Ok, here's a basic model with a simple joint setup I would use for something like this. With this setup, the "origin spheres" are acutally redundant; the pins themselves actually function as the "origins". You can see how the rotation propagates down the parent-child chain by selecting one of the pins and dragging around the rotate button in the edit palette (stick to only X-axis rotations as these are one-axis joints).

The way I was telling you earlier to set up the scene (copying "origin sphere" locations and whatnot) is wrong. Like I said above..."It's been a while since I've been in Bryce...I'm a little rusty."

The way you should do it is to parent the objects you want to rotate and translate to the "origin objects" (be they spheres, pins, bushings, etc.). Any rotation or translation is then accomplished by rotating or translating the "origin objects"; their children will follow accordingly. This method makes it easier to adjust your rotation points also. If your joint is in the wrong place, just un-parent it's children, drag it to wherever it goes, and re-parent.
What you are doing is essentially building a skeletal structure. The "origin objects" define the joints and moving them forces the bones (their children) to go where they are supposed to be.

Take a look at the file (Bryce4 and Rhino2 files are both included in the archive) and notice how the parenting is done.
You could go even more crazy with this and do some more advanced stuff. I've included a more advanced joint setup (one with a piston) in the "Advanced" folder of the archive. That one did require me to adjust the origin Z values for the arm_piston_lower and arm_piston_upper; I used the Z-values from the origin_arm_piston_lower and origin_arm_piston_upper, respectively. Make sure to click the lock icon to "unlocked" before changing origin values; otherwise you'll end up moving your object in addition to changing it's origin.

Rename the attached file (only 80KB) to "Digger_Arm.zip" to open it (the forum only takes images or text files).

Note: In the advanced file I've deleted the redundant origins and haven't bothered to hide the piston origins.