Personally, I haven't had a problem with the lower shaft having a little wobble. If the coil cable is not coiled but taped straight up the shaft for the first 18 inches along the lower rod, then coiled, any movement on the rod will all be relative and shouldn't produce any falsing. This has been my experience with the 10" x 14" DD, the 8" Mono coil and the 3" x 7" DD coil. In fact, the slight wobble can actually cushion a sudden hit on a rock and prevent some falsing. If you do get falsing in the water, try lowering the electronics in the water while you are swinging the coil. That will quite often stop the falsing immediately. You may have to re-tune the machine to a quieter frequency and properly ground balance it a second time.
However, if that slight wobble does bother you, you can wrap 1-2 layers of tape around the male end of the shaft and insert this into the female (outer) tube for greater stability. You can also drill another hole in both shafts and add another nylon bolt. Keep in mind that if you are already using a lower rod with a tight fit on the infinium and use it in the water often, you will have one heck of a challenge trying to remove/adjust the lower rod, as you get a buildup of salt and calcium that acts like cement. I suggest you clean that lower rod by running it under tap water to remove some of that buildup after each hunt.
If you plan to hip mount the Infinium, you should tether the cable coming off the electronics after about 12-18 inches so that the cable connection does not receive all the cable movement while swinging the coil. I have had units fail in the past from constant stress on the cable just prior to where it attavches to the electronics.
If you want to read up some more on the Infinium, ask questions or just post, click on the Infinium Forum link below:
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