force Jacobian matrix, J h is the Jacobian matrix of the hydraulic connecting rod force.

[0097] The driving force vector can be expressed as:

[0098]

[0099] This shows that if the external forces and the forces applied by the hydraulic linkage are known, the magnitude of the driving force vector can be determined.

[0100] The parameter synthesis of the 6-PSS / 3SPS parallel mechanism becomes the following optimization problem:

[0101]

[0102] Although the optimization goal is to minimize the root mean square error of the horizontal projection and hydraulic pressure of all links, which is not directly related to high stiffness; according to the design criteria proposed by S2 and S3, the design criteria is to maximize the normal and lateral stiffness. Therefore, the physical meaning of the optimization goal can be regarded as maximizing both the normal stiffness and the lateral stiffness.

[0103] Example

[0104] Combining the above-mentioned design method of a six-DOF parallel mechanism with high main and lateral stiffness, a flexible redundant 6-PSS / 3-SPS parallel mechanism with high normal stiffness and lateral stiffness is designed. The design parameters are shown in Table 3. The basic structure is shown in Figure 1 As shown in Figure 2 shown.

[0105] Table 3 Design parameters of 6-PSS / 3-SPS parallel mechanism.

[0106]

[0107] According to the design parameters, the normal and lateral stiffness performance of the new 6-PSS / 3-SPS parallel mechanism was analyzed. First, in order to evaluate the normal stiffness performance of the new 6-PSS / 3-SPS, the normal external force is set to F n =4~8MN, the force arm is Re =45~90mm, lateral force is 0, and the maximum error of the moving platform is calculated, such as Figure 3 As shown in Figure 2, the dynamic platform error under different normal forces and different force arms is further analyzed, as shown in Figure 2. Figure 4 As shown; Figure 5 The normal stiffness of the 6-PSS / 3-SPS under different force arms and normal forces is given. It is observed that the normal stiffness decreases with the increase of the force action radius, while the change of the normal force has no significant effect on it. The maximum stiffness of the 6-PSS / 3-SPS mechanism is very high, ranging from about 21.5N / nm to 29.2N / nm, and is not affected by the change of the normal force. Further, in order to evaluate the lateral stiffness performance of the new 6-PSS / 3-SPS, the lateral force coefficient is designed to be ξ r =0~0.1 and ξ t =0~0.1. Figure 6 The error distribution of the 6-PSS parallel mechanism moving platform under different radial and tangential forces is described, and the error distribution is between 245 and 809 um. Figure 7 The error distribution of the 6-PSS / 3-SPS parallel mechanism dynamic platform under different radial and tangential forces is described, and the error distribution is 207~454um. Figure 8 The lateral stiffness of the 6-PSS and 6-PSS / 3-SPS parallel mechanisms is summarized. It can be seen that the lateral stiffness of the 6-PSS increases from about 0.21N / nm to 2.1N / nm, while the lateral stiffness of the 6-PSS / 3-SPS parallel mechanism increases from 1.3N / nm to 12.9N / nm, an increase of about 6 times. In summary, the proposed 6-PSS / 3-SPS parallel mechanism design has high normal stiffness and is suitable for heavy load conditions.

[0108] The embodiments of the present invention are described above in conjunction with the accompanying drawings, but the present invention is not limited to the above-mentioned specific implementation modes, which are merely illustrative rather than restrictive. Under the guidance of the present invention, ordinary technicians in this field can also make many forms without departing from the scope of protection of the present invention and the claims, all of which are within the protection of the present invention.

Claims

1. A design method for a parallel mechanism with both high normal stiffness and high lateral stiffness, characterized in that: The following steps are involved: S1. Determine the motion freedom requirements of the parallel mechanism dynamic platform, establish the mechanism motion screw system and constraint screw system, on this basis, establish the branch constraint screw system and motion screw system of the parallel mechanism, and select the motion branch and mechanism configuration that meet the design constraints and motion requirements of the parallel mechanism; S2. Establish a force transmission model of the parallel mechanism and determine the maximum design criterion for normal stiffness; S3. Establish the force balance equation of the parallel mechanism, provide an additional force system by introducing auxiliary configuration to adjust the overall force state of the mechanism, and determine the design criteria for maximizing lateral stiffness; S4. Combining the design criteria of maximum normal stiffness and maximum lateral stiffness with the static and dynamic force model, a parallel mechanism with both high normal stiffness and high lateral stiffness is obtained.

2. The design method of a parallel mechanism with both high normal stiffness and high lateral stiffness according to claim 1, characterized in that: In step S1, arbitrary spatial motion is characterized by a six-dimensional motion spinor: In the formula, The system of kinematic spinors representing spatial motion, S mpi Represents the orthogonal spinor of spatial motion; based on the spinor theory, the relationship between the spinor system of the parallel mechanism motion platform and the spinor of the branch joint motion is expressed as: In the formula, represents the constrained screw system that is reciprocal with the moving platform motion screw system, represents the constrained screw system of the parallel mechanism branch chain, The motion screw system of the parallel mechanism branch chain; various types of branches are generated by using the linear combination of the branch chain motion screws, and the parallel mechanism that meets the motion requirements is obtained through system assembly and drive design.

3. The design method of a parallel mechanism with both high normal stiffness and high lateral stiffness according to claim 2, characterized in that: In step S2, the total static balance of the parallel mechanism is expressed as: in, represents the constraint force of the drive joint on the platform, represents the drive provided by the driving joint, Σ represents the angle of the base guide, and F n represents the normal force; the overall static equilibrium of the parallel mechanism can be expressed as: in, represents the components of the connecting rod along the x, y, and z directions, J g Represents the Jacobian matrix of the connecting rod force transmission of the parallel mechanism; the design criterion for maximizing the normal stiffness of the parallel mechanism is:

4. The design method of a parallel mechanism with both high normal stiffness and high lateral stiffness according to claim 3, characterized in that: In step S3, by specifying the point of action of the external force as the force analysis origin, when the parallel mechanism is acted upon by the lateral force, the force system of the parallel mechanism is expressed as: Among them, ξ r The coefficient representing the radial force, ξ t The coefficient representing the tangential force, the driving force provided by each branch chain is expressed as follows: in, represents the connecting rod force rotation, Represents the three components of the connecting rod lever arm; the force balance condition is: because, F n > 0, the force balance in the z-axis is expressed as: In order to minimize the connecting rod force, the optimization goal is: Another parallel mechanism is introduced to avoid the motion singularity and withstand the lateral force. The force balance condition of the other parallel mechanism is: in, The sub-table represents the vector components of the hydraulic connecting rod, Represents the forces of the three hydraulic connecting rods and is solved by the following equation: Among them, J h is the force transmission Jacobian matrix of the two parallel mechanisms; in order to maximize the lateral stiffness, the design criteria of the other parallel mechanism are as follows:

5. The design method of a parallel mechanism with both high normal stiffness and high lateral stiffness according to claim 4, characterized in that: In step S4, the torque of the six connecting rods and the torque of the hydraulic connecting rod are calculated as follows: in, and is the force twist and The unit spin of and Represents the direction vector of the connecting rod and the hydraulic connecting rod, d l0 Indicates the length of the connecting rod, d h0 and They represent the initial length and extension length of the hydraulic connecting rod respectively; the static equilibrium equation is expressed as follows: Among them, J g is the connecting rod force Jacobian matrix, J h is the Jacobian matrix of the hydraulic connecting rod force. The driving force vector is expressed as: The parameters of the two parallel mechanisms are integrated into the following optimization problem: 。

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