CN114722531B - Progressive optimization design method, system and mechanism for flexible parallel micro-operation mechanism - Google Patents
Progressive optimization design method, system and mechanism for flexible parallel micro-operation mechanism Download PDFInfo
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Abstract
The invention discloses a progressive optimization design method, a progressive optimization design system and a progressive optimization design mechanism for flexible parallel micro-operation mechanisms, wherein a closed vector method is utilized to establish a kinematic model of the flexible parallel micro-operation mechanisms, and the kinematic performance of the flexible parallel micro-operation mechanisms is analyzed; then defining a design parameter range and a global dexterity limiting condition, taking the minimum ratio of the mechanism volume to the working space volume as an optimization index, establishing a scale parameter optimization model, and optimally designing the scale parameters; then, a dynamic model of the flexible parallel micro-operation mechanism is established by utilizing a Lagrangian equation, and an expression of the driving force of the flexible parallel micro-operation mechanism is solved; and finally, based on the optimized scale parameters, taking the natural frequency limit, the stress limit and the flexible hinge design parameter range of the flexible parallel micro-operation mechanism as limiting conditions, taking the minimum linear weighted value of the total mass and the rigidity as an optimization target, and optimizing the flexible hinge structure parameters to ensure that the dynamic performance of the flexible parallel micro-operation mechanism is optimal.
Description
Technical Field
The invention belongs to the technical field of mechanical equipment design, relates to a method, a system and a mechanism for designing a flexible parallel micro-operation mechanism, and particularly relates to a method, a system and a mechanism for progressively optimizing design of a flexible parallel mechanism based on kinematic performance and dynamic performance.
Background
Because the flexible parallel micro-operation mechanism combines a flexible mechanism and a parallel mechanism, the flexible parallel micro-operation mechanism has a series of advantages of no friction, no impact, simple assembly and the like. At present, the flexible parallel micro-operation mechanism is applied to the fields of microelectronics, microbiological experiments, precise measurement, aerospace, and the like. Although flexible parallel connection has been focused on some fields to achieve a certain market, it has not been widely used like parallel mechanisms, wherein an issue is very important in optimizing design of the mechanism, which can reduce manufacturing cost of the mechanism, improve working space of the mechanism, optimize flexibility of the mechanism, reduce inertia force of the mechanism, and the like. Therefore, the research on the optimal design method of the flexible parallel micro-operation mechanism has important significance.
Most of researches are limited to optimization design based on kinematic performance or dynamic performance, so that the optimization of the flexible parallel mechanism is difficult to meet the requirements of practical application environments. Therefore, in order to meet the design requirements of the kinematics and the dynamics performance of the optimized flexible parallel micro-operation mechanism, the flexible parallel micro-operation mechanism is subjected to orderly progressive optimization design based on the kinematics performance and the dynamics performance, so that the overall performance of the mechanism can meet the practical application requirements.
Disclosure of Invention
The invention mainly aims to ensure that the kinematic performance and the dynamic performance of a flexible parallel micro-operation mechanism meet the design requirements, and provides a progressive optimization design method, a progressive optimization design system and a progressive optimization design mechanism based on the kinematic performance and the dynamic performance of the mechanism. The optimized mechanism meets the design requirement of multiple performances.
The technical scheme adopted by the method is as follows: a progressive optimization design method for flexible parallel micro-operation mechanisms comprises the following steps:
step 1: establishing a flexible parallel micro-operation mechanism kinematic model;
Establishing a kinematic model of the flexible parallel micro-operation mechanism by using a closed vector method, and analyzing the kinematic performance of the flexible parallel micro-operation mechanism;
step 2: based on the kinematic performance, establishing a scale parameter optimization model;
defining a design parameter range and a global dexterity limiting condition, and optimally designing the scale parameters by taking the minimum ratio of the mechanism volume to the working space and the volume as an optimization index;
step 3: based on the kinematic performance, establishing a dynamic model of the flexible parallel micro-operation mechanism;
Establishing a dynamic model of the flexible parallel micro-operation mechanism by using a Lagrangian equation, and solving an expression of the driving force of the flexible parallel micro-operation mechanism;
Step 4: establishing a flexible hinge structure parameter optimization model;
Based on the optimized scale parameters, the dynamic performance is based on the limiting conditions of the natural frequency limit, the stress limit and the flexible hinge design parameter range of the flexible parallel micro-operation mechanism, the linear weighting of the total mass and the rigidity is used as an optimization target, and the flexible hinge structure parameters are optimized, so that the dynamic performance of the flexible parallel micro-operation mechanism is optimal.
