The problems related to self-collision detection and optimal collision-free trajectory planning for a robot arm subjected to dynamic constraints is investigated. First, a computed-torque method is used to obtain a linearized closed-loop system. For this linearized system, the reference state that the robot arm is capable of reaching is verified through phase plane analysis. This will ensure that the robot arm can be stopped before self-collision occurs, Dynamic constraints are taken into account for a continuous motion of deceleration by calculating the bounds of the commanded force/torques with interval evaluations. When the reference state at t + ${delta}t$ is not valid for self-collision avoidance, a new feasible state is determined by adhering to an interval-based method which allows decomposition of a complex constrained optimization problem into a simple two-stage optimization problem with relaxed constraints. The optimized feasible state not only secures the robot arm against self-collision but also allows the robot arm to track the original reference trajectory closely. Simulation and experimental results of a 2-dof robot arm show the effectiveness of the proposed interval-based approach.