A Variational Approach for Modeling Flexibility Effects in Manipulator Arms

This paper presents a general technique to model flexible components (mainly links and joints flexibilities are considered) of manipulator arms based on the Castigliano’s theorem of least work. The robotic arms flexibility properties are derived and represented by the matrix of compliance coefficients. Such expressions can be used to determine the errors due to the robotic tip deformations under the application of a set of applied loads at the tip in Cartesian space. Once these deformations are computed, they may be used to correct for the positional errors arisen from the robotic structural deformations in the motion control algorithms.