Abstract: In this paper we introduce a theory of spherical frame vectors.There is a one-to-one correspondence between the set of all right-handed coordinate frames with acentre O and the set of all spherical frame vectors at every point on the unit sphere with the centre O.The rotation trans formation from Ox₀y₀z₀ to Oxyz can be described using spherical frame vectors,Then we study how to solve the spherical vector tri-angles,We can develope a method for writing kinematic equations and solving kine-matic equations for manipulators.Our methods are quite different from the methods of "Rotation matrices" and "Rotation vectors"(Quaternion).Finally we give some examples illustrating the solution of practical manipulators.