Design of a mechanical system for unequal periodic cycles

I want to perform an experiment of a material testing. For the experiment, I require to move the testing specimen in a solution for 10 minutes and then out of it for next 50 minutes. This should be a repeated process for 24 hours and 20 days and should be completely mechanical. No electric input should be required to perform this experiment. This mechanical assembly can be done using weight fraction, hour glass, water dropper or any other approach. If anybody comes up with an assembly which is relatively simpler, he would be of great help to me. It is requested to make keen efforts. Your efforts would be appreciated.