Abstract: This paper investigates the nature and forming method of the singular surfaces inthe workspace of robot manipulators,which can have indefinite degrees of freedom andconsist of revolute(limited or unlimited)and prismatic,joints by the method of staticforce balancing analysis.The reasons which cause the phenomenon of singular posi-tions are discussed.An algorithm which can determine the section graphs of singularsurfaces in the workspace of robot manipulators on indefinite arbitrarily appointedplanes is developed,and corresponding computer programs——the WARM softwarepackage is compiled and applied to a practical example.