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}.
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