The advancement of cable-driven robot technology broadens their application scope, showcasing significant developmental promise. This study addresses the kinematic control precision deficit in quaternion joint cable-driven continuum robots by reconceptualizing the quaternion joint as a dual universal joint. Through systematic error analysis and modeling, it introduces a kinematic calibration method leveraging optimized trajectories to refine algorithmic precision. This approach streamlines calibration data acquisition, ensuring data quality and enhancing computational accuracy. Both simulations and experiments verify the proposed calibration algorithm’s efficacy in augmenting cable-driven robots’ kinematic accuracy.