优化行走机构设计,在提升步态质量的同时显著降低关节磨损。
Durability-Aware Multi-Objective Optimization of the Jansen Linkage: Trading Gait Quality Against Joint Wear

- 构建多体动力学与磨损模型,联合评估步态与关节磨损。
- 调整连杆长度可使总磨损降低约56%,同时改善步态平顺性。
- 结果对制造误差鲁棒,适合长期服役的仿生机器人设计。
Jansen连杆是一种单自由度平面腿机构,其十一个关键参数由Theo Jansen通过优化足部轨迹获得,但未考虑铰链磨损问题。本文将耐久性目标引入设计过程,构建参数化正向运动学模型(两圆交点求解器)、逆动力学模型(七体十铰系统,基于约束雅可比与拉格朗日乘子法,经能量法独立验证)以及Archard磨损模型,用于评估任意连杆长度下的步态质量与每个销轴的每周期滑动磨损。由于磨损计算基于理想无间隙铰链,结果为相对排序而非绝对寿命预测。在步长、离地高度、占空比和装配约束下,采用NSGA-II求解双目标优化问题:复合步态误差与总关节磨损。经典Jansen设计在该指标下被帕累托支配:代表性设计中,连杆长度在±29%范围内调整,可使支撑期平坦度提升28%、支撑期速度更平稳58%,总磨损降低约56%。敏感性分析表明磨损优势在曲柄转速×载荷范围内保持48%-56%;全局方差分析(Sobol)确认两个连杆长度主导磨损方差,蒙特卡洛制造公差研究显示磨损优势在真实制造误差下仍能稳健保持。该框架为实现更长寿的行走连杆提供可行路径,并为未来磨损-间隙耦合研究奠定基础。
原文摘要 · Abstract (English)
The Jansen linkage is a single-degree-of-freedom planar leg mechanism whose eleven "holy numbers" were evolved by Theo Jansen to optimize the foot-path gait alone, with no regard for the wear of its revolute joints. This paper introduces a durability objective into the design of the Jansen leg. A parametric forward-kinematic model (two-circle-intersection solver), an inverse-dynamic model (constraint-Jacobian / Lagrange-multiplier formulation of a seven-body, ten-joint system, independently cross-verified by a reduced-DOF energy method), and an Archard wear model are coupled to evaluate, for any set of link lengths, both gait quality and the per-cycle sliding wear at every pin. Because the wear is computed on ideal, clearance-free revolute joints, the resulting wear figures are a relative comparative ranking rather than an absolute life prediction. A bi-objective problem -- composite gait error versus total joint wear, subject to step-length, ground-clearance, duty-factor and assembly constraints -- is solved with NSGA-II. Under the adopted gait metric the classical Jansen design is Pareto-dominated: for a representative design, link-length adjustments within +/-29% simultaneously flatten the stance (-28%), smooth the stance velocity (-58%) and reduce total joint wear by ~56%. A sensitivity study shows the wear advantage is robust across a crank-speed x payload envelope (48%-56%) and identifies the link lengths that most strongly govern wear. A variance-based global (Sobol) analysis confirms that two link lengths dominate the wear variance, and a Monte-Carlo manufacturing-tolerance study shows the wear advantage degrades gracefully under realistic fabrication error. The framework provides a practical route to longer-lived walking linkages and a baseline for future wear-clearance-impact coupled studies.
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