Abstract: This paper analyzes the motion space of pantograph leg mechanism in order todesign and manufacture a quadruped walking robot.We get the space motion of legwith three rectilineal motion in Cartesian coordinates.The paper gives the conclusionthat K₂=1 and K₁（>1）should be as large as possible,and gives also three optimizingmotion distance and loction of each actuator with optimizing methods.