平行回转副广义杆组的有效分量研究及应用

Research and Application on the Effective Component of the Parallel R General Link Group

结合基于广义杆组理论已提出的机构自由度计算公式—GOM公式,为完善其应用中的集合求交问题,对两组夹角小于90°的平行回转副(R)广义杆组运动参数的交集运算进行了分析,把一组的运动参数分解为垂直和平行于另一杆组的运动参数分量,将垂直分量作为该杆组的有效运动参数,与另一杆组运动参数求交集,得到的计算结果符合机构的实际情况,证明了含平行R杆组的机构,符合交集运算规则;并将该结论应用于含平行R杆组的机构自由度计算及消极构件的判定:当平行R杆组的自由度与输出参数的维数之和小于等于零时,输出构件成为消极构件;最后通过分析一组7R机构的自由度,理论分析与实际一致,验证了所提理论的正确性。

Combining with the pre-research of a new mobility formula-GOM presented previously, to perfect the list intersection in calculation, the intersection calculation of motion parameters of parallel R general link group(link group including revolute joints with parallel rotation axis) of which the angle is less than 90° is analyzed. Decomposing a set of motion parameters into vertical and parallel to which of another link group, and one vertical set should be taken as the valid motion parameter to do intersection calculation. Furthermore, the conclusion is applied to mobility calculation and the determination of passive components: when the mobility of the parallel R link group and the dimension of the output parameter is less than zero, the output member becomes a passive component. Thereafter, there 7R mechanisms are taken as instances, and the results coincide with the prototype data, which proves the validity of the proposed theory.