Abstract
A mathematical model of a crane with a tree structure of a kinematic chain and with closed-loop sub-chains is presented in the paper. The formulated model takes into account the flexibility of supports, link, rope and drives. Dry friction in joints is also considered. It is assumed that the clearances in joints are neglected. The formalism of joint coordinates and homogeneous transformation matrices, based on the Denavit–Hartenberg notation, are used to describe the kinematics of the crane. The equations of motion are derived using the Lagrange equations of the second kind. These equations are supplemented by the Lagrange multipliers and constraint equations formulated for each cut-joint. The flexible link is modelled using the Rigid Finite Element Method.
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Urbaś, A., Augustynek, K. (2020). Mathematical Model of a Crane with Taking into Account Friction Phenomena in Actuators. In: Kecskeméthy, A., Geu Flores, F. (eds) Multibody Dynamics 2019. ECCOMAS 2019. Computational Methods in Applied Sciences, vol 53. Springer, Cham. https://doi.org/10.1007/978-3-030-23132-3_36
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DOI: https://doi.org/10.1007/978-3-030-23132-3_36
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