Taka
means essentially to take, 
hold, receive, to have. 

Its subtler shades reveal interesting meanings in combination with various propositions:
Taka á means to make effort, to strain as in "hold tight" or "hold on".  Example: "Ég tók á eins og ég gat" (I tried as hard as I could).  This meaning is intransitive. 

Að taka á einhverju (transitive) means to take something firmly, do something properly and with due effort, not give an inch.  Literally it means to take on something.  Picture a man having a firm grip on a bull´s horns. 

Then we can add the agent to the equation.  Að taka sig á means to strive harder, apply oneself harder.   Ég verð að taka mig á (I must do better).  Literally this is to take oneself to face something ("á" meaning "at", "towards"). 
 



REFLEXIVE: It would be interesting to take something reflexive like "take oneself seriously "(taka sjálfan sig alvarlega) and change it into middle voice, and say: Takast alvarlega.  But that is only technically correct.  This is not used.  Taka sig is only turned into middle voice with the proposition á as in að taka sig á (face the challenge, do better).  When used that way, it adds another preposition (við), "takast á við eitthvað", which means to face a particular challenge, to tackle, deal with.  Literally you take yourself towards something (to face something).  Example: Maður flýr ekki frá vandamálunum, þau eru til að takast á við (one should not run away from the problems, they are to be tackled and dealt with). 
  

RECIPROCAL: This is used.  When you shake someone´s hand, he shakes yours, so inevitably you take each other´s hand in your hands. We say:"Takast í hendur" as in "Þeir tókust í hendur til að staðfesta sáttmálann"(they shook their hands to confirm the treaty). Taka á can also be turned into a reciprocal, when you strive against something and it strives back.  This is a fight.  Þeir tókust kröftuglega á" (They fought forcefully).  Literally this is to take on each other. 

PASSIVE: Taka has yet another middle voice here.  Takast means to succeed.  Here, the meaning of "take" has to be altered a little.  With the help of some imagination one might see a link between "take" and "do", as in "deal with" as in "How did you take it? When you passively are capable of taking something (doing it) you "succeed".  Thus "takast" is to succeed.  Example:  Þeim tókst ekki að verja titilinn (They were unsuccessful in defending the title).  Mér tekst alltaf allt sem ég tekst á við (I always succed in doing what I´m doing (tackling)). 

INCHOATIVE: This does not apply.  Taka is not a state that one can develop into. 


Conclusion, 4 middle voices:
Takast á við (reflexive = tackle, deal with)
Takast á (reciprocal = fight)
Takast í hendur (reciprocal = shake each other´s hands)
Takast (passive = succeed)