Kinematics of single-degree-of-freedom closed-loop systems with C2 Hermite Spline interpolation

This paper presents a procedure for computing the kinematics of closed-loop multibody subsystems when their kinematics cannot be analytically expressed in terms of the system’s degrees of freedom (DOF). The approach expresses the kinematics by a separate interpolation in translation and rotation. Firstly, the kinematics of the system is formulated through constraint equations in Cartesian coordinates. Then, the Newton-Raphson algorithm is used to solve the constraint equations and determine positions and orientations, followed by computing the solution at velocity and acceleration levels. Furthermore, an incremental interpolation method using fifth-order Hermite splines, between the reference configurations, ensures C2 continuity. The proposed interpolation approach is compared with rotation interpolation based on Tait-Bryant angles and applied to two benchmark systems: a double wishbone suspension and a slider-crank mech- anism. The results showed that interpolation with Bryant angles provide better accuracy for the slider-crank mechanism, reducing velocity and acceleration oscillations.