  It has been supposed that the interplay of elasticity and activity plays a
key role in triggering the non-equilibrium behaviors in biological systems.
However, the experimental model system is missing to investigate the
spatiotemporally dynamical phenomena. Here, a model system of an active chain,
where active eccentric-disks are linked by a spring, is designed to study the
interplay of activity, elasticity, and friction. Individual active chain
exhibits longitudinal and transverse motion, however, it starts to self-rotate
when pinning one end, and self-beats when clamping one end. Additionally, our
eccentric-disk model can qualitatively reproduce such behaviors and explain the
unusual self-rotation of the first disk around its geometric center. Further,
the structure and dynamics of long chains were studied via simulations without
steric interactions. It was found that hairpin conformation emerges in free
motion, while in the constrained motions, the rotational and beating
frequencies scale with the flexure number (the ratio of self-propelling force
to bending rigidity), ~4/3. Scaling analysis suggests that it results from the
balance between activity and energy dissipation. Our findings show that
topological constraints play a vital role in non-equilibrium synergy behavior.
