@Rufus_t_Doofus, let’s talk about linear mechanism binding!
I derived this equation for estimating the likelihood of binding a linear mechanism.
A way to reconfigure this free body diagram to be more applicable to this year’s likely mechanism is as a laterally-extending telescope mechanism. It may be the case that a and b change as a mechanism is deployed, so you should use the smallest b and largest a values to be conservative.
The conclusions are intuitive:
- As the eccentricity of the load increases (a) the chance of binding increases
- As the wheelbase of the linear device increases (b) the chance of binding decreases
- A the coefficient of friction increases (µf) the chance of binding increases
How does this inform mechanism choices in FRC? In bearing selection of course!
A plain bearing, like Igus Drylin from the KoP makes a great example: best-case we’re looking at a coefficient of friction of 0.05-0.12.
Ball bearings/roller contact bearings also have an ‘effective coefficient of friction’ that is well understood. There are numerous sources for these numbers, the first one I found through google is here.
While 0.05 is impressive for a plain material contact pair, it is more than an order of magnitude higher than the effective coefficient of a ball bearing. To move the earlier equation around:
As the bearing friction decreases we can support a larger eccentric load and/or reduce the base of support without binding.
If you have a linear mechanism it is worth running your configuration through this quick calculation to see if it is likely to bind. For our intake we have a bearing spacing (center-to-center) of 4.5in=b and a total intake reach past the bearing center of ~16.5in=a. So we get:
4.5/(2*16.5) = 0.13 = µf likely to cause binding
So we would be REALLY close to binding if we used plain bearings with a µf of 0.05-0.12, but super comfortable with a roller contact bearing with an effective µf of 0.002. Looking at the factor of safety:
0.13/0.12 = 1.08
0.13/0.05 = 2.6
0.13/0.002 = 65 for the win