Takt is the target, cycle is the result
Takt time follows from demand: available working time divided by the number of units needed in that time. With 450 minutes of net working time and 300 parts per shift it is 90 seconds. It is a requirement placed on the workstation.
Cycle time is the time the operation actually takes. If it exceeds takt, the line backs up. For handling, what counts is therefore not how fast a unit lifts but whether the whole handling operation fits into the share that takt leaves for it.