%0 Journal Article
%T Automatic formulation of falling multiple flexible-link robotic manipulators using 3×3 rotational matrices
%J Journal of Theoretical and Applied Vibration and Acoustics
%I Iranian Society of Acoustics and Vibration and Avecina
%Z 2423-4761
%A Shafei, Ali Mohammad
%D 2017
%\ 01/01/2017
%V 3
%N 1
%P 15-40
%! Automatic formulation of falling multiple flexible-link robotic manipulators using 3×3 rotational matrices
%K Recursive formulation
%K Gibbs-Appell
%K Flight phase
%K Impact phase
%K 3×3 rotational matrices
%R 10.22064/tava.2017.35085.1032
%X In this paper, the effect of normal impact on the mathematical modeling of flexible multiple links is investigated. The response of such a system can be fully determined by two distinct solution procedures. Highly nonlinear differential equations are exploited to model the falling phase of the system prior to normal impact; and algebraic equations are used to model the normal collision of this open-chain robotic system. To avoid employing the Lagrangian method which suffers from too many differentiations, the governing equations of such complicated system are acquired via the Gibbs-Appell (G-A) methodology. The main contribution of the present work is the use of an automatic algorithm according to 3×3 rotational matrices to obtain the system’s motion equations more efficiently. Accordingly, all mathematical formulations are completed by the use of 3×3 matrices and 3×1 vectors only. The dynamic responses of this system are greatly reliant on the step sizes. Therefore, as well as solving the obtained differential equations by using several ODE solvers, a computer program according to the Runge-Kutta method was also developed. Finally, the computational counts of both algorithms i.e., 3×3 rotational matrices and 4×4 transformation matrices are compared to prove the efficiency of the former in deriving the motion equations.
%U http://tava.isav.ir/article_24846_2a40bd187532386edf8c72184f117ea9.pdf