An Ｒ + { 2-UPＲ + ＲPＲ} leg mechanism was designed to improve the mobility and adaptability of quadruped robots in complex environment． The spiral theory analysis showed that the mechanism has 3 freedom degrees of two rotations and one movement． Then，the inverse kinematics solution and the positive solution equation were derived based on the position relationship between the member and the motion pair in space，and the velocity and acceleration of the driving member were solved． Then，with the help of Matlab calculation software and ADAMS simulation software，the accuracy of the positive and negative solution model was verified through the comparison of kinematics positive and negative solution theoretical calculation results and simulation results． Finally，the motion trajectory and velocity changes of the leg mechanism were obtained through the motion simulation of the robot's single leg． And the working space of the leg mechanism was analyzed to obtain the working range and motion characteristics of the foot end． The results show that the proposed leg mechanism with less independent joints has better working adaptability and movement flexibility．