A recursive algorithm for dynamics of multiple frictionless impact-contacts in open-loop robotic mechanisms

•Dynamic modeling of multiple impact-contacts in open kinematic chains has been studied.•Recursive Gibbs–Appell formulation has been used to derive the motion equations.•In order to model the impact phenomenon, the regularized method has been utilized.•Detecting the impact moments and solving the st...

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Bibliographic Details
Published in:Mechanism and machine theory Vol. 146; p. 103745
Main Authors: Ahmadizadeh, M., Shafei, A.M., Fooladi, M.
Format: Journal Article
Language:English
Published: Elsevier Ltd 01.04.2020
Subjects:
Contact force model
Gibbs–Appell formulation
Impact moment
Multibody system
Recursive algorithm
Impact moment
Multibody system
Gibbs–Appell formulation
Recursive algorithm
Contact force model
ISSN:0094-114X
Online Access:Get full text
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Summary:•Dynamic modeling of multiple impact-contacts in open kinematic chains has been studied.•Recursive Gibbs–Appell formulation has been used to derive the motion equations.•In order to model the impact phenomenon, the regularized method has been utilized.•Detecting the impact moments and solving the stiff differential equations are investigated.•Nine of the famous contact force models have been compared to select a more suitable one. In this paper, the phenomenon of multiple impact-contacts has been dynamically modeled for an open kinematic chain with rigid links and revolute joints. The dynamic equations of the mentioned system have been extracted based on the recursive Gibbs–Appell formulation. The impact-contact phenomenon has been formulated by the regularized method in which the force of impact is a continuous function of the relative penetration and relative velocity of two colliding surfaces with respect to each other. The geometrical specifications and the mechanical properties of colliding surfaces are the two main parameters used in the modeling of viscoelastic contact force models. In this work, a recursive algorithm, which has been developed based on 3 × 3 rotation matrices to reduce the computational load, symbolically derives the motion equations of a multibody system that collides with surrounding surfaces at several points. The system under study includes the non-impact (flight) phase and the impact phase. Going from the flight phase to the impact phase and back, detecting the exact moment of impact, and also solving the differential equations of motion during a very short impact time have their particular challenges and complexities, which are dealt with in this work. In the next step, nine famous contact force models have been compared in order to select the most suitable model for simulation work. Finally, to show the accuracy and the capability of the presented algorithm, the dynamic behavior of an open-chain robotic mechanism consisting of 4 rigid links connected by revolute joints has been simulated and analyzed.
ISSN:0094-114X
DOI:10.1016/j.mechmachtheory.2019.103745