Enabling novel dispersion and topological characteristics in mechanical lattices via stable negative inertial coupling

Mechanical topological insulators have enabled a myriad of unprecedented characteristics that are otherwise not conceivable in traditional periodic structures. While rich in dynamics, new developments in the domain of mechanical topological systems are hindered by their inherent inability to exhibit negative elastic or inertial couplings owing to the inevitable loss of dynamical stability. The aim of this paper is, therefore, to remedy this challenge by introducing a class of architected inertial metamaterials (AIMs) as a platform for designing mechanical lattices with novel topological and dispersion traits. We show that carefully coupling elastically supported masses via moment-free rigid linkages invokes a dynamically stable negative inertial coupling, which is essential for topological classes in need of such negative interconnection. The potential of the proposed AIMs is demonstrated via three examples: (i) a mechanical analogue of Majorana edge states, (ii) a square diatomic AIM that can sustain the quantum valley Hall effect (classically arising in hexagonal lattices), and (iii) a square tetratomic AIM with topological corner modes. We envision that the presented framework will pave the way for a plethora of robust topological mechanical systems.

Stiffness Optimization of redundant mechanism based on elastic coupling and inertial coupling characteristics

Aiming to redundant parallel mechanism, on the basis of the kinetic energy method, virtual work principle and perturbation method, the generalized mass matrix and generalized stiffness matrix are obtained, respectively. Two indices on inertial coupling and elastic coupling are defined to measure the decoupling level of the redundant parallel mechanism in terms of two generalized matrices. Furthermore, an algebraic solution method for natural frequency equation of the mechanism is utilized to obtain the natural frequency by means of the Cholesky decomposition method. And then, in order to minimize inertial coupling and elastic coupling, and maximize the natural frequency of the mechanism, two indices and natural frequency are taken as objective functions to optimize the structural parameters of the redundant mechanism, so that optimal dynamic performance of the mechanism is acquired. In the optimization of natural frequency, two optimal solutions are selected. One is to consider inertial coupling and elastic coupling and the other is to ignore inertial coupling and elastic coupling. Finally, the dynamic performance of the two indexes is better by comparing the dexterity of the two solutions

Distributed force feedback in the spinal cord and the regulation of limb mechanics

This review is an update on the role of force feedback from Golgi tendon organs in the regulation of limb mechanics during voluntary movement. Current ideas about the role of force feedback are based on modular circuits linking idealized systems of agonists, synergists, and antagonistic muscles. In contrast, force feedback is widely distributed across the muscles of a limb and cannot be understood based on these circuit motifs. Similarly, muscle architecture cannot be understood in terms of idealized systems, since muscles cross multiple joints and axes of rotation and further influence remote joints through inertial coupling. It is hypothesized that distributed force feedback better represents the complex mechanical interactions of muscles, including the stresses in the musculoskeletal network born by muscle articulations, myofascial force transmission, and inertial coupling. Together with the strains of muscle fascicles measured by length feedback from muscle spindle receptors, this integrated proprioceptive feedback represents the mechanical state of the musculoskeletal system. Within the spinal cord, force feedback has excitatory and inhibitory components that coexist in various combinations based on motor task and integrated with length feedback at the premotoneuronal and motoneuronal levels. It is concluded that, in agreement with other investigators, autogenic, excitatory force feedback contributes to propulsion and weight support. It is further concluded that coexistent inhibitory force feedback, together with length feedback, functions to manage interjoint coordination and the mechanical properties of the limb in the face of destabilizing inertial forces and positive force feedback, as required by the accelerations and changing directions of both predator and prey.