Space manipulator arms often exhibit significant joint flexibility and limited motor torque. Future space missions, including satellite servicing and large structure assembly, may involve the manipulation of massive objects, which will accentuate these limitations. Currently, astronauts use visual feedback on-orbit to mitigate oscillations and trajectory following issues. Large time delays between orbit and Earth make ground teleoperation difficult in these conditions, so more autonomous operations must be considered to remove the astronaut resource requirement and expand robotic capabilities in space. Trajectory planning for autonomous systems must therefore be considered to prevent poor trajectory tracking performance. We provide a model-based trajectory generation methodology that incorporates constraints on joint speed, motor torque, and base actuation for flexible-joint space manipulators while minimizing total trajectory time. Full spatial computer simulation results, as well as physical experiment results with a single-joint robot on an air bearing table, show the efficacy of our methodology.