The system of the invention adopts the technical proposal that: a progressive optimization design system of a flexible parallel micro-operation mechanism comprises the following modules:
The module 1 is used for establishing a flexible parallel micro-operation mechanism kinematic model;
Establishing a kinematic model of the flexible parallel micro-operation mechanism by using a closed vector method, and analyzing the kinematic performance of the flexible parallel micro-operation mechanism;
the module 2 is used for establishing a scale parameter optimization model;
defining a design parameter range and a global dexterity limiting condition, and optimally designing the scale parameters by taking the minimum ratio of the mechanism volume to the working space and the volume as an optimization index;
The module 3 is used for establishing a dynamic model of the flexible parallel micro-operation mechanism;
Establishing a dynamic model of the flexible parallel micro-operation mechanism by using a Lagrangian equation, and solving an expression of the driving force of the flexible parallel micro-operation mechanism;
The module 4 is used for establishing a flexible hinge structure parameter optimization model;
Based on the optimized scale parameters, the dynamic performance is based on the limiting conditions of the natural frequency limit, the stress limit and the flexible hinge design parameter range of the flexible parallel micro-operation mechanism, and the minimum linear weighting value of the total mass and the rigidity is used as an optimization target, so that the dynamic performance of the flexible parallel micro-operation mechanism is optimized.
The mechanism of the invention adopts the technical scheme that: the flexible parallel micro-operation mechanism is manufactured by using the progressive optimization design method of the flexible parallel micro-operation mechanism.
Compared with the prior art, the invention has the beneficial effects that: most of the optimal designs of the flexible parallel micro-operation mechanisms are focused on the optimal designs of the dimensional parameters of the mechanisms based on the kinematic performance, and few design requirements of the kinematic performance are considered, and meanwhile, the design of the two is rare. The invention provides a progressive optimization design method based on kinematic performance and dynamics requirements aiming at a flexible parallel micro-operation mechanism, so that the performance of the optimized mechanism has the kinematic and dynamics performance requirements.
Drawings
FIG. 1 is a schematic diagram of a 3-PSS flexible parallel micro-operation mechanism employed in an embodiment of the present invention; wherein, 1 is a frame, 2 is a piezoelectric moving platform, 3 is a sliding block, 4 is a supporting rod, 5 is a flexible spherical hinge, and 6 is a moving platform;
FIG. 2 is a flow chart of a method according to an embodiment of the present invention;
FIG. 3 is a simplified pseudo-rigid body model schematic diagram of an embodiment of the present invention;
FIG. 4 is an ith branch vector diagram of an embodiment of the present invention;
FIG. 5 is a schematic diagram of a mechanism working space according to an embodiment of the present invention;
FIG. 6 is a maximum cross-section of an optimized mechanism workspace of an embodiment of the invention;
FIG. 7 is a comparison of maximum cross-sections of working spaces of the front and rear mechanism optimized according to an embodiment of the present invention;
FIG. 8 is a schematic diagram showing the working space contrast of the front and rear mechanism according to the embodiment of the present invention;
Fig. 9 is a schematic diagram of driving force of the mechanism before and after optimization under a specific trajectory in the embodiment of the present invention.
Detailed Description
In order to facilitate the understanding and practice of the invention, those of ordinary skill in the art will now make further details with reference to the drawings and examples, it being understood that the examples described herein are for the purpose of illustration and explanation only and are not intended to limit the invention thereto.
The embodiment is illustrated by taking a progressive optimization design of the 3-PSS flexible parallel micro-operation mechanism as shown in fig. 1 as an example, wherein the mechanism mainly comprises a frame, a piezoelectric moving platform, a sliding block, a flexible spherical hinge, a supporting rod and a moving platform. Three PSS (P-moving pairs; S-ball pairs) branched chains distributed at 120 degrees are connected with the moving platform and the static platform, wherein the moving pairs P are driving pairs, and the flexible deformation of the flexible ball hinge (S) is utilized to transmit force and motion. The parameters are defined as: the radius of the movable platform is r p =25mm; rod length l=65 mm; static plateau radius r a =45 mm.
