Recent quadruped robots achieve high performance motion control relying on optimization and reinforcement learning. However, there's ongoing research to achieve high performance motion control through dynamic motion implementation based on simple and dominant principles. In this paper, a control approach is proposed that employs admittance control in the rotating workspace to project the SLIP dynamics onto articulated legs, which describes the dynamic behavior of the compliant leg. Furthermore, a comprehensive control framework is presented that allows the motion control of the quadruped robot exploiting the SLIP dynamics by establishing a Jacobian that relates the motions of trunk and SLIP-realized legs. Notably, the robotic leg used in this work features high reduction ratio gears, typically unsuitable for the legged robots due to low backdrivability and significant joint nonlinearity. Through the vertical jumping motion, the effectiveness of the proposed method is validated, which enables the quadruped robot motion control with SLIP-realized legs, even with high gear ratio actuators.