独立杆组参数矩阵的表达方法

Expressing Method for an Independent Link Group Parameter Matrix

并联机构中由于各杆组间的约束类型不同导致部分杆组参数向量中含有不独立的混合参数,使得对机构中输出构件自由度数目及性质、机构过约束判断的直观性变差。为构建仅含独立运动参数的杆组参数向量,分别就向量中非独立的"角运动参数"、"非衍生线运动参数"、"衍生线运动参数"展开讨论,基于螺旋理论,通过研究螺旋系的相关性,得到线性无关的基螺旋系,并等价到杆组参数矩阵中,建立独立杆组参数矩阵,最终提出参数垂直分量有效准则。结合该准则,基于GOM自由度新公式,对几种典型机构进行自由度分析,验证这些理论在独立杆组参数矩阵确定、机构自由度求解、输出构件自由度及运动性质分析、过约束判断等方面的应用。

The different types of constraints among the link groups in parallel mechanisms led to the independent and mixed parameters in part of link group parameter vectors,which made the number and engendered nature of DOFs（degree of freedoms）of output components along with the intuitiveness of judging overconstraints in the mechanisms worse.To construct the parameter vectors which only included independent motion parameters,dependent parameters in vectors such as＂angular motion parameters＂,＂non-derivative line motion parameters＂and＂derivative line motion parameters＂were discussed.Meanwhile based on the screw theory,the relevance of screw system was deduced to obtain the linear independent basic screw system which was equivalent into the matrix of link group parameters.Independent matrix of link group parameters was constructed.Furthermore the rule named＂the validity of vertical component＂was proposed.Finally based on a new mobility formula—GOM,combined with the rules mentioned above,the DOFs of several kinds of typical mechanisms were analysed.The applications of the theories presented before and herein were verified in the following parts：determination of independent matrix for link group parameters,calculations of the mobility and mobility property of output components,and determination of overconstraints.