A method for modeling three-dimensional flexible mechanisms based on an equivalent rigid-link system

Accurate modeling of flexible mechanisms is an open research topic, and different models have been presented since the 1970s. In this work, a novel approach for modeling of three-dimensional flexible mechanisms is presented, based on an equivalent rigid-link system, with respect to which elastic deformations are defined and computed. Concepts of three-dimensional kinematics are used in order to define an effective relationship between the rigid body and the elastic motion. The model is based on a compact kinematic formulation and, for a specific mechanism, there is no need for customizing the formulation. By using the principle of virtual work, a coupled dynamic formulation is found. A crucial advantage of this method is that it is not necessary to explicitly formulate the compatibility equations expressing the link connections, since they are included in the matrices of the system dynamics. The model was applied to a specific three-dimensional flexible mechanism. The results, compared with the Adams-Flex™ software, show a good agreement, thus proving the effectiveness of the methodology.