The previous research regarding the gait planning of quadruped robot focuses on the sequence for lifting off and placing the feet, but neglects the influence of body height. However, body height affects gait performance significantly, such as in terms of the stride length and stability margin. We herein study the performance of a quadruped robot using the equivalent mechanism concept based on metamorphosis. Assuming the constraints between standing feet and the ground with hinges, the ground, standing legs and robot body are considered as a parallel mechanism, and each swing leg is regarded as a typical serial manipulator. The equivalent mechanism varies while the robot moves on the ground. One gait cycle is divided into several periods, including step forward stages and switching stages. There exists a specific equivalent mechanism corresponding to each gait period. The robot’s locomotion can be regarded as the motion of these series of equivalent mechanisms. The kinematics model and simplified model of the equivalent mechanism is established. A new definition of the multilegged robot stability margin, based on friction coefficient, is presented to evaluate the robot stability. The stable workspaces of the equivalent mechanism in the step forward stage of trotting gait under different friction coefficients are analyzed. The stride length of the robots is presented by analyzing the relationship between the stable workspaces of the equivalent mechanisms of two adjacent step forward stages in one gait cycle. The simulation results show that the stride length is larger with increasing friction coefficient. We herein propose a new method based on metamorphosis, and an equivalent mechanism to analyze the stability margin and stable workspace of the multilegged robot.