A combination of static and kinematic maths could help design buildings and structures able to withstand high winds and earthquakes better than current techniques. Stuart Nathan reports.

Combining the mathematical basis for designing moving and static structures could be the key to making more stable machinery, according to researchers from PurdueUniversity in Indiana.

It could lead to buildings and structures which can withstand high winds and earthquakes better, and at a lower cost, than current design techniques, claims research leader Gordon Pennock.

The system bridges the gap between civil engineering principles, which depend on the way forces interact with static objects (known as the science of statics) and mechanical engineering, which largely uses theorems dealing with the science of motion, or kinematics.

Pennock, a mechanical engineer, has been working with Israeli civil engineer, Offer Shai of Tel Aviv University, to derive new theorems which combine the mathematics of statics and kinematics.

‘These new theorems represent a common language and provide an understanding of what we call the duality between kinematics and statics,’ said Pennock. ‘The practical result is that engineers can use this knowledge to design better structures and better machines.

‘Civil engineers understand the mathematics of forces and moment, and mechanical engineers understand velocity and acceleration maths,’ he said. ‘We have shown that these concepts are, in fact, analoguous.’

A particular strength of the technique is that it will allow civil engineers to take account of the moving forces, such as torque, which affect buildings and structures during earthquakes. Static structures are built to be extremely strong in one position, but if the position changes, because of a twisting or pushing force, the strength might become compromised.

‘Today, if you want to design a sturdy structure that does not become unstable, you have several choices,’ explained Pennock. ‘You can use the highest quality materials and add many supporting members.’ However, he said that combining static and kinematic mathematics will give designers more insight into the physics that govern how the structure will react to the forces affecting it, and its stability. ‘This, in turn, should enable the designer to create a safer structure, at or below the cost of current designs.’

The system could also be used in the design of engineering robots, particularly those that work on ‘multiple platforms’. One example of this might be a spherical robot, with three curved plates nested inside each other, for space applications; these could be used for structures which need to be compact for launch, but expanded for deploying in orbit, such as solar panels and antennae.

Another could be a robot with two platforms at different heights — the lower one standing on four legs, all on the ground, and the upper with two legs on the ground and two on the upper platform.

‘In robotics,’ explained Pennock, ‘you want the payload to have at least six degrees of freedom, like you have with your arm or shoulder. But what if something happens to impair the motion of a robot, so that it can no longer use all of its joints, and it gets locked in a position that makes it vulnerable to collapse?

‘Kinematics alone cannot solve such a problem,’ he said, ‘so you want to include the mathematics of statics in the design to ensure that your multiple-platform robot remains stable in a variety of configurations.’