In this paper, an adaptive motion-force control scheme is presented for a networked ultrasound robotic manipulator to perform a transversal abdomen scan. An adaptive backstepping position controller is designed to ensure the stability of the ultrasound robot in the presence of parametric uncertainties and external disturbances. A proportional-integral-derivative force controller is proposed to maintain a constant interaction force during the scan process. Rather than periodic time-triggered implementation, the Lyapunov-based triggering condition is derived to update the control inputs in an aperiodic manner, reduce the communication burden, and preserve the stability of the robotic system during the task. The effectiveness of the proposed control strategy is investigated based on a comparison study with different time-triggered adaptive control schemes. Moreover, the proposed event-triggered mechanism is compared with the most common triggering conditions in literature, i.e., fixed and relative thresholds. These schemes are devoted to carry out the transversal ultrasound scan in the simulation environment. Additional validation of the proposed control scheme is performed in the virtual robot experimentation platform (V-REP). From the results of simulation and experimental runs, the proposed event-triggered control scheme is found to be more promising and efficient in robot-assisted ultrasound imaging.