An apparatus for generating motion around a remote center of motion, comprising: - a distal link (L12, LR) arranged to revolve about the remote center of motion and to translate through the remote center of motion; - a proximal link (L10, LI) arranged to revolve about a proximal center of motion through a rotational joint and a sliding joint to effect rotation about an axis of rotation comprising the proximal center of motion and to effect translation relative to the proximal center of motion in a plane of motion of the proximal link perpendicular to the axis of rotation; - a base link adapted to be coupled to a mounting fixture, wherein the proximal center of motion is coupled to the base link; - a first mechanism comprising a first link (L9, BE) pivotally coupled to the proximal link (L10, LI) and to the distal link (L12, LR), wherein pivotal coupling between the first link and the proximal link defines an intermediate point in constant relative relation to the first link and pivotal coupling between the first link and the distal link defines a remote point in constant relative relation to the first link, wherein the first mechanism is operable to transfer motion of the proximal link relative to the proximal center of motion to a motion of the distal link relative to the remote center of motion by maintaining a parallelogram between orthogonal projections of the proximal center of motion, the remote center of motion, the intermediate point, and the remote point on the plane of motion of the proximal link (L10, LI), wherein a length between the intermediate point and the proximal center of motion is adjustable; - a second mechanism having at least two degrees of freedom, coupled to the first link (L9, BE) and operable to move the first link with two degrees of freedom in a plane parallel to the plane of motion of the proximal link (L10, LI), wherein the second mechanism comprises one link or a serial connection of links (L4, L8, L3, L7, L2, L6) connecting the base link to the first link (L9, BE), and wherein the one link or the links of the serial connection is or are configured to have an orientation of instant motion which is different from an orientation of instant motion of the proximal link (L10, LI), relative to the base link. - a distal link (L12, LR) arranged to revolve about the remote center of motion and to translate through the remote center of motion; - a proximal link (L10, LI) arranged to revolve about a proximal center of motion through a rotational joint and a sliding joint to effect rotation about an axis of rotation comprising the proximal center of motion and to effect translation relative to the proximal center of motion in a plane of motion of the proximal link perpendicular to the axis of rotation; - a base link adapted to be coupled to a mounting fixture, wherein the proximal center of motion is coupled to the base link; - a first mechanism comprising a first link (L9, BE) pivotally coupled to the proximal link (L10, LI) and to the distal link (L12, LR), wherein pivotal coupling between the first link and the proximal link defines an intermediate point in constant relative relation to the first link and pivotal coupling between the first link and the distal link defines a remote point in constant relative relation to the first link, wherein the first mechanism is operable to transfer motion of the proximal link relative to the proximal center of motion to a motion of the distal link relative to the remote center of motion by maintaining a parallelogram between orthogonal projections of the proximal center of motion, the remote center of motion, the intermediate point, and the remote point on the plane of motion of the proximal link (L10, LI), wherein a length between the intermediate point and the proximal center of motion is adjustable; - a second mechanism having at least two degrees of freedom, coupled to the first link (L9, BE) and operable to move the first link with two degrees of freedom in a plane parallel to the plane of motion of the proximal link (L10, LI), wherein the second mechanism comprises one link or a serial connection of links (L4, L8, L3, L7, L2, L6) connecting the base link to the first link (L9, BE), and wherein the one link or the links of the serial connection is or are configured to have an orientation of instant motion which is different from an orientation of instant motion of the proximal link (L10, LI), relative to the base link.