Automatic Soap Dispenser

This is a prototype in progress.  I have managed to get the circuit working correctly, but making a motor actually pump soap is challenging my skills.

This circuit is based on expired circuit US4989755 A, which was invented by Shiau Guey Chuan.  It has been modified by JackANDJude for prototyping with littleBits.  First, with the roller switch already depressed, the user places a hand in front of the sensor.  The light trigger senses a change in light and turns on the motor.  The motor turns the gears and cam, releasing the roller switch and moving the plunger up and down.  Finally, if the user has moved away from the sensor, the cam re-presses the roller switch, thus turning off the motor and "resetting" the bistable flip flop circuit. 

The littleBits shown in this video include "double AND" and "inverter", which are my substitutes for NAND.  Unfortunately, the legos cannot push my soap dispenser even when I adjust the gears for more torque or use a dollar store dispenser with water in it.  The legos strain and break apart.  I need to come up with a design beyond the circuit.  Any ideas on solving this pumping problem would be appreciated.  :)

 

For reference, here is an image of the originally patented circuit: