When a manipulator works in dynamic environments, it may be affected by obstacles and may cause danger to people around. This requires the manipulator to be able to plan the obstacle avoidance motion in real time. Therefore, the problem solved in this paper is dynamic obstacle avoidance with the whole body of the redundant manipulator. The difficulty of this problem is how to model the manipulator to reflect the motion relationship between the manipulator and the obstacle. In order to describe accurately the occurrence conditions of the collision, we propose the triangular collision plane, a predictable obstacle avoidance model based on the geometric configuration of the manipulator. Based on this model, three cost functions, including the cost of the motion state, the cost of a head-on collision, and the cost of the approach time, are established and regarded as optimization objectives in the inverse kinematics solution of the redundant manipulator combined with the gradient projection method. The simulations and experiments on the redundant manipulator and the comparison with the distance-based obstacle avoidance point method show that our method improves the response speed of the manipulator and the safety of the system.