The book that I found in my martial arts library from 1974, teaching the movements of two basic karate forms (kata), is interesting to read. Some basic applications are included, and I'd like to add an application to one of the techniques.
In these books, a simple view of karate forms was shown in great step-by-step photos. For those of us caught up in the Bruce Lee craze in 1973 and 1974, there was really no distinction between arts. Karate and kung-fu and Taekwondo all seemed exotic and exciting -- we didn't really focus at all on the differences between these arts. And I had no idea how much I would be drawn to the internal arts.
One of the katas demonstrated in this book is Heian 1 -- the other is Tekki 1. In this form, the teacher does a move showing him defending against two attackers (photo 1), bringing his foot up and inward (photo 2), and the application shows him evading a kick.
This is a perfectly good application. Please forgive the crease -- the photo was placed between pages. The application itself is obvious and it's level 1.
There are some good karate and TKD teachers around who teach beyond the basic applications. They are few and far between but there are a couple here in my area (Jai Johnson and Hector Lareau, for example).
So let's go to the next level with this application.
Remember, level one of a movement is basic -- a punch is a punch and a kick is a kick. A step is a step.
Let's look at level two of this movement.
An attacker punches. You block with the forearm (photo 3) and position your leg behind the attacker's leg.
Then you kick your foot up and sweep your opponent (photo 4).
One of the main goals of the internal arts, particularly tai chi, is to unbalance the opponent, then take advantage of him when he's unbalanced. When the opponent punches and you deflect it, he is easier to unbalance at that moment. Here's a hint -- your foot doesn't have to rise like it does in the photo, and it always helps to exert opposite energy on the upper part of his body.
There are many similarities between karate and tai chi, karate and Shaolin, etc. It's well known that one term used for karate was "China Hand" because of the influence of kung-fu masters on the development of karate. The body mechanics of tai chi are far different, but similarities exist if you look for them.
Take a look at the forms (kata) that you do in your art and see if you can find movements that could be sweeps hidden in the form. It's possible that your teacher doesn't even know, but that shouldn't stop you from seeing deeper.