In order to achieve safer and more dexterous performance, collision avoidance is a key element in manipulator trajectory planning. The obstacle detection and avoidance for traditional rigid-link manipulators have already been studied thoroughly, but it is still a challenging problem addressing soft and continuum manipulators with arbitrary arm shapes. In this paper, a real-time collision-free trajectory planning is proposed for manipulators with arbitrary shapes in point-to-point tasks. To deal with collisions on the whole body of the manipulator, a novel obstacle avoidance algorithm is proposed using Signed Distance Function (SDF). An articulated version of SDF is adopted in our scenario for easy implementation by taking advantage of the articulated manipulator structure. The articulated SDF offers critical points in an accurate and efficient way and can be used to obtain the evasive velocity conveniently according to gradient. Lastly, simulation results in both rigid-link manipulator and a 4-DoF deformable manipulator verified the effectiveness of our method.