Solving the Kinematics of Planar Mechanisms

1999 ◽  
Vol 121 (3) ◽  
pp. 387-391 ◽  
Author(s):  
C. W. Wampler
Keyword(s):  
Eigenvalue Problem ◽  
Complex Plane ◽  
Generalized Eigenvalue Problem ◽  
System Of Equations ◽  
Polynomial Equations ◽  
Input Output ◽  
Planar Mechanisms ◽  
Generalized Eigenvalue ◽  
General Method

This paper presents a general method for the analysis of planar mechanisms consisting of rigid links connected by rotational and/or translational joints. After describing the links as vectors in the complex plane, a simple recipe is outlined for formulating a set of polynomial equations which determine the locations of the links when the mechanism is assembled. It is then shown how to reduce this system of equations to a generalized eigenvalue problem, or in some cases, a single resultant polynomial. Both input/output problems and tracing-curve equations are treated.

Solving the Kinematics of Planar Mechanisms

1998 ◽  
Author(s):  
Charles W. Wampler
Keyword(s):  
Eigenvalue Problem ◽  
Complex Plane ◽  
System Of Equations ◽  
Polynomial Equations ◽  
Input Output ◽  
Planar Mechanisms ◽  
General Method

Abstract This paper presents a general method for the analysis of planar mechanisms consisting of rigid links connected by rotational and/or translational joints. After describing the links as vectors in the complex plane, a simple recipe is outlined for formulating a set of polynomial equations which determine the locations of the links when the mechanism is assembled. It is then shown how to reduce this system of equations to a standard eigenvalue problem, or if preferred, a single resultant polynomial. Both input/output problems and tracing-curve equations are treated.

scholarly journals Solving the Kinematics of Planar Mechanisms by Dixon Determinant and a Complex-Plane Formulation

2000 ◽  
Author(s):  
Charles W. Wampler
Keyword(s):  
Eigenvalue Problem ◽  
Complex Plane ◽  
Numerical Solutions ◽  
Generalized Eigenvalue Problem ◽  
Minimal Size ◽  
Input Output ◽  
Planar Mechanisms ◽  
Planar Mechanism ◽  
Generalized Eigenvalue ◽  
General Method

Abstract This paper presents a general method for the analysis of any planar mechanism consisting of rigid links connected by revolute and slider joints. The method combines the complex plane formulation of Wampler (1999) with the Dixon determinant procedure of Nielsen and Roth (1999). The result is simple to derive and implement, so in addition to providing numerical solutions, the approach facilitates analytical explorations. The procedure leads to a generalized eigenvalue problem of minimal size. Both input/output problems and the derivation of tracing curve equations are addessed.

scholarly journals Solving the Kinematics of Planar Mechanisms by Dixon Determinant and a Complex-Plane Formulation

2000 ◽  
Vol 123 (3) ◽  
pp. 382-387 ◽  
Author(s):  
Charles W. Wampler
Keyword(s):  
Eigenvalue Problem ◽  
Complex Plane ◽  
Numerical Solutions ◽  
Minimal Size ◽  
Input Output ◽  
Planar Mechanisms ◽  
Planar Mechanism ◽  
Revolute Joints ◽  
Generalized Eigenvalue ◽  
General Method

This paper presents a general method for the analysis of any planar mechanism consisting of rigid links connected by revolute joints. The method combines a complex plane formulation [1] with the Dixon determinant procedure of Nielsen and Roth [2]. The result is simple to derive and implement, so in addition to providing numerical solutions, the approach facilitates analytical explorations. The procedure leads to a generalized eigenvalue problem of minimal size. Both input/output problems and the derivation of tracing curve equations are addressed, as is the extension of the method to treat slider joints.

Efficient and Flexible Finite Element Procedure for Free and Forced Vibration Problems of a Plate Coupled With Fluid

2020 ◽  
Author(s):  
Ming Ji ◽  
Kazuaki Inaba
Keyword(s):  
Finite Element ◽  
Eigenvalue Problem ◽  
Forced Vibration ◽  
Natural Frequencies ◽  
Coupled System ◽  
Generalized Eigenvalue Problem ◽  
Symmetric System ◽  
System Of Equations ◽  
Generalized Eigenvalue ◽  
Finite Element Procedure

Abstract Identifying the coupled system natural frequencies and dynamic behavior of systems in the presence of fluid-structure interaction is one of the most important issues in the engineering design of buildings, road vehicles and aircraft. This paper presents an efficient and flexible finite element procedure using fully vectorized codes for the free and forced vibration analysis of a rectangular plate in contact with fluid. The 4-node MITC plate finite element (MITC4) based on the Mindlin plate theory is used to simulate the plate, while the 8-node acoustic pressure element is used to simulate the fluid. The derived system of equations using structural displacements and fluid pressures yields a non-symmetric system of equations. Solving the generalized eigenvalue problem for the non-symmetric system is more computationally intensive compared to solving the generalized eigenvalue problem for symmetric systems. The modal expansion technique is used to reduce the model size. Then the reduced non-symmetric system is symmetrized by right eigenvectors. The Newmark method is used to solve the forced vibration problem of the coupled systems. The effect of the height of the fluid on the natural frequencies is discussed. The natural frequencies and transient responses are in good agreement with those obtained from the commercial finite element software. Moreover, the technique is proved to be effective to solve the coupled system.

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