Kinematic and dynamic modeling of viscoelastic robotic manipulators using Timoshenko beam theory: theory and experiment

Korayem, M. H.; Shafei, A. M.; Absalan, Farshid; Kadkhodaei, B.; Azimi, Alireza

doi:10.1007/s00170-013-5391-1

Cited by 50 publications

(16 citation statements)

References 48 publications

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“…where j = 3, 4, ρ j is the link material density, A j is the cross-section area of the flexible link. The strain term caused by the deflection moment is given in (13)…”

Section: Dynamic Modelmentioning

confidence: 99%

“…Moreover, according to the type of modeling, some uncertainties could appear such as truncation of flexible modes, control and observation spillover, [9]. There are many methods for solving the flexible body modeling problem, such as the Finite Element Method (FEM) [10], Lumped Parameter Method (LPM) [11], Assumed Modes Method (AMM) [12], Gibbs-Appell formulation and AMM [13]. Besides, analyzing the effects of impact on the closed-loop mechanisms have significantly attracted [14].…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Concurrent Design of a 2 Dof Five-Bar Parallel Robot a Hybrid Design of Rigid and Flexible Links

et al. 2021

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In this paper, the concurrent optimal design of a planar five-bar parallel robot for a highspeed pick and place task is considered. A trade-off between trajectory tracking, energy consumption and deformation of the flexible links is sought. Due to the high-speed operation, the minimization of the vibratory effect is considered since the design stage. Thus, the design is stated as a non-linear multiobjective dynamic optimization problem that is solved through the Differential Evolution (DE) algorithm, as well as, feasibility rules for constraints handling. Mechanical structural variables that modify the inertial parameters of the rigid and flexible links, as well as, control variables related to gains of a PID controller are considered as independent variables. This problem is subject to maximum torque that each motor could provide; inherent constraints for link manufacture; dimensional synthesis; Grashof's criterion and initial and boundary conditions. Results show that it is possible, despite the vibrational phenomenon, to reduce the energy consumption without loss of precision through an appropriate mass balance of the actuated links.

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“…where j = 3, 4, ρ j is the link material density, A j is the cross-section area of the flexible link. The strain term caused by the deflection moment is given in (13)…”

Section: Dynamic Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Concurrent Design of a 2 Dof Five-Bar Parallel Robot a Hybrid Design of Rigid and Flexible Links

et al. 2021

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“…The tip has mass m and there is an angle α between the cantilever and sample surface. The beam tapers linearly from a height

h_{0} to h_{1}

and from a breadth b_{0} to b_{1}

Based on the Timoshenko beam theory, the governing differential equations of motion for the rectangular cantilever with constant cross section are written as (Korayem et al ., 2014):

\begin{matrix} true \\ left \frac{\partial}{\partial x} ([], {kGA}_{0} ((), \frac{\partial v false(x, t false)}{\partial x} - ψ (x, t))) \\ left - ρ A_{0} \frac{\partial^{2} v (x, t)}{\partial t^{2}} - c \frac{\partial v false(x, t false)}{\partial t} \\ left + f_{d_{1}} (x, t) = 0, \end{matrix}

\begin{matrix} true \\ left \frac{\partial}{\partial x} ([], {IE}_{y 0} ((), \frac{\partial ψ (x, t)}{\partial x})) \\ left + {kGA}_{0} ((), \frac{\partial v false(x, t false)}{\partial x} - ψ (x, t)) \\ left - ρ I_{y 0} \frac{\partial^{2} ψ (x, t)}{\partial t^{2}} = 0 \end{matrix}

…”

Section: Theoretical Modelmentioning

confidence: 99%

Experimental and theoretical studies of frequency response function of dagger‐shaped atomic force microscope cantilever in different immersion environments

Pasha

Sadeghi

2020

Journal of Microscopy

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Summary In this study, the amplitude of frequency response functions of vertical and rotational displacements and resonant frequency of a dagger‐shaped atomic force microscope cantilever have been investigated. To increase the accuracy of theoretical model, all necessary details for cantilever and sample surface have been taken into account. In this paper, carbon tetrachloride (CCL4), methanol, acetone, water and air have been considered as the environments. In the most cases, presence and absence of tip–sample interaction force have studied. For a sample cantilever immersed in air, both of the Euler–Bernoulli and Timoshenko beam theories have been compared. The results indicate that the tip–sample interaction force raises the resonant frequency. Increasing the liquid viscosity leads to a decrease in the resonant frequency and the amplitude of frequency response functions of vertical and rotational displacements. Increasing the rectangular and tapered parts lengths, decreases the resonant frequency and amplitude of frequency response functions of vertical and rotational displacements. By increasing the cantilever thickness the resonant frequency and amplitude of frequency response functions of vertical and rotational displacements increases. Theoretical model for air and water has been compared with experimental work. Results show good agreement.

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“…However, redundant manipulators usually have a large number of joints and long slender links, which means the pose will be affected by the transmission gap, mechanical vibration, elastic deformation, and other factors that deviate from the calculated value. As a result, the manipulators are in an uncertain state of kinematics and dynamics, so complex control models need to be established to ensure control accuracy [8][9][10].…”

Section: Introductionmentioning

confidence: 99%

End‐Effector Pose Estimation in Complex Environments Using Complementary Enhancement and Adaptive Fusion of Multisensor

Luo

Guo

et al. 2021

Journal of Sensors

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Redundant manipulators are suitable for working in narrow and complex environments due to their flexibility. However, a large number of joints and long slender links make it hard to obtain the accurate end-effector pose of the redundant manipulator directly through the encoders. In this paper, a pose estimation method is proposed with the fusion of vision sensors, inertial sensors, and encoders. Firstly, according to the complementary characteristics of each measurement unit in the sensors, the original data is corrected and enhanced. Furthermore, an improved Kalman filter (KF) algorithm is adopted for data fusion by establishing the nonlinear motion prediction of the end-effector and the synchronization update model of the multirate sensors. Finally, the radial basis function (RBF) neural network is used to adaptively adjust the fusion parameters. It is verified in experiments that the proposed method achieves better performances on estimation error and update frequency than the original extended Kalman filter (EKF) and unscented Kalman filter (UKF) algorithm, especially in complex environments.

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Kinematic and dynamic modeling of viscoelastic robotic manipulators using Timoshenko beam theory: theory and experiment

Cited by 50 publications

References 48 publications

Concurrent Design of a 2 Dof Five-Bar Parallel Robot a Hybrid Design of Rigid and Flexible Links

Concurrent Design of a 2 Dof Five-Bar Parallel Robot a Hybrid Design of Rigid and Flexible Links

Experimental and theoretical studies of frequency response function of dagger‐shaped atomic force microscope cantilever in different immersion environments

End‐Effector Pose Estimation in Complex Environments Using Complementary Enhancement and Adaptive Fusion of Multisensor

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