Static forces in bongo

I wonder if it is possible to apply some kind of constraint that simulates static forces like gravity.
I am working on an IK linkage that requires gravity to bring the assembly back to its home position to repeat a cycle. I have successfully rigged the chain and it animates in accordance to the constraints, however without a load on the end arm, it has too much freedom and travels all over the place instead of the desired orbit.

Anyone have thoughts on this?