Flexible Bar Flexible Hinge Robot Rigid-flexible Coupling Dynamics

With the trend of high speed, high precision, light weight and large scale of manipulators, the effects of flexible components become more important than before. While the component is undergoing large overall motion, its elastic deformations couples with the motion, which brings some problems such as "dynamic stiffening" effect to increase the accuracy of dynamic analysis. These problems become the general problems and key technologies in the area of manipulator engineering. The discussing about the manipulators with flexible links and flexible joints is based on the former researches. The flexible effects of links and joints are both taken into account. To the deformation of the links, not only the tension and bending deflection are considered, but also the torsion deflection. Then the model of flexible manipulators with more consideration is given. 4×4 homogeneous transformation matrices are used to describe the positions and orientations of components. The dynamic stiffening item and the mass of joints can be brought into the matrices. The first-order rigid-flexible coupling dynamic model of flexible manipulators is built for the first time, from which the Lagrange dynamic equations in the form of matrices have been deduced. The equations with a nice form and clear arrangement are effective for programming. During the modeling, the recursive relation among the matrices is analyzed, so that the matrices can be calculated in an efficient way. Several examples are simulated and analyzed under different conditions.