This study proposed the development of a quadruped cat robot designed to achieve straight-line walking motion inspired by a cat’s gait. The objective was to enhance cat-like robotic mobility by addressing challenges in gait planning and joint coordination. The robot was constructed with 2 degrees of freedom (DoF) for each leg, using lightweight materials such as acrylic, plywood, and aluminum to balance strength and maneuverability. Geometric kinematic equations were applied to model the end-effector positions, and a Fourier series was employed to generate a smooth, periodic trajectory for the foot’s end-effector, minimizing jerky movements. The Fourier series fitting achieved high accuracy (R² ≈ 0.99) for the joint angles. The resulting prototype, controlled by an Arduino microcontroller, successfully demonstrated a stable and periodic gait cycle generated through the Fourier series approach, confirming the viability of this kinematic method for straight-line motion.