Analytic modelling of the dynamics of the four-bar mechanism

A comparison of some methods

Conference paper (2018)

Authors

J.P. Meijaard Olton Engineering Consultancy
V. van der Wijk Mechatronic Systems Design - Mechanical, Maritime and Materials Engineering
Research Group
Mechatronic Systems Design (Mechanical, Maritime and Materials Engineering) (TU Delft)
Modeling Algebra Equations of motion Dynamics (Mechanics) Linkages Virtual work principle
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Published Date

2018

Language

English

Reuse Rights

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Faculty

Mechanical, Maritime and Materials Engineering

Department

Precision and Microsystems Engineering

Research Group

Mechatronic Systems Design

Abstract

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.