Nylon Fishing Line Artificial Muscles VI

I've finally done some characterization of these muscles. My primary goal was to investigate the relationship between the diameter of the secondary coils and various muscle properties/behaviors.

The Test Muscles

I made three rod-coiled test muscles, of different internal diameters determined by the size of the rods on which they were coiled. I attempted to keep other variables constant, including the following:

• Materials: All muscles were made from Trilene Big Game “Solar Collector” fishing line (50 lb. test, 711 um in diameter), with a single heating element of 10/46 litz wire twisted in.
• Secondary Coils: I tried to cut the filament to a length that would produce the same number of secondary coils in each muscle when finished (ensuring all muscles would have the same length when at rest). Due to a lack of preciseness in my manufacturing methods, I could not get them quite the same, but corrected for this by reporting relative contraction distance instead of absolute contraction distance in the weight lifting results.
• Primary Coils: I measured the coiling time required, going at the speed of the drill I was using, before a length of filament would begin to spontaneously form secondary coils. I then used this time as a guide for coiling subsequent muscles, scaling it by the length of filament used. Ideally, this would ensure that each muscle had almost enough tension to begin self-coiling, but not quite. In practice, again, the results were less than precise; for instance, two of the muscles developed a few secondary coils at the top. (I treated these as part of the muscle's “tail”, so they did not affect measurements. However, they show that these muscles ended up with a higher primary coiling tension than the remaining one.)
• Tension: I used the same 2 lb. weight as a load for each muscle during the coiling process. Unfortunately this does not entirely guarantee a consistent tension, because some of the nylon filaments were too long to suspend the weight for all or part of the coiling process – meaning it was acting as more of an anchor, and the force on the line would depend on the weight's friction with the floor as well.
• Secondary Coil Spacing: When coiling each muscle around its rod, I packed all of the coils as tightly as possible, so that the muscle would be fully contracted when at rest.
• Annealing: All muscles were annealed at a temperature of 300°F for 20 minutes.
• Chirality: All muscles were homochiral.

Experimental Setup

The passive spring constant test involved suspending various weights from a muscle and measuring the amount of deformation (stretching) produced. The muscles were not powered for this test.

The weight lifting test was intended to measure each muscle's ability to lift weight under power. One muscle was tested at a time. It received its current through a power MOSFET switched by an ATTiny85 microcontroller. A multimeter was included in the circuit to measure current. I had programmed the ATTiny to read an analog voltage, which I could adjust by turning the dial on a potentiometer. The ATTiny sent a PWM signal to the gate of the transistor, varying the duty cycle based on the value of the analog voltage. I hand-adjusted the value of the potentiometer to get the same (effective) current value for each muscle. The distance through which the weight was lifted was measured at steady-state, after the load had risen as far as was possible for that current.

Results

Passive Spring Constant Tests

Each data set has been fitted with a cubic curve.  A spring constant can be obtained for each muscle by taking the slope of the linear portion of the curve.

Weight Lifting Tests

Each data set has been fitted with a parabolic curve.  The (0,0) data point is assumed.

Summary

Muscle	Coil Diameter	Spring Constant	Optimum Load*	Max. Possible Contraction**
1	4.763 mm	8.63 N/m	32.4 g	22.7%
2	3.175 mm	40.12 N/m	60.3 g	14.3%
3	1 mm	237.62 N/m	82.8 g	11.1%

*Averaged over all currents tested on this muscle
**At highest current tested on this muscle, computed from curve

Conclusions

I am going to emphasize again that I'm not working with the greatest equipment here. Distances moved by all of these muscles were on the order of millimeters, and difficult to measure. Muscles can be reshaped by the heat, making the repeatability of the measurements imperfect. Couple that with the possibility of varying ambient temperatures in the house between test sessions, and you have a recipe for a lot of error. Nonetheless, I hope the data is useful in a rough, qualitative way. I'll posit the following:

• All else being equal, muscles with a smaller secondary coil diameter have a larger spring constant.
• Every muscle has an optimum load, a “sweet spot” on the curve, which allows for maximum lift distance when the muscle is powered. Too little weight doesn't stretch the coils far enough apart to provide a working distance, and too much begins to exceed the muscle's strength. I'm sure the optimum loads found for these muscles are dependent on the fact that they all have close-packed secondary coils. It would be interesting to re-try the experiment using muscles that are not fully contracted at rest, and thus have less need to be stretched by the weight.
• The size of the optimum load increases as the secondary coil diameter decreases. I don't know whether the optimum load is related to the amount of current as well, or is the same regardless of current; the data is too irregular to tell.
• At a given current, muscles with a large secondary coil diameter, lifting their optimum load, will lift higher than muscles with a small secondary coil diameter, lifting their optimum load. However, note that large-diameter muscles may have access to a smaller range of currents due to the risk of “going flat” (see yesterday's post).

I now have better answers to a couple of questions that have been asked previously:

Q: Once you've made a muscle contract, can you continue to run current through it and hold it in position?

A: Yes! Just be careful not to overheat the muscle. Current values that are tolerated in brief bursts may be enough to make the muscle flatten or go limp if they are applied for too long.

Q: What is the advantage of rod-coiled muscles over self-coiled muscles, or vice versa? What is the best secondary coil diameter?

A: The best diameter depends on your application. As I suspected, muscles with smaller diameters (including the self-coiled ones, which have the smallest diameter possible) can manage heavier weights, but can't lift them as far as large-diameter muscles can lift their optimal lighter weights (though I do wonder how the more tightly coiled muscles would perform if they were annealed with their coils spread out). The new revelation here is that diameter plays in to current requirements as well – large muscles working at their optimum point need less current than small muscles working at theirs.

Until the next cycle,
Jenny