- Sajiv Shah

# Modifications to a SEA (Spring System) That Could Potentially Breed Variable Stiffness

After accumulating for the errors in our previous actuator design by adding a belt with teeth which wrapped around the joint pulley, we found that the experimental data began to resemble the mathematical prediction: extending the initial length of a standard extension spring between a motor and actuator does not change the torque achieved at the joint.

Let's take a look back at the math that we used from __a past article__.

Looking at the final equation that determines torque, we are presented with two different methods of achieving different stiffnesses at a small deflection (compliance). We can either change the radius of the pulley, which would cause the spring to act a force on a longer lever, or use a non-linear elastic material, such as a conical spring, which has a non-linear relationship between the spring extension and output force.

The first method, changing the pulley radius, has many benefits but also many problems.

It allows us to use standard extension springs, which are found easily

It requires the implementation of springs in between toothed-belts

Changing the pulley radius also changes the ratio between the motor and joint, meaning torques and speeds change.

Different kinematic models would be needed for different pulley radii

A non-standard belt, such as a V-shape toothed belt, would be necessary

The second method, which I am obviously leaning toward, is much simpler and has fewer cons

It requires the implementation of springs in between toothed-belts

It does not allow us to use standard extension springs, which may be difficult to come across.

Many non-linear elastics, such as rubber bands and conical springs, are not easily implementable into a mechanical system that must be predictable and reliable. In order to use this method in comparison to varying pulley radius, we must find a non-linear elastic system that can be used between the joint and motor to create variable stiffness.