绳牵引并联机构的自由度和奇异性

绳牵引并联机构是将若干驱动器的运动和力以绳为介质，转换成末端执行器的运动和力的封闭机械装置。可控性是绳牵引并联机构的主要问题，在其基础上，通过建立机构的静力学平衡方程，将末端执行器的自由度定义为结构矩阵的所有列矢量正张成的空间的维数；同时给出并证明末端执行器自由度的类型；说明绳牵引并联机构的奇异类型仅有过运动性的奇异，证明了纯平动机构不存在奇异位姿；最后，根据无奇异机构的设计原理，列举了无奇异性的3个1R2T机构、2个2R3T机构和1个3R3T机构。

Degree of freedom and singularity of rope-pulling parallel mechanism

Rope-pulling parallel mechanism is a closed mechanical device that taking the rope as a medium to let the motions and forces of a certain number of drivers be transformed as the motions and forces of end executor. At first, it is shown that controllability is the main issue of rope-pulled parallel mechanism, and on this basis by means of establishing the statics equilibrium equation of the mechanism, the degree of freedom of end executor is defined as the dimension of the space which is positively spanned by all column vectors of the structural matrix, and at the same time the types of degree of freedom of end executor are presented and verified. After that, it has been explained that only the over mobilized singularity can happen in the singularity types of rope-pulled parallel mechanism, and it is proved that there exists no singularity posture in pure translation mechanism. Finally, in accordance with the designing principle of singularity-free mechanism, three 1R2T mechanisms, two 2R3T mechanisms and one 3R3T mechanism, which are all singularity-free, were listed.