Wolfgang Höbarth, Hubert Gattringer, Hartmut Bremer,
"A Dynamic Model for a Hybrid Articulated Robot"
: PAMM Proceedings in Applied Mathematics and Mechanics / 79th Annual Meeting of the International Association of Applied Mathematics and Mechanics (GAMM), Bremen 2008, Vol. 8, Nummer 1, WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim, Seite(n) 10123-10124, 2008, ISSN: 1617-7061
A Dynamic Model for a Hybrid Articulated Robot
Sprache des Titels:
PAMM Proceedings in Applied Mathematics and Mechanics / 79th Annual Meeting of the International Association of Applied Mathematics and Mechanics (GAMM), Bremen 2008
The dynamic modeling of hybrid systems, consisting of flexible and rigid
parts and increasing numbers of bodies is resulting in large partial differential
equation systems (PDE). With the assumption of small deflections and the Ritz
expansion the PDE can be approximated by an ordinary differential equation
system (ODE) but the number of degrees of freedom is generally high.
In this paper a hybrid articulated robot with 2 flexible links and 6 joints is under
consideration. The joints are equipped with Harmonic Drive gears with high
gear ratio but relative low stiffness. Therefore additionally degrees of freedom
are introduced for the elastic deflection of the gears. The links are modeled with
flexibility in two bending directions and in torsional sense.
To be able to achieve structured equations the projection equation in subsystem
representation is used. The projection equation is based on the momentum and
the angular momentum equations of each single finite or infinite body which are
projected into the space of minimal coordinates and subsequently are summed
up. Groups of bodies are collected to the so called subsystems with separated
describing velocities. These subsystems are linked together with the kinematical
chain. Because the robot is tree structured it is possible to obtain an explicit
expression for the second derivatives of the minimal coordinates with a recursive
scheme (O(n) efficiency).
The robot is controlled with a feed forward controller and a linear PD joint
controller. Simulation results and measured data are presented and compared.