Perpetual motion of zeroth kind? Perpetual motions are classified by which law it breaks:

Perpetual motion of first kind breaks the first law of TD. It generates energy from nowhere.
Perpetual motion of second kind breaks the second law of TD. Examples of those include an engine or a pump with efficiency 100%.
Perpetual motion of third kind breaks the third law of TD. It conserves kinetic energy forever.

Then what about the zeroth kind? Since the zeroth law of TD defines temperature, the breakage of it will make the temperature of the motion undefined.
What kind of impossible motion could have undefined temperature?
 A: The zeroth low states that "The Zeroth Law of Thermodynamics states that if two bodies are each in thermal equilibrium with some third body, then they are also in equilibrium with each other."
now if you can a machine which contains three parts (let's say A, B , and C) and A is in thermal equilibrium with B and B is also in the thermal equilibrium with C but A and C are not in equilibrium then you have violated the zeroth law.
Can this ever happen? no. But there is an interesting fact in probability which is similar but different. if drug A cure more people than drug B and drug B cures more people than drug C then you CANNOT conclude that A cures more people than C. You can learn more about this aspect of probability in the following video.
https://www.youtube.com/watch?v=zzKGnuvX6IQ&t=3s 
A: Violating the zero law implies that you can create a perpetual heat transfer from the environment to some simple system (such as a gas in a container). And then you can use this increased internal energy of the system to generate work. So it is basically very similar to the second kind, you can transform random motion into macroscopical work. But it is simpler in the sense that the heat transfer happens spontaneously by simple contact between the environment and the system. 
