基于几何约束条件过约束并联机构自由度瞬时性的简便判别方法

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The mobility of the parallel mechanism calculated by using the screw theory tool is instantaneous, especially for the overconstrained parallel mechanism, not only the nature of the mobility may be changed, but also movement of some mobility could not realized at all, so whether the mobility is instantaneous or not must be checked. Since there have been very few investigations on the methods for distinguishing mobility＇s instantaneity of the overconstrained parallel mechanism home and abroad, a simple method for distinguishing the mobility＇s instantaneity of the overconstrained parallel mechanism is put forward based on the geometric constraint conditions of their own. For this method, the geometric constraint equations are established according to geometric constraint conditions of the different limbs of the overconstained parallel mechanism, and then whether the geometric constraint equations exist nonzero real solution is examined to determine the instantaneity of the mobility, and five overconstrained parallel mechanisms are taken as examples to elaborate the specific steps of the method. Then a simulation analysis method for distinguishing mobility＇s instantaneity of the overconstrained parallel mechanism is proposed based on the simulation software ADAMS. And for this method, the extra degrees of freedom that are automatically added in the simulation model are firstly detected, then whether the extra degrees of freedom produce displacement is examined to judge the instantaneity of the mobility. Similarly, the above five overconstrained parallel mechanisms are analyzed by using this simulation analysis method. The results obtained by using these two kinds of distinguishing methods are consistent, which effectively verifies the correctness of the two distinguishing methods.由于采用螺旋理论工具计算得到的并联机构自由度是瞬时的，特别对于过约束并联机构，不仅其自由度性质可能改变，而且有些自由度的运动可能根本实现不了，所以必须对其自由度的瞬时性进行判别。鉴于国内外对过约束并联机构自由度瞬时性的判别方法的研究非常少，基于机构自身的几何约束条件提出一种判别过约束并联机构自由度瞬时性的简便方法。该方法根据各分支的几何约束条件建立几何约束方程，通过检查几何约束方程是否存在非零实数解来判别机构自由度的瞬时性，并以五种过约束并联机构为例，阐述该方法的具体判别步骤。基于仿真软件ADAMS提出一种判别过约束并联机构自由度瞬时性的仿真分析方法，该方法检测仿真模型自动添加的多余自由度，检查自动添加的多余自由度是否产生位移来判别自由度是否为瞬时的，同样采用这种仿真分析方法对上述五种过约束并联机构的自由度瞬时性进行判别。结果表明两种判别方法得到的结果是一致的，有力地验证了两种判别方法的正确性。