Robotic arms and surgical robotic systems incorporating such arms are described. A robotic arm includes a roll joint connected to a prismatic link by a pitch joint and a tool drive connected to the prismatic link by another pitch joint. The prismatic link includes several prismatic sublinks that are connected by a prismatic joint. A surgical tool supported by the tool drive can insert into a patient along an insertion axis through a remote center of motion of the robotic arm. Movement of the robotic arm can be controlled to telescopically move the prismatic sublinks relative to each other by the prismatic joint while maintaining the remote center of motion fixed. Other embodiments are also described and claimed.