Mathematical Method to design better robots, structures

WEST LAFAYETTE, Ind. – Mechanical and civil engineers have created a new mathematical method to design better structures, machines and versatile computer-controlled robots called "robot manipulators."

Civil engineers design structures such as buildings and bridges using mathematical formulas, or theorems, that deal with the science of statics. Mechanical engineers designing robots, machinery and mechanisms use their own set of theorems dealing with kinematics, or the science of motion

The research is detailed in a technical paper that will appear in the January issue of the Journal of Mechanical Design(or another version here pdf), published by the American Society of Mechanical Engineers. The paper was written by Gordon Pennock at Purdue University and Offer Shai, a civil engineer in the Department of Mechanics, Materials and Systems at Tel Aviv University.

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.

"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.


Engineers create mathematical method to design better robots, structures