I think you could make your own drawings from the diagrams on this page:
I would dimension the design such that the exhaust ports open before the inlet port. The animation shows the inlet port opening before the exhaust.
I see a few challenges with the linear free piston engine concept:
How would one couple the linear motion and turn it into rotation to drive a vehicle?
Also, the operating rod acts as an inlet valve by means of a step in its diameter. The larger of the two rod diameters needs to be a gas tight seal with the inlet port. I don't see how you can maintain a good seal here with low friction unless rings are used. If a ring is used, it will tend to catch as it re-enters the port during the compression stroke.
The diagrams do show a cone combustion chamber, but I think the cone angle at expanded ring diameter needs to be much shallower to cam the rings back down to port diameter without breaking them.
How do you start a free piston engine? If you can couple the pistons to a vehicle transmission, then that same mechanism could be used in reverse to start it.