Method for solving three positions of connecting rods of planar four-rod mechanism with fixed double-rack hinge points

Abstract

The invention belongs to the technical field of mechanical design, and particularly relates to a two-rack hinge point fixed planar four-bar mechanism connecting rod three-position solving method, which comprises the following steps of: drawing an auxiliary line segment at any position by adopting computer-aided software; geometric constraints are added to one circle at one ends of the same sides of the three auxiliary line segments, and three movement positions of the planar four-bar mechanism corresponding to the three movement tracks are obtained by connecting the line segments and deleting the auxiliary lines; by means of computer-aided design software which is widely popularized and applied at the present stage, design constraints of the planar four-bar mechanism are converted into geometric constraints in the computer-aided design software, and the planar four-bar mechanism meeting the requirements of double-rack hinge point coordinates and three-position connecting rods is automatically solved through software calculation. On one hand, the method overcomes blindness of a conventional experimental method, track accuracy is high, and cost is low; and on the other hand, the defect that an analytical method is complex in algorithm is overcome, operation is easy, design efficiency is high, and application and popularization are facilitated.

Description

Technical Field

[0001] The present application belongs to the field of mechanical design technology, and in particular relates to a method for solving three positions of connecting rods of a planar four-bar mechanism with double-frame hinge points fixed. Background Art

[0002] The planar four-bar mechanism is a widely used mechanism in the field of mechanical design. It has many advantages, such as simple and reliable principle, and can realize complex motion trajectories. However, the design method of the planar four-bar mechanism is not perfect at present. The conventional experimental method is relatively blind, has low trajectory accuracy and high cost. Although the analytical method has high accuracy, the algorithm is complex and the design efficiency is low, which is not conducive to its promotion and application.

[0003] Therefore, a method for solving the planar four-bar mechanism that is efficient, high-precision, simple to operate and easy to promote and apply is needed. Summary of the invention

[0004] The purpose of this application is to provide a method for solving the three positions of the connecting rods of a planar four-bar mechanism with fixed hinge points of two frames, so as to solve the problem that the design method of the existing stage planar four-bar mechanism is not perfect.

[0005] The technical solution of the present application is: a method for solving the three positions of the connecting rods of a planar four-bar mechanism with fixed hinge points of two racks, comprising:

[0006] Use computer-aided software to draw a known fixed connecting rod AB and at least three motion trajectories P1, Q1; P2, Q2; P3, Q3;

[0007] Draw auxiliary line segments at any positions on the known line segments, including C1D1, C2D2, and C3D3; and add geometric constraints so that the distances between the connected motion trajectories and the auxiliary line segments are the same; and control the three quadrilaterals enclosed by the three motion trajectories and the three auxiliary line segments to be congruent;

[0008] Draw two circles of arbitrary radius with the two end points of the fixed connecting rod as the center;

[0009] One end of the same side of the three auxiliary line segments adds a geometric constraint on one of the circles, and the other end of the same side of the three auxiliary line segments adds a geometric constraint on another circle, and the line segments that can be connected are automatically calculated and updated by computer-aided software;

[0010] Delete the redundant auxiliary lines to obtain three groups of quadrilaterals formed by different auxiliary line segments and motion trajectories in the required planar four-bar mechanism;

[0011] Connect the two ends of the fixed link to the two ends of the auxiliary line segment respectively, and obtain three motion trajectories corresponding to the three motion positions of the planar four-bar mechanism, thus completing the solution of the planar four-bar mechanism.

[0012] Preferably, the distances between the connected motion trajectories and the auxiliary line segments are the same, including P1C1=P2C2=P3C3, P1D1=P2D2=P3D3, Q1C1=Q2C2=Q3C3, Q1D1=Q2D2=Q3D3.

[0013] Preferably, the three quadrilaterals enclosed by the three motion trajectories and the three auxiliary line segments are congruent, including quadrilateral P1C1Q1D1≌quadrilateral P2C2Q2D2≌quadrilateral P3C3Q3D3.

[0014] Preferably, two ends of the fixed connecting rod are respectively connected to two ends of the auxiliary line segment, including AC1, AC2, AC3, BD1, BD2, and BD3.

