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The optimal tuning of high-order motion parameters has emerged as a promising strategy for actively controlling the kinematics/dynamics of high-speed cam mechanisms. However, accomplishing this task remains challenging with current low-order interpolation or tuning methods. This study proposes an integrated high-order interpolation and tuning methodology for the optimal construction of high-speed motion curves. Initially, an explicit <i>C</i>⁴-spline interpolant (C4SI) is developed. This interpolant utilizes four-order continuous (<i>C</i>⁴) splines to synthesize a high-fidelity motion curve that satisfies the predefined motion constraints up to the fourth order, including dimensionless displacement, velocity, acceleration, jerk, and quirk. Concerning the reduction of motion peaks, a unique C4SI-based global kinematics optimization strategy is designed, using the definite integral of the motion curve (free of the time variable) as the objective function. This facile time-free optimization strategy could yield a simultaneous reduction in multiple motion peaks (up to five), which is currently inaccessible with conventional motion tuning strategies. Concerning the improvement of dynamic characteristics, the C4SI-based time-free global dynamics optimization of variable motion parameters is further performed. The results indicate that the optimized fourth-order motion curve offers minimal high-speed transmission error and residual vibration over the whole rise-dwell-return-dwell cycle, which outperforms the standard motion curves and other low-order counterparts.