A robotic surgery system comprising: an orienting platform; a support linkage movably supporting the orienting platform; a plurality of manipulators; each of the manipulators including an instrument holder; each of the manipulators being configured to support an associated surgical instrument mounted to the instrument holder, to insert the associated surgical instrument along an insertion axis into a patient through an associated remote center of manipulation, RC, to rotate the instrument holder around a first manipulator axis that intersects the associated RC, and to rotate the instrument holder around a second manipulator axis that intersects the associated RC, each of the first and second manipulator axes being transverse to the insertion axis, the second manipulator axis being transverse to the first manipulator axis; and a plurality of set-up linkages, each of the set-up linkages coupling one of the manipulators to the orienting platform and operable to reposition the associated manipulator relative to the orienting platform and fixedly support the associated manipulator in a selected position relative to the orienting platform, wherein each of the set-up linkages is coupled to the orienting platform and comprises a manipulator support coupled to the associated manipulator, at least one of the set-up linkages comprising a tornado mechanism and a tornado mechanism support link, wherein the tornado mechanism includes a tornado joint and a coupling link having a coupling link proximal end coupled to the tornado joint and a coupling link distal end coupled to the associated manipulator support, wherein actuation of the tornado joint rotates the coupling link about a tornado axis that intersects the associated RC and that is not aligned with either of the first and second manipulator axes, so as to reposition and reorient the coupling link distal end relative to the coupling link proximal end, and wherein the coupling link is configured to maintain the associated RC in a fixed position relative to the tornado mechanism support link in response to actuation of the tornado joint. an orienting platform; a support linkage movably supporting the orienting platform; a plurality of manipulators; each of the manipulators including an instrument holder; each of the manipulators being configured to support an associated surgical instrument mounted to the instrument holder, to insert the associated surgical instrument along an insertion axis into a patient through an associated remote center of manipulation, RC, to rotate the instrument holder around a first manipulator axis that intersects the associated RC, and to rotate the instrument holder around a second manipulator axis that intersects the associated RC, each of the first and second manipulator axes being transverse to the insertion axis, the second manipulator axis being transverse to the first manipulator axis; and a plurality of set-up linkages, each of the set-up linkages coupling one of the manipulators to the orienting platform and operable to reposition the associated manipulator relative to the orienting platform and fixedly support the associated manipulator in a selected position relative to the orienting platform, wherein each of the set-up linkages is coupled to the orienting platform and comprises a manipulator support coupled to the associated manipulator, at least one of the set-up linkages comprising a tornado mechanism and a tornado mechanism support link, wherein the tornado mechanism includes a tornado joint and a coupling link having a coupling link proximal end coupled to the tornado joint and a coupling link distal end coupled to the associated manipulator support, wherein actuation of the tornado joint rotates the coupling link about a tornado axis that intersects the associated RC and that is not aligned with either of the first and second manipulator axes, so as to reposition and reorient the coupling link distal end relative to the coupling link proximal end, and wherein the coupling link is configured to maintain the associated RC in a fixed position relative to the tornado mechanism support link in response to actuation of the tornado joint.