An original 4—PTT parallel mechanism with threedimensional translations and rotational motion about Z axis was presented. Its positional inverse expressions were established using the conversion of coordinates and projection in analytic geometry, and the method of the forward solution of the mechanism and corresponding numerical examples were given. Subsequently, the workspace of standing pose was analyzed by programming with Matlab and LabVIEW. The analytical results indicate that the workspace of the 4—PTT parallel mechanism has advantages of smooth boundary, big volume, no cavity and regular cross section in the fields of industrial robots, micromanipulators, virtual axis machine tools, damping platform, rehabilitation robot and etc.  