综合运动求交与约束求并的机构自由度分析方法

Combined Motion Intersection and Constraint Merging Method of Mechanism Degrees of Freedom Analysis

过约束的存在是导致机构实际自由度和计算自由度出现不一致的根本所在,针对这个问题提出一种综合运动求交与约束求并的自由度分析方法。首先,借助数学符号描述机构的运动特征和约束特征,明确分支和动平台相关参数的表示形式,阐述自由度分析求解的基本步骤;其次,基于图谱法的线图元素清晰、直接的表达机构运动和约束的关系,从避开过约束的角度提出基于运动求交的机构自由度直接分析方法;然后,面向多自由度分支组成的并联机构,将过约束视作一般约束,提出基于约束求并的机构自由度间接分析方法;最后,建立综合运动求交与约束求并的机构自由度分析方法,并通过两种典型的机构算例验证了其应用于复杂机构自由度分析的高效性和实用性。该自由度分析方法统一两种思路的表达形式,计算简单,逻辑严谨,不仅为含过约束机构的自由度求解提供了思路,也为后续的机构综合研究提供了参考。

In response to the problem that the theoretical calculation of degrees of freedom and the actual motion are contradictory due to the existence of over-constraints in the mechanism,a degree of freedom analysis method that integrates the intersection of motion and constraint solving is proposed.The motion characteristics and constraint characteristics of the mechanism are described with the help of mathematical symbols.The relation between mechanism motion and constraints is clearly and directly expressed by the line diagram elements of the atlas method.The direct analysis method of mechanism degrees of freedom based on motion seeking intersection is proposed from the perspective of avoiding over-constraint.The mechanism degree of freedom analysis method of integrated motion intersection and constraint merging is established,and the efficiency and practicality of its application to complex mechanism degree of freedom analysis is verified by two typical mechanism cases.The method unifies the expressions of the two ideas with simple calculation and rigorous logic,which not only provides ideas for solving the degrees of freedom of the mechanism with over-constraint,but also provides reference for the subsequent comprehensive study of the mechanism.