Results of Implementing Torsion Springs Linearly as Elastics
After measuring the data we specified would be necessary in the last post, we physically placed a pair of torsion springs in between a timing belt and a servo motor. On the joint side of the actuator, the timing belt wrapped around a pulley with a short lever attached to it. From that lever we measured the stiffness, or essentially the torque at very small angles, and plotted them against the expected values that we generated from the equation we derived .in my last post.
As visible from the data below, the spring is stiffer than calculated and the difference in value increases. This could possibly be because the angle that the stiffness was measured at was much larger than expected, and came closer to about 12 degrees. At this angle, the torsion springs on one side have a different spring constant than those on the other, so we cannot simply calculate the stiffness value assuming that the the spring stiffness value is the same on each side. We would actually have to measure the length of each pair of springs and calculate the spring stress value at that length and then multiply it by that length to find the force that spring applies. Once we do that for both springs we can then only calculate the stiffness value.
An important measurement that I did not mention in the last post was the effective stiffness range. As shown by the graph of the stress/strain value compared to extension, the value grows exponentially in comparison to the extension meaning that a greater change in the stress/strain is achieved by a small extension of the springs at a larger value in comparison to a smaller value. That said, in the extension range of 0-4cm for that spring, there is little to no effective change in the stress/strain value that would prove beneficial. Setting up a system where the initial extension is 4cm and a motor is optimized to extend the springs to 8cm would prove far more useful.
In this case above, the effective range of stiffness is even smaller. From 0 to 3cm, there is almost no change in the stiffness of the system. From 3-4.5cm, the stiffness goes from about 3 Ncm/rad to 60 Ncm/rad. This means that gearing a extension motor that requires a short amount of travel means that less speed is required from the motor if one wants to change the stiffness quickly (which can be beneficial for releasing stored energy), and therefore less energy is required from the extension motor.
Overall this spring system effectively works as a Variable Stiffness Actuator, and creates a predictable and controllable actuator. Although worthy on the test bench, we still need a multi-link system or realistic application of this actuator to test how it compares to other methods and what the costs of the simplicity of the design are.