There is a specific position in which my headjoint is kept when I play my flute. Should this position apply to my piccolo as well? Also, do the same rules for embouchure shape on flute go for piccolo as well?

yes, pretty much, you obviously need a small apeture to play picc, try to keep as relaxed as possible to avoid a pinched tone

I just got a piccolo a few weeks ago. It was one of those dreaded no name brands. But thats all I could afford. But, I have that pinched tone. I tried relaxing alittle but I have trouble making such a small embouchure without closing my throught. It seems impossible.

To Tiffloser, I don't recommend having one absolute position for the headjoint, as circumstances will change day to day (same goes for flute and picc). You should have a pretty good idea of where the head needs to be, but not to the point where you develop the mindset that if you move the head in a bit or out a bit, terrible things will happen. Your lips will change slightly from day to day...They may be slightly dehydrated or chapped, or whatever, and you still need to get the best tone possible, so if that means moving the head, go for it. Patrick's right on the embouchure bit. Your embouchure should be firm, but not tensed, and your throat open to help facilitate a decent sound. The overall shape will be much like a flute embouchure, but slightly smaller.

To Penny, just keep trying! Piccolo is a tough beast to tame, especially at first (and when you don't have the optimal equipment), but well worth the effort. Try doing tone exercises, and separating the muscles forming your embouchure from those controlling your throat. The two should not be connected....A small aperture should be possible without pinching, just as a larger aperture can be produced while you pinch. Once you get the hang of the picc (and hopefully a better quality instrument somewhere down the line), things should become much easier.

Well, when I first started I had an arrow on my head joint and body that you alligned them up with but its the same as flute. About the embouchure when you play the flute your mouth is further back and the hole for your airstream is wider (because the instrument is bigger than picc) when you play picc move it up so the sides of your mouth are alligned with the 3rd tooth on each side of your mouth (on the tope line). GOOD LUCK!

Such concrete rules may work for you, but they don't often transfer between players well. There's such a variety of mouth sizes and shapes that the 3rd tooth rule almost certainly would not hold, and in any case is not the best way to go about setting an embouchure. That should become part of muscle memory....You should not have to consciously think "Hmm....Are the sides of my mouth aligned with the 3rd tooth back?" The more you play piccolo the less difficult it becomes to find a picc embouchure that works, and to go back and forth between the flute and picc. As for the arrow on the body and head, these are pretty common, but since every player is different, they will need the head positioned slightly differently than other players, meaning that these arrows don't have a whole lot of meaning. Also, I'm not sure what you mean about your mouth being further back (perhaps you mean the lower jaw is further back?), but just to clarify, jaw movement should be very slight (if there is any at all), and changes in air direction and use should be dictated mostly by the lips.

I was told by my college flute teacher to think of the piccolo as an extension of the flute. She would have me play middle octave long tones on flute, and then pick up my piccolo and play the lower octave (sounding in the same register). The upper register of the flute, middle register of the piccolo, etc. The changes from one register to the next on flute are extended for the highest register on the piccolo. I hope that made sense! It is much easier to explain in person. This seemed to work well for developing the embouchure on piccolo for me!