Mamma mia!
We try to suppress gears wherever possible, and you add one...
Drawbacks: shocks, wear, noise, uncomfortable lateral force.
Advantages?

Sorry forgot to add the gears

A and B are front view and c is side view.
The system has to be setup with the one pistons teeth all ways on the crank shaft (8 pistons one of the pistons teeth should be connected(teeth for piston 1 are at the right side of the crank shaft teeth for 2 are at the bottom 3 are at the left side and four are at the top)).
c the gears should keep the pistons moveing at the same speed as the crank shaft.

I tried that design myself and found the draw back was a dead zone of releasing and reconnecting. Having two opposite means of transference working against eachother meant a dead zone was needed. And a dead zone needs to keep momentum to align itself for reconnection. The momentum has no guarantee of alignment. My hat is off to you though. My conflict with the typical crankshaft is the TDC and BDC. I have come up with another replacement to transfer motion from the piston to the driveshaft. This engine design though is unlike the typical 4 stroker. What I have created is a design rendering 2 combustions per cylinder per revolution. A four cylinder rendering 8 combustions per engine revolution. And with the new "crankshaftless" configuration there are 2 parts per cylinder of moving parts. No timing chain, or cams or valves. this site is nice, any of you been able to connect with manufacturers out there?

Here is a link to an old post of mine where I discuss another interesting rotary engine, the Bricklin-Turner. In fact, people on this thread may be interested in reading that entire old thread. It's from about a year and a half ago, and one poster has a huge list of all the alternate engine designs he's been able to find. Interesting reading!

--Stuart Anderson