How to find the orientation of a 6DOF robot optimizing manipulability with a fixed position constraints ?

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Hello,

I am trying to find the orientation of my 6DOF robot that maximizes the manipulability at a given endeffector postition and a known orientation of my z axis.

What I am trying to do, is to use a TOF-camera that moves around the center of an object with a fixed radius and records pointclouds from that Object from different positions, that I want to register later on. So the camera should always be looking towards the center of the object, while the endeffector is positioned on a sphere with a given radius. Furthermore the orientation i want to use should be optimized by its manipulability.

Any idea how I could solve this Problem? Maybe a IK-solver with equality-constraints?

Thanks for your help