Dynamics of flexible mechanisms with mutual dependence between rigid body motion and longitudinal deformation of links

Hać, M.

doi:10.1016/0094-114x(95)00001-f

Cited by 13 publications

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“…This procedure increases the dimension of the problem considerably and yields to the set of equations composed of both differential and algebraic equations, which are not easy to solve. Later works by Nagarajan and Turcic [8,9] and others [10,11] allowed for the rigid-body motion and the elastic motion to influence each other, and both rigidbody degrees of freedom and elastic degrees of freedom are considered as generalized coordinates in the derivation.…”

Section: Introductionmentioning

confidence: 99%

On Equations of Motion of Elastic Linkages by FEM

Hać

2013

Mathematical Problems in Engineering

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Discussion on equations of motion of planar flexible mechanisms is presented in this paper. The finite element method (FEM) is used for obtaining vibrational analysis of links. In derivation of dynamic equations it is commonly assumed that the shape function of elastic motion can represent rigid-body motion. In this paper, in contrast to this assumption, a model of the shape function specifically dedicated to the rigid-body motion is presented, and its influence on elastic motion is included in equations of motion; the inertia matrix related to the rigid-body acceleration vector depends on both shape functions of the elastic and rigid elements. The numerical calculations are conducted in order to determine the influence of the assumed shape function for rigid-body motion on the vibration of links in the case of closed-loop and open-loop mechanisms. The results of numerical simulation show that for transient analysis and for some specific conditions (e.g., starting range, open-loop mechanisms) the influence of assumed shape functions on vibration response can be quite significant.

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