The objective of this diploma thesis, which was completed in 2001 at the Institute of Mechanics at Graz University of Technology in Austria under the supervision of Prof. Dr. Peter Dietmaier, was to develop a computer software serving as an educational synthesis- and design tool which deals with the kinematics of the simple planar four-bar mechanism and two of its special cases, namely the slider-crank mechanism and the Cardan mechanism. In order to guarantee its usability on several hardware platforms, the prospering JAVA™ object-oriented programming language was chosen to realize this project. The big advantage of this program lies in its interactivity as well as in its simplicity of handling. Joints and parts of the analyzed mechanism can easily be displaced on the screen by dragging the mouse. The whole set of possible positions and all curves are steadily calculated. Several analysis features which are basically known from the introductory courses on Kinematical Geometry such as the coupler curve, the pole-curves, the envelope of a straight-line fixed to the coupler, the theorem of Roberts-Chebyshev, the Circles of Bresse and de la Hire as well as the cubic of stationary curvature can be shown. Synthesis tasks for desired coupler point positions, coupler positions as well as transmission functions of the cranks are solved by means of the well-known Hooke-Jeeves optimization algorithm. In 1999 a paper on this computer software was published at the 10th World Congress on the Theory of Machines and Mechanisms (IFToMM) in Oulu, Finland.
Description of the program:
The planar four-bar mechanism consists of four rotational joints and a coupler. Both elements can be dragged with the mouse.
This video shows an example of animation of a mechanism traversing its coupler curve.
The so-called coupler point traverses the coupler curve. In general there are two coupler curves depending on the closure mode of the mechanism. There is an additional four-bar mechanism of same dimensions which can be closed on an alternative coupler curve. The second closure mode is steadily shown in light grey.
The threefold generation of a coupler curve , or more commonly known as theorem of Roberts, can be visualized.
Synthesis tasks are solved for coupler points, coupler positions and transmission functions of the cranks. In order to realize this optimization problem the Hooke-Jeeves algorithm was implemented to minimize the sum of the squares of distance. The advantage of this algorithm lies in the fact that no derivatives of function are needed to find a local minimum of the objective function.
This video shows an example of a coupler curve optimization in which all dimensions of the mechanism are supposed to be modified. It is however possible to lock several elements of the mechanism as coupler, cranks and pivot positions during the optimization process.
Example of a coupler position synthesis: Several coupler positions are given, we search for a four-bar mechanism whose coupler traverses the given set of coupler positions in the right order without changing the size of the coupler.
After the optimization process a mechanism was found which complies with all requirements.