Dynamic modeling of SCARA robot based on Udwadia–Kalaba theory

Xu, Yujie; Liu, Rong

doi:10.1177/1687814017728450

Cited by 11 publications

(6 citation statements)

References 25 publications

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“…The formulation can be used to model a mechanical system as a system of rigid bodies, with geometrical constraint equations governing their physical kinematical motions. Previous investigations of this dynamic modelling approach [6,7,8] showed convincing agreement of simulated system dynamic results with reference data. Udwadia and Phohomsiri in [9] note that alternative analytical formulations of constrained system motion were offered by Gibbs and Appell, Gauss and Dirac, however emphasise that a key feature of the U-K formulation is that it may provide an explicit set of equations for generic constrained systems.…”

Section: Introductionsupporting

confidence: 54%

Modeling Flexible Multi-Body Systems Within the Udwadia–Kalaba Framework, a Lumped Parameter Approach

Yap

Rezgui

Löwenberg

et al. 2022

Journal of Computational and Nonlinear Dynamics

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It is common practice within Multi-Body Dynamic (MBD) modelling to assume that individual bodies are rigid however this can be an oversimplification especially when slender bodies are present resulting in inaccurate estimations of the system's natural frequencies and overall behaviour. To address this shortfall, we extend the Udwadia-Kalaba (U-K) MBD formulation in this paper to model flexible multibody systems for purposes of exploring system natural frequencies. To model the flexibility, a lumped parameter approach is proposed, which in this work idealises a flexible beam as a series of discrete rigid elements connected by torsional springs. In the U-K formulation, a mechanical system can also be discretised into rigid elements and adapted. This is viewed as a benefit for incorporating a lumped parameter approach within the U-K formulation to model flexible multibody systems. A flexible crank-slider mechanism is introduced and modelled within the Udwadia-Kalaba formulation to capture the dynamics of flexibility through linkage compliance. The model is validated against an alternatively formulated MBD model and system natural frequencies and mode shapes numerically predicted. Results of the study show the effectiveness and potential of extending the application of the Udwadia-Kalaba modelling approach to dynamically model flexible multibody systems. Results also highlight the importance of considering flexible body modes within dynamic analysis of multibody systems, which would otherwise be overlooked under rigid body assumption models.

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Section: Introductionsupporting

confidence: 54%

Modeling Flexible Multi-Body Systems Within the Udwadia–Kalaba Framework, a Lumped Parameter Approach

Yap

Rezgui

Löwenberg

et al. 2022

Journal of Computational and Nonlinear Dynamics

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“…acceleration constraints brought into play to ensure that the system satisfies the geometric constraints it is subjected to. This dynamic modelling approach has also previously been investigated by Nielsen et al [14], Li et al [15] and Xu et al [16] who all found convincing agreement of simulated system dynamic results with reference data. In 2019, previous work of the authors [7] provided an application study of the Udwadia-Kalaba modelling approach to a rigid nonlinear planar crank-slider linkage mechanism.…”

Section: The Udwadia-kalaba Mbd Modelling Approachmentioning

confidence: 66%

Towards development of a nonlinear and flexible multi-body helicopter inceptor model: a resonant frequency tuning study.

Yap

Rezgui

Lowenberg

et al. 2021

AIAA Scitech 2021 Forum

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This paper presents an investigation into the mathematical modelling of the dynamics of a generic candidate inceptor mechanism when system linkage flexibilities are represented. The lumped parameter approach for modelling the flexibility is proposed and applied within the multi-body dynamic modelling framework formulated by Udwadia-Kalaba to explore system resonances. A low-order multi-body mathematical model of an inceptor system is derived and frequency response characteristics numerically obtained. Through a parametric design study, results show how resonance frequencies can be tuned to meet specified levels by identifying and recommending modifications in system design configurations at early design stages. The work presented in this paper provides a framework to identify acceptable design configurations of a system and offers parametric design insights within a multi-body dynamic environment.

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“…It is relatively simple to establish and to solve system motion equations, 15 is relatively simple for the precise tracking and controlling of nonlinear systems, [16][17][18] and has been widely used recently. By the Udwadia-Kalaba equation method, some scholars have studied and discussed some problems in the modeling and control of the planar three-link manipulator, 19,20 the planar multi-link manipulator, 21 the dual-arm cooperating manipulators, 22 the manipulator with redundant degrees of freedom, 23 the SCARA manipulator, 24 and so on.…”

Section: Introductionmentioning

confidence: 99%

Precise torques and sliding mode compensation for trajectory tracking of manipulator with uncertainty

Lyu

Wang

Li³

et al. 2022

International Journal of Advanced Robotic Systems

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The control based on dynamic model could improve the dynamic performance of manipulators and obtain better control effects than the control based on kinematic model. As manipulators are complex online multivariable systems, there are various uncertainties in different environments and working conditions. Accurate dynamic parameters are difficult to obtain in practical engineering applications. In this article, a controller is designed by combining the precise control torques obtained by the analytical dynamics method with the compensation control torques obtained by sliding mode method for trajectory tracking of the manipulator with bounded uncertainty. Precise control torques obtained from the Udwadia–Kalaba modeling method could be applied for the control of the ideal manipulator tracking the desired trajectory. Compensation control torques obtained from the sliding mode concept and the Lyapunov stability theory could be applied to compensate the uncertainties of parameters and external disturbances, thus enhancing the robustness of the system. By combining precise control torques with compensation control torques, the end point of the manipulator with uncertainty could track the end of the ideal manipulator and then track the desired trajectory. The simulation results of the three-link manipulator with uncertainty show that the control method can make the controlled target approach the desired trajectory in relatively small torque ranges and obtain high stability accuracy, and the chattering is effectively reduced at the stage of approaching the sliding mode surface.

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Dynamic modeling of SCARA robot based on Udwadia–Kalaba theory

Cited by 11 publications

References 25 publications

Modeling Flexible Multi-Body Systems Within the Udwadia–Kalaba Framework, a Lumped Parameter Approach

Modeling Flexible Multi-Body Systems Within the Udwadia–Kalaba Framework, a Lumped Parameter Approach

Towards development of a nonlinear and flexible multi-body helicopter inceptor model: a resonant frequency tuning study.

Precise torques and sliding mode compensation for trajectory tracking of manipulator with uncertainty

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