[0015] Preferably, the computer-aided software is CAD.

[0016] Preferably, the CAD software is: Inventor, UG or CATIA.

[0017] The method for solving the three positions of the connecting rod of the planar four-bar mechanism with a fixed double-frame hinge point in the present application, with the help of the computer-aided design software that has been widely popularized and applied at this stage, converts the design constraints of the planar four-bar mechanism into geometric constraints in the computer-aided design software, and automatically solves the planar four-bar mechanism that meets the requirements of the double-frame hinge point coordinates and the three positions of the connecting rod through software calculation. On the one hand, this method overcomes the blindness of the conventional experimental method, with high trajectory accuracy and low cost; on the other hand, it overcomes the shortcomings of the complex algorithm of the analytical method, is easy to operate, has high design efficiency, and is conducive to promotion and application. It can be widely used in the aviation field and many mechanical engineering fields, and can produce good economic and social benefits. BRIEF DESCRIPTION OF THE DRAWINGS

[0018] In order to more clearly illustrate the technical solution provided by the present application, the following is a brief introduction to the accompanying drawings. Obviously, the accompanying drawings described below are only some embodiments of the present application.

[0019] Figure 1 This is a schematic diagram of the overall process of this application;

[0020] Figure 2 A fixed connecting rod and at least three motion trajectory position diagrams for this application;

[0021] Figure 3 This is a schematic diagram of the structure of three planar four-bar mechanisms of this application;

[0022] Figure 4 Draw a schematic diagram of two circles of arbitrary radius for this application;

[0023] Figure 5 Add geometric constraint diagrams on three auxiliary line segments for this application;

[0024] Figure 6 Delete the auxiliary line segment diagram for this application;

[0025] Figure 7 This is a schematic diagram of the quadrilateral P1C1Q1D1 structure of this application;

[0026] Figure 8 This is a schematic diagram of the quadrilateral P2C2Q2D2 structure of this application;

[0027] Fig. 9 This is a schematic diagram of the quadrilateral P3C3Q3D3 structure of this application. DETAILED DESCRIPTION

[0028] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0029] A method for solving the three positions of the connecting rods of a planar four-bar mechanism with fixed hinge points of two racks is used for solving circular constraints. The three motion trajectories P1, Q1; P2, Q2; P3, Q3 of the fixed connecting rod AB and the moving connecting rod positions of the planar four-bar mechanism are known; based on these, a planar four-bar mechanism ACDB that can meet the above requirements is obtained.

[0030] like Figure 1 , the specific steps are as follows:

[0031] Step S100, as Figure 2 , use computer-aided software to draw the known fixed connecting rod and at least three motion trajectories, including AB; P1, Q1; P2, Q2; P3, Q3. The available computer-aided software is preferably CAD, and the specific CAD software is: Inventor, UG or CATIA, etc.

[0032] Step S200, as Figure 3, draw auxiliary line segments at arbitrary positions on the known line segments, including C1D1, C2D2, and C3D3; and add geometric constraints so that the distances between the connected motion trajectories and the auxiliary line segments correspond to the same, including P1C1=P2C2=P3C3, P1D1=P2D2=P3D3, Q1C1=Q2C2=Q3C3, Q1D1=Q2D2=Q3D3; and control the three quadrilaterals formed by the three motion trajectories and the three auxiliary line segments to be congruent, that is, quadrilateral P1C1Q1D1≌quadrilateral P2C2Q2D2≌quadrilateral P3C3Q3D3; the positions of C2D2 and C3D3 are not fixed, but when dragging any line segment, the lengths of the three remain equal, and they maintain the same relative positions with P1Q1, P2Q2, and P3Q3, respectively.

[0033] Step S300, as Figure 4 , draw two circles of arbitrary radius with the two end points of the fixed connecting rod as the center.

[0034] Step S400, as Figure 5 , one end of the same side of the three auxiliary line segments adds a geometric constraint on one of the circles, and the other end of the same side of the three auxiliary line segments adds a geometric constraint on another circle, and the line segments that can be connected are automatically calculated and updated through computer-aided software.

