Dynamics and vibration of a 3- P SP parallel robot with flexible moving platform

J Braz. Soc. Mech. Sci. Eng.

2018

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In the present study, a simple and efficient finite element approach is presented for large deflection analysis of both the straight and curved Euler-Bernoulli beams in the planar static problems. The linear stress-strain relationship is assumed for the Euler-Bernoulli beam. In some of finite element methods, displacements together with rotations, and in some others, positions are considered as the main fields of interpolation. However, in the present study, the main idea for the interpolation is using the dimensions of the deformed element instead of the displacements. Therefore, the slope angle (like the previous works) and the length of beam centroidal axis (unlike the previous works) are used as the main field parameters. This treatment creates simplicity in the constitutive equations. Next, using the weighted residual method, the constitutive equations are applied to the element. Using the equilibrium equations and kinematic equations, the position coordinates of the nodes are related to the internal forces and the main field parameters. In the present study, three-node element and, consequently, Simpson's 1/3 rule is used for integration. For solving nonlinear equations of the beam, the Newton-Raphson method is used. Finally, several numerical examples are presented and compared with the previous works to illustrate the validity and efficiency of the new element.

Section: And Mahdi Sharifniamentioning

confidence: 99%

A new beam element for analysis of planar large deflection

J Braz. Soc. Mech. Sci. Eng.

2018

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“…Finally, it seems that the prismatic joint constraints are not used in mesh-free methods such as assumed modes method. Authors of the present paper previously performed dynamic and vibration of PR-PRP, 3-PRP and 3-PSP parallel robots in which flexible moving platforms have prismatic joints [23][24][25].…”

Section: Introductionmentioning

confidence: 99%

A constrained assumed modes method for solution of a new dynamic equation for an axially moving beam

Computers & Mathematics with Applications

Akbarzadeh

2016

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a b s t r a c tFlexible beams with prismatic joints have complicated differential equations. This complexity is mostly due to axial motion of the beam. In the present research, a horizontal flexible link sliding through a passive prismatic joint while attached to a rigid link of a robot moving in a vertical direction is considered. A body coordinate system is used which aids in obtaining a new and rather simple form of the differential equation without the loss of generality. To model the passive prismatic joint, the motion differential equation is written in a form of virtual displacement. Next, a solution method is presented for the lateral vibrations of the beam referred to as ''constrained assumed modes method''. Unlike the traditional assumed modes method, in the proposed constrained assumed modes method, the assumed mode shapes do not each satisfy the geometrical boundary conditions of the point where passive prismatic joint is located. Instead, by writing additional constraint equations the combination of the assumed modes will satisfy the geometrical boundary conditions at location of the passive prismatic joint. Two case studies for the effect of axial motion on lateral vibration of the beam are presented. Approximate analytical results are compared with FEM results.

“…Two main computational methods are used in flexible multibody dynamics: assumed mode method (AMM) and finite element method (FEM). The AMM can still be extended for use in more complicated systems (Sharifnia and Akbarzadeh, 2014, 2016a, 2016b, 2016c, 2017). Some researchers compared the results of the AMM with experimental results (Ettefagh et al, 2018; Korayem et al, 2014, 2016; Luo, 1993; Nagaraj et al, 1997; Yim et al, 1993).…”

Section: Introductionmentioning

confidence: 99%

Nonlinear dynamics of flexible links in planar parallel robots using a new beam element

Journal of Vibration and Control

2020

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In the present research, a previously presented beam element in planar static problems is extended to planar dynamic problems. As investigated in the previous work of the author, formulation of the presented Euler–Bernoulli beam element is simpler and the beam element more efficient than similar elements in large deflection problems. In the present element, the main idea is estimating the dimensions of the body in the deformed configuration, instead of estimating its absolute or relative positions. Therefore, two parameters, the length and slope angle of the beam centroid curve, are selected to be estimated by interpolating polynomials. To verify the efficiency of the element, obtained results for the flexible pendulum are compared with previous works. Because of the simple and efficient formulation of the element, it can be efficiently used for dynamic analysis of planar flexible linkages, and especially in flexible parallel robots, which are the main aims of the present research. Finally, the inverse dynamic of the flexible 3-RRR parallel robot is presented.