Overcoming Obstacles in Passive Handcart Systems: A Quasi-Static Analysis and Passive Module Development

This study develops a first-order quasi-static framework for climbing initiation in passive handcarts and proposes two passive modules to relax the resulting geometric constraints. Unlike motorized platforms that apply torque directly at the wheel axle, passive handcarts rely solely on handle-applied forces, making climbing initiation strongly dependent on force direction and system geometry. As a result, even small obstacles such as a 15 mm step for a 90 mm wheel can be difficult to negotiate in practice despite substantial manual effort. Starting from an isolated single passive wheel, the analysis is extended progressively to a single-wheel-and-link configuration and a two-row-wheel handcart. We establish geometric and force-direction&#x2013;based conditions governing climbing initiation and identify structural scenarios associated with forward tipping or stalled motion. The analysis highlights the role of the contact angle (<inline-formula> <tex-math notation="LaTeX">$\theta $ </tex-math></inline-formula>) and shows how handcart structures restrict the feasible force-direction region relative to that of an isolated wheel. A parametric analysis highlights geometry sensitivity, practical force-direction margins, and observed front-rear asymmetry. Based on these insights, two passive modules, RHINO and PIZZA, are proposed to locally modify the effective wheel&#x2013;obstacle contact geometry while preserving the passive nature of the system. Experiments with a commercial rollator show baseline success at 10 mm but failure at 15 mm, whereas RHINO and PIZZA extend feasibility to 50 and 30 mm, respectively. The results provide a first-order analytical basis for passive handcart obstacle-negotiation and support geometry-guided passive module design.