Please refer to fig. 2, a progressive optimization design method for a flexible parallel micro-operation mechanism provided in this embodiment includes the following steps:
step 1: establishing a flexible parallel micro-operation mechanism kinematic model;
Establishing a kinematic model of the flexible parallel micro-operation mechanism by using a closed vector method, and analyzing the kinematic performance of the flexible parallel micro-operation mechanism;
According to the kinematic performance of the 3-PSS flexible parallel micro-operation mechanism, each flexible hinge is simplified into two ideal rotating joints which are distributed in an orthogonal mode and have constant bending rigidity, the supporting rods are equivalent to rigid rods, and the supporting rods on each branched chain of the mechanism are equivalent to one supporting rod because the motion states of the supporting rods are the same, so that a simplified rigid body model can be built, as shown in figure 3, Is the angle between OA i and the x-axis of the reference frame. The angle between the axis of the link B iPi and the z-axis of the reference frame is defined as θ l.
The vector diagram of the ith branched chain of the mechanism is shown in fig. 4, and based on the vector relation, a closed vector equation of the ith branched chain is established as follows:
raai+bi+lci-rpdi＝P (1)
Wherein r a、rp and l are respectively the radius of the static platform, the radius of the movable platform and the length of the support rod, B i is the input displacement of the sliding block, P is the center of a circle circumscribed by the movable platform, and a i、ci and d i are respectively the direction vectors of the static platform OA i, the support rod B iPi and the radius PP i of the movable platform; The included angle between OA i and the x-axis of the reference coordinate system, and the included angle between the B iPi axis of the connecting rod and the z-axis of the reference coordinate system; o is the center of a circle circumscribed by the static platform; wherein the reference frame x-axis coincides with OA 1;
And (3) sorting and deriving the formula (1) to obtain the relationship between the input and output of the mechanism:
where J is the Jacobian matrix of the mechanism. A velocity matrix representing the slider; /(I)Representing a velocity matrix of the moving platform.
The actuator of the selection mechanism is a piezoelectric moving platform with a stroke of 200 mu m, the limit rotation angle of the flexible spherical hinge is assumed to be 1 degree, and the working space of the mechanism obtained according to the cylindrical limit searching method is shown in figure 5.
In order to quantify the size of the working space volume, a cube covering the whole working space is selected, the cube volume V is divided into N small unit bodies with the volume V N, the center point of each small unit is used as a reference point, judgment is carried out according to the constraint condition of the working space, the number of the center points of the unit bodies in the working space is reserved and counted, and the total number is N. The volume V w of the workspace can be expressed as:
The dexterity of a mechanism is the ability of the mechanism to change its position, direction, or apply force, moment in any direction. In micro-nano scale operation, the dexterity is an important motion performance of the designed flexible parallel micro-operation mechanism. The general Jacobian matrix condition number k is a measure of the mechanism's dexterity, where k= |j|·|j -1 |, and|·| is the two norms of the matrix. In addition, the dexterity of the mechanism is typically represented by the reciprocal of the jacobian condition number, i.e., u=1/k. When u=0, the mechanism is in a singular configuration, and when u=1, the mechanism is in isotropy. From the given mechanism model parameters, a dexterity profile on the maximum cross-section of the mechanism workspace (z=z max/2) is obtained, as shown in fig. 6.
To evaluate the global dexterity index in the workspace context, the global dexterity of an organization may be expressed as:
Where w is one of the points of all the rendezvous points N w that are uniformly distributed over the workspace.
Step 2: establishing a scale parameter optimization model;
defining a design parameter range and a global dexterity limiting condition, and optimally designing the scale parameters by taking the minimum working space and volume as optimization indexes;
According to kinematic analysis, the structural parameters of the mechanism, which mainly affect the working space and the flexibility of the mechanism, are the radius difference of the dynamic platform and the static platform and the length of the rod. For simplicity, the radius of the movable platform is assumed to be unchanged, and the radius r a of the static platform and the length l of the rod are taken as optimization parameters. In order to enable the mechanism to be minimized in volume and the mechanism to be maximized in working space volume while being within the design parameters and meeting the design requirements in terms of the overall dexterity of the mechanism. Thus, constraints and objective functions are established as shown in the following equation: given the constraint of global dexterity GDI, the maximum working space of the mechanism and the minimum mechanism volume are taken as optimization targets, so that the constraint conditions and the objective functions are as follows:
Where GDI is global dexterity, l is the lever length of the mechanism, and r a is the static platform radius. V is the volume of the mechanism and V w is the volume of the mechanism working space.
