Kinematic and inverse dynamic analysis using mixed and fully Cartesian coordinates with a generic rigid body

Abstract

The propagation of errors along a kinematic chain, caused by using drivers computed from noisy data, can affect the accuracy of the kinematic and dynamic outcomes. Minimizing the effect of such errors is crucial, particularly when traditional smoothing techniques prove to be ineffective. This work expands the multibody formulation with Fully Cartesian Coordinates and a Generic Rigid Body (FCC-GRB) to the inverse dynamic analysis of spatial mechanical systems using mixed coordinates (MC). This method considers the incorporation of angular variables, enabling the determination of the kinematic consistent positions that best fit the reference data, while simultaneously computing the joint angular drivers. The accuracy and computational performance of the formulation are evaluated using both numerical- and optimization-based methods in the study of two mechanisms guided with perturbed data. The results show that implementing an MC methodology with FCC-GRB can be easily performed without compromising the theoretical foundations of the classical formulation. This approach efficiently computes both the positions and drivers of the model simultaneously, avoiding the propagation of errors along the kinematic chain. Numerical methods based on the Newton-Raphson algorithm generated positions closely matching the reference data, while optimization-based methods ensured a stricter fulfillment of the topological constraints.