Here's a rocking chair i made for my girlfriend's birthday using Russian plywood.
After spending too much time reading about the perfect chair height/leg length/radius ratio i decided to search pinterest for a chair with similar proportions to what i had in mind for my girlfriend. once i found the perfect profile picture i imported it in Illustrator to figure out the seat and seat back angles, and the rocker radius. It gave me a good starting point but i still wanted to be able to try it before committing to a final shape so i started thinking about a way to create a structure i could modify and then build on top of it for the final chair instead of starting over and wasting time and material.
To do that, i decided to double the plywood on each sides of the chair, one ply would be modified until i had the prefect seat angle, and the other glued on top of it would make the arm rests and create the final overall look.
After a dry assembly i didn't like the proportions, the seat back was way too high and the sides with the armrests made it look too bulky for my taste. instead of just cutting down the seat back, i decided to cut a notch in the side panels to slide it down which also added structural rigidity. then using a router i cut a notch in the seat back where the seat panel can sit (forgot to take a picture of this, but you can see the notch in the top view of the deconstructed chair). then i took a pen and drew some holes in the sides until i had something i liked, screwed both sides together (screws placed in the middle of the material i was going to remove) and took the jig saw to it. then it was just a matter of sanding it down and rounding the corners with the router. in the next "step" you can see a special sanding tool i made for the inside corners.
Final assembly was made using only carpenter glue. the way its designed the weight is never pulling it appart so it should last for a long time and screws can always be added if necessary.
for the cushions i used a 2in foam covered with some plushy type material. Its made with a lot of love so it compensates for my lack of expert sowing machine skills. there's plenty of instructables out there covering that part so i won't even try ;)
this isn't exactly a step by step but should give you enough insight to start your own!
Step 1: Special Sanding Tool
i made a special sanding tool to be able to sand the inside corners of the holes by using a piece of 3/4in aluminium rod. i used the lathe to make one end smaller so it could fit my drill chuck, then just taped a bit of sanding paper on it. worked surprisingly well and only took minutes to make. this is actually my 2nd version, the first one was just a bit of wood dowel with a screw half way screwed in the end with the head cut off. it worked ok too but my screw wasn't centred so it bounced a lot which was annoying.