A remote center manipulator for use in minimally invasive robotic surgery includes a base link held stationary relative to a patient, an instrument holder, and a linkage coupling the instrument holder to the base link. First and second links of the linkage are coupled to limit motion of the second link to rotation about a first axis intersecting a remote center of manipulation. A parallelogram linkage portion of the linkage pitches the instrument holder around a second axis that intersects the remote center of manipulation. The second axis is not coincident with the first axis. Third and fourth links of the linkage are coupled to limit motion of the fourth link to rotation about a third axis intersecting the remote center of manipulation. The third axis is not coincident with either of the first and second axes. Various combinations of hardware-constrained remote center of motion robotic manipulators with redundant mechanical degrees of freedom are disclosed.