In robot-assisted minimally invasive laparoscopic surgery, dexterity has a high relevance. Ideally, the surgeon should feel like in open surgery with the robotic instrument able to perform all tool motions in a suitably wide workspace. The avoidance of the surrounding organs and the adaptation of the motion of the instrument to the space available in the patient should be carried out by the robot and should not interest the surgeon. The dexterity is improved by increasing the number of degrees of freedom available in the portion of the surgical instrument inside the patient. The trend has been to date to actuate the joints in the instrument using actuators located outside the patient and tendons or other transmissions to reach the joints. This approach presents intrinsic limitations that can be overcome only with a change of the architecture. The article presents a design of surgical arm made of modules joined together in a chain. Each module embeds its actuation and sensing. The arm architecture can be selected to be optimal for a specific patient and surgery. The major criticality of this architectural rethink is if small actuators could provide enough torque to move the chain and apply sufficient surgical forces. Preliminary experiments are presented proving that embedded actuation can be strong and powerful enough. The designs of a variety of modules are carefully described.