Modeling and analysis of flexible link manipulators using the algebra of rotations

In this paper, a complete model of the elasto-kinematics is formulated in terms of a new kinematic notation, called the algebra of rotations. Based on this formulation, the elegant and concise expressions are derived for the displacement equation and especially the Jacobians governing the motion mapping between the manipulator tip and joint variables and link deflections. Introduction of the elasto-kinematics into the elasto-dynamics can directly take into consideration the nonlinear coupling between joint variables and link deflections, and thus improve the result of the elasto-dynamics