Recursive modeling of serial flexible manipulators

This paper discusses the modeling of serial manipulators with flexible links and joints. The model of a flexible link includes bending in two perpendicular directions and torsion around the longitudinal axis. Second-order strain-displacement relationships, coupled with curvatures' as generalized coordinates, are used to represent the foreshortening effect. Then, the dynamic equations are exact to first order in terms of the generalized coordinates associated with the flexible links. These generalized coordinates and their first time-derivatives are assumed to be small (of first order). The model developed captures all the important phenomena, such as stiffening due to the angular speed or buckling due to large payloads. The dynamic equations are developed recursively using Jourdain's principle to allow an efficient symbolic implementation. The equations associated with the flexible links are reformulated to enable off-line symbolic integration. The gyroscopic effects of motors with reducers are included.