In this paper, we focus on the design requirement of a high-precision magnetic resonance imaging-compatible robot for prostate needle-insertion surgery, which is actuated by five ultrasonic motors to achieve the goal of needle posture adjustment and prostate puncture. After a brief introduction to the robot, the direct and inverse kinematic equations are deduced. In order to show the relationship of the velocity between the actuators and the end effector, the Jacobian matrix is derived by formulating a velocity closed-loop equation for each limb. The kinematics is carried out by minimizing a global and comprehensive dimensional synthesis conditioning index subject to transmission angle and range of motion of the mechanism constraints. The dimensional parameters are obtained for achieving a good kinematic performance throughout the entire task workspace by an example, and finally the reachable workspace of the robot is calculated.