Ellipsoid Centrodes

Matlab File

Click the figure above to activate the associated video simulation file.

Software copyright © 2004 by The McGraw-Hill Companies, Inc. All rights reserved.

Info

The centrode of instant center of I₂₄ of a special-case Grashof linkage with crossed links (also called an anti-parallelogram linkage), traces ellipses, as shown in the figures on the left and in the middle. Note that the centrode of I₂₄ on link 2 or 4 can be plotted by fixing the respective link.

The motion of the output link (in blue) with respect to the input link (in green) could be duplicated by causing these two centrodes to roll against one another without slipping, as shown in the figure on the right. 

For more information on the ellipsoid geometry generated, click here.

Source

This Working Model file is adapted from Figure 6.15b on p.290 in Design of Machinery, 3rd ed. by Norton, R.L., McGraw-Hill, 2004, and from Figure 5.13-6 on p.161 in Kinematics and Dynamics of Planar Machinery by Paul, B. K., Prentice-Hall, 1979.

Credits

This Working Model file was first developed by Jie (Jeff) Yang.