Dynamic Model of a Mobile Robot with Long Spatially Flexible Links


Department of Mechanical Engineering,Sharif University of Technology


Abstract. Using some agent variables, the general structure of the dynamic model of a spatial mobile
robot with N long spatially
exible links and N revolute joints has been exposed. It is composed of a
set of 5N + 6 nonlinear coupled partial di erential motion equations under the in
uence of the boundary
conditions. Non-conservative forces/moments have been neglected. While being considered, the general
structure of the dynamic model will not change, but a few exciting/damping terms will arise within
the agent variables. The base of the robot is an unconstrained rigid body in space and the links as
3D Euler-Bernoulli beams undergo tension-compression, torsion and two spatial bendings while elastic
orientation is considerable and the nonlinear part of the geometric Green-Lagrange strain is ignored.
When the elastic orientation is neglected, the dynamic model of each link remains more accurate than
that of a nonlinear 3D Euler-Bernoulli beam within which the elastic orientation is actually negligible.
The obtained dynamic model is capable of creating the nonlinear 3D long Euler-Bernoulli beam and the
fully-enhanced/enhanced/generalized nonlinear 3D Euler-Bernoulli beam theories, considering a
ying or
a xed support.