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<p>This paper systematically investigates numerical strategies for updating dependent coordinates in multibody dynamics simulations, focusing on resolving the inherent conflict between computational efficiency and numerical accuracy within coordinate partitioning frameworks. Addresses this gap by evaluating three representative methods—Exact coordinate update, Newton increment, and Newton-Raphson—under a unified framework. Benchmark cases include planar two-bar and four-bar mechanisms as well as a spatial slider-crank mechanism. Computational efficiency, constraint violation, energy error, and kinematic accuracy are compared across varying time-step sizes. Results show that the exact update achieves the highest accuracy but at high computational cost, the increment update provides superior speed but deteriorates with larger steps, and the Newton-Raphson update offers a balanced trade-off suitable for general-purpose simulations. Furthermore, we identify dependent coordinate update operations as the dominant computational bottleneck (60%–90% of runtime). These findings provide practical guidelines for selecting update strategies in real-time versus high-accuracy simulations and highlight avenues for performance optimization in complex multibody systems.</p>

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Multibody simulation of mechanical systems using the coordinate partitioning method

  • 期刊论文

  • 出版模式：

    开放获取

  • 发表日期：

    2026年7月29日

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  • Li Zhang,
  • Suraj Jaiswal,
  • Yongjun Pan,
  • Aki Mikkola

摘要

This paper systematically investigates numerical strategies for updating dependent coordinates in multibody dynamics simulations, focusing on resolving the inherent conflict between computational efficiency and numerical accuracy within coordinate partitioning frameworks. Addresses this gap by evaluating three representative methods—Exact coordinate update, Newton increment, and Newton-Raphson—under a unified framework. Benchmark cases include planar two-bar and four-bar mechanisms as well as a spatial slider-crank mechanism. Computational efficiency, constraint violation, energy error, and kinematic accuracy are compared across varying time-step sizes. Results show that the exact update achieves the highest accuracy but at high computational cost, the increment update provides superior speed but deteriorates with larger steps, and the Newton-Raphson update offers a balanced trade-off suitable for general-purpose simulations. Furthermore, we identify dependent coordinate update operations as the dominant computational bottleneck (60%–90% of runtime). These findings provide practical guidelines for selecting update strategies in real-time versus high-accuracy simulations and highlight avenues for performance optimization in complex multibody systems.