Recursive modeling of serial flexible manipulators

This paper discusses the modeling of serial manipulators with flexible link s and joints. The model of a flexible link includes bending in two perpendi cular directions and torsion around the longitudinal axis. Second-order str ain-displacement relationships, coupled with curvatures' as generalized coo rdinates, are used to represent the foreshortening effect. Then, the dynami c equations are exact to first order in terms of the generalized coordinate s associated with the flexible links. These generalized coordinates and the ir first time-derivatives are assumed to be small (of first order). The mod el developed captures all the important phenomena, such as stiffening due t o the angular speed or buckling due to large payloads. The dynamic equation s are developed recursively using Jourdain's principle to allow an efficien t symbolic implementation. The equations associated with the flexible links are reformulated to enable off-line symbolic integration. The gyroscopic e ffects of motors with reducers are included.