Abstract: Concept of manipulator solution space is first presented in this paper.By applying screw theory,we derive a sufficient and necessary condition of manipulators with three degrees of freedom locating on the boundary surfaces of solution-space.That is the screws representing the instant motion of pairs must be reciprocal to ascrew passing through the centre of the terminal with zero screw parameter.Thenthe equation of the generator of manipulator solution-space boundary surfaces arederived.Next,the relationship between solution-space boundary surfaces and singularity is discussed.And some examples of mapping are given.