In order to improve the safety of digital subtraction angiography (DSA) equipment in the treatment of cardiovascular diseases, a hybrid collision detection algorithm based on separation distance is proposed by combining oriented bounding box (OBB) algorithm with GJK algorithm. Firstly, according to the structure of DSA equipment, the real-time position of DSA equipment is simulated in robot operating system (ROS); Then, the OBB is used to envelope the moving parts, and then the generated OBB model is applied to GJK algorithm to calculate the separation distance between the moving parts and quickly eliminate the detection pairs outside the threshold; Finally, for the detection pairs within the threshold, the real model is applied with GJK algorithm to calculate the separation distance between the real models and judge whether the models collide. The experimental results show that the average detection time of the hybrid collision detection algorithm is 15ms. The application of the algorithm in practical equipment has achieved good anti-collision effect.