Hello everybody, I'm a final year student in mechanical engineering. For my final year project, I'm designing a spring system to store energy when stopping a hand wagon and use this to boost the wagon when starting. This involves a pinion attached to the axle of rotation for the wheels, and a rack connected to the spring such that the rack drives the pinion which in turn moves the wheels. In my calculations, I need to know what the relationship between the downwards movement of the rack and the torque of the pinion is. For example, assuming I need the wagon to accelerate at "a" metres per second, with a load of M, I will need a thrust of F, obviously. To provide this thrust, I know the wheels have to turn at a certain angular velocity, but I do not know how to calculate this, nor do I know how to relate the necessary torque to this velocity or to the downwards force required by the rack. Any help would be immensely appreciated.