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Method for confirming motion mode of corresponding free node at singular configuration part of hinge bar system mechanism

A technology of mechanism movement and node movement, which is applied in the direction of mechanical equipment, transmission devices, belts/chains/gears, etc., can solve problems such as the uncertainty of mechanism movement, and achieve significant propulsion, broad application prospects, and strong operability

Inactive Publication Date: 2012-09-19
ZHEJIANG UNIV
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Problems solved by technology

The existence of the singularity of the mechanism makes the movement of the mechanism uncertain

Method used

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  • Method for confirming motion mode of corresponding free node at singular configuration part of hinge bar system mechanism
  • Method for confirming motion mode of corresponding free node at singular configuration part of hinge bar system mechanism
  • Method for confirming motion mode of corresponding free node at singular configuration part of hinge bar system mechanism

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Embodiment Construction

[0027] by figure 1 The one-plane hinged four-bar system shown is taken as an example, member AB is the driving rod, node B is the driving node, and node C is the driven node. Correspondingly, α is the control variable, and β is the state variable, both of which are positive in the counterclockwise direction.

[0028] According to the length of the BC rod in the closed loop, the independent coordination equation of the movement of this mechanism can be established as follows:

[0029] F(β;α)=(b+bcosβ-bcosα) 2 +(bsinβ-bsinα) 2 -b 2 =0 (3)

[0030] Wherein, b is the length of each rod. The singular conditions are (α=0, β=0), (α=0, β=π), (α=π, β=π), and the corresponding singular configurations are shown in Figure 2, and they are all structural singularities type.

[0031] The coordination equation (3) with respect to the state variable Doing second-order analysis, we can get:

[0032] ∂ 2 F ...

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Abstract

The invention discloses a method for confirming the motion mode of a corresponding free node at a singular configuration part of a hinge bar system mechanism. The method comprises the following steps of: carrying out second-order derivation on a coordination function which is dependent from a mechanism to describe the corresponding free node variable quantity, to judge whether the second-order derivative is equal to zero or not at the singular configuration place, if the second-order derivative is equal to zero, the corresponding free node at the singular configuration part can move like a limiting mechanism; and if the second-order derivative is not equal to zero, the corresponding free node can move like a first-order infinite small mechanism. According to the method, the motion mode of the corresponding free node at the singular configuration place of the hinge bar system mechanism can be confirmed, the motion mode of the mechanism at the singular configuration place can be basically confirmed, the method is high in operability, the basis is provided for the singularity avoidance and the structure design of the novel space structure, and the research of the mechanism singularity and the motion bifurcation has an important impelling action, so that the method is wide in application prospect.

Description

technical field [0001] The invention relates to a method for determining the motion mode of a free node at a singular configuration of a mechanism, and belongs to the technical field of engineering analysis and design of new space structures. Background technique [0002] The simulation analysis of the whole process of construction and forming of the bar system has become a hot spot in the research of modern space structures. The existence of the singularity of the mechanism makes the movement of the mechanism uncertain. At the singular configuration of mechanism motion, the corresponding free nodes have two motion modes: finite mechanism motion and first-order infinitesimal mechanism motion. Different motion modes have different effects on the entire structural system, and the avoidance measures taken in structural design are also different. Therefore, The research on the motion mode of the corresponding free nodes at the singular configuration of the mechanism is also one...

Claims

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Application Information

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IPC IPC(8): F16H21/10
Inventor 袁行飞周练
Owner ZHEJIANG UNIV
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