Heart and cerebrovascular diseases such as arteriosclerosis and myocardial ischemia dysfunction are currently among the main causes of death in developed countries. Recently, wave intensity (WI), which is an index used to obtain the force of cardiac contraction, has been investigated as a method for early-stage diagnosis of the above-mentioned diseases. Nevertheless, experimental tests have proven that the manual measurements of WI by means of commercial ultrasonic diagnostic systems require too much time and can be affected by the operator's skills. For this purpose, the introduction of robotic-assisted technology has advantages in terms of repetitiveness and accuracy of the measurement procedure. Therefore, at Waseda University, the development of a carotid blood flow measurement system has been proposed to support doctors while using ultrasound diagnostic equipment to measure the WI. This robotic system is composed of a serial robot with a wrist having a six-degree-of-freedom (6-DOF) parallel mechanism. The main focus is to obtain a suitable workspace performance of the 6-DOF parallel mechanism wrist. In this paper, a workspace analysis is carried out on a wrist prototype built for the Waseda-Tokyo Women's Medical Aloka Blood Flow Measurement System No.1 Refined (WTA-1R). Then, mechanical design enhancements are proposed and validated to provide a suitable workspace performance both as reachable workspace and dexterity, and a refined prototype WTA-1RII has been built.