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Kinematic modeling, linearization and first-order error analysis

: Pott, Andreas; Hiller, Manfred

Wu, H.:
Parallel manipulators. Towards new applications
Vienna: InTech Education and Publishing, 2008
ISBN: 978-3-902613-40-0
Book Article
Fraunhofer IPA ()
Parallelkinematik; parallel kinematic machine; PKM; Manipulator; Fertigung; Montage; Modellsimulation; Kinematik; Fehleranalyse

This chapter deals with a modular method for the kinematic analysis of parallel kinematic machines (PKM) at discrete points within their workspace. Firstly, a modular approach is presented for calculating the forward kinematic transmission function of some widely used parallel kinematic machines. This includes the well-known Stewart-Gough-platforms of general geometry, the Delta-robots, and parallel machines with legs of constant length. The kinematic analysis is based on the kinetostatic method and permits to calculate the position, velocity, and acceleration transmission from the articulated joints towards the moveable platform of the machine. Furthermore, a force transmission is defined based on kinetostatic duality. By means of a simple numerical calculation schema, a comprehensive first-order sensitivity analysis is performed. Finally, it is shown how to set up the stiffness matrix for the aforementioned robots. Computational examples of the proposed algorithms are presented.