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Are two weapon fighting penalties assessed to a character with multiple attaks who switches between kicks and sword blows? He doesn't take the extra attack granted to a 2-wpn fighter, so what gives?
A fighter with base attack of 11 gets three attacks at +11/+6/+1. If he has unarmed combat and decides to punch with his right hand, kick with his left foot , and then end on an elbow strike your fine. You will need ambidexterity for the off hand attacks or else they would be a -4.
But if joe fighter switches between two-handed sword blows and kicks, does he assess penalties. The gimmick for the character is: Unarmed Trip, use the Improved trip feat and disarm the enemy, take 3 attacks. (BAB 16/11/6/1)
No matter how it works out, you can't get free attacks without some sort of penalty. By the rules you can't really get any other attacks if you are using a two handed weapon (no "off-hand" attacks that is).
But if joe fighter switches between two-handed sword blows and kicks, does he assess penalties. The gimmick for the character is: Unarmed Trip, use the Improved trip feat and disarm the enemy, take 3 attacks. (BAB 16/11/6/1)
That's legal. You can always substitute a Trip, Disarm, or Grapple attack for a normal melee attack. A trip attack is assumed to be unarmed unless you are using a "trip weapon", but I don't believe you would be assessed the off-hand penalty for a normal trip attack (unless you used the extra attack granted from two-weapon fighting to make the trip attack.)
If you were to try and use one of the attacks from your BAB to make a damaging attack (such as an actual kick) with a different limb than your primary attack, you would get all the normal off-hand penalties (including 1/2 strength bonus to damage). I don't believe you would get the additional two-weapon fighting penalties unless you actually made an extra attack.
(Basically anything other than your primary hand is an off-hand. The PHB doesn't go into this, but that's how it's treated in the MM.)