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Method for detecting singular and movement bifurcation of articulated bar system mechanism by utilizing mechanism displacement modal submatrix method

A technology of displacement mode and motion bifurcation, applied in the field of determination of singularity and motion bifurcation, can solve the problems of structural system instability, large additional load, etc., and achieve the effect of broad application prospects and strong operability

Inactive Publication Date: 2012-10-24
ZHEJIANG UNIV
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Problems solved by technology

When the mechanism moves according to the non-design path, due to the contradiction between the control and the actual movement, a large additional load will be generated in the system, which will lead to the instability of the entire structural system and cause serious consequences.

Method used

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  • Method for detecting singular and movement bifurcation of articulated bar system mechanism by utilizing mechanism displacement modal submatrix method
  • Method for detecting singular and movement bifurcation of articulated bar system mechanism by utilizing mechanism displacement modal submatrix method
  • Method for detecting singular and movement bifurcation of articulated bar system mechanism by utilizing mechanism displacement modal submatrix method

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Embodiment Construction

[0026] Take a planar hinged four-bar system as shown in Figure 1 as an example, the coordinates of each point are A (0, 0), B (3, -4), C (5, -20 / 3), D (7, -4) , E (10, 0), rod length AB=5, BC=10 / 3, CD=10 / 3, DE=5, AE=10.

[0027] Choose AB and DE rods as driving rods, then nodes B and D are driving nodes, and node C is a driven node. A vertical upward unit force is applied to nodes B and D, and the lifting motion process is simulated by MATLAB programming. The motion path is as follows figure 2 Shown.

[0028] Establish the balance matrix of the articulated linkage mechanism according to the configuration in the motion path A , The balance matrix of the articulated rod system A Is a 2n×b order matrix:

[0029] (3)

[0030] Then obtain the displacement modal matrix of the overall mechanism by singular value decomposition:

[0031] (4)

[0032] Among them, n is the number of free nodes in the plane rod system, b is the number of rods, m is the nu...

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Abstract

The invention provides a method for detecting singular and movement bifurcation of an articulated bar system mechanism by utilizing a mechanism displacement modal submatrix method. The method comprises the following steps of (1) determining a driving node and a driven node in free nodes of the articulated bar system mechanism; (2) according to configuration generated in the moving process of the articulated bar system mechanism, establishing a balance matrix of the articulated bar system mechanism, and obtaining a whole mechanism displacement modal matrix through singular value decomposition; (3) decomposing the whole mechanism displacement modal matrix into a mechanism displacement modal matrix Ua (2l*m) corresponding to the driving node and a mechanism displacement modal matrix Up (2k*m) corresponding to the driven node; and (4) computing a singular value of a mechanism displacement modal submatrix, and judging that the singular and movement bifurcation happen to the articulated bar system mechanism if the minimum singular value tends to zero. The method is strong in operability, provides structural design and construction design basis for a novel space structure-mechanism, and has wide application prospect.

Description

Technical field [0001] The invention relates to a method for determining the singularity and motion bifurcation of a novel space structure-mechanism, and belongs to the technical field of engineering analysis and design of a novel space structure. Background technique [0002] With the continuous development of structural forms, many movable systems have appeared in modern structures, such as tensioned overall structures, cable domes, climbing domes, and deployable structures. These new systems have variable initial forms, and the construction process is accompanied by geometric displacements that are different from elastic displacements, so they are often associated with "mechanisms". Studies have found that there are singularities and bifurcations in the movement of the mechanism. The mechanism may have motion "dead spots" at the singular and bifurcated configurations, or it may lose controllability when moving along an undesigned motion path. When the mechanism moves accordin...

Claims

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Application Information

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IPC IPC(8): G06F17/16
Inventor 袁行飞周练李阿龙
Owner ZHEJIANG UNIV
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