  We study the impact of cosmological scale modifications to General Relativity
on the dynamics of halos within voids by comparing N-body simulations
incorporating Hu-Sawicki $f(R)$ gravity, with $|f_{R0}|=10^{-6}$ and $10^{-5}$,
to those of $\Lambda$CDM. By examining the radial velocity statistics within
voids classified based on their size and density-profile, as "rising"
($R$-type) or "shell" ($S$-type), we find that halo motions in small $R$-type
voids, with effective radius $<15 Mpc/h$, reveal distinctive differences
between $f(R)$ and $\Lambda$CDM cosmologies.
  To understand this observed effect, we study the linear and nonlinear fifth
forces, and develop an iterative algorithm to accurately solve the non-linear
fifth force equation. We use this to characterize the Chameleon screening
mechanism in voids and contrast the behavior with that observed in
gravitationally collapsed objects.
  The force analysis underscores how smaller $R$-type voids exhibit the highest
ratios of fifth force to Newtonian force, which source distinguishable
differences in the velocity profiles and thereby provide rich environments in
which to constrain gravity.
