How to use and interpret the Coupler Curve and Centrode Atlas

In order to view the images, your browser must be able to interpret frames, and you will have to have Adobe Acrobat Reader installed on your computer. It is available for free download .

Once you have Acrobat working properly on your machine, the atlas page should work properly. You may peruse the images by varying the parameters in the left frame by obvious means. In order to obtain the best possible scale for your image in the right hand frame, I suggest that you go to Acrobat in a separate window, and excecute the following: File--> Preferences--> General--> Default Magnification--> Fit Page. Once you have a set of curves which appears interesting, you may zoom in or out using the soft buttons provided within your browser by Acrobat.

Each image has lines and curves of several different colors. Below is an explanation of the meaning of these colors as well as the four-bar linkage parameters which determine the shapes of the curves.

Four-bar mechanism (not to scale)
The image shown here is a four-bar mechanism with parameters labeled. The two double (concentric) circles represent pin joints located on a fixed link. This ground link is labelled d. Links a (the input link) and c (the output link) pivot about these pin joints. In turn, the coupler link (the blue triangle) is pinned to link a at A and to link c at B. The coupler point P is located at some interesting position on the coupler link. As link a is rotated, the coupler point will trace out a special path called the coupler curve.

The following parameters are necessary to determine a unique four-bar mechanism coupler curve: the lengths a, b, c, d, and BP; and the angle gamma which line segment BP forms with line segment AB. In order to pack more information on each image, several values of BP are shown on each graph. In the atlas, they are all indicated by small black circles on the edge of the coupler triangle, all originally located along the x-axis.

To further reduce the number of images necessary, the value of a is set to 1 cm on all graphs. To obtain results for a different length a, simply scale the whole graph.

If the double circles represent fixed pivots, why are they shown in different positions on various pages of the atlas? For the purpose of easy comparison, the various coupler points in the mechanism's starting position are always plotted along the x-axis. The rest of the mechanism is rotated enough to be plotted in a congruent starting position.

The colors' meanings are below.

Each dash in the curves mentioned above represents 5o of rotation of line a, as does each of the gaps between the dashes.

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