  Controlling material properties by modulating the crystalline structure has
been attempted using various techniques, e.g., hydrostatic pressure, chemical
pressure, and epitaxy. These techniques succeed to improve properties and
achieve desired functionalities by changing the unit cell in all dimensions. In
order to obtain a more detailed understanding on the relation between the
crystal lattice and material properties, it is desirable to investigate the
influence of a smaller number of parameters. Here, we utilize the combination
of chemical pressure and epitaxy to modify a single lattice parameter of the
multiferroic orthorhombic RMnO$_3$ (R = rare-earth, o-RMnO$_3$) system. By
growing a series of o-RMnO$_3$ (R = Gd - Lu) films coherently on (010)-oriented
YAlO$_3$ substrates, the influence of chemical pressure is reflected only along
the $b$-axis. Thus, a series of o-RMnO$_3$ with $a$ ~ 5.18 {\AA}, 5.77 {\AA} <
$b$ < 5.98 {\AA}, and $c$ ~ 7.37 {\AA} were obtained. Raman spectra analysis
reveals that the change of the $b$-axis parameter induces a shift of the oxygen
in the nominally "fixed" $ca$-plane. Their ferroelectric ground state is
independent on the $b$-axis parameter showing polarization of ~ 1 $\mu$C
cm$^{-2}$ along the $a$-axis for the above-mentioned range, except for $b$ ~
5.94 {\AA} which corresponds to TbMnO$_3$ showing ~ 2 $\mu$C cm$^{-2}$. This
result implies that multiferroic order of o-RMnO$_3$ is almost robust against
the $b$-axis parameter provided that the dimension of the $ca$-plane is fixed
to 7.37 {\AA} $\times$ 5.18 {\AA}.
