  Based on the Maxwell-Beatty reciprocity theorem, static non-reciprocity has
been realized by using nonlinearity, but this non-reciprocity has strict
restrictions on input amplitude and structure size (number of units). Here, we
propose a robotic metamaterial with two components of displacement and
rotation, which uses active control to add external forces on the units to
break reciprocity at the level of the interactions between the units. We show
analytically and simulatively that breaking reciprocity at the level of the
interactions directly leads to a strong asymmetric response of displacement in
a static system, this displacement-specific characteristic not only has no
restrictions on size, input amplitude, and suitable geometric asymmetry, but
also can be transmitted to rotation by coupling under large deformation. After
the evolution from statics to dynamics, asymmetric transmission and
unidirectional amplification of vector solitons are both implemented in this
system. Our research uncovers the evolution of static non-reciprocity to
dynamic non-reciprocity while building a bridge between non-reciprocity physics
and soliton science.
