One of the most important problems in space based robotics is the disturbance to the satellite attitude caused by satellite mounted manipulators operation. In this paper the dynamic equations and conservation of angular momentum of a space manipulator system which are considered subject conditions are developed by using the“Virtual Manipulator Mode”;According to skew Matrix about skew motion of rigid body, we put out with a function to comment on the attitude change of rigid body; the we present a technique called“periods motion“to find an globally optimal path planning in form of analytic function solution.