Study on the Direct Differential Method in Constraint Violations for the Reduced Multibody System Transfer Matrix Method

The Reduced Multibody System Transfer Matrix Method (RMSTMM) is a technique that utilizes relative coordinates and formulates kinetic equations at the acceleration level to solve dynamics problems in mechanical systems. However, in the presence of closed loops, the generalized coordinates of the RMSTMM using relative coordinates may not be independent, necessitating the introduction of constraint equations at the displacement and velocity levels to rectify this issue. Alternatively, the Direct Differentiation Method (DDM) is a widely employed software-based approach for tackling dynamics problems, and can also be employed to address anomalies in closed-loop multi-body systems. In this study, the DDM is utilized to correct for violations in closed-loop multi-body systems. This proposed approach differentiates the required parameters along the kinematic equation until the cut-off hinge. Utilizing this method offers several benefits, such as increased universality, simplicity, and convenience, which significantly expands the range of applications for the transfer matrix method.