You will notice that most chairs do their reclining feature through the use of pulling a handle and allowing you to freely recline the chair while you hold that handle, and it relocks when you release it.

So what you do is you use a hinge, and you attach a ridged circle at the end, and then you attach another ridged circle that locks with the hinge, and connect it to a handle that has a pivot just before the second ridged circle, and a spring to keep it in place until moved. Then pivoting the handle will allow you to recline.

NOTE: I'll draw you a diagram and attach it in a few minutes.