Computational kinematics of multibody systems: Two formulations for a modular approach based on natural coordinates

Saura, Mariano; Segado, P.; Dopico, Domingo Calvo

doi:10.1016/j.mechmachtheory.2019.103602

Cited by 10 publications

(6 citation statements)

References 58 publications

(82 reference statements)

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“…The successive inverse displacements can be obtained with equation ( 25), the successive inverse velocities can be updated by equation ( 22) and the successive inverse accelerations can be iterated from equation (26).…”

Section: Kinematics Of a Planar Four-bar Slider-crank Linkagementioning

confidence: 99%

Kinematics of a planar slider-crank linkage in screw form

Zhao

Wei

2021

Proceedings of the Institution of Mechanical Engineers, Part C:

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This paper investigates the forward and inverse kinematics in screw coordinates for a planar slider-crank linkage. According to the definition of a screw, both the angular velocity of a rigid body and the linear velocity of a point on it are expressed in screw components. Through numerical integration on the velocity solution, we get the displacement. Through numerical differential interpolation of velocity, we gain the acceleration of any joint. Traditionally, position and angular parameters are usually the only variables for establishing the displacement equations of a mechanism. For a series mechanism, the forward kinematics can be expressed explicitly in the variable of position parameters while the inverse kinematics will have to resort to numerical algorithms because of the multiplicity of solution. For a parallel mechanism, the inverse kinematics can be expressed explicitly in the variable of position parameters of the end effector while the forward kinematics will have to resort to numerical algorithms because of the nonlinearity of system. Therefore this will surely lead to second order numerical differential interpolation for the calculation of accelerations. The most prominent merit of this kinematic algorithm is that we only need the first order numerical differential interpolation for computing the acceleration. To calculate the displacement, we also only need the first order numerical integral of the velocity. This benefit stems from the screw the coordinates of which are velocity components. The example of planar four-bar and five-bar slider-crank linkages validate this algorithm. It is especially suited to developing numerical algorithms for forward and inverse velocity, displacement and acceleration of a linkage.

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Section: Kinematics Of a Planar Four-bar Slider-crank Linkagementioning

confidence: 99%

Kinematics of a planar slider-crank linkage in screw form

Zhao

Wei

2021

Proceedings of the Institution of Mechanical Engineers, Part C:

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“…Kinematic analysis of a linkage requires the algebraic equations that might be iterated numerically. Computational kinematic analysis plays a vital role in the study of a mechanical system (Saura et al, 2019). It is the most straightforward procedure for kinematics and dynamics to select the absolute coordinates of the reference point as the variables (García de Jalón and Bayo, 1994).…”

Section: Introductionmentioning

confidence: 99%

“…To understand the kinematic performance of a linkage, many scholars have been proposing different theories (McCarthy, 1990;Duffy, 1996;Davidson and Hunt, 2004;Dai, 2014;Zhao et al, 2016;Amiri and Mazaheri, 2020;Faghidian and Mohammad-Sedighi, 2020), methods (Angeles, 1982;Kong et al, 2018;Yang et al, 2018;Kong et al, 2019;Shen et al, 2020), algorithms (García de Jalón and Bayo, 1994;Kong et al, 2016;Saura et al, 2019) and software (Brát and Lederer, 1973;García de Jalón and Bayo, 1994;Wu et al, 2009;Wu et al, 2017). This paper focuses on an algorithm in the screw coordinates to solve the velocity of articulated planar linkage and investigates the displacement and acceleration.…”

Section: Introductionmentioning

confidence: 99%

Kinematics of Articulated Planar Linkages

Zhao

Wei

2021

Front. Mech. Eng.

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This paper proposes a kinematics algorithm in screw coordinates for articulated linkages. As the screw consists of velocity and position variables of a joint, the solutions of the forward and inverse velocities are the functions of position coordinates and their time derivatives. The most prominent merit of this kinematic algorithm is that we only need the first order numerical differential interpolation for computing the acceleration. To calculate the displacement, we also only need the first order numerical integral of the velocity. This benefit stems from the screw the coordinates of which are velocity components. Both the forward and the inverse kinematics have the similar calculation process in this method. Through examples of planar open-chain linkage, single closed-chain linkage and multiple closed-chain linkage, the kinematics algorithm is validated. It is particularly fit for developing numerical programmers for forward and inverse kinematics in the same procedures, including the velocity, displacement and acceleration which provide the fundamental information for dynamics of the linkage.

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“…Previous classifications mentioned in the literature usually consider the types of coordinates involved [12]. The research focus is on four main approaches, namely "reference point coordinates," [2,13,14] "relative coordinates," [15] "natural coordinates," [16,17] and particle-based formulations [9,10,11,18]. Furthermore, in this paper, we associate mechanical models to these formulations and four distinctive classes of models were identified.…”

Section: Introductionmentioning

confidence: 99%

Computational efficiency of multi-body systems dynamic models

Antonya¹,

Boboc²

2021

Robotica

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For several decades, simulation and analysis of mechanisms have been performed with dedicated computer-aided engineering software that implements general dynamic formulations, known in the literature as multi-body systems (MBS) formulations. The MBS name is related to the structure of the mechanism, which is often considered to be a collection of bodies interconnected by mechanical joints (pairs). Nevertheless, only a few formulations are really based on a true multi-body mechanical model, while many others instantiate mathematically quite different mechanical concepts. This paper aims to identify and discuss the mechanical models that fundament the main multi-body mathematical formulations known in the literature. The main features of each model are outlined, based on a detailed presentation of the structure and equations of motion, together with their link with the kinematic and dynamic formulations. A comparative study related to computational efficiency is then presented for the identified main models, based on a test mechanism. Comparative advantages and disadvantages are discussed at the end, considering the identified mechanical models.

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Computational kinematics of multibody systems: Two formulations for a modular approach based on natural coordinates

Cited by 10 publications

References 58 publications

Kinematics of a planar slider-crank linkage in screw form

Kinematics of a planar slider-crank linkage in screw form

Kinematics of Articulated Planar Linkages

Computational efficiency of multi-body systems dynamic models

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