A NEW METHOD OF DETERMINING THE REACHABLE SPACE OF PARALLEL MANIPULATORS USED IN PRECISION MACHINING AND ASSEMBLY IS DISCUSSED. THE METHOD IS BASED ON TASK MANIFOLDS OF THE PARALLEL CHAINS OF THE MANIPULATOR. IT IS IMPLEMENTED USING THE SIMPLE INVERSE KINEMATICS, A MODIFIED FORM OF THE FORWARD KINEMATICS OF THE PARALLEL ROBOTS, AND A COMPUTER GRAPHICS TECHNIQUE. THE WORKSPACE DETERMINATION OF A GENERAL 6 DOF PARALLEL ROBOT IS DISCUSSED IN DETAIL. AN EXAMPLE ILLUSTRATING THE APPLICATION OF THE METHOD IS ALSO PROVIDED. IT IS BELIEVED THAT THE PROPOSED METHOD IS MORE GENERAL, MORE EFFICIENT, AND EASIER TO IMPLEMENT THAN ANY OF THE EXISTING METHODS.