"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 dual theorems could enable civil engineers to design structures that better withstand the forces and "moments," or torque, associated with motions such as those caused by earthquakes, perhaps at less expense than today's designs.
The mathematics associated with kinematics must factor in the effects of velocity and acceleration resulting from motion. Static structures, on the other hand, are inherently strong in one position but could become weak if that position changes due to unpredictable motion. Combining the mathematics of kinematics and statics provides the best of both worlds by enabling engineers to better design structures that can withstand the "loads" resulting from motion-related forces.
The theorems offer promise in creating a new class of "multiple-platform robots" that maintain their strength even when damaged or otherwise compromised. 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.
One 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.
"In robotics, you want the payload to have at least six degrees of freedom, like you have with your arm and shoulder, allowing your arm to move up and down, side to side, and forward and backward," Pennock said. "In order to ensure that your multiple-platform robot remains stable in a variety of configurations, you want to include the mathematics of statics in the design."
COMPAMED.de; Source: Purdue University