I have made a little progress on characterizing the arm's dynamics for feed-forward control as discussed at the end of the last update. To start out I took some measurements to characterize the friction in the belt reductions. Somehow in the past month my data from the 72 tooth reduction disappeared, but I still have everything from the 60 tooth one, and I remember they were virtually identical:

The process for calculating the friction was pretty simple. I ran the motor off a bench supply at a constant current. I then had the mbed spit back the steady-state angular velocity to my computer over serial. Since I know the torque constant of my motor, I can convert the current draw read off the bench supply into torque produced by the motor. Plotting all this data gives me a nice linear curve representing the friction in the belt reduction as a function of angular velocity.

While doing all this testing, all of a sudden the readings from one of my encoders got stuck. I probed the encoder outputs, and found that one channel was stuck high. I cracked open the encoder to investigate further, and found this:

Further probing around the inside told me something was wrong with the 339N comparator (the chip on the right). Fortunately MITERS had some of these same chips floating around. I cut the leads off the original and soldered a new one in its place:

This seems to have fixed things. I can't imagine why the chip would have died in the first place though.

In terms of actual mechanical progress, I machined a new linkage to replace the carbon fiber one. It's basically an aluminum I-beam, with clamping mounts at each end:

I also worked out the inertia terms for the arm. At the end of the last post I stated that the inertia would change as a function of arm configuration. Fortunately, this actually isn't really true. The inertia

*as seen by the motors*is actually independent of the configuration the arm is in. Let me demonstrate.

First let's look at the inertia as seen by motor 1, which drives the arm's first link. When that motor (driving link 1) rotates, the following happens: The link 1 rotates about its pivot (C). Link 4 rotates about its pivot (D). Link 2

*translates,*following the motion of the end of the first link (B). This is shown by the diagram below:

So, the inertia seen by motor 1 (ignoring the effects of the belt reduction) it I

Now the inertia seen by the second motor, which drives link 3: Link 3 rotates about its pivot (C). Link 2 rotates about its pivot (B). Link 4 translates, following the motion of point (D).

_{D}+ I_{C}+ m_{2}*L_{1}^{2}.Now the inertia seen by the second motor, which drives link 3: Link 3 rotates about its pivot (C). Link 2 rotates about its pivot (B). Link 4 translates, following the motion of point (D).

_{C}+ I

_{B}+ m

_{4}*L

_{3}

^{2}.

The values of the various masses, lengths, and inertias can be determined form my Solidworks models of all the parts. By assigning appropriate material properties to all the parts, and defining reference coordinate systems at the pivot points, can just click on "mass properties" and read off the values for moment of inertia.

Finally, to figure out the inertia

*as seen by the motor*, I just take the values computed by the two formulas above, and multiply them by the square of the gear ratio between the motor and the links. So ((18/72)

^{2})

^{2}for the first link and ((18/60)

^{2})

^{2}for the second link.