Conforming to safety standards often limits collaborative robots' performance and size, restricting their applications despite their capabilities. Planning their motions in human environments involves a trade-off between optimal trajectory planning and quick adaptation to dynamic, unstructured spaces. Traditional trajectory planning methods either use simplified robot models and sacrifice robot's abilities for computational efficiency, or exploit robots' abilities fully but have high computational complexity and rely on substantial pre-computation. This paper introduces an approach for trajectory planning that exploits robot's full motion abilities while planning on-the-fly. In each step of the trajectory execution, it evaluates robot's movement ability using polytope algebra and calculates a time-optimal Trapezoidal Acceleration Profile (TAP) on the remaining trajectory. The method is shown to be near time-optimal (around 5% slower trajectories) by benchmarking it against the state-of-the-art time-optimal method TOPP-RA. The method allows reaching higher velocities (able to plan up to 100% of the robot's kinematic limits) while at the same time lowering the tracking error (under 4mm) than traditional Cartesian Space planning methods. A mock-up experiment demonstrates its efficiency in collaborative waste sorting using a Franka Emika Panda robot.