Here is an exploded view of a pair of purlin joints where they meet the rafter.
Each frame design should be reviewed by an experienced timber framing engineer for the exact design of this joint.
Loads, spans, type of wood, and possibly other factors will have to be considered when designing this joint.
My examples are only examples of two different types. One cut with a curved cut on the bottom and one is just reduced.
Only an engineer can give the exact sizes of these joints.