Abstract
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.