There are 3 main disassemblers, plus a recipe for a fourth. The three main type each allow 3 disassembles per day, and each has its own counter, so if you own two different types you get 6 disassemblies, if you own all three types, you get 9. Furthermore, if you own all three main types you can combine them to create the fourth, and gain more disassemblies that way. The fourth type can disassemble itself, so in total 3+3+3+20-1=28 disassemblies total per day if you have all three.
on odd days, use 9 disassembles from the 3 base disassemblers, then assemble the big disassembler and disassemble 20 times
on even days, use the big disassembler to disassemble the big disassembler and 19 other disassemblable things, then use 3 base disassemblers to disassemble 9 more.
That's (9+20+19+9)/2=57/2=28.5 disassemblies per day