Discrete Body Dynamics: A Numerical Method for Multibody Systems Investigated on Closed-Chain Problems

Discrete Body Dynamics (DBD) is a recently developed approach for solving multibody dynamics problems that aims to improve the numerical treatment of systems with joint compliance. Conventional multibody formulations typically rely on kinematic constraints, which can increase numerical complexity and sensitivity, particularly in closed-chain systems. In this work, DBD is presented as a unified framework that combines a new modeling approach with a new numerical solution strategy. Mechanical joints are modeled explicitly using sets of springs and dampers, replacing ideal constraints and transforming the governing equations from a differential-algebraic system into a purely differential one. Based on this modeling framework, the numerical solution avoids global matrix operations and relies on element-wise computations, resulting in linear computational complexity with respect to the number of bodies. The numerical performance of the DBD method is investigated using a set of closed-chain benchmark systems, which are known to be challenging for conventional constraint-based solvers. The analysis examines the influence of joint stiffness, system dynamics, time-step selection, and mechanism topology on numerical stability, energy dissipation, and computational efficiency. The results show that DBD maintains robust and accurate solutions across the examined scenarios and exhibits a well-defined operating region with low numerical dissipation. Across the examined compliant-joint benchmarks, DBD shows the potential for up to three orders of magnitude lower energy drift at comparable simulation-time-to-real-world time (SRT), or up to about one order of magnitude higher SRT at comparable energy drift, relative to ADAMS/View. These findings indicate that DBD is well suited for the simulation of realistic multibody systems with compliant joints, including closed-chain configurations.