This paper proposed a novel spatial-motion-constraints virtual fixtures (VFs) method for the human-machine interface collaborative technique. In our method, two 3D flexible VFs have been presented: warning pipe and safe pipe. And a potential-collision-detection method based on two flexible VFs has been proposed. The safe pipe constructs the safe workspace dynamically for the robot, which makes it possible to detect the potential collision between the robot and the obstacles. By calculating the speed and the acceleration of the robot end-effecter (EE), the warning pipe can adjust its radius to detect the deviation from the EE to the reference path. These spatial constraints serve as constraint conditions for constrained robot control. The approach enables multiobstacle manipulation task of telerobot in precise interactive teleoperation environment. We illustrate our approach on a teleoperative manipulation task and analyze the performance results. The performance-comparison experimental results demonstrate that the control mode employing our method can assist the operator more precisely in teleoperative tasks. Due to the properties such as collision avoidance and safety, operators can complete the tasks more efficiently along with reduction in operating tension.