Computational Mechanics

, Volume 59, Issue 3, pp 459–481 | Cite as

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

  • Alfredo Gay NetoEmail author
Original Paper


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.


Mechanisms Joints Geometrically-exact Beam Rodrigues Cam/follower 



The author would like to acknowledge Prof. Paulo de Mattos Pimenta for the discussions. The author also acknowledges the financial support by FAPESP (Fundação de Amparo à Pesquisa do Estado de São Paulo) under the Grant 2015/11655-3 and by CNPq (Conselho Nacional de Desenvolvimento Científico e Tecnológico) under the Grant 308190/2015-7.

Supplementary material

Supplementary material 1 (mp4 486 KB)

Supplementary material 2 (mp4 1997 KB)

Supplementary material 3 (mp4 1085 KB)

466_2016_1355_MOESM4_ESM.mp4 (13.3 mb)
Supplementary material 4 (mp4 13630 KB)


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Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.Polytechnic School at University of São PauloSão PauloBrazil

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