Path defined directed graph vector (Pgraph) method for multibody dynamics

Abstract

Dynamical modeling of complex systems may include multiple combinations of serial and tree topologies, as well as closed kinematic chain systems. Simulating of such systems is a costly task not only for run time but also for construction time when a model description and constraints are introduced. This paper presents a systematic framework of a construction time efficient modeling methodology for complex systems by introducing a path defined directed graph vector ($\mathit{Pgraph}$) and the associated methodology based on Linear Graph Theory (LGT). Updating of body coordinate frame vectors which can be a challenge in complex topology systems is easily performed using the proposed method. This technique is especially useful for systems changing topology, such as walking mechanisms where bilateral and unilateral constraints are conditionally embedded. Although this is a general methodology, to be combined with many dynamical modeling algorithms available in the literature, here we demonstrate it using Spatial Operator Algebra (SOA), which is a recursive algorithm based on the Newton–Euler formalism.