Analytical Modelling of the Dynamics of the Four-Bar Mechanism: A Comparison of Some Methods

2018 ◽  
Author(s):  
J. P. Meijaard ◽  
V. van der Wijk
Keyword(s):  
Virtual Work ◽  
Equations Of Motion ◽  
Differential Algebraic Equations ◽  
Force Balance ◽  
Dynamic Force ◽  
Algebraic Equations ◽  
Principle Of Virtual Work ◽  
Principal Vector ◽  
Reaction Forces ◽  
Principal Points

Some thoughts about different ways of formulating the equations of motion of a four-bar mechanism are communicated. Four analytic methods to derive the equations of motion are compared. In the first method, Lagrange’s equations in the traditional form are used, and in a second method, the principle of virtual work is used, which leads to equivalent equations. In the third method, the loop is opened, principal points and a principal vector linkage are introduced, and the equations are formulated in terms of these principal vectors, which leads, with the introduced reaction forces, to a system of differential-algebraic equations. In the fourth method, equivalent masses are introduced, which leads to a simpler system of principal points and principal vectors. By considering the links as pseudorigid bodies that can have a uniform planar dilatation, a compact form of the equations of motion is obtained. The conditions for dynamic force balance become almost trivial. Also the equations for the resulting reaction moment are considered for all four methods.

scholarly journals On the Weyl transform for rotationally invariant symbols

2019 ◽  
Vol 10 (4) ◽  
pp. 769-791 ◽  
Author(s):  
Norbert Ortner ◽  
Peter Wagner
Keyword(s):  
Asymptotic Behavior ◽  
Differential Operators ◽  
Symmetric Distributions ◽  
Yield Criteria ◽  
Weyl Transform ◽  
Pseudo Differential Operators ◽  
Weyl Transforms ◽  
Rotationally Invariant

Abstract Several formulas for the eigenvalues $$\lambda _j$$ λ j of the Weyl transforms $$W_\sigma $$ W σ of symbols $$\sigma $$ σ given by radially symmetric distributions are derived. These yield criteria for the boundedness and the compactness, respectively, of the pseudo-differential operators $$W_\sigma .$$ W σ . We investigate some examples by analyzing the asymptotic behavior of $$\lambda _j$$ λ j for $$j\rightarrow \infty $$ j → ∞ .

Sign in / Sign up

Export Citation Format

Share Document