  Via numerical simulation and experimental assessment, this study examines the
use of origami folding to develop robotic jumping mechanisms with tailored
nonlinear stiffness to improve dynamic performance. Specifically, we use
Tachi-Miura Polyhedron (TMP) bellow origami -- which exhibits a nonlinear
"strain-softening" force-displacement curve -- as a jumping robotic skeleton
with embedded energy storage. TMP's nonlinear stiffness allows it to store more
energy than a linear spring and offers improved jumping height and airtime.
Moreover, the nonlinearity can be tailored by directly changing the underlying
TMP crease geometry. A critical challenge is to minimize the TMP's hysteresis
and energy loss during its compression stage right before jumping. So we used
the plastically annealed lamina emergent origami (PALEO) concept to modify the
TMP creases. PALEO increases the folding limit before plastic deformation
occurs, thus improving the overall strain energy retention. Jumping experiments
confirmed that a nonlinear TMP mechanism achieved roughly 9% improvement in air
time and a 13% improvement in jumping height compared to a "control" TMP sample
with a relatively linear stiffness. This study's results validate the
advantages of using origami in robotic jumping mechanisms and demonstrate the
benefits of utilizing nonlinear spring elements for improving jumping
performance. Therefore, they could foster a new family of energetically
efficient jumping mechanisms with optimized performance in the future.
