Andrea Arena and Marco Lepidi
J. Comput. Nonlinear Dynam. August 2025, 20(8): 081011
https://doi.org/10.1115/1.4067702

A parametric lattice model is formulated to describe the dispersion properties of harmonic elastic waves propagating in two-dimensional textile metamaterials. Within a weak nonlinear regime, the free undamped motion of the textile metamaterial, starting from a spatially periodic prestressed configuration, is governed by nonlinear differential difference equations, where nonlinearities arise from the elastic contact between plain woven yarns. Within the linear field, the linear dispersion properties characterizing the regime of small oscillation amplitudes are obtained, by applying the Bloch's theorem. Parametric analyses are carried out to study the influence of the mechanical parameters on wavefrequencies, waveforms and group velocities. As major outcome, the dispersion spectrum is found to possess two distinct passbands, covering the low- and the high-frequency ranges, respectively, while a complete mid-frequency bandgap exists for large parameter regions. Within the nonlinear field, the nonlinear wavefrequencies and the multi-harmonic non-resonant response in the time domain are described, by means of perturbation techniques. As interesting finding, the free wave are shown to propagate with a systematic softening behavior. The wave polarization exalts the nonlinear effects in the high-frequency passband.

Thomas Kordik, Hubert Gattringer, and Andreas Müller
J. Comput. Nonlinear Dynam. Aug 2025, 20(8): 081008
​https://doi.org/10.1115/1.4068321

A major field of industrial robot applications deals with repetitive tasks that alternate between operating points. For these so-called pick-and-place operations, parallel kinematic manipulators (PKM) are frequently employed. These tasks tend to automatically run for a long period of time and therefore minimizing energy consumption is always of interest. As recent research addresses the use of elastic elements, this paper explores the possibilities of minimizing energy consumption of pick-and-place task performing PKM that are driven by series elastic actuators (SEA). The basic idea is to excite eigenmotions that result from the actuator springs and exploit their oscillating characteristics. To this end, a prescribed cyclic pick-and-place operation is analyzed and a dynamic model of SEA driven PKM is derived. Subsequently, an energy minimizing optimal control problem is formulated where operating trajectories as well as SEA stiffnesses are optimized simultaneously. Here, optimizing the actuator stiffness does not account for variable stiffness actuators. It serves as a tool for the design and dimensioning process. The hypothesis on energy reduction is tested on two (parallel) robot applications where redundant actuation is also addressed. The results confirm the validity of this approach.