Simulation of mechanisms modeled by geometrically-exact beams using Rodrigues rotation parameters

We present mathematical models for joints, springs, dashpots and follower loads, to be used together with geometrically-exact beam finite elements to simulate mechanisms. The rotations are described using Rodrigues parameters. An updated-Lagrangian approach is employed, leading to the possibility of finite rotations involving many turns, overcoming possible singularities in the rotation tensor. We present formulations for spherical, hinge and universal (Cardan) joints, which are enforced by Lagrange multipliers. For the hinge joint, a torsional spring with a nonlinear damper model is presented. A geometric-nonlinear translational spring/dashpot model is proposed, such as follower loads. All formulations are presented detailing their contribution to the model weak form and tangent operator. These are employed together with implicit time-integration schemes. Numerical examples are performed, showing that the proposed formulations are able to model complex spatial mechanisms. Usage of the models together with contact interaction between beams is explored by a cam/follower mechanism example.