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Research Papers

Planar Multibranch Open-Loop Robotic Manipulators Subjected to Ground Collision

[+] Author and Article Information
A. M. Shafei

Department of Mechanical Engineering,
Shahid Bahonar University of Kerman,
Kerman 76188-68366, Iran
e-mail: shafei@uk.ac.ir

H. R. Shafei

Department of Mechanical Engineering,
Shahid Bahonar University of Kerman,
Kerman 76188-68366, Iran

1Corresponding author.

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received September 4, 2016; final manuscript received February 22, 2017; published online September 7, 2017. Assoc. Editor: Stefano Lenci.

J. Comput. Nonlinear Dynam 12(6), 061003 (Sep 07, 2017) (14 pages) Paper No: CND-16-1416; doi: 10.1115/1.4036197 History: Received September 04, 2016; Revised February 22, 2017

In this article, a recursive approach is used to dynamically model a tree-type robotic system with floating base. Two solution procedures are developed to obtain the time responses of the mentioned system. A set of highly nonlinear differential equations is employed to obtain the dynamic behavior of the system when it has no contact with the ground or any object in its environment (flying phase); and a set of algebraic equations is exploited when this tree-type robotic system collides with the ground (impact phase). The Gibbs–Appell (G–A) formulation in recursive form and the Newton’s impact law are applied to derive the governing equations of the aforementioned robotic system for the flying and impact phases, respectively. The main goal of this article is a systematic algorithm that is used to divide any tree-type robotic system into a specific number of open kinematic chains and derive the forward dynamic equations of each chain, including its inertia matrix and right-hand side vector. Then, the inertia matrices and the right-hand side vectors of all these chains are automatically integrated to construct the global inertia matrix and the global right-hand side vector of the whole system. In fact, this work is an extension of Shafei and Shafei (2016, “A Systematic Method for the Hybrid Dynamic Modeling of Open Kinematic Chains Confined in a Closed Environment,” Multibody Syst. Dyn., 38(1), pp. 21–42.), which was restricted to a single open kinematic chain. So, to show the effectiveness of the suggested algorithm in deriving the motion equations of multichain robotic systems, a ten-link tree-type robotic system with floating base is simulated.

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Figures

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Fig. 1

A tree-type robotic system with multiple branches

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Fig. 2

Dividing the tree-type robotic system in Fig. 1 into four branches

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Fig. 3

Branch m of the tree-type robotic system as an open kinematic chain

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Fig. 4

Inertia matrix of the mth branch in the flying phase

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Fig. 5

Right-hand side vector of the governing equations of the mth branch

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Fig. 6

A tree-type robotic system with 12 degrees-of-freedom

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Fig. 7

Inertia matrices of each branch of the tree-type robotic system shown in Fig. 6

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Fig. 8

Right-hand side vectors of each branch of the tree-type robotic system shown in Fig. 6

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Fig. 9

Global inertia matrix of the tree-type robotic system shown in Fig. 6

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Fig. 10

Global right-hand side vector of the tree-type robotic system shown in Fig. 6

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Fig. 11

Computational efficiencies of Lagrangian and G–A algorithms when considering the same number of branches

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Fig. 12

Computational efficiencies of Lagrangian and G–A algorithms when considering the same number of links

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Fig. 13

Configurations of the examined tree-type system during the simulations

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