Scaling a physical device's geometry results in mechanical properties changing in various ways (e.g. the cubed-squared law states that for a scaling factor C, mass scales with C3 and surface area with C2). These scaling effects can result in a device's inconsistent and unplanned mechanical behavior when varying its fabricated size, thereby necessitating unique designs at different scales. We show that for displacement-driven compliant mechanisms, mechanical stress is uniquely invariant with scale. This effect is described theoretically, verified through computer models and physical testing, and is demonstrated in three examples: a parallel-guiding mechanism, a projectile launcher, and a deployable chair. This enhanced understanding of stress invariance provides innovative insight into the way devices can be designed for systems that operate across different scales.
Hunter et al. (2026) studied this question.