Modeling of Flexible Robotic Systems

Filipovic, Mirjana; Vukobratović, Miomir

doi:10.1109/eurcon.2005.1630169

Cited by 11 publications

(23 citation statements)

References 7 publications

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“…Based on the same principle, elasticity of gears is introduced into the mathematical model in this paper, as in papers [27] - [31] also. However, when the introduction of link flexibility into the mathematical model is concerned, it is necessary to point out to some essential problems in this domain.…”

mentioning

confidence: 98%

“…The LMA (used in [5],) gives the possibility to analyze the motion of the any point of each mode. We consider that EBA and LMA, are two comparable methods addressing the same problem but from different aspects [27], [28], [30], [31]. As the equation of equilibrium for the mode tip point is essentially LMA and it follows directly from the equation of flexible line obtained via EBA for the preset boundary conditions, it clearly comes out that the structures of these equations are the same (whereas the content of elements of these structures is not the same).…”

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confidence: 99%

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New interpretation of the Euler-Bernoulli equation

Filipovic

Vukobratović

2008

2008 6th International Symposium on Intelligent Systems and Informatics

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A new notion of joint, defined in terms of the state of motor (active or locked) and type of the elastic or rigid element, gear and/or link that follows after the motor, is introduced. Special attention is paid to the motion of the flexible links in the robotic configuration. The article is concerned with the relationship between the Euler-Bernoulli equation, the "Euler-Bernoulli approach" (EBA), and equation of equilibrium at the point of elastic line tip, the "Lumped-mass approach" (LMA). The Euler-Bernoulli equations (which have for a long time been used in the literature) should be expanded according to the requirements of the motion complexity of elastic robotic systems. The Euler-Bernoulli equation (based on the known laws of dynamics) should be supplemented with all the forces that are participating in the formation of the bending moment of the considered mode. This yields the difference in the structure of Euler-Bernoulli equations for each mode. The stiffness matrix is a full matrix. Mathematical model of the actuators also comprises coupling between elasticity forces. Particular integral of Daniel Bernoulli should be supplemented with the stationary character of elastic deformation of any point of the considered mode, caused by the present forces. General form of the elastic line is a direct outcome of the system motion dynamics, and can not be described by one scalar equation but by three equations for position and three equations for orientation of every point on that elastic line. Simulation results are shown for a selected robotic example involving the simultaneous presence of elasticity of the joint and of the link (two modes), as well the environment force dynamics.

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mentioning

confidence: 98%

mentioning

confidence: 99%

New interpretation of the Euler-Bernoulli equation

Filipovic

Vukobratović

2008

2008 6th International Symposium on Intelligent Systems and Informatics

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“…There are two aspects in defining the reference trajectory of the motor angle (see [10][11][12]), viz. :…”

Section: Reference Trajectorymentioning

confidence: 99%

“…Mathematical model of a mechanism with one degree of freedom (DOF), with one elastic gear was defined by Spong [29] as early as in 1987.Based on the same principle, elasticity of gears is introduced into the mathematical model in this paper, as in paper [10][11][12] also. However, when the introduction of link flexibility into the mathematical model is concerned, it is necessary to point to some essential problems in this domain.…”

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confidence: 99%

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Complement of Source Equation of Elastic Line

Filipovic

Vukobratović

2008

J Intell Robot Syst

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A new notion of joint, defined in terms of the state of motor (active or locked) and type of the elastic or rigid element, gear and/or link that follows after the motor, is introduced. Special attention is paid to the motion of the flexible links in the robotic configuration. The paper deals with the relationship between the equation of elastic line equilibrium, the "Euler-Bernoulli approach" (EBA), and equation of motion at the point of elastic line tip, the "Lumped-mass approach" (LMA). The Euler-Bernoulli equations (which have for a long time been used in the literature) should be expanded according to the requirements of the motion complexity of elastic robotic systems. The Euler-Bernoulli equation (based on the known laws of dynamics) should be supplemented with all the forces that are participating in the formation of the elasticity moment of the considered mode. This yields the difference in the structure of Euler-Bernoulli equations for each mode. The stiffness matrix is a full matrix. Mathematical model of the actuators also comprises coupling between elasticity forces. Particular integral of Daniel Bernoulli should be supplemented with the stationary character of elastic deformation of any point of the considered mode, caused by the present forces. General form of the elastic line is a direct outcome of the system motion dynamics, and cannot be described by one scalar equation but by three equations for position and three equations for orientation of every point on that elastic line. The choice of reference trajectory is analyzed. Simulation results are shown for a selected robotic example involving the simultaneous presence of elasticity of the gear and of the link (two modes), as well as the environment force dynamics.

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Introduction

Guo¹,

Lee²

2018

Flexonics for Manufacturing and Robotics

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Modeling of Flexible Robotic Systems

Cited by 11 publications

References 7 publications

New interpretation of the Euler-Bernoulli equation

New interpretation of the Euler-Bernoulli equation

Complement of Source Equation of Elastic Line

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