Venipuncture is the most common invasive medical procedure performed in the United States and the number one cause of hospital injury. Failure rates are particularly high in pediatric and elderly patients, whose veins tend to deform, move, or roll as the needle is introduced. To improve venipuncture accuracy in challenging patient populations, we have developed a portable device that autonomously servos a needle into a suitable vein under image guidance. The device operates in real time, combining near-infrared and ultrasound imaging, computer vision software, and a 9 degrees-of-freedom robot that servos the needle. In this paper, we present the kinematic and mechanical design of the latest generation robot. We then investigate in silico and in vitro the mechanics of vessel rolling and deformation in response to needle insertions performed by the robot. Finally, we demonstrate how the robot can make real-time adjustments under ultrasound image guidance to compensate for subtle vessel motions during venipuncture.