The Characteristics of Void Cavites and Holes in the Workspace of (n--R) Manipulator Wang ZhongzhengUsing the recurrence relations, this paper successively analysedthe influence which the constructional parameters of the links in the(n-R) manipulator exerted on void cavities and holes in the corresp-onding subworkspace and presented a set of discriminants on voidcavities and holes by means of the enveloping surface theory of differ-ential geometry. This paper has developed a new idea and a new way to under-stand the process in which the workspace of a (n-R) manipulator iscreated and to discriminante the characteristics of void cavities andholes in the entire workspace of (n-R) manipulator.