Optimizing by utilizing a MATLAB genetic algorithm tool box, and obtaining an optimized scale parameter of r a =38.66 mm; l=50.13 mm. Performance before and after comparative scale optimization is shown in table 1. Global dexterity u=0.204 for the optimized mechanism, the dexterity distribution of the optimized mechanism over the largest cross-section in the workspace is shown in fig. 7; the working space volume of the mechanism after optimization is increased by 14.17% compared with the mechanism before optimization, and the working space volume pairs before and after optimization are shown in FIG. 8; the comparison shows that the kinematic performance is obviously improved.
Table 1 comparison of performance before and after optimization of scale parameters
Step 3: establishing a dynamic model of the flexible parallel micro-operation mechanism;
Establishing a dynamic model of the flexible parallel micro-operation mechanism by using a Lagrangian equation, and solving an expression of the driving force of the flexible parallel micro-operation mechanism;
According to a dynamic model of the 3-PSS flexible parallel micro-operation mechanism, the dynamic equation of the mechanism is as follows:
Wherein M is a mass matrix of the flexible parallel micro-operation mechanism, K is a rigidity matrix of the flexible parallel micro-operation mechanism, G is an inertia force of the flexible parallel micro-operation mechanism, and F is a generalized driving force matrix of the flexible parallel micro-operation mechanism; s is the generalized coordinates of the system, Is the generalized acceleration of the system.
The generalized driving force F is actually the driving force generated by the sliding block, and according to the virtual work principle, the driving force of the flexible parallel micro-operation mechanism is as follows:
Fb＝J-1F (8)
where J is the Jacobian matrix of the mechanism.
According to dynamics analysis, the dynamics performance of the flexible parallel micro-operation mechanism is related to the dimensional parameters of the mechanism and the structural parameters of the flexible spherical hinge. But in order to ensure that the kinematic performance of the mechanism is not changed, the structural parameters of the flexible spherical hinge are selected as optimization parameters based on the optimization of the dynamic performance.
Step 4: establishing a flexible hinge structure parameter optimization model;
based on the optimized scale parameters, natural frequency limitation, stress limitation and flexible hinge design parameter range of the flexible parallel micro-operation mechanism are defined as limiting conditions, the minimum linear weighted value of total mass and rigidity is taken as an optimization target, and the flexible hinge structure parameters are optimized to enable the dynamic performance of the flexible parallel micro-operation mechanism to be optimal;
In order to prevent resonance, low order resonance, the natural frequency of the mechanism is required to be larger than the fundamental frequency of the actuator (piezoelectric moving platform) Multiple times. At the same time, in order for the design of the mechanism to meet fatigue strength, it is required that the maximum stress should be less than the allowable stress. The machining of the mechanism and the practical application requirements are considered, and a certain size range (unit: mm) of the flexible spherical hinge structural parameter is given. Thus its constraints can be written as:
Wherein ω is the natural frequency of the flexible parallel micro-operation mechanism, and ω b is the fundamental frequency of the piezoelectric mobile platform; sigma is the maximum stress of the flexible spherical hinge, and [ sigma ] is the allowable stress of the flexible spherical hinge; t is the minimum thickness of the flexible spherical hinge, and R s is the cutting radius of the flexible spherical hinge.
From the kinetic model, the driving force of the mechanism is mainly related to the total mass of the mechanism and the rigidity of the mechanism. Generally, the smaller the mass of the mechanism, the lower the inertial force of the mechanism. The mass of the moving platform of the mechanism is set to be a fixed value, and the total mass of the mechanism is mainly related to the length of a mechanism rod and the mass of a sliding block. Based on the optimized scale parameters, the quality of the strut is only related to the diameter of the strut. In the analysis of the flexible parallel micro-operating mechanism, a pseudo rigid body model method is adopted, so the diameter D of the rod is required to be larger than the sum of the minimum thickness t of the flexible spherical hinge and the double cutting radius R s in the design, and the diameter D=t+2R s +2mm of the supporting rod is agreed. The size of the slider is known to be directly related to the diameter of the strut. In summary, the total mass of the mechanism is mainly related to the dimensional parameters of the flexible spherical hinge. The smaller the total mass of the component, the smaller the driving force required by the mechanism under the same kinematic conditions, thus taking the minimum total mass of the mechanism M as one of the optimization targets.
