Introducing the 4R equivalent circuit into parallel mechanism,the kinematics and dynamics property of the mechanism can be effectively improved. Meanwhile,the change of singular position in parallel mechanism may be caused. The singular position of 4R mechanism is analyzed by using screw theory. The 4R circuit is introduced into 3- PRS parallel mechanism to form a new 3- P（ 4R） RS parallel mechanism. The force Jacobian matrix is established,and the possible singular positions of actuator,platform and branched chain are obtained by using Jacobian algebra method. On this basis,the effect of rod length relationship on the singular position is investigated,and the 3- dimensional model and motion simulation of 3- P（4R） RS parallel mechanism are established by Pro / E. The result validates the conclusion that the introduction of 4R circuit can effectively avoid part of the singular position of the mechanism.