Simulating large-scale articulated assemblies poses a significant challenge due to the numerical stiffness and geometric complexity of jointed structures. Conventional rigid body solvers struggle with the high nonlinearity induced by rotation parameterization. This difficulty becomes more pronounced for multiple two-way-coupled bodies. This paper introduces a novel framework that leverages the linear kinematic mapping of Affine Body Dynamics (ABD). As ABD targets near-rigid objects, the constitutive variations of different materials become negligible, which justifies a co-rotational approach to isolate geometric nonlinearities of the system. This insight enables the use of constant system matrices that can be pre-factorized throughout the simulation, even with fully implicit integration schemes. To manage the high DOF counts of large-scale systems, we map primal body coordinates onto a compact dual space defined by minimal joint degrees of freedom. By solving the resulting KKT systems, our method ensures exact constraint enforcement and physically accurate motion propagation. We provide a suite of specialized solvers tailored for diverse joint topologies, including chains, trees, closed loops, and irregular networks. Experimental results show that our approach achieves interactive rates for systems with hundreds of thousands of bodies on a single CPU core, while maintaining excellent stability at large time steps.

翻译：模拟大规模铰接装配体因其关节结构的数值刚性与几何复杂性而构成重大挑战。传统刚体求解器难以处理由旋转参数化引入的高度非线性问题，对于多个双向耦合体而言，这一困难尤为显著。本文提出一种新颖框架，该框架利用仿射体动力学（ABD）的线性运动学映射特性。由于ABD针对近刚体对象，不同材料的本构变化可忽略不计，这为采用共旋方法以隔离系统几何非线性提供了理论依据。该洞见使得系统矩阵可保持恒定，并能在整个模拟过程中进行预分解，即使采用完全隐式积分方案亦如此。为处理大规模系统的高自由度数量，我们将原始体坐标映射到由最小关节自由度定义的紧凑对偶空间。通过求解所得KKT系统，本方法能确保约束的精确执行与物理精确的运动传播。我们提供了一套针对不同关节拓扑结构（包括链式、树状、闭环及不规则网络）的专用求解器。实验结果表明，该方法在单CPU核心上对包含数十万体的系统实现了交互级计算速率，同时在大时间步长下保持了优异的稳定性。