两层两环空间耦合链机构自由度分析原理

Principle of Mobility Analysis of Two-level and Two-loop Spatial Mechanisms with Coupling Chains

自由度分析是机构构型综合、运动学和动力学研究的基础。过去的几十年,国内外学者主要对空间并联机构自由度分析开展了研究。研究比空间并联机构更加复杂的两层两环空间耦合链机构的自由度分析原理。通过推导两层两环空间耦合链机构的运动螺旋方程,建立耦合链带来的耦合关系的数学模型。基于运动螺旋方程,建立空间耦合机构中刚性子结构的判别方法和自由度分析原理。利用两层两环空间耦合链机构的等效子并联机构的分支运动螺旋系线性组合的特点可以实现自由度性质分析。两个典型的例子被用来说明提出方法的有效性。

Mobility is one of the most fundamental concepts in type synthesis, kinematics and dynamics of mechanisms. In the past several decades, strong interest of many scholars at home and abroad has been mainly shown in mobility analysis of spatial parallel mechanisms. A principle of mobility analysis is introduced for two-level and two-loop spatial mechanisms with coupling chains, which contains more complex coupling relations than spatial parallel mechanisms. Through deriving the twist equation of two-level and two-loop spatial mechanisms with coupling chains, the mathematic model of coupling relations caused by coupling chains is established. Based on the twist equation, the method for rigid substructure detection and the principle of mobility analysis of the class of mechanisms are proposed. Mobility property can be determined by the characteristics of the linear combinations of the limb twist system of the equivalent sub-parallel mechanisms of two-level and two-loop spatial mechanisms with coupled chains. Two typical examples are used to illustrate effectiveness of the proposed method.