According to a dynamics model, the bending rigidity k m of the flexible spherical hinge directly influences the integral rigidity of the mechanism, and further influences the driving force, the natural frequency and the dynamic stress of the mechanism of the system. Therefore, the bending stiffness k of the flexible spherical hinge is taken as a characteristic value of the flexibility of the mechanism; when the bending rigidity k of the flexible spherical hinge meets the design requirement of the mechanism, the smaller the bending rigidity k is, the smaller the driving force required by the mechanism is. Therefore, the minimum rigidity is one of the optimization targets.
In summary, in order to meet the design objective of minimum driving force of the mechanism, the optimization objective function is set as a weighted combination of the total mass M (t, R s) of the flexible parallel micro-operation mechanism and the bending stiffness k (t, R s) of the flexible spherical hinge, and then the expression of the optimization objective function is as follows:
Wherein, the weight parameter alpha represents the proportion of bending rigidity in optimization, and alpha is [0,1]; k min and M min represent the minimum values of bending stiffness and total mass, respectively, under constraint conditions such that the two optimization goals are within the same order of magnitude;
and optimizing by utilizing an MATLAB genetic algorithm tool box, so that the optimization results of the flexible spherical hinge size under different weights can be obtained.
In order to obtain the flexible spherical hinge structural parameters with optimal dynamic performance, the embodiment calculates the maximum absolute value F bM of the driving force of different model parameter mechanisms under the same motion track (as shown in the formula).
Wherein ω=pi/4, and the movement locus unit is m.
In contrast, when the dimensions of the flexible spherical hinge are t=0.8 mm and R s =1.82 mm, the absolute maximum F bM of the driving force required is minimum under the same movement track. The driving force variation law of the mechanism before and after optimization under the same trajectory (formula (11)) can be obtained using the driving force expression, as shown in fig. 9. It is known that the driving force of the mechanism is consistent in change rule before and after secondary optimization; the driving force of the mechanism after optimization is reduced to different degrees at each moment, compared with the mechanism before secondary optimization, the maximum absolute value F bM of the driving force required by the mechanism after secondary optimization is reduced by 37.13%, and the dynamic performance is obviously improved.
Table 2 comparison of performance before and after optimization of flexible spherical hinge structural parameters
The dynamic performance of the front and rear mechanisms is optimized by the flexible spherical hinge structure parameters, as shown in table 2. Comparing, the overall mass of the mechanism is reduced by 20.62% after the secondary optimization, which reduces the inertia force of the mechanism; the rigidity after the secondary optimization is reduced by 33.04%, so that the natural frequency of the mechanism after the secondary optimization is properly reduced, and the design requirement is still met; and the limit rotation angle of the flexible spherical hinge after secondary optimization is far larger than the size of the design requirement.
It should be understood that the foregoing description of the preferred embodiments is not intended to limit the scope of the invention, but rather to limit the scope of the claims, and that those skilled in the art can make substitutions or modifications without departing from the scope of the invention as set forth in the appended claims.
Claims (6)
1. A progressive optimization design method for flexible parallel micro-operation mechanisms is characterized by comprising the following steps:
step 1: establishing a flexible parallel micro-operation mechanism kinematic model;
Establishing a kinematic model of the flexible parallel micro-operation mechanism by using a closed vector method, and analyzing the kinematic performance of the flexible parallel micro-operation mechanism;
aiming at the 3-PSS flexible parallel micro-operation mechanism, simplifying each flexible hinge into two ideal rotating joints which are orthogonally distributed and have constant bending rigidity, enabling the supporting rods to be equivalent to rigid rods, enabling the supporting rods on each branched chain to be equivalent to one supporting rod, and obtaining a simplified rigid body model of the mechanism;
Based on the vector relation, establishing a closed vector equation of the ith branched chain as follows:
raai+bi+lci-rpdi＝P (1)
Wherein r a、rp and l are respectively the radius of the static platform, the radius of the movable platform and the length of the support rod, B i is the input displacement of the sliding block, P is the center of a circle circumscribed by the movable platform, and a i、ci and d i are respectively the direction vectors of the static platform OA i, the support rod B iPi and the radius PP i of the movable platform; The included angle between OA i and the x-axis of the reference coordinate system, and the included angle between the B iPi axis of the connecting rod and the z-axis of the reference coordinate system; o is the center of a circle circumscribed by the static platform; wherein the reference frame x-axis coincides with OA 1;
and (3) sorting and deriving the formula (1) to obtain the input and output relation of the flexible parallel micro-operation mechanism:
Wherein J is the Jacobian matrix of the mechanism, A velocity matrix representing the slider; /(I)A velocity matrix representing the moving platform;
Obtaining a working space of the flexible parallel micro-operation mechanism according to a cylindrical limit searching method; for quantifying the size of the working space volume, selecting a cube covering the whole working space, dividing the cube volume V into N small unit bodies with the volume V N, taking the center point of each small unit as a reference point, judging according to the constraint condition of the working space, reserving and counting the number of the center points of the unit bodies in the working space, and recording the total number as N; the volume V w of the workspace is:
The method comprises the steps of adopting a Jacobian matrix condition number k as a measure of the flexibility of the flexible parallel micro-operation mechanism, wherein k＝||J||·||J-1 I and I are two norms of a matrix; the dexterity of the flexible parallel micro-actuator is represented by the reciprocal of the jacobian condition number, i.e., u=1/k; when u=0, the mechanism is in a singular configuration, and when u=1, the mechanism is in isotropy;
the global flexibility of the flexible parallel micro-operating mechanism is as follows:
wherein w is one of all the rendezvous points N w uniformly distributed over the workspace;
step 2: based on the kinematic performance, establishing a scale parameter optimization model;
defining a design parameter range and a global dexterity limiting condition, and optimally designing the scale parameters by taking the minimum ratio of the mechanism volume to the working space and the volume as an optimization index;
step 3: based on the kinematic performance, establishing a dynamic model of the flexible parallel micro-operation mechanism;
Establishing a dynamic model of the flexible parallel micro-operation mechanism by using a Lagrangian equation, and solving an expression of the driving force of the flexible parallel micro-operation mechanism;
Step 4: establishing a flexible hinge structure parameter optimization model;
Based on the optimized scale parameters, the dynamic performance is based on the limiting conditions of the natural frequency limit, the stress limit and the flexible hinge design parameter range of the flexible parallel micro-operation mechanism, the linear weighting of the total mass and the rigidity is used as an optimization target, and the flexible hinge structure parameters are optimized, so that the dynamic performance of the flexible parallel micro-operation mechanism is optimal.
2. The progressive optimization design method of the flexible parallel micro-operation mechanism according to claim 1, which is characterized in that: in the step 2, the radius of the movable platform is unchanged, and the radius r a of the static platform and the length l of the rod are taken as optimization parameters; given the constraint of global dexterity GDI, the maximum working space of the mechanism and the minimum mechanism volume are taken as optimization targets, so that the constraint conditions and the objective functions are as follows:
Wherein GDI is global dexterity, l is the rod length of the mechanism, and r a is the radius of the static platform; v is the volume of the mechanism, and V w is the volume of the working space of the mechanism;
And optimizing by utilizing a MATLAB genetic algorithm tool box to obtain optimized scale parameters r a and l.
3. The progressive optimization design method of the flexible parallel micro-operation mechanism according to claim 1, wherein the dynamic model of the flexible parallel micro-operation mechanism in the step 3 is as follows:
Wherein M is a mass matrix of the flexible parallel micro-operation mechanism, K is a rigidity matrix of the flexible parallel micro-operation mechanism, G is an inertia force of the flexible parallel micro-operation mechanism, and F is a generalized driving force matrix of the flexible parallel micro-operation mechanism; s is the generalized coordinates of the system, Generalized acceleration for the system;
The generalized driving force F is the driving force generated by the sliding block, and according to the virtual work principle, the driving force of the flexible parallel micro-operation mechanism is as follows:
Fb＝J-1F (8)
Wherein J is the Jacobian matrix of the mechanism;
And selecting structural parameters of the flexible spherical hinge as optimization parameters according to the dynamic performance of the mechanism.
4. The progressive optimization design method of the flexible parallel micro-operation mechanism according to claim 1, which is characterized in that: in step 4, a certain size range of the flexible spherical hinge structural parameter is given, and the unit is: mm; the constraint conditions are as follows:
Wherein ω is the natural frequency of the flexible parallel micro-operation mechanism, and ω b is the fundamental frequency of the piezoelectric mobile platform; sigma is the maximum stress of the flexible spherical hinge, and [ sigma ] is the allowable stress of the flexible spherical hinge; t is the minimum thickness of the flexible spherical hinge, and R s is the cutting radius of the flexible spherical hinge;
The optimization objective function is set as a weighted combination of the total mass M (t, R s) of the flexible parallel micro-operation mechanism and the bending stiffness g (t, R s) of the flexible spherical hinge, and is as follows:
wherein, the weight parameter alpha represents the proportion of bending rigidity in optimization, and alpha is [0,1]; g min and M min represent the minimum values of bending stiffness and total mass, respectively, under constraint conditions such that the two optimization goals are within the same order of magnitude;
And optimizing by utilizing an MATLAB genetic algorithm tool box to obtain the optimization results of the flexible spherical hinge sizes under different weights.
5. A progressive optimization design system of a flexible parallel micro-operation mechanism is characterized by comprising the following modules:
The module 1 is used for establishing a flexible parallel micro-operation mechanism kinematic model;
Establishing a kinematic model of the flexible parallel micro-operation mechanism by using a closed vector method, and analyzing the kinematic performance of the flexible parallel micro-operation mechanism;
aiming at the 3-PSS flexible parallel micro-operation mechanism, simplifying each flexible hinge into two ideal rotating joints which are orthogonally distributed and have constant bending rigidity, enabling the supporting rods to be equivalent to rigid rods, enabling the supporting rods on each branched chain to be equivalent to one supporting rod, and obtaining a simplified rigid body model of the mechanism;
Based on the vector relation, establishing a closed vector equation of the ith branched chain as follows:
raai+bi+lci-rpdi＝P (1)
Wherein r a、rp and l are respectively the radius of the static platform, the radius of the movable platform and the length of the support rod, B i is the input displacement of the sliding block, P is the center of a circle circumscribed by the movable platform, and a i、ci and d i are respectively the direction vectors of the static platform OA i, the support rod B iPi and the radius PP i of the movable platform; The included angle between OA i and the x-axis of the reference coordinate system, and the included angle between the B iPi axis of the connecting rod and the z-axis of the reference coordinate system; o is the center of a circle circumscribed by the static platform; wherein the reference frame x-axis coincides with OA 1;
and (3) sorting and deriving the formula (1) to obtain the input and output relation of the flexible parallel micro-operation mechanism:
Wherein J is the Jacobian matrix of the mechanism, A velocity matrix representing the slider; /(I)A velocity matrix representing the moving platform;
Obtaining a working space of the flexible parallel micro-operation mechanism according to a cylindrical limit searching method; for quantifying the size of the working space volume, selecting a cube covering the whole working space, dividing the cube volume V into N small unit bodies with the volume V N, taking the center point of each small unit as a reference point, judging according to the constraint condition of the working space, reserving and counting the number of the center points of the unit bodies in the working space, and recording the total number as N; the volume V w of the workspace is:
Adopting the Jacobian matrix condition number k as the measure of the flexibility of the flexible parallel micro-operation mechanism, wherein k＝||J||·||J||-1, |·| is the two norms of the matrix; the dexterity of the flexible parallel micro-actuator is represented by the reciprocal of the jacobian condition number, i.e., u=1/k; when u=0, the mechanism is in a singular configuration, and when u=1, the mechanism is in isotropy;
the global flexibility of the flexible parallel micro-operating mechanism is as follows:
wherein w is one of all the rendezvous points N w uniformly distributed over the workspace;
the module 2 is used for establishing a scale parameter optimization model;
defining a design parameter range and a global dexterity limiting condition, and optimally designing the scale parameters by taking the minimum ratio of the mechanism volume to the working space and the volume as an optimization index;
The module 3 is used for establishing a dynamic model of the flexible parallel micro-operation mechanism;
Establishing a dynamic model of the flexible parallel micro-operation mechanism by using a Lagrangian equation, and solving an expression of the driving force of the flexible parallel micro-operation mechanism;
The module 4 is used for establishing a flexible hinge structure parameter optimization model;
Based on the optimized scale parameters, the dynamic performance is based on the limiting conditions of the natural frequency limit, the stress limit and the flexible hinge design parameter range of the flexible parallel micro-operation mechanism, the linear weighting of the total mass and the rigidity is used as an optimization target, and the flexible hinge structure parameters are optimized, so that the dynamic performance of the flexible parallel micro-operation mechanism is optimal.
6. A flexible parallel micro-operation device, characterized in that: manufactured by the progressive optimization design method of the flexible parallel micro-operation mechanism according to any one of claims 1-4.
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