According to this news release from Purdue University, civil engineers, who deal with statics, and mechanical engineers, who deal with kinematics, have unified their efforts to create dual theorems which combine the mathematics of both kinematics and statics. In other words, they've shown that these concepts are in fact analogous. By applying these new theorems, it should be possible to design better automotive transmissions or new classes of 'multiple-platform' robots which "maintain their strength even when damaged or otherwise compromised."
Before looking at better robots, here are some quotes about these new theorems.
A mechanical engineer at Purdue University [Gordon Pennock], and a civil engineer at Tel Aviv University in Israel [Offer Shai] have created new theorems that improve the design process by combining the mathematics of both kinematics and statics.
"These new theorems represent a common language and provide an understanding of what we call the duality between kinematics and statics," said Gordon R. Pennock, a Purdue associate professor of mechanical engineering. "The practical result is that engineers can use this knowledge to design better structures and better machines."
And when he says better machines, he really means better robots.
The theorems offer promise in creating a new class of "multiple-platform robots" that maintain their strength even when damaged or otherwise compromised.
So-called robot manipulators currently in use in manufacturing are controlled by sophisticated computer software and can perform a range of tasks.
"Current robots, however, have a single platform, but we showed how the dual theorems will enable engineers to design more functional robots with more than one platform," Pennock said.
Below is a picture showing one of these "multiple-platform" robot designs (Credit: Purdue University School of Mechanical Engineering). Here is a link to a larger version.
And here are some examples of some future robotic designs.
One example is a spherical robot that contains three curved plates nested inside each other. Such a design might be useful in space applications for compact structures that expand into larger structures, such as antennas. Another example is a 12-legged robot that has two flat platforms: a lower platform that has six legs standing on the ground and an upper platform that is connected to the ground by four legs and to the lower platform by two legs.
This research work has been published by the Journal of Mechanical Design under the name "Extension of Graph Theory to the Duality Between Static Systems and Mechanisms" (Volume 128, Issue 1, pp. 179-191, January 2006). Here is a link to the abstract.
Sources: Purdue University news release, January 11, 2006; and various web sites
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