On equations of motion of flexible mechanisms

Hać, M.

doi:10.1016/0093-6413(93)90029-n

Cited by 2 publications

(8 citation statements)

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“…where is the angle between and the global coordinate systems. Since the longitudinal displacements of nodes in the case of rigid motion are equal, the shape function for the rigid-body motion (4) can be presented in other forms as shown in [22].…”

Section: Equations Of Motionmentioning

confidence: 99%

“…By comparing (22) and (25) it can be seen that, assuming the shape function for rigid-body motion (4), the inertia matrices related to the rigid-body acceleration vector at right-hand side of equations of motion differ considerably in the two cases considered. The solution { } of matrix (22) and (25) is obtained by using Newmark method for integrating the equations. In the numerical examples, the gravity and damping effects are not taken into account.…”

Section: Equations Of Motionmentioning

confidence: 99%

“…Case 1. By solving equations of motion (22) which have been formulated for the shape function for the rigid-body motion given by (4).…”

Section: Illustrative Examplesmentioning

confidence: 99%

“…During numerical simulations the equations of motion given by (22) and (25) were solved. In both cases the vector of the unknown functions (nodal displacement vector { }) consists of eighteen elements: displacements and in the and directions, respectively, of moving nodes 2, 3, 4, 5, and 6 and the nodal deformation angles Θ The order of the nodal displacement vector for the rigid-body motion { 0 } differs depending on the case considered.…”

Section: Four-bar Linkagementioning

confidence: 99%

“…In both cases the vector of the unknown functions (nodal displacement vector { }) consists of eighteen elements: displacements and in the and directions, respectively, of moving nodes 2, 3, 4, 5, and 6 and the nodal deformation angles Θ The order of the nodal displacement vector for the rigid-body motion { 0 } differs depending on the case considered. In (22) it consists of ten elements, that is, the displacements of moving nodes in the and direction, respectively, due to the rigid-body motion (i.e., all displacements are with the index 0):…”

Section: Four-bar Linkagementioning

confidence: 99%

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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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Section: Equations Of Motionmentioning

confidence: 99%

Section: Equations Of Motionmentioning

confidence: 99%

“…Case 1. By solving equations of motion (22) which have been formulated for the shape function for the rigid-body motion given by (4).…”

Section: Illustrative Examplesmentioning

confidence: 99%

Section: Four-bar Linkagementioning

confidence: 99%

Section: Four-bar Linkagementioning

confidence: 99%