At Petruchio's country home, Grumio complains about how cold it is and prepares to start a fire. He tells another servant, Curtis, to help start a fire, since Petruchio and Katherine will be arriving soon. He asks if everything is ready for their arrival, the house cleaned, the supper ready, and all the servants properly dressed. Curtis tells him everything is ready, and asks him for news.
All of Petruchio's servants hastily prepare for his arrival, as Petruchio (and other noblemen) are liable to insult, abuse, and hit the servants upon whom they rely if those servants do not meet their expectations.
Grumio tells Curtis that, on her way to the house, Katherine fell off her horse into the mud. Instead of helping Katherine up, Petruchio beat Grumio, whom he blamed for the horse falling. Katherine finally had to pull Petruchio off Grumio, while the horses all ran away. Grumio calls an assortment of servants to come line up and be prepared to welcome Katherine and Petruchio.
Petruchio continues to irritate Katherine, by irrationally punishing his servant Grumio when her horse falls in the mud, instead of helping her up. This would seem to be more of Petruchio's deliberate act, but given his propensity for treating servants harshly at other times, it is unclear to what degree Petruchio is simply performing.
Petruchio and Katherine arrive. Petruchio is angry that the servants did not meet him outside and immediately begins to insult them. He sends the servants off to bring him his dinner and continues to act rudely toward them. When he hits a servant, Katherine tells him not to be so harsh toward them. Petruchio tells her not to worry and takes her to the bedroom. Curtis reports that Petruchio is constantly correcting, scolding, and berating Kate.
Petruchio treats Katherine and his servants equally harshly, showing how both women and those of lower social classes are in similarly oppressed positions in the play.
Petruchio re-enters and announces, "Thus have I politicly begun my reign," (iv.1.188). He says that he will train Katherine as falconers tame falcons: he will not let her eat or sleep until she obeys him. He will pretend to find something wrong with her food and with the bed, whenever she tries to eat or sleep. This is his plan to reform Katherine's behavior and thus "tame a shrew," (iv.1.210).
Petruchio uses animal imagery both to degrade Katherine and to suggest the complete mastery over her he desires in marriage. He also compares his relationship to Katherine to a king ruling over a subject, implying that the subservient role of women is similar to that of people lower on the social hierarchy. Meanwhile, to tame Katherine he is literally denying her food and sleep, which seems like a kind of torture.