考虑关节间隙后，优化设计仍更耐久，但磨损集中且影响复杂。
Wear-Clearance-Impact Coupling in the Jansen Linkage: A Gait-Durability-Optimized Design Slows Joint Loosening
- 构建含间隙的动态模型，耦合磨损-间隙-冲击反馈循环。
- 间隙使最大接触力翻倍至426N，单点磨损降低7倍以上。
- 磨损集中在10度弧段，非均匀性导致误判风险36倍。
前序研究将关节耐久性引入 Theo Jansen 走路连杆的尺寸设计，发现其经典“圣数”被超越，但该研究假设铰链为理想无间隙状态，因此磨损结果仅为相对排序而非服役退化预测。本文放宽此理想化假设，建立包含间隙的正向动力学模型：铰链以连续法向接触律（Lankarani-Flores，滞后阻尼）和 Ambrosio 摩擦建模，并作为约束稳定微分代数系统集成，与 Archard 磨损定律构成磨损→间隙→冲击反馈回路。三个发现：第一，忽略间隙会低估峰值载荷——有间隙时承载销处最大接触力约104N，理想铰链仅48N（放大约2倍），双关节同时有间隙时升至426N；第二，耦合具有强冲击敏感性——单条轨迹非单调且可逆转设计排名，呈现混沌特征，需统计比较；在16组随机相位下，优化设计在群体均值中更鲁棒，单间隙时每周期磨损低9-7倍（峰值力低4倍），双间隙时仍低1.7倍（p<0.01）；第三，磨损极不均匀——集中于约10°载荷弧段，假设均匀间隙增长会低估局部增长约36倍。因此，尽管存在混沌、多关节、非均匀磨损耦合，无间隙耐久优势在群体平均中仍成立。本文首次提供 Jansen 腿的间隙耦合正向动力学模型，并给出可验证的测试协议。
原文摘要 · Abstract (English)
A companion study introduced joint durability into the dimensional design of the Theo Jansen walking linkage and found its classical "holy numbers" Pareto-dominated, but it modelled the revolute joints as ideal, clearance-free pins, so its wear figures were relative rankings, not a prediction of in-service degradation. Here we relax that idealization. We build a forward-dynamic model of the Jansen leg in which a revolute joint becomes a clearance joint with a continuous normal contact law (Lankarani-Flores, hysteresis-damped) and Ambrosio friction, integrated as a constraint-stabilized differential-algebraic system, and couple it to the Archard law in a wear->clearance->impact feedback loop. Three findings emerge. First, neglecting clearance underestimates the peak joint load: the clearance model gives a peak contact force of ~104 N at the load-bearing pin against ~48 N for the ideal joint (~2x amplification), rising to ~426 N when two joints carry clearance at once. Second, the coupling is strongly impact-sensitive--single trajectories are non-monotonic and can reverse the design ranking, a chaos consistent with the literature--so designs must be compared statistically; over an ensemble of 16 randomized phases the optimized joint is robustly more durable, with per-cycle wear ~9-7x lower (peak force ~4x lower) at one clearance joint and still ~1.7x lower on both with two (p<0.01 throughout). Third, the wear is strongly non-uniform--it concentrates on a ~10 deg load arc--so assuming uniform clearance growth underestimates local clearance growth by ~36x. The clearance-free durability advantage thus survives the chaotic, multi-joint, non-uniformly-worn coupling in the ensemble mean. We deliver the first clearance-coupled forward-dynamic model of the Jansen leg and specify a falsifiable protocol to test each prediction.
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