Parallel Kinematics Machines (PKMs) are a new type of CNC machines, and it has many advantages over the conventional serial machines. But PKMs also have lots of theoretical and practical problems to be solved because it was just several years away from the 90s metaphase of last centuries when it was published first. Focused on the development of new PKMs, relative theory and design method were studied in the dissertation. The 3-degree of freedom (DOF) mechanism has difference kinematics characteristics from the 6-DOF Stewart platforms, and its kinematics characteristics must be determined first. The screw theory and anti-screw theory were applied to analyze the 3-PSS mechanism kinematics characteristics, and a constraint from three linearly independent anti-screw moments was shown to act on the moveable platform of the 3-PSS mechanism, which then could move only in three-translation direction. Based on the 3-PSS kinematics equation, the 3-PSS mechanisms was simplified to such a simple mechanism that its forward kinematics could be solved easily by analytical approach. As for 6-SPS parallel manipulators, a predictor-corrector method to get the forward solution was proposed based on the principle of position tracking, and all the 16 forward solutions of 3-6 Stewart platform were obtained through difference initial values when the lengths of six legs were specified. In this dissertation every forward solution was defined as an assembly configuration, and the parallel manipulator could move only in one configuration space. A new viewpoint concerning parallel manipulator's singularity was put forward. The reason for the singularities was its multiple kinematics's solutions and the singularities existed on the borders of different configuration space. All the famous singularities of Stewart platform found before were studied based on the forward solutions. It was demonstrated that all the singularities did exist on the borders of different configuration space. The singular