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.
Original language | English |
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Title of host publication | Proceedings ASME 2018 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference |
Subtitle of host publication | Volume 5A: 42nd Mechanisms and Robotics Conference |
Place of Publication | New York, NY , USA |
Publisher | ASME |
Number of pages | 10 |
ISBN (Electronic) | 978-0-7918-5180-7 |
DOIs | |
Publication status | Published - 2018 |
Event | ASME 2018 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, IDETC/CIE 2018 - Quebec City, Canada Duration: 26 Aug 2018 → 29 Aug 2018 |
Conference
Conference | ASME 2018 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, IDETC/CIE 2018 |
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Abbreviated title | IDETC/CIE 2018 |
Country/Territory | Canada |
City | Quebec City |
Period | 26/08/18 → 29/08/18 |
Keywords
- Dynamics (Mechanics)
- Modeling
- Equations of motion
- Linkages
- Virtual work principle
- Algebra