Non-dimensional variables are very useful as they reduce the number of variables when analyzing physical phenomenon. In this paper, the solutions to the frequency equation of multilink flexible robots with elastic constraints is analyzed in a compact form using the dimensional analysis. First, dimensionless governing differential equation of motion is presented. Second, dimensionless boundary conditions are obtained. Third, the dimensionless frequency equation and the orthogonality conditions among the mode shapes are derived. Fourth, some degenerate cases are developed and compared against some existing models. Finally, dimensionless wave numbers are plotted for various joint stiffness ratio to show the influence of various dimensionless parameters on the natural vibrational behavior of the planar multilink flexible robots.