Parametric Synthesis of Compliant Joints for Impact-Robust Shaftless Leg Mechanisms

This paper describes a novel parametric optimization procedure for three flexure cross hinges (TFCH) integrated into multi-link leg mechanisms with closed-loop kinematics. Despite advantages such as compliance, no need for joint lubrication, light weight and cost-efficiency, such shaftless mechanisms have not been widely used, especially in the field of dynamic locomotion, also because their design is challenging and barely studied. Using a morphological computation approach, we have optimized the TFCH geometry to achieve the desired joint stiffness using frequency analysis, ensuring safe and stable hopping under external perturbations. We combined rigid body dynamics with lumped stiffness model and finite element modeling using the SPACAR toolbox to simulate various designs within our optimization pipeline. To illustrate the efficiency of the resulting designs, we built a prototype and conducted a series of full-scale experiments with ramp jumps whose trajectories were recorded by a motion capture system. The experiments showed that TFCH can be effectively integrated into leg mechanisms, providing benefits such as impact robustness, energy recuperation, and the ability to work in extreme conditions.