This pattern, "Cogwheel Insertion", is from "The Home Art Crochet Book" (1912) edited by Flora Klickmann. The book is available freely at The Antique Pattern Library. The edging is found on page 15 Section II, Uncommon Insertions, described as "Useful for Many Purposes."
I reproduce the original antique pattern here (above) and provide a version I have edited for the modern crocheter. For the sample shown, I used crochet cotton thread size 8 and steel hook size 1.2mm.
UK crochet terminology
Ch 7, sl st in first ch to make a ring.
Row 1: Ch 5, in ring make 8 tr, ch 5, 1 tr.
Row 2: Ch 7, turn, in ch sp make (2 tr, 5 ch, 4 tr); ch 2, make tr, ch 2, in each of the next 8 tr; 4 tr in next sp.
Row 3: Ch 5, turn, make 2 dc in each of the next 2-ch sps; ch 5, sk 4 tr in next sp make (8 tr, ch 5, 1 tr).
Rep Rows 2-3 four more times to make 5 spokes plus the first row of the 6th spoke of the cogwheel. To finish the last (sixth) spoke and join to the first spoke:
Next Row: Ch 7, turn, in ch sp make (2 tr, 5 dc in 7-ch ring of first spoke, 4 tr); ch 2, make tr, ch 2, in each of the next 8 tr; 4 tr in next sp.
Last Row: Ch 5, turn, make 2 dc in each of the next 2-ch sps; sl st in 5-ch turning ch of first spoke to join. Fasten off.
To join the cogwheels:
Cogwheels arranged alternately (cogwheel facing right side is joined to cogwheel facing wrong side, etc.) and are joined at the third row along two succeeding spokes. Make the cogwheel in the usual way and join at two succeeding spokes as follows (refer to photos for guide):
Row 3: Ch 5, turn, make 2 dc in each of the next 2-ch sps joining to corresponding dc on previous cogwheel at the fourth and fifth sps; ch 5, sk 4 tr in next sp make (8 tr, ch 5, 1 tr).
Row 3: Ch 2, turn, sl st in corresponding 5-ch on previous cogwheel to join, ch 2, turn, in working cogwheel make 2 dc in each of the next 2-ch sps; ch 5, sk 4 tr in next sp make (8 tr, ch 5, 1 tr).
Care must be taken in joining as the pattern meets exactly.