This paper presents a method for computing the kinematics of single–degree-of-freedom closed-loop mechanisms using minimal coordinates combined with $C^{2}$ -continuous Hermite spline interpolation. Instead of solving nonlinear constraint equations at every time step, the proposed approach evaluates exact kinematics only at selected values of the independent parameter and reconstructs intermediate configurations through interpolation. Several rotational interpolation strategies are examined, including incremental and normalized quaternion schemes as well as Tait–Bryant angle interpolation. Two benchmark systems—a double wishbone suspension and a 3D slider-crank mechanism—are used to assess the accuracy of the interpolated kinematics. The results show that $C^{2}$ interpolation significantly improves the smoothness of angular velocities and accelerations, reducing oscillations in curvature terms. Dynamic simulations further demonstrate that interpolation continuity has a direct impact on mechanical-energy conservation: $C^{2}$ interpolation allows stable integration with larger step sizes, whereas $C^{1}$ interpolation produces noticeable energy drift and requires stricter time-step control. The study highlights the importance of interpolation smoothness for both kinematic accuracy and dynamic robustness. The conclusions provide perspectives for extending the method to multiple DOFs, comparing additional orientation-spline formulations, and systematically analysing which interpolation strategies, integrators, and solver parameters are best suited for different multibody system configurations.
