In this paper, a parallel manipulator is comprised of two sliders and four links. Sliders execute a linear reciprocating motion depending on parallel guides and make the connected links rotate. A couple of links connected by sliders do coupling motion. The end-effector called a link tip has orientation angle. Through the kinematics analysis of this manipulator, we found displacement, velocity and acceleration using direct and inverse kinematics. We used equations that derived from this analysis and determined five constraint conditions. These conditions had much to do with rotation states of links, the relative relation of link length and coupling motion state. To verify those, we suggest a new algorithm regarding constraint conditions of a manipulator. With the result which performed the algorithm, we found out that operation range of coupled links was limited by relative relation of link length and that manipulator was not able to carry out a series of link motion, in case of being the link vertical between two parallel guides.