Telerobotic, telesurgical, and/or surgical robotic devices, systems, and methods employ surgical robotic linkages that may have more degrees of freedom than an associated surgical end effector in space. A processor can calculate a tool motion that includes pivoting of the tool about an aperture site. Linkages movable along a range of configurations for a given end effector position may be driven toward configurations which inhibit collisions. Refined robotic linkages and methods for their use are also provided.