[0035] Step S500, as Figure 6 , delete the redundant auxiliary lines, and obtain three sets of quadrilaterals formed by different auxiliary line segments and motion trajectories in the required planar four-bar mechanism, such as Figure 7-Figure 9 As shown in quadrilateral P1C1Q1D1, quadrilateral P2C2Q2D2, and quadrilateral P3C3Q3D3.

[0036] Step S600, connect the two ends of the fixed link to the two ends of the auxiliary line segment, including AC1, AC2, AC3, BD1, BD2, BD3, obtain three motion trajectories corresponding to the three motion positions of the planar four-bar mechanism, and complete the solution of the planar four-bar mechanism.

[0037] Through the above design, with the help of computer-aided design software that has been widely used at this stage, the design constraints of the planar four-bar mechanism are transformed into geometric constraints in the computer-aided design software, and the planar four-bar mechanism that meets the requirements of the double-frame hinge coordinates and the three-position of the connecting rod is automatically solved through software calculation. On the one hand, this method overcomes the blindness of the conventional experimental method, with high trajectory accuracy and low cost; on the other hand, it overcomes the shortcomings of the complex algorithm of the analytical method, is easy to operate, has high design efficiency, and is conducive to promotion and application. It can be widely used in the aviation field and many mechanical engineering fields, and can produce good economic and social benefits.

[0038] Finally, it should be noted that: the drawings of the embodiments disclosed in the present invention only involve structures related to the embodiments disclosed in the present invention, and other structures can refer to the general design. In the absence of conflict, the same embodiment and different embodiments of the present invention can be combined with each other;

[0039] Finally: The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the protection scope of the present invention.

Claims

1. A method for solving the three positions of the connecting rods of a planar four-bar mechanism with fixed hinge points of two racks, characterized in that: include: Use computer-aided software to draw a known fixed connecting rod AB and at least three motion trajectories P1, Q1; P2, Q2; P3, Q3; Draw auxiliary line segments at any positions on the known line segments, including C1D1, C2D2, and C3D3; and add geometric constraints so that the distances between the connected motion trajectories and the auxiliary line segments are the same; and control the three quadrilaterals enclosed by the three motion trajectories and the three auxiliary line segments to be congruent; Draw two circles of arbitrary radius with the two end points of the fixed connecting rod as the center; One end of the same side of the three auxiliary line segments adds a geometric constraint on one of the circles, and the other end of the same side of the three auxiliary line segments adds a geometric constraint on another circle, and the line segments that can be connected are automatically calculated and updated by computer-aided software; Delete the redundant auxiliary lines to obtain three groups of quadrilaterals formed by different auxiliary line segments and motion trajectories in the required planar four-bar mechanism; Connect the two ends of the fixed link to the two ends of the auxiliary line segment respectively, and obtain three motion trajectories corresponding to the three motion positions of the planar four-bar mechanism, thus completing the solution of the planar four-bar mechanism.

2. The method for solving the three positions of the connecting rods of the planar four-bar mechanism with two fixed hinge points as claimed in claim 1, characterized in that: The distances between the connected motion trajectories and the auxiliary line segments correspond to the same, including P1C1=P2C2=P3C3, P1D1=P2D2=P3D3, Q1C1=Q2C2=Q3C3, Q1D1=Q2D2=Q3D3.

3. The method for solving the three positions of the connecting rods of the planar four-bar mechanism with two fixed hinge points as claimed in claim 2, characterized in that: The three quadrilaterals enclosed by the three motion trajectories and the three auxiliary line segments are congruent, including quadrilateral P1C1Q1D1≌quadrilateral P2C2Q2D2≌quadrilateral P3C3Q3D3.

4. The method for solving the three positions of the connecting rods of the planar four-bar mechanism with two fixed hinge points as claimed in claim 2, characterized in that: Connect the two ends of the fixed link to the two ends of the auxiliary line segments, including AC1, AC2, AC3, BD1, BD2, and BD3.

5. The method for solving the three positions of the connecting rods of the planar four-bar mechanism with two fixed hinge points as claimed in claim 1, characterized in that: The computer-aided software is CAD.

6. The method for solving the three positions of the connecting rods of the planar four-bar mechanism with two fixed hinge points as claimed in claim 5, characterized in that: The CAD software is specifically: Inventor, UG or CATIA.

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