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M3 M2 M1 t ins 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 −0.8 −0.6 −0.4 −0.2 0 0.2 0.4 0.6 0.8 1 e3 e2 e1 t ins 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 ×10−3 −3 −2 −1 0 1 2 3 4 5 6 Figure4. SimulationresultswithanaugmentedPD-controller inredundantcoordinates formulation References [1] H.Bremer.Elasticmultibodydynamics: AdirectRitzapproach. Springer-Verlag,2008. [2] H.Cheng,Y.K.Yiu, andZ.Li. Dynamics andcontrol of redundantly actuatedparallelmanipu- lators.Mechatronics, IEEE/ASMETransactionson, 8(4):483–491,2003. [3] H. Gattringer. Starr-elastische Robotersysteme: Theorie und Anwendungen. Springer-Verlag, 2011. [4] T.Hufnagel andA.Mu¨ller. A realtimecoordinate switchingmethod formodel-based control of PKM. InMultibodyDynamics 2011, ECCOMASThematic Conf. Brussels, Belgium, 4-7 July, 2011. [5] A.Mu¨ller. Internalpreloadcontrolof redundantlyactuatedparallelmanipulators– itsapplication tobacklashavoidingcontrol.Robotics, IEEETransactionson, 21(4):668–677,2005. [6] A.Mu¨ller. Stiffness control of redundantly actuatedparallelmanipulators. InRobotics andAu- tomation, 2006. ICRA2006.Proceedings2006 IEEE InternationalConference on, pages 1153– 1158. IEEE,2006. [7] A.Mu¨ller. Arobust inversedynamics formulation for redundantlyactuatedPKM. In13thWorld Congress inMechanismandMachineScience,Guanajuato,Mexico, pages19–25,2011. [8] A.Mu¨ller andT.Hufnagel. Model-based control of redundantly actuated parallelmanipulators in redundant coordinates.RoboticsandAutonomousSystems, 60(4):563–571,2012. [9] B. J. Yi, R. A. Freeman, and D. Tesar. Open-loop stiffness control of overconstrainedmech- anisms/robotic linkage systems. InRobotics and Automation, 1989. Proceedings., 1989 IEEE InternationalConferenceon, pages1340–1345. IEEE,1989. 216