How to make a human character model grab a random moving object?

Hi. I am working on a Virtual Reality project (hand tracking with Kinect) . I am using the rigged human character Justin (Part of Male character pack from Asset store). My requirement is as follows. I have the human character model Justin and a sphere object. The location of the sphere keeps changing, but is always near the character Justin. I need to apply transformations to the left arm and the left forearm of the character model, so that the sphere object is held by the arm of the character model (sphere needs to be grabbed). I need to do this transformation to the arm and forearm, for every changing position of the sphere object.

I worked out the math involved and everything basically narrowed down to rotations of the arm and the forearm. But I face a lot of problems performing the rotations. Is there any simple solution (already existing in Unity) to perform this 'grab' operation?? Also, which rotate function would be the apt choice in order to rotate the arm and the forearm?

Thanks!