A single link robotic manipulator is modeled as a rotating flexible beam with a rigid mass at the tip and accurate energy expressions are derived. The resulting partial differential equations are solved using an approximate method of weighted residuals. From the solutions, coupling between axial and flexural deformations and the interactions with rigid body motions are rigorously analyzed.
The emphasis in the current paper is not on an exhaustive analysis of existing systems but it is rather intended to compare and highlight the various flexibility effects in a relatively simple system. Hence, a nondimensional parametric analysis is performed to determine the effect of several parameters (including the rotating speed) on the errors and the individual interaction effects are discussed. Comparison with previous work in the field shows important phenomena often ignored or buried in large scale numerical analyses. Future work including application to multi-link robots is outlined.