用穷举法求过约束机构存在的充要条件

Using Exhaustive Method to Find the Necessary and Sufficient Conditions for the Existance of Over-constrained Mechanisms

本文给出求过约束机构存在的充要条件的一种方法——穷举法,并以4R、RPRP机构为例,说明这种方法的应用.文中的结果表明,除了平面4R机构、球面4R机构以及Bennett机构外,不存在其它4R机构;除平面RPRP机构外,还存在且只存在一种RPRP机构.文中的方法也可用于求其它过约束机构存在的充要条件.

In this paper the 4R and RPRP mechanisms are used as examples to illustrate the application of the exhaustive method for deriving the necessary and sufficient conditions to the existance of over-constrained mechanisms. The results obtained in this paper show that except for the planar or spherical mechanism and the Bennett mechanism non-existance of other 4R mechanism, and besides the planar mechanism there is one, and only one, RPRP mechanism. The exhaustive method can also be used to find the necessary and sufficient conditions for other over-constrained mechanisms.