A system arranged to: obtain a plurality of positions defined by a radiotherapy treatment plan; obtain a set of position related constraints for a plurality of mechanical and radiation producing components of a radiation treatment delivery system, the constraints applicable to the radiation treatment delivery system delivering the radiotherapy treatment plan by synchronous motion of the plurality of mechanical and radiation producing components traversing a prescribed sequence of the plurality of positions in a predetermined time, as defined by the radiotherapy treatment plan; determine a trajectory (200; 220) and a minimum duration for the radiation treatment delivery system to traverse the prescribed sequence of the plurality of positions and deliver the radiotherapy treatment plan as defined by the radiotherapy treatment plan while adhering to the position related constraints for the plurality of mechanical and radiation producing components of the radiation treatment delivery system and being within a predetermined tolerance limit of a linear trajectory along the prescribed sequence of the plurality of positions; generate a record of the determined trajectory (200; 220) and minimum duration for the radiation treatment delivery system to traverse the prescribed sequence of the plurality of positions (205; 210) and deliver the radiotherapy treatment plan; and control the plurality of mechanical and radiation producing components of the radiation treatment delivery system to execute, in synchronous motion, the determined trajectory (200; 220) within the determined minimum duration, as indicated in the record characterized in that adhering to further constraints to determine the trajectory (200, 220), the further constraints including constraints of a jerk parameter, an acceleration parameter, and a velocity between different position of the plurality of positions, and the motion of the plurality of mechanical and radiation producing components is defined by a velocity model having three phases, including, in order, a first monotonic velocity change phase, a constant velocity phase, and a second monotonic velocity change phase, the first monotonic velocity change phase and the second monotonic velocity change phase being either an acceleration phase or a deceleration phase and being different from each other. obtain a plurality of positions defined by a radiotherapy treatment plan; obtain a set of position related constraints for a plurality of mechanical and radiation producing components of a radiation treatment delivery system, the constraints applicable to the radiation treatment delivery system delivering the radiotherapy treatment plan by synchronous motion of the plurality of mechanical and radiation producing components traversing a prescribed sequence of the plurality of positions in a predetermined time, as defined by the radiotherapy treatment plan; determine a trajectory (200; 220) and a minimum duration for the radiation treatment delivery system to traverse the prescribed sequence of the plurality of positions and deliver the radiotherapy treatment plan as defined by the radiotherapy treatment plan while adhering to the position related constraints for the plurality of mechanical and radiation producing components of the radiation treatment delivery system and being within a predetermined tolerance limit of a linear trajectory along the prescribed sequence of the plurality of positions; generate a record of the determined trajectory (200; 220) and minimum duration for the radiation treatment delivery system to traverse the prescribed sequence of the plurality of positions (205; 210) and deliver the radiotherapy treatment plan; and control the plurality of mechanical and radiation producing components of the radiation treatment delivery system to execute, in synchronous motion, the determined trajectory (200; 220) within the determined minimum duration, as indicated in the record characterized in that adhering to further constraints to determine the trajectory (200, 220), the further constraints including constraints of a jerk parameter, an acceleration parameter, and a velocity between different position of the plurality of positions, and the motion of the plurality of mechanical and radiation producing components is defined by a velocity model having three phases, including, in order, a first monotonic velocity change phase, a constant velocity phase, and a second monotonic velocity change phase, the first monotonic velocity change phase and the second monotonic velocity change phase being either an acceleration phase or a deceleration phase and